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If the ellipse is not circular, then ρℰsubscript𝜌ℰ\rho_{{\mathcal{E}}}italic_ρ start_POSTSUBSCRIPT caligraphic_E end_POSTSUBSCRIPT is smaller than the asymptotic convergence rate of Orthomin(1)1(1)( 1 ). | those of Orthomin(4). Note that, in general, the first k𝑘kitalic_k steps of Orthomin(k+1𝑘1k+1italic_k + 1) are identical to those of Orthomin(k𝑘kitalic_k). | similar to the ones for Orthomin(1), and in practice the two methods converge comparably fast for SPD systems. Analogously, | Two facts are notable about the behavior of Orthomin(k)𝑘(k)( italic_k ) on the systems in Conjecture 4. | The main goal of this article is to examine the behavior of Orthomin(k𝑘kitalic_k) on a family of examples, and to show | C |
For each s∈S𝑠𝑆s\in Sitalic_s ∈ italic_S, (Run(s),ℱ,𝒫)𝑅𝑢𝑛𝑠ℱ𝒫(Run(s),\mathcal{F},\mathcal{P})( italic_R italic_u italic_n ( italic_s ) , caligraphic_F , caligraphic_P ) is a probability space, where ℱℱ\mathcal{F}caligraphic_F is the σ𝜎\sigmaitalic_σ-field generated by all basic cylinders Cyl(π)𝐶𝑦𝑙𝜋Cyl(... | Model checking [5] is an essential tool for formal verification, which is an interesting and important topic in the research field of logic in computer science and particularly plays an important role in verification of digital circuit (chips), in which one describes the system to be verified as a model of some logic, ... | The logic PCTL was originally introduced in [9], where the corresponding model-checking question has been focused mainly on finite-state Markov chains. | Among the probabilistic infinite-state systems, one is the probabilistic pushdown systems, which were dubbed “probabilistic pushdown automata” in [4, 3, 6], the input alphabet of which contains only one symbol. Throughout the paper, such a limited version of probabilistic pushdown automata will be dubbed “probabilistic... | The logic PCTL∗ extends PCTL by deleting the requirement that any temporal operator must be proceeded by a state formula (Thus, the logic PCTL can be regarded as a sublogic of PCTL∗), and its path formulas are generated by the following syntax: | B |
The convergence results on Gaussian process regression presented in section 3 are mainly known results from the theory of scattered data interpolation [43, 37, 28]. The error bounds are given in terms of the fill distance of the design points used to construct the Gaussian process emulator, and depend in several ways o... | Gaussian process emulators are frequently used as surrogate models. In this work, we analysed the error that is introduced in the Bayesian posterior distribution when a Gaussian process emulator is used to approximate the forward model, either in terms of the parameter-to-observation map or the negative log-likelihood.... | The remainder of this paper is organised as follows. In section 2, we set up the Bayesian inverse problem of interest. We then recall some results on Gaussian process regression in section 3. The heart of the paper is section 4, where we introduce the different approximations to the posterior and perform an error analy... | The main focus of this work is to analyse the error introduced in the posterior distribution by using a Gaussian process emulator as a surrogate model. The error is measured in the Hellinger distance, which is shown in [41, 15] to be a suitable metric for evaluation of perturbations to the posterior measure in Bayesian... | The convergence results on Gaussian process regression presented in section 3 are mainly known results from the theory of scattered data interpolation [43, 37, 28]. The error bounds are given in terms of the fill distance of the design points used to construct the Gaussian process emulator, and depend in several ways o... | B |
After initialization, logπ≥−2𝜋2\log\pi\geq-2roman_log italic_π ≥ - 2 by Lemma 1. | τ𝜏\tauitalic_τ. For each k∉G𝑘𝐺k\notin Gitalic_k ∉ italic_G, we have, by definition of G𝐺Gitalic_G, | By definition of G𝐺Gitalic_G, whenever we add an item to W𝑊Witalic_W, we decrease | and irrevocably) whether to add i𝑖iitalic_i to the set W𝑊Witalic_W, subject to the | see an item with value at least 2OPT2𝑂𝑃𝑇2OPT2 italic_O italic_P italic_T, we select it. For item i𝑖iitalic_i, | B |
Recall that Wk(G,x)subscript𝑊𝑘𝐺𝑥W_{k}(G,x)italic_W start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT ( italic_G , italic_x ) is the set of closed walks in G𝐺Gitalic_G of length k𝑘kitalic_k starting from x𝑥xitalic_x. | A random rooted graph (G,∘)𝐺(G,\circ)( italic_G , ∘ ) is a unimodular network if | The spectral radius of (G,∘)𝐺(G,\circ)( italic_G , ∘ ) can also be formulated in terms of the spectral | on (G,x)𝐺𝑥(G,x)( italic_G , italic_x ) started from vertex x𝑥xitalic_x. The spectral radius of the SRW on a unimodular network (G,∘)𝐺(G,\circ)( italic_G , ∘ ) is | The spectral radius of a unimodular network (G,∘)𝐺(G,\circ)( italic_G , ∘ ) is defined to be | D |
Decide the corresponding k𝑘kitalic_k random variables as the anomalous random variables. | Algorithm 1 Maximum likelihood estimation with fixed time-invariant measurements | Consider fixed time-invariant measurements Yj=𝐚jT𝐗j=𝐚T𝐗jsuperscript𝑌𝑗superscriptsuperscript𝐚𝑗𝑇superscript𝐗𝑗superscript𝐚𝑇superscript𝐗𝑗Y^{j}={{\boldsymbol{a}}^{j}}^{T}{\boldsymbol{X}}^{j}={\boldsymbol{a}}^{T}{% | Algorithm 5 Maximum likelihood estimation with deterministic time-varying measurements | We propose the maximum likelihood estimate method with random time-varying measurements over (nk)binomial𝑛𝑘\binom{n}{k}( FRACOP start_ARG italic_n end_ARG start_ARG italic_k end_ARG ) hypotheses in Algorithm 3. For the purpose of analyzing the error probability of the maximum likelihood estimation, we further propose... | A |
There are tools to estimate posture by analyzing acceleration acquired from these sensors (e.g., NTT Docomo provides hitoe SDK [18] for hitoe data analysis). However, acceleration of vehicles is added to acceleration of wearable sensor in vehicles, it is vague to estimate drivers’ posture accurately by tools of wearabl... | In Japan, a fatal accident of long distance bus occurred in which 15 people were dead in January 2016 [14]. Thus, needs for safety management with wearable sensors for drivers are increasing because dangerous driving posture like picking up things or fatigue accumulation of bus or taxi (hereafter, vehicle) drivers may ... | This paper studied methods to estimate postures of drivers on vehicles using wearable acceleration sensor hitoe and conducted field tests. The method to subtract vehicle acceleration using hitoe and smart phone has problems of accuracy differences between them. On the other hand, posture changes such as picking things ... | For drivers’ posture estimation in vehicles, we need to consider two things. The first is that acceleration data of wearable sensor includes acceleration of vehicle. The second is that considering safety management of vehicles, specific dangerous posture such as picking up things during driving needs to be detected. | There are tools to estimate posture by analyzing acceleration acquired from these sensors (e.g., NTT Docomo provides hitoe SDK [18] for hitoe data analysis). However, acceleration of vehicles is added to acceleration of wearable sensor in vehicles, it is vague to estimate drivers’ posture accurately by tools of wearabl... | C |
Step 1: In parallel with shoplifting detection using camera movie, a sales management terminal sends sales information to a product management application on a cloud via a network. A product management application is SaaS which provides business application of ERP, and information of sales and product item stock is sto... | Step 2: Stream data of security camera movie is sent to a small computer in a shop. A small computer is a computer which has a certain degree of computation power, memory size and communication capability. For example, Rasbpberry Pi can be used for this to analyze images. | Based on these backgrounds, this paper targets a low cost shoplifting prevention SaaS service for small shops using cloud technology and data analysis technology. In our proposal, machine learning framework Jubatus[6] on a small computer deployed in a shop analyzes security cameras movie, detects anomaly behavior and n... | Saburo-kun Ace[7] is a shoplifting prevention system using security camera movie. Saburo-kun Ace detects a shoplifting from security camera movie when customers’ actions match pre-defined 50 patterns of suspicious behaviors, and notifies it to staffs of shops. Shop staffs question or say something to the suspicious cus... | Step 3: A small computer cuts off each image from movie and extracts feature values from the image data. To extract feature values, libraries of dlib, OpenCV can be used. | A |
Recently, a scheme for faithful quantum communication in quantum wireless multihop networks, by performing quantum teleportation between two distant nodes which do not initially share entanglement with each other, was proposed by Wang et al. MA2 . Xiong et al. MA3 proposed a quantum communication network model where a... | \rangle=1/(4\varrho\gamma)⟨ caligraphic_G start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT | caligraphic_P start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT | caligraphic_G start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ⟩ = 1 / ( 4 italic_ϱ italic_γ ), then the node finds that the state of qubits J1J3subscript𝐽1subscript𝐽3J_{1}J_{3}italic_J ... | In this section, we establish the quantum channel linking the nodes. As it can be seen in Figs. 2 (a) and (b), A denotes the source node while the destination node is denoted by J. In the source node A, there exists two-qubit of unknown state |χ⟩A1A2=a0|00⟩+d0|11⟩subscriptket𝜒subscript𝐴1subscript𝐴2subscript𝑎0ket... | The cluster state MA6 , which is a type of highly entangled state of multiple qubits, is generated in lattices of qubits with Ising type interactions. On the basis of single qubit operation, the cluster state serves as initial resource for a universal computation scheme MA7 . Cluster state has been realized experimenta... | To sum it up, in this paper, we propose a quantum routing protocol with multihop teleportation for wireless mesh backbone networks. The quantum channel that linked the intermediate nodes has been realized through entanglement swapping based on four-qubit cluster state. After quantum entanglement swapping, quantum link ... | C |
For example of Tacit Computing, let us consider tracking cameras. Tracking cameras are usage that movies of small children in schools or roads are taken by security cameras near the children and parents can see the movies by their mobile terminals. Tracking cameras can satisfy parents’ needs to confirm children’s safet... | In device layer, it is necessary to switch a device that satisfies the needs of user at first. In the case of tracking cameras, it means to select the camera in which the image of the child appears based on location of the child. At this time, if we analyze images with all cameras connected to the network and use only ... | For example of Tacit Computing, let us consider tracking cameras. Tracking cameras are usage that movies of small children in schools or roads are taken by security cameras near the children and parents can see the movies by their mobile terminals. Tracking cameras can satisfy parents’ needs to confirm children’s safet... | As a processing of tracking cameras, Tacit Computing discovers the camera in which the child appears, and delivers movies of the camera to the parents’ mobile terminals when the parents request movies. And for watching, image analyzing functions such as OpenCV library are arranged on gateways or network edge SSE (Subsc... | In cloud layer, where to process in the cloud greatly affects cost and performance. Firstly, we deploy the processing function to the cloud of the DC (Data Center) that has a small delay from the network edge that accommodates devices frequently used. Furthermore, since the size of the cloud resource also affects the o... | C |
While the problem has been formulated for all dimensions n≥2𝑛2n\geq 2italic_n ≥ 2, the study in this paper has been limited to n=2𝑛2n=2italic_n = 2. This is for the following reasons. (i) n=2𝑛2n=2italic_n = 2 this is the smallest dimension in which the shape of a Voronoi cell plays a role in the communication cost, ... | We study the dependence of the communication cost of our protocols on the lattice structure. In particular, we show that the lattice which is best in two dimensions for both coding and quantization, namely, the hexagonal lattice, requires the largest amount of communication in a two-node distributed setting. | For interactive protocols with an unbounded number of rounds, we exhibit a construction which results in zero error probability with finite average bit cost. This is a surprising result, when compared to the single-round protocol, which can only achieve a strictly positive error probability at a finite rate. | While the problem has been formulated for all dimensions n≥2𝑛2n\geq 2italic_n ≥ 2, the study in this paper has been limited to n=2𝑛2n=2italic_n = 2. This is for the following reasons. (i) n=2𝑛2n=2italic_n = 2 this is the smallest dimension in which the shape of a Voronoi cell plays a role in the communication cost, ... | We have considered the problem of interactively computing the nearest lattice point for a lattice in two dimensions. A two-party model of communication is assumed and expressions for the error probability have been obtained for a single round of communication (i.e. two messages). We have also considered an unbounded nu... | D |
The analysis of different studies about motor control revealed some parallels with current theories about NS anatomy physiology, and this paragraph is dedicated to describe such findings. However, the authors would like to remark that the proposed organisation is not the structure of the NS but an architecture that can... | We proposed a structure of a semi-autonomous controller organised in a hierarchical architecture that has a parallelism in the biological motor control Figure 6. At the apex of the hierarchy is the TS planner, which acts on the input of walking towards a target. The TS planning appears to be based on stereotyped optimi... | Figure 6: The parallel between the proposed architecture and the human nervous system based on literature information [17, 42, 8, 47, 16, 11, 13, 5, 10]. The full lines in the schematic represent information involved in the control, while the dotted lines indicate a supervision signal. Both types of connection are ofte... | The dynamic motion primitives theory was developed as an extension of the motor primitives and, until now, it is unclear how they are connected[5]. Our theory is based on the integration of our task-space planner with the joint-space planner λ0−PMPsubscript𝜆0𝑃𝑀𝑃\lambda_{0}-PMPitalic_λ start_POSTSUBSCRIPT 0 end_PO... | Our results describe how the proposed deterministic model, based on a harmonic oscillator centred in the saddle point, produces human-like gait trajectories for both the CoM and the foot swing at different gait speeds. Furthermore, it identifies the ankle strategies as the mechanism that allows to control of the vertic... | A |
E𝐸Eitalic_E is partitioned into p𝑝pitalic_p disjoint sets E1,…,Epsubscript𝐸1…subscript𝐸𝑝E_{1},\ldots,E_{p}italic_E start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , … , italic_E start_POSTSUBSCRIPT italic_p end_POSTSUBSCRIPT, where |Ei|=risubscript𝐸𝑖subscript𝑟𝑖|E_{i}|=r_{i}| italic_E start_POSTSUBSCRIPT italic_i end_P... | Hence, and from |X|=LP𝑋subscript𝐿𝑃|X|=L_{P}| italic_X | = italic_L start_POSTSUBSCRIPT italic_P end_POSTSUBSCRIPT, we get that the number of connected components is reduced by LPsubscript𝐿𝑃L_{P}italic_L start_POSTSUBSCRIPT italic_P end_POSTSUBSCRIPT. Then, | (with p=LP𝑝subscript𝐿𝑃p=L_{P}italic_p = italic_L start_POSTSUBSCRIPT italic_P end_POSTSUBSCRIPT), | We will denote by k^^𝑘\hat{k}over^ start_ARG italic_k end_ARG the number of rounds performed by the algorithm (Steps 1-1). | We will denote by [p]delimited-[]𝑝[p][ italic_p ] the set {1,2,…,p}12…𝑝\{1,2,\ldots,p\}{ 1 , 2 , … , italic_p }. | D |
Compatibility with R and Bioconductor. The results returned by EBIC could be easily saved into a format loadable by Bioconductor R package biclust in order to perform biological validation. In Supplementary Material we provide detailed workflow presenting how to use EBIC, all within R environment. | Workflow for analysis of methylation data. EBIC was capable to capture bio-meaningful signals in methylation data. A tutorial is presented in a Supplementary Material. | In this paper we introduce the open source package built on top of the upgraded version of the method. First and foremost, a full support for multi-GPUs is added, which allows to analyze datasets with almost unlimited numbers of rows (available memory is a constraint). Secondly, the method has been integrated with Bioc... | Compatibility with R and Bioconductor. The results returned by EBIC could be easily saved into a format loadable by Bioconductor R package biclust in order to perform biological validation. In Supplementary Material we provide detailed workflow presenting how to use EBIC, all within R environment. | In this paper we present the recent advancements in one of the leading biclustering methods. The algorithm was wrapped into a framework, which is conveniently integrated with R and allows multiple input file formats. In Supplementary Material we also demonstrate that even for such a large genomic dataset, the results p... | A |
Similar reasoning leads to the result that the above non-generic game possesses no strictly perfect equilibria; see van Damme (1991, p. 16). | it follows that this outcome can be destabilized by the “secret handshake” entrants. | Then it is obvious that σ∗superscript𝜎\sigma^{*}italic_σ start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT is a strictly perfect equilibrium of G¯¯𝐺\bar{G}over¯ start_ARG italic_G end_ARG. | Motivated by this, it can be shown that a strictly perfect equilibrium actually ensures that | Suppose that σ∗superscript𝜎\sigma^{*}italic_σ start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT is a strictly perfect equilibrium of G𝐺Gitalic_G, | C |
\Delta}_{r},\tilde{\Lambda}_{1},\ldots,\tilde{\Lambda}_{s}caligraphic_S start_POSTSUPERSCRIPT italic_s end_POSTSUPERSCRIPT = ! start_POSTSUPERSCRIPT italic_β start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT end_POSTSUPERSCRIPT over~ start_ARG roman_Δ end_ARG start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , … , ! start_POSTSUPERSCRIPT ... | The formulas in the conclusion are called the main formulas and the formulas in the premises are called the active formulas of the rule. Usually, we work with the rules with exactly one main formula. A rule is called single-conclusion if all of its meta-sequents are single-conclusion. Define the single-conclusion versi... | Such a setting is required to define the multiplicative rules, like the left implication or right fusion rules, where the contexts of the premises are merged in the conclusion. | The left and middle premises are in the same family with the context Π~~Π\tilde{\Pi}over~ start_ARG roman_Π end_ARG in the antecedent. Thus, one copy of Π~~Π\tilde{\Pi}over~ start_ARG roman_Π end_ARG appears in the antecedent of the conclusion. A generic example of a right multi-conclusion semi-analytic rule is: | condition of occurrence-preservation is a weaker version of the usual analyticity property. Furthermore, recall that the usual sequent calculi for substructural logics have two basic ways to handle the contexts. For the additive connectives, namely the conjunction and disjunction, the contexts in the premises of the ru... | B |
\widetilde{q},r)-\left(\frac{\sqrt{3}}{2}+\epsilon_{1}+\epsilon_{2}\right)\deltaoverOVERACCENT start_ARG < end_ARG roman_dist start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT ( italic_p , over~ start_ARG italic_q end_ARG ) + italic_ϵ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT italic_δ + italic_ϵ start_POSTSUBSCRIPT 2 end_PO... | <distx(c,q).absentsubscriptdist𝑥𝑐𝑞\displaystyle<\operatorname{dist}_{x}(c,q).< roman_dist start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT ( italic_c , italic_q ) . | <distx(p,c)absentsubscriptdist𝑥𝑝𝑐\displaystyle<\operatorname{dist}_{x}(p,c)< roman_dist start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT ( italic_p , italic_c ) | =distx(p,r)−distx(r,c)+distx(r,c)−32δ≤4distx(p,c).absentsubscriptdist𝑥𝑝𝑟subscriptdist𝑥𝑟𝑐subscriptdist𝑥𝑟𝑐32𝛿4subscriptdist𝑥𝑝𝑐\displaystyle=\operatorname{dist}_{x}(p,r)-\operatorname{dist}_{x}(r,c)+% | dist(p,rp)+dist(sq,q)+dist(r,s)<distx(p,c)+distx(c,q)+dist(r,s)=dist(p,q)+dist(r,s)dist𝑝superscript𝑟𝑝distsuperscript𝑠𝑞𝑞dist𝑟𝑠subscriptdist𝑥𝑝𝑐subscriptdist𝑥𝑐𝑞dist𝑟𝑠dist𝑝𝑞dist𝑟𝑠\displaystyle\operatorname{dist}(p,r^{p})+\operatorname{dist}(s^{q},q)+% | C |
If the shape functions are in the pre-image basis, then F𝐹Fitalic_F won’t in general | H𝐻Hitalic_H and V𝑉Vitalic_V, the univariate functions H(0,y)𝐻0𝑦H(0,y)italic_H ( 0 , italic_y ) and V(x,0)𝑉𝑥0V(x,0)italic_V ( italic_x , 0 ) | compute for ζ(x,y)𝜁𝑥𝑦\zeta(x,y)italic_ζ ( italic_x , italic_y ) that are straightforward to evaluate. | polynomial on 𝐑2superscript𝐑2\mathbf{R}^{2}bold_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT and so will H𝐻Hitalic_H and V𝑉Vitalic_V and since each curve | To evaluate G𝐺Gitalic_G, we must also evaluate H𝐻Hitalic_H and V𝑉Vitalic_V numerically. | D |
In this section, we will provide the details of the contextual hourglass module and our Contextual Hourglass Network (CxtHGNet). | In this work, we choose to utilize the encoding layer [13, 21] as our channel-wise attention mechanism to test the network performance, which has the ability to selectively highlight class-dependent featuremaps. It may be worthwhile to mention that it is convenient to replace the channel-wise attention used here with o... | 1) We design a novel contextual hourglass module which incorporates attention mechanism on processed low-resolution featuremaps to exploit the contextual semantics and therefore improve the robustness of the prediction. | Our contextual hourglass module is a symmetric structure inspired by hourglass module [12]. It firstly processes features down to a low resolution by a set of convolutional and pooling layers, then applies channel-wise, point-wise or other attention mechanisms on the processed low-resolution featuremap, and finally bi-... | We develop a novel Contextual Hourglass Network (CxtHGNet) for semantic segmentation of high-resolution aerial imagery. Our CxtHGNet can extract rich multi-scale features of the image and learn the contextual semantics in scenes, due to the incorporation of bottom-up, top-down inference across various scales, attention... | C |
On the applications side, the results herein can be used to solve infinite horizon versions of online network revenue management where the retailer must price several unique products, each of which may consume common resources (e.g., inventories of different products) that have limited availability and are replenished ... | O(logn)𝑂𝑙𝑜𝑔𝑛O(logn)italic_O ( italic_l italic_o italic_g italic_n )) for cases in which activation costs are bandit-dependent iid random variables. Applications of MAB models include problems of online revenue management: Ferreira et al. (2018), Wang et al. (2014), Johnson et al. (2015) of dynamic procurement:... | search-based and targeted advertising online learning, cf. Rusmevichientong and Williamson (2006), Agarwal et al. (2014) and references therein. | For versions of such problems with no resource (inventory) replenishment we refer to Ferreira et al. (2018) and references therein. Additional applications include | refer to: Guha and Munagala (2007); Tran-Thanh et al. (2012); Thomaidou et al. (2012); Lattimore et al. (2014); Sen et al. (2015); Pike-Burke and Grunewalder (2017); Zhou et al. (2018); Spencer and Kevan de Lopez (2018) and | C |
5: S∗←S∗∪{v}←superscript𝑆superscript𝑆𝑣S^{*}\leftarrow S^{*}\cup\{v\}italic_S start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT ← italic_S start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT ∪ { italic_v }; | In this section, we present the algorithm designed based on the hybrid sampling method for solving the MP problem and provide theoretical analysis. | In this paper, we present a hybrid sampling method which is designed particularly for the misinformation prevention problem. We show that the new sampling method can be used to design an approximation algorithm which outperforms the state-of-the-art solutions. | In this sampling method, the frequency that a node can be collected in the first step is proportional to the probability that it will be affected by the misinformation. Thus, the samples produced by the second step are more likely to be the protectors of the nodes which are prone to be misinformation-influenced. Note t... | There are three most related existing works, [2, 4, 15], which aim at solving Problems 1 and 2 by designing approximation algorithms. C. Budak et al. [2] first proposed the problem of limiting the spread of information and they considered Problem 2. In [2], it is shown that Problem 2 is monotone and submodular, and the... | A |
Detection Trigger Module: If the confidence score surpasses a predefined threshold and the frame-skipping counter hasn’t reached its limit, the system skips detection and relies solely on the Kalman filter’s prediction for the current frame (detection is skipped). This approach improves processing speed. Conversely, if... | Data Association: The Hungarian algorithm is employed for the data association task, effectively matching the detection results from the current frame with the predicted object locations provided by the Kalman filter. This process ascertains the continuity of object identity between consecutive frames, ensuring that ea... | Figure 1: illustrates the tracking outcomes for frames 55 to 61 utilizing the CTD approach. The analysis is illustrated with cropped image frames, where white bounding boxes denote predictions made by the Kalman filter, and blue bounding boxes indicate detections from the object detector. Between frames 56 and 60, no n... | Hungarian Assignment: This algorithm plays a crucial role in object association and ID attribution. It essentially determines whether an object detected in the current frame corresponds to the same object tracked in the previous frame. | Kalman Filter: When a new frame arrives, the Kalman Filter predicts the object’s location in the current frame based on its detection information from the previous frame. This prediction helps maintain object tracking during periods when detection is skipped. | A |
KF4subscript𝐾subscript𝐹4K_{F_{4}}italic_K start_POSTSUBSCRIPT italic_F start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT end_POSTSUBSCRIPT | 1.5×10−51.5superscript1051.5\times 10^{-5}1.5 × 10 start_POSTSUPERSCRIPT - 5 end_POSTSUPERSCRIPT | 1.2×10−51.2superscript1051.2\times 10^{-5}1.2 × 10 start_POSTSUPERSCRIPT - 5 end_POSTSUPERSCRIPT | 1.7×10−51.7superscript1051.7\times 10^{-5}1.7 × 10 start_POSTSUPERSCRIPT - 5 end_POSTSUPERSCRIPT | 1.6×10−51.6superscript1051.6\times 10^{-5}1.6 × 10 start_POSTSUPERSCRIPT - 5 end_POSTSUPERSCRIPT | A |
In this section our goal will be to leverage sublevel set persistence for the selection of τ𝜏\tauitalic_τ for both state space reconstruction and permutation entropy. | Specifically, our goal is to automate the frequency analysis method [27] for selecting τ𝜏\tauitalic_τ for state space reconstruction by analyzing both the time and frequency domain of the signal using sublevel set persistence. | The goal in this section is to relate the distribution of permutations formed from a given delay τ𝜏\tauitalic_τ to the state space reconstruction with the same delay τ𝜏\tauitalic_τ. This connection will show the time delay for both permutations and state space reconstruction are related. | In this section our goal will be to leverage sublevel set persistence for the selection of τ𝜏\tauitalic_τ for both state space reconstruction and permutation entropy. | The first approach we implement for estimating the maximum significant frequency of a signal is based on a time domain analysis of the sublevel set persistence. | A |
Specifically, they require that r≥2m+ς+(2ℓ−1)d𝑟superscript2𝑚𝜍superscript2ℓ1𝑑r\geq 2^{m+\varsigma}+(2^{\ell}-1)ditalic_r ≥ 2 start_POSTSUPERSCRIPT italic_m + italic_ς end_POSTSUPERSCRIPT + ( 2 start_POSTSUPERSCRIPT roman_ℓ end_POSTSUPERSCRIPT - 1 ) italic_d, which implies log2(d)∼log2(r)/(1+1/s)similar-tosubscrip... | We have verified numerically that it agrees with the analysis in [8] when d∼rsimilar-to𝑑𝑟d\sim\sqrt{r}italic_d ∼ square-root start_ARG italic_r end_ARG, see App. B.1.2. | The analyses in [7, 8] are exact, but they rely on d∼rsimilar-to𝑑𝑟d\sim\sqrt{r}italic_d ∼ square-root start_ARG italic_r end_ARG or smaller when s=1𝑠1s=1italic_s = 1. | By comparison, the heuristic analysis in this paper covers the case where d∼rsimilar-to𝑑𝑟d\sim\sqrt{r}italic_d ∼ square-root start_ARG italic_r end_ARG or greater. | To see why we need d∼rsimilar-to𝑑𝑟d\sim\sqrt{r}italic_d ∼ square-root start_ARG italic_r end_ARG or greater, note that the heuristic assumes δb=(e+bd)/r mod 1subscript𝛿𝑏𝑒𝑏𝑑𝑟 mod 1\delta_{b}=(e+bd)/r\text{ mod }1italic_δ start_POSTSUBSCRIPT italic_b end_POSTSUBSCRIPT = ( italic_e + italic_b italic_d ) / itali... | C |
Collect lists of srsuperscript𝑠𝑟s^{r}italic_s start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT for every Pisubscript𝑃𝑖P_{i}italic_P start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT | with a similar list of transactions (i.e., xij=yjsuperscriptsubscript𝑥𝑖𝑗superscript𝑦𝑗x_{i}^{j}=y^{j}italic_x start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_j end_POSTSUPERSCRIPT = italic_y start_POSTSUPERSCRIPT italic_j end_POSTSUPERSCRIPT), and | yjsuperscript𝑦𝑗y^{j}italic_y start_POSTSUPERSCRIPT italic_j end_POSTSUPERSCRIPT=set of verified transactions by remaining cooperative | yjsuperscript𝑦𝑗y^{j}italic_y start_POSTSUPERSCRIPT italic_j end_POSTSUPERSCRIPT=set of verified transactions by remaining cooperative | transactions yjsuperscript𝑦𝑗y^{j}italic_y start_POSTSUPERSCRIPT italic_j end_POSTSUPERSCRIPT that is different from his own vector of transactions | B |
|f(x)∧f(z)|≥i𝑓𝑥𝑓𝑧𝑖|f(x)\wedge f(z)|\geq i| italic_f ( italic_x ) ∧ italic_f ( italic_z ) | ≥ italic_i implying continuity of f𝑓fitalic_f. | Moreover, if f𝑓fitalic_f is uniformly computable, then the modulus of continuity of M𝑀Mitalic_M is in particular a modulus of continuity for f𝑓fitalic_f and is thus uniformly continuous. | We only have left to show that if f𝑓fitalic_f is moreover uniformly continuous, then M𝑀Mitalic_M has a computable modulus of continuity. | Moreover if there exists a computable function m:ℕ→ℕ:𝑚→ℕℕm\colon\mathbb{N}\rightarrow\mathbb{N}italic_m : blackboard_N → blackboard_N (called a modulus of continuity for M𝑀Mitalic_M) | Hence in each of the next i𝑖iitalic_i steps, we are guaranteed to output a letter. Hence m′superscript𝑚′m^{\prime}italic_m start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT is a modulus of continuity for M𝑀Mitalic_M and f𝑓fitalic_f is uniformly computable. | A |
Note that for all r∈[1,2]𝑟12r\in[1,2]italic_r ∈ [ 1 , 2 ], if |δ|=Θ(|Q|r)𝛿Θsuperscript𝑄𝑟|\delta|=\Theta(|Q|^{r})| italic_δ | = roman_Θ ( | italic_Q | start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT ) then the second approach is faster by at least a factor of |Q|𝑄|Q|| italic_Q |. | In the rest of the paper we analyse the general case of model checking a given Markov chain against a given unambiguous Büchi automaton. | Perhaps more significantly, model checking Markov chains against Büchi automata, i.e., computing the probability that the random word generated by the Markov chain is accepted by the automaton, is a key problem in the verification of probabilistic systems. | In this paper we obtain a faster algorithm (recall that E𝐸Eitalic_E is the set of transitions in the Markov chain): | Although it is not the main focus of this paper, we have analysed also the model-checking problem, where a non-trivial Markov chain is part of the input. | D |
2.9×1072.9superscript1072.9\times 10^{7}2.9 × 10 start_POSTSUPERSCRIPT 7 end_POSTSUPERSCRIPT | 2×1062superscript1062\times 10^{6}2 × 10 start_POSTSUPERSCRIPT 6 end_POSTSUPERSCRIPT | 2×1062superscript1062\times 10^{6}2 × 10 start_POSTSUPERSCRIPT 6 end_POSTSUPERSCRIPT | 2×1062superscript1062\times 10^{6}2 × 10 start_POSTSUPERSCRIPT 6 end_POSTSUPERSCRIPT | 3.5×1063.5superscript1063.5\times 10^{6}3.5 × 10 start_POSTSUPERSCRIPT 6 end_POSTSUPERSCRIPT | D |
Multivariate analysis of variance (Manova) [38, 24] and Hotelling T2superscript𝑇2T^{2}italic_T start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT (Hotelling) [39]. | Mean Embedding Test [40]: A test based on the analytical mean embeddings between two distributions. | The evaluation uses a spiral simulation with 1000 samples and 2 dimensions for each test and compares test statistics over 20 repetitions. Figure 1b shows the difference between the hyppo implementation of the independence test and the respective R package implementation of the independence test. | Smooth CF Test [40]: A test using analytic analogues of characteristic functions. | tools contains common helper functions, simulations, and finite-sample statistical power functions to test differences between each test in hyppo. | C |
A pixelated “Game Over” was the message that flashed across our CRT televisions when we ran out of lives. We would start again, play until the next “Game Over,” and repeat until our mothers told us our eyeballs would turn into squares if we played any longer. The same “Game Over” also signaled the conclusion of a game.... | To test our hypothesis, we consider how to gamify the vehicle routing problem with stochastic requests (VRPSR). The VRPSR is an important problem in modern logistics. It is the problem of dynamically routing a vehicle to service customer requests that occur at random times across an operating horizon and in random plac... | Game worlds, playable areas, zoom views, minimaps, deep-Q𝑄Qitalic_Q networks. These things are not the end. This is only level one. New quests await us. Games, like optimization problems, have always been about discovery of a winning policy. Whether that happens through theorems and proofs, or by sitting an agent in f... | DRL methods have been applied to a variety of tasks involving sequential decisions and uncertainty. These tasks span the domains of healthcare (Liu et al., 2017), image recognition (Choi et al., 2018), and autonomous driving (Sallab et al., 2017), to name a few. In the operational realm, members of our team have applie... | Though some of our game designs allow agents to outperform benchmark policies, our aim is not to develop a state-of-the-art procedure. Rather, our contribution is a connection between the seemingly disparate worlds of video games and logistics. More generally, our work points to the representation of dynamic and stocha... | B |
We next discuss the role of the symmetric generations structure in the bound of two additional signals per generation. We have implicitly imposed three restrictions on the network, beyond the basic generations structure: the observation structures are the same across generations, all generations are the same size, and ... | is worse with larger generation sizes, as illustrated in Figure 1. We also show that even early generations learn slowly in maximal generations networks. Social learning accumulates no more than three signals per generation starting with the third generation. If everyone in the first generation observes a single additi... | We next discuss the role of the symmetric generations structure in the bound of two additional signals per generation. We have implicitly imposed three restrictions on the network, beyond the basic generations structure: the observation structures are the same across generations, all generations are the same size, and ... | The arbitrarily large information loss we have highlighted in Section 4 can have large welfare consequences. To illustrate this, we give an example comparing complete networks to maximal generations networks with large generations. | Jadbabaie (2006)). We could also allow different sized generations and obtain bounds on aggregative efficiency. For example, the logic of Example 2 would extend to maximal generation networks with generations of varying sizes. | D |
We therefore impose an ℓ1subscriptℓ1\ell_{1}roman_ℓ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT-norm constraint to the first layer of 𝐖hsuperscript𝐖ℎ\mathbf{W}^{h}bold_W start_POSTSUPERSCRIPT italic_h end_POSTSUPERSCRIPT which includes the fully connected weights. | We expect that this constraint will set many elements in the first layer of 𝐖hsuperscript𝐖ℎ\mathbf{W}^{h}bold_W start_POSTSUPERSCRIPT italic_h end_POSTSUPERSCRIPT to zeros and identify the edges that | We therefore impose an ℓ1subscriptℓ1\ell_{1}roman_ℓ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT-norm constraint to the first layer of 𝐖hsuperscript𝐖ℎ\mathbf{W}^{h}bold_W start_POSTSUPERSCRIPT italic_h end_POSTSUPERSCRIPT which includes the fully connected weights. | and 𝐖hsuperscript𝐖ℎ\mathbf{W}^{h}bold_W start_POSTSUPERSCRIPT italic_h end_POSTSUPERSCRIPT in the FC layer (embedded in olsubscript𝑜𝑙o_{l}italic_o start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT) | and 2) weight 𝐖hsuperscript𝐖ℎ\mathbf{W}^{h}bold_W start_POSTSUPERSCRIPT italic_h end_POSTSUPERSCRIPT within the FC for prediction. | A |
A retired region is a region in the old reference genome that does not map to any region in the new reference genome (colored in pink). | An updated region is a region in the old reference genome that maps to at least one region in the new reference genome within a reasonable error rate, i.e., differences from the old reference (colored in orange with some differences marked with black bars). | A new region is a region in the new reference genome that does not map to any region in the old reference genome (colored in green). | A constant region is a region of the genome that is exactly the same in both old and new reference genomes (colored in blue). The start and end positions of a constant region are not necessarily the same in the old and new reference genomes. | A retired region is a region in the old reference genome that does not map to any region in the new reference genome (colored in pink). | B |
Khaligh-Razavi, S.-M., and Kriegeskorte, N.: Deep supervised, but not unsupervised, models may explain IT cortical representation. PLOS Computational Biol. 10 (2014). | Khaligh-Razavi, S.-M., and Kriegeskorte, N.: Deep supervised, but not unsupervised, models may explain IT cortical representation. PLOS Computational Biol. 10 (2014). | Kriegeskorte, N. and Douglas, P. K.: Interpreting Encoding and Decoding Models. arXiv:1812.00278 [q-bio] (2018). | Evtimov, I et al. “Robust physical-world attacks on deep learning models,” arXiv:1707.08945, 2017. | Kriegeskorte, N. and Douglas, P. K.: Cognitive Computational Neuroscience. Nature Neuroscience. 21. 1148-1160 (2018). | B |
Nusubscript𝑁𝑢N_{u}italic_N start_POSTSUBSCRIPT italic_u end_POSTSUBSCRIPT bits by applying Theorem 3.3 (with parameters N=Nu𝑁subscript𝑁𝑢N=N_{u}italic_N = italic_N start_POSTSUBSCRIPT italic_u end_POSTSUBSCRIPT, k=ku𝑘subscript𝑘𝑢k=k_{u}italic_k = italic_k start_POSTSUBSCRIPT italic_u end_POSTSUBSCRIPT and 1logn... | D.𝚠𝚛𝚒𝚝𝚎(u,X)formulae-sequence𝐷𝚠𝚛𝚒𝚝𝚎𝑢𝑋D.\mathtt{write}(u,X)italic_D . typewriter_write ( italic_u , italic_X ). | dense rank to replace the self-delimiting number in D.𝚟𝚎𝚌𝚝𝚘𝚛(u)formulae-sequence𝐷𝚟𝚎𝚌𝚝𝚘𝚛𝑢D.\mathtt{vector}(u)italic_D . typewriter_vector ( italic_u ) by the | operations 𝚛𝚎𝚊𝚍𝚛𝚎𝚊𝚍\mathtt{read}typewriter_read(u𝑢uitalic_u) and 𝚠𝚛𝚒𝚝𝚎𝚠𝚛𝚒𝚝𝚎\mathtt{write}typewriter_write(u𝑢uitalic_u) in constant time as | vector q𝑞qitalic_q by calling D.𝚠𝚛𝚒𝚝𝚎(u,(h+1,rq))formulae-sequence𝐷𝚠𝚛𝚒𝚝𝚎𝑢ℎ1subscript𝑟𝑞D.\mathtt{write}(u,(h+1,r_{q}))italic_D . typewriter_write ( italic_u , ( italic_h + 1 , italic_r start_POSTSUBSCRIPT italic_q end_POSTSUBSCRIPT ) ). | A |
As an alternative approach, relative localization based on wireless communication between drones has the advantage of being lightweight and suitable for resource-constrained aerial vehicles. | To support relative localization, the ranging message must carry additional velocity, yaw rate, and height information of the sender, so that the neighbors can utilize such information for relative localization estimations. | Figure 1: The scheme of the multi-robot system and all onboard sensors. Specifically, each robot has an inertial measurement unit (IMU), an optical flow sensor, and a downward-pointing laser sensor for obtaining acceleration, rotation rates, velocities, and height. This information is fused by an onboard filter to get ... | In this simulation, the relative state between two robots is estimated and compared to the ground-truth relative position and yaw to verify the localization accuracy. | The aerial robots use wireless antennas to exchange state information (e.g., velocity, yaw rate, height) and combine these with relative range measurements obtained from the antennas, which attracts recent attensions [11, 12, 13]. | D |
The paper is organized as follows. We start by discussing the related background and our previous work (Section 2). We introduce the grammar of IEMA that bases on a new taxonomy of explanations (Section 3) and present its applicability on two real-world predictive tasks (Section 4). We then report the results from a us... | 2.1 A theory-practice mismatch in explainable and interpretable machine learning | The topic of explainable machine learning brings much attention recently. However, related work is dominated by contributions with a technical approach to XIML or works focused on providing a list of requirements for its better adoption. | Complex machine learning predictive models, often referred to as black-boxes, demonstrate high efficiency in a rapidly increasing number of applications. Simultaneously, there is a growing awareness among machine learning practitioners that we require more comprehensive tools for model interpretability and explainabili... | Contrastively, Yan et al. (2020) create an interpretable decision tree that supports decision-making in a hospital, concerning COVID-19 mortality. We applied the methodology of IEMA to showcase the potential human-model dialogue with a machine learning black-box in this use-case (Baniecki and Biecek, 2021). It results ... | A |
The pump and dumps on currencies with higher market capitalization are typically carried out on Binance, the ones with lower market capitalization on Cryptopia. | Once a pump is detected we pause our classifier for 30303030 minutes to avoid multiple alerts for the same event. | YoBit is the exchange where most of pump and dump operations happen, while Binance is the most popular exchange among all groups. | The pump and dumps on currencies with higher market capitalization are typically carried out on Binance, the ones with lower market capitalization on Cryptopia. | In particular, the median market capitalization of the cryptocurrencies for exchange is $25,574,192currency-dollar25574192\$25,574,192$ 25 , 574 , 192 for Binance, $2,619,703currency-dollar2619703\$2,619,703$ 2 , 619 , 703 for YoBit, $2,512,627currency-dollar2512627\$2,512,627$ 2 , 512 , 627 for BitTrex, and $144,373cu... | D |
Note that there are different possible ways of constructing computational models | In particular, we can then apply the construction of cohomological information as in | higher mutual information functionals of cohomological information, in the same way as the | One interprets then the rest of the cohomological integrated information as measures | with respect to which one can compute the cohomological integrated information as | A |
In this paper, we argue that applying neurotechnology for human augmentation to augment physicians and surgeons, and can cause personal identity, discrimination and financial issues for physicians and surgeons, and lead to patients being harmed. The way that the paper is structured is as followed: we first describe the... | For our case, we will only mainly focus on (1) and (4) as (2) and (3) are more distant to the scope of the paper. However, those are areas that can and should be further investigated. With there being four different groups, there is the change that those that physicians and surgeons that are fully augmented (i.e. have ... | Knowing how neurotechnology can realize augmentations within humans enables us to address how such technology and augmentations will impact medical practice. For this section, we will specifically focus on the practice of surgery. In this case, the users of the neurotechnology are surgeons. Within surgical settings, au... | For this section, we will focus on medical practice that do not involve surgery. In this case, the users of the neurotechnology would be physicians. Within non-surgical settings, augmented vision and augmented cognition will allow physicians to better perform diagnoses. For instance, given that the physician will have ... | Human augmentation can be formally defined as an interdisciplinary field that addresses methods, technologies and their application for enhancing cognitive abilities, senses and actions of humans [32]. In enhancing these leads us to augmented cognition, augmented senses, and augmented actions. Augmented senses focus on... | D |
In Section 5, we prove that the first fall degree of a multi-graded polynomial system is bounded by a certain value determined from its multi-degree if the order of the coefficient field is sufficiently large, and provide the theoretical assumption for applying the XL algorithm with a kernel search. | In Section 5, we prove that the first fall degree of a multi-graded polynomial system is bounded by a certain value determined from its multi-degree if the order of the coefficient field is sufficiently large, and provide the theoretical assumption for applying the XL algorithm with a kernel search. | In this article, we mainly investigate an upper bound of the first fall degree for a polynomial system over a sufficiently large field. Upper bounds given in this article are actually that of the minimal degree d𝐾𝑆𝑦𝑧subscript𝑑𝐾𝑆𝑦𝑧d_{{\it KSyz}}italic_d start_POSTSUBSCRIPT italic_KSyz end_POSTSUBSCRIPT at the f... | In Section 6, we provide actual examples that satisfy the condition for the order of the coefficient field. | In Section 4, we prove that the first fall degree is smaller than the degree of regularity in the semi-regular case if the order of the coefficient field is sufficiently large. | C |
Antic, J.: A deep learning based project for colorizing and restoring old images (2018) | Anwar, S., Khan, S., Barnes, N.: A deep journey into super-resolution: A survey. | Anwar, S., Khan, S., Barnes, N.: A deep journey into super-resolution: A survey. | Anwar, S., Khan, S., Barnes, N.: A deep journey into super-resolution: A survey. | Therefore, inspired by surveys in deep image super-resolution [6], VQA [1], etc., we provide a comprehensive survey of deep image colorization. | A |
In Section 4.1 we show that the factor 2 is essentially optimal in the worst case, unless P = NP. | We study the computational complexity of finding φ∗superscript𝜑\varphi^{*}italic_φ start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT and polynomial-time approximation algorithms. In general, approximating φ∗superscript𝜑\varphi^{*}italic_φ start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT can be an extremely hard problem, even in... | For the constrained delegation problem, we show two interesting non-trivial approximation results in Section 4.2. For instances with degree-d𝑑ditalic_d states we give a (2−1d2)21superscript𝑑2(2-\frac{1}{d^{2}})( 2 - divide start_ARG 1 end_ARG start_ARG italic_d start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG )-ap... | We discuss tractable special cases in Section 4.3. Sher [32, Theorem 7] shows that in instances with foresight the optimal decision scheme can be found in polynomial time by solving a network flow problem. Unique rejects and degree-1 accepts are special cases, so the same result holds. For proof of membership, the opti... | In Section 4.2 we present our results on approximation algorithms. The results on special cases with optimal schemes are discussed in Section 4.3. | D |
In contrast with the setting in this paper where memory involves the dependence of the output time series on the input, the Hurst exponent measures temporal variations and dependence within the input time series itself. | This may serve to justify or improve current heuristic methods (Tseng et al., 2016; Dieng et al., 2017; Trinh et al., 2018) developed in applications to deal with the difficulty in training with long-term memory. | Recurrent neural networks (RNNs) (Rumelhart et al., 1986) are among the most frequently employed methods to build machine learning models on temporal data. Despite its ubiquitous application (Baldi et al., 1999; Graves & Schmidhuber, 2009; Graves, 2013; Graves et al., 2013; Graves & Jaitly, 2014; Gregor et al., 2015), ... | Much of the time series literature investigates statistical properties and estimation methods of data with long range dependence (Samorodnitsky, 2006; Taqqu et al., 1995; Beran, 1992; Doukhan et al., 2003). One can also combine these classic statistical methodologies with the RNN-like architectures to design hybrid mod... | In the literature, a number of results have been obtained pertaining to the analysis of training dynamics of RNNs. A positive result for training by GD is established in Hardt et al. (2018), but this is in the setting of identifying hidden systems, i.e. the target functional comes from a linear dynamical system, hence ... | C |
The uniform distribution on {(1,1,−1),(1,−1,1),(−1,1,1)}111111111\{(1,1,-1),(1,-1,1),(-1,1,1)\}{ ( 1 , 1 , - 1 ) , ( 1 , - 1 , 1 ) , ( - 1 , 1 , 1 ) } has the same pairwise biases. | It suffices to show that for every clause, there exists a distribution of satisfying assignments that agrees with the global (pairwise) biases. | The uniform distribution on {(1,1,−1),(1,−1,1),(−1,1,1)}111111111\{(1,1,-1),(1,-1,1),(-1,1,1)\}{ ( 1 , 1 , - 1 ) , ( 1 , - 1 , 1 ) , ( - 1 , 1 , 1 ) } has the same pairwise biases. | Our intuition for this conjecture is that this configuration comes from taking the uniform distribution over satisfying assignments where all but one of the Xisubscript𝑋𝑖X_{i}italic_X start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT are the same, which we expect are the hardest satisfying assignments to distinguish fro... | The following distribution on satisfying assignments has the same pairwise biases. | D |
Even in the case of the smaller Coppersmith-Winograd tensor CW1𝐶subscript𝑊1CW_{1}italic_C italic_W start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT, the known limitations are weaker, and it is not ruled out that one could achieve ω<2.239𝜔2.239\omega<2.239italic_ω < 2.239 using it (see [ambainis, Table 1]). | The main contribution of this paper is a new refined version of the laser method which we then use to obtain the new bound on ω𝜔\omegaitalic_ω. The laser method (as coined by Strassen [laser]) is a powerful mathematical technique for analyzing tensors. In our context, it is used to lower bound the “value” of a tensor ... | After the preliminary version of this paper, subsequent work [duan2023faster, williams2024new] designed a further improved matrix multiplication algorithm, achieving ω<2.371552𝜔2.371552\omega<2.371552italic_ω < 2.371552. The key idea behind these improvements is a new asymmetric way to apply the laser method to CWq𝐶... | We present our new probabilistic argument for dealing with distributions β∈Dα𝛽subscript𝐷𝛼\beta\in D_{\alpha}italic_β ∈ italic_D start_POSTSUBSCRIPT italic_α end_POSTSUBSCRIPT other than α𝛼\alphaitalic_α in Section 3, and then we show how to incorporate it into the laser method in Section 4. We then get into the det... | In this subsection, we give an overview of our improvement to the laser method. We assume familiarity with basic notions related to tensors and matrix multiplication; unfamiliar readers may want to read Section 2 first. | D |
=ℒsup,absentsubscriptℒsup\displaystyle=\mathcal{L}_{\mathrm{sup}},= caligraphic_L start_POSTSUBSCRIPT roman_sup end_POSTSUBSCRIPT , | Π1subscriptΠ1\displaystyle\Pi_{1}roman_Π start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT | For the sets Σ1subscriptΣ1\Sigma_{1}roman_Σ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT, ℒsupsubscriptℒsup\mathcal{L}_{\mathrm{sup}}caligraphic_L start_POSTSUBSCRIPT roman_sup end_POSTSUBSCRIPT, Π1subscriptΠ1\Pi_{1}roman_Π start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT, ℒsubsubscriptℒsub\mathcal{L}_{\mathrm{sub}}caligraphic_L sta... | \underline{r}_{n}=x_{*}roman_inf start_POSTSUBSCRIPT italic_n ∈ blackboard_N end_POSTSUBSCRIPT start_ARG start_FLOATSUPERSCRIPT ′ end_FLOATSUPERSCRIPT end_ARG under¯ start_ARG italic_r end_ARG start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT = italic_x start_POSTSUBSCRIPT ∗ end_POSTSUBSCRIPT. Hence, x∗∈Π1subscript𝑥subsc... | The following lemma is a basic result by Zheng and Weihrauch, characterizing the sets Σ1subscriptΣ1\Sigma_{1}roman_Σ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT and Π1subscriptΠ1\Pi_{1}roman_Π start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT through the suprema and infima of computable sequences of rational numbers. | A |
\mathcal{R}\}.italic_L start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT ( italic_D start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , … , italic_D start_POSTSUBSCRIPT italic_K end_POSTSUBSCRIPT ) ≜ roman_inf start_POSTSUBSCRIPT ( italic_R , italic_L ) end_POSTSUBSCRIPT { italic_L | ( italic_R , italic_L , italic_D start_POSTSUBSCRIP... | In addition to the privacy and utility, the released rate, which represents the necessary number of bits per letter to transmit the privatized data, is also an important metric of a privatization mechanism as mentioned in Section II-A. We have studied the optimal tradeoff between privacy and utility. The next interesti... | Due to the lack of information of which task to be carried out, a robust privatization based on a given set of possible tasks is considered. We first derive the single-letter characterization of the optimal privacy-utility tradeoff. By applying log-loss distortion as the utility metric, the minimum privacy leakage prob... | that can achieve the minimum released rate in problem (44), and the minimum rate is | Note that in the above definition, L∗superscript𝐿L^{*}italic_L start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT is not a function of the released rate R𝑅Ritalic_R. Instead, it is the minimum leakage with arbitrarily large released rate. The impact of the released rate and the sufficient condition to achieve the optimal pr... | D |
Additionally, we need a way to increase and decrease the approximation level (the n𝑛\mathit{{\color[rgb]{0,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,0}% | \pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}{n}}}italic_n index), for reasons we explain below. | \pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}{n-2}}}italic_n - italic_2 steps. | \pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}{n=3}}}italic_n = italic_3) for this type is: | \pgfsys@color@gray@stroke{0}\pgfsys@color@gray@fill{0}{t^{\prime}}}}italic_t start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT. | A |
While the fact that ERM relies on spurious correlations has become empirical folk wisdom, only a few studies have made efforts to carefully model this. Broadly, there are two kinds of existing models that explain this phenomenon. One existing model is to imagine that both the invariant and the spurious features are onl... | Spurious correlations. Empirical work has shown that deep networks find superficial ways to predict the label, such as by relying on the background (Beery et al., 2018; Ribeiro et al., 2016) or other kinds of shortcuts (McCoy et al., 2019; Geirhos et al., 2020). Such behavior is of practical concern because accuracy ca... | While the fact that ERM relies on spurious correlations has become empirical folk wisdom, only a few studies have made efforts to carefully model this. Broadly, there are two kinds of existing models that explain this phenomenon. One existing model is to imagine that both the invariant and the spurious features are onl... | The other existing model is based on the “simplicity bias” of gradient-descent based deep network training (Rahaman et al., 2018; Neyshabur et al., 2015; Kalimeris et al., 2019; Arpit et al., 2017; Xu et al., 2019; des Combes et al., 2018). In particular, this model typically assumes that both the invariant and spuriou... | The most popular strategy is to learn useful features while constraining them to have similar distributions across domains (Ganin et al., 2016; Li et al., 2018b; Albuquerque et al., 2020). Other works constrain these features in a way that one can learn a classifier that is simultaneously optimal across all domains (Pe... | C |
There is a constant c𝑐citalic_c such that for any d⩾3𝑑3d\geqslant 3italic_d ⩾ 3 it holds that any graph | Given any graph Gdsubscript𝐺𝑑G_{d}italic_G start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT that is drawn in a d𝑑ditalic_d-dimensional grid, we construct a | n𝑛nitalic_n variables, we can generate a graph Gdsubscript𝐺𝑑G_{d}italic_G start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT of degree at most 4444 drawn in a | G𝐺Gitalic_G of maximum degree 2d2𝑑2d2 italic_d on n𝑛nitalic_n vertices can be drawn in a d𝑑ditalic_d-dimensional | cover on graphs drawn in a d𝑑ditalic_d-dimensional grid. In the second stage, given | C |
In order to make the download rate decision of each user, the physical layer subproblem (PHY-LS) is solved before the download of every chunk. Note that a beam alignment period is considered before the download of each chunk, and that the beam coherence time is assumed to be longer than the chunk download time. Therefo... | Our objective twofold: (i) minimize Max(𝒲)Max𝒲\text{Max}(\cal{W})Max ( caligraphic_W ) and, (ii) use the remaining resources to maximize the available rate for each user, so the application layer subproblem (APP-LS) can use the rate to maximize the QoE of each user. Since a user’s QoE is a concave function with resp... | The problem defined in (5a)-(5k) is a non-convex optimization problem that has integer (non-convex) constraints. Integer-constrained problems are known to be NP hard in general [27]. Very limited problems in this class of discrete optimization are known to be solvable in polynomial time. Moreover, the FoV of each user ... | The PHY-LS described in the previous subsection finds which user is scheduled to use the resources during the time slots comprised in the next beam coherence interval. Hence, the achievable rate for each user during the next beam coherence period is exposed to the application layer algorithm which leverages this knowle... | In this paper, we have proposed a cross layer optimization approach for multi-user 360 degree video streaming. The proposed framework maximizes the available rate to each user and allows each user to efficiently utilize the available rate to maximize its QoE. A QoE metric that maintains a tradeoff between maximizing ea... | A |
Table 10: Prediction results on the training set by the generalised beta-CoRM models with vague gamma, objective Lomax, Lomax and half-Cauchy type priors respectively. | To analyse the effects of the prior on the beta-CoRM models proposed in the previous sections we consider a synthetic data set composed of 5 imbalanced groups with 250 total observations and 300 binary features as graphically represented in Figure 2. We are interested in looking at the computational cost of posterior i... | With respect the feature selection it is further interesting to notice that the four generalised models coincide in 98 features, and this number increases to 119 common features if we just consider the generalised beta-CoRM models with gamma-gamma priors. To fully understand the process of feature selection on this noi... | Now that we have compared the posterior inference of the beta-CoRM models and the impact of the prior we can turn our attention to the feature selection procedure of the generalised beta-CoRM models. To this end we are mainly interested on the optimal number of features, the threshold at which they are found and of cou... | Of course, it is important to remember that the main advantage of the generalised models is that they allow us to find an optimal number of features to reduce the uncertainty in the data and which can be further used to improve the predictive performance of the model. To this end and contrary to the synthetic data we o... | B |
To further improve modelling, in-depth extraction of indicator features and using high-quality data are suggested, which may involve a broader range of risk potentials and driving scenarios, such as lane changing. Methodologically, new algorithms on clustering and AutoML can be integrated to refine the solution. | The occurrence of risk conditions (i.e., the minority class) is usually much lower than the number of safety instances (i.e., the mass majority class). Incorrect assignment of risk instances into a safety class entails a great misclassification cost [17]. Machine learning on imbalanced data is challenging, since algori... | In view of a large number of real-world applications suffering from the challenges of class imbalance and lack of ground truth (e.g., expensive or difficult to obtain beforehand), we demonstrate a reliable solution with a case on road safety, which holds great potentials. | Early risk diagnosis and effective anomaly detection play a key role in a range of advanced solutions towards Smart Road, especially with the development of autonomous and connected vehicles (CAV) and roadside sensing [1]. Smart road will add huge benefits and synergistic effects to standalone smart vehicles, which can... | The quality of clustering can be generally measured by two ways, namely, external validation and internal validation. External validation is by comparing the clustering result to the ground truth or well-defined reference. However, in most real applications, one can hardly claim that a complete knowledge of ground trut... | B |
The experimental conditions of the GA for GPU and many core CPU loop statement offload are as follows. | Number of generations T: No more than the gene length. 16 for 3mm, 20 for NAS.BT and 6 for tdFIR. | First, as a preparation, I proposed an automatic offload method for loop statements for a many core CPU as one of various offloading destination environments, with reference to the evolutionary computation method for a GPU. Next, I studied the order of offload trials for each offloading device and the speedup method wh... | Gene length: Number of GPU and many core CPU processable loop statements. 18 for 3mm, 120 for NAS.BT and 6 for tdFIR. | Number of individuals M: No more than the gene length. 16 for 3mm, 20 for NAS.BT and 6 for tdFIR. | C |
γλ3𝛾superscript𝜆3\gamma\lambda^{3}italic_γ italic_λ start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT | γλ3𝛾superscript𝜆3\gamma\lambda^{3}italic_γ italic_λ start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT | γλ5𝛾superscript𝜆5\gamma\lambda^{5}italic_γ italic_λ start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT | γλ3/2𝛾superscript𝜆32\gamma\lambda^{3/2}italic_γ italic_λ start_POSTSUPERSCRIPT 3 / 2 end_POSTSUPERSCRIPT | \varsigma\lambda^{3}}.italic_λ start_POSTSUBSCRIPT italic_μ end_POSTSUBSCRIPT = 1 , italic_λ start_POSTSUBSCRIPT italic_J end_POSTSUBSCRIPT = italic_γ italic_λ start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT , italic_λ start_POSTSUBSCRIPT caligraphic_P end_POSTSUBSCRIPT = italic_γ italic_ς italic_λ , italic_λ start_POSTSUB... | C |
Ecsuperscript𝐸𝑐E^{c}italic_E start_POSTSUPERSCRIPT italic_c end_POSTSUPERSCRIPT, one character bigram cici+1subscript𝑐𝑖subscript𝑐𝑖1{c_{i}}{c_{i+1}}italic_c start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT italic_c start_POSTSUBSCRIPT italic_i + 1 end_POSTSUBSCRIPT, its representation Ebcsuperscript𝐸𝑏𝑐{E^{bc}}i... | Table 4: An example of a Sindhi sentence, all words end with the non-joiner letters. (i) denote the words with white space (the tokens are separated with ‘-’ symbol), (ii) without white space (iii) Roman transliteration of Sindhi sentence (iv) is the English translation of a Sindhi sentence. | Table 5: Sindhi word types with an example of space insertion, along with English translation. (i) represent the words with white space (‘-’ symbol represents space), and (ii) without space. The Roman transliteration is given for ease of reading. | Table 6: An example of employed character-level sequence tagging scheme for SWS task. The [X] label represents the white spaces. The given Sindhi sentence can be read from right to left, and the Roman transliteration of each Sindhi token can be read from left to right. | Table 7: An example of Sindhi subword decomposition for subword representation learning | D |
Since the SDP relaxation is exact, it holds that rank(P∗)=1ranksuperscript𝑃1\operatorname{rank}(P^{*})=1roman_rank ( italic_P start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT ) = 1. Therefore, P∗superscript𝑃P^{*}italic_P start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT can be expressed as | P=[1xz][1x⊤z⊤]∈𝕊nx+nz+1.𝑃matrix1𝑥𝑧matrix1superscript𝑥topsuperscript𝑧topsuperscript𝕊subscript𝑛𝑥subscript𝑛𝑧1P=\begin{bmatrix}1\\ | P∗=[1x∗z∗][1x∗⊤z∗⊤]superscript𝑃matrix1superscript𝑥superscript𝑧matrix1superscript𝑥absenttopsuperscript𝑧absenttopP^{*}=\begin{bmatrix}1\\ | P∗=[1vw][1v⊤w⊤]=[1v⊤w⊤vvv⊤vw⊤wwv⊤ww⊤]superscript𝑃matrix1𝑣𝑤matrix1superscript𝑣topsuperscript𝑤topmatrix1superscript𝑣topsuperscript𝑤top𝑣𝑣superscript𝑣top𝑣superscript𝑤top𝑤𝑤superscript𝑣top𝑤superscript𝑤topP^{*}=\begin{bmatrix}1\\ | V=[e⊤XZ],e∈ℝr,X∈ℝnx×r,Z∈ℝnz×r,formulae-sequence𝑉matrixsuperscript𝑒top𝑋𝑍formulae-sequence𝑒superscriptℝ𝑟formulae-sequence𝑋superscriptℝsubscript𝑛𝑥𝑟𝑍superscriptℝsubscript𝑛𝑧𝑟V=\begin{bmatrix}e^{\top}\\ | C |
The paper is organized as follows: Section II covers key concepts, Section III introduces the BE-RAN framework, Section IV details core security mechanisms, Section V provides performance analysis, Section VI discusses challenges, and Section VII concludes the paper. | Current 5G RAN typically comprises Centralized Units (CU), Distributed Units (DU), and Radio Units (RU) operating at different OSI layers [7], with the RAN Intelligent Controller (RIC) operating at upper OSI layers. This disaggregated architecture is expected to evolve further in 6G, potentially introducing new functio... | The functional split of RAN at lower layers opens up possibilities for distributed features that could enhance privacy and security in decoupled RAN architectures. In this context, the adoption of distributed ledger technology in RAN presents an opportunity for implementing blockchain-native infrastructure [10, 11, 12]... | To address the growing demand for distributed communication in both industrial and consumer applications, we propose Blockchain-enabled Radio Access Network (BE-RAN). This system incorporates blockchain-enabled identity management and mutual authentication (BeMutual) as core functions, evolving RAN with a decentralizat... | BE-RAN incorporates key RAN features and blockchain concepts to implement core network functions at the RAN level, laying a foundation for future 6G networks. While current 5G architectures form the basis of our research, the principles and innovations proposed in BE-RAN are designed with forward compatibility in mind,... | D |
Function sorted_adjacency_list_rt(Tr)superscript𝑇𝑟(T^{r})( italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT ) is | In: Trsuperscript𝑇𝑟T^{r}italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT rooted tree. | In: Trsuperscript𝑇𝑟T^{r}italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT rooted tree. | In: Trsuperscript𝑇𝑟T^{r}italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT rooted tree at r𝑟ritalic_r. | In: Trsuperscript𝑇𝑟T^{r}italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT rooted tree at r𝑟ritalic_r. | A |
In what follows, we aim to quantify the tradeoffs between excess adversarial risk, privacy, and runtime for output perturbation. We begin by considering the conceptual output perturbation algorithm, in which we assume that we can compute an exact (α=0𝛼0\alpha=0italic_α = 0) saddle point of HD(w,𝐯).subscript𝐻𝐷𝑤𝐯H... | 5.2.2 Conceptual output perturbation for differentially private adversarial training | Algorithm 6 Black Box Output Perturbation Algorithm for Implementing DP Adversarial Training | 5.2.3 Efficiently Implementing Output Perturbation for Private Adversarial Training | In the next subsection, we present a practical, efficient algorithm for implementing differentially private adversarial training with runtime bounds for attaining the above robustness guarantees. | A |
Fig.3 demonstrates the benefit of using our combined localization loss compared to regression only on Carvana dataset (Carvana, 2010). Higher accuracy has been obtained using the combined loss. Fig.4 shows our instance segmentation results on Cityscapes dataset. It is worth noting that our results are reported on "vehi... | Insta-YOLO does not have this limitation. Since the four box points are independent of each other, the resulting polygon will be oriented without additional parameter to learn and free of the angle encoding problem. Table 3 shows that our algorithm supersedes (Ali et al., 2018) in accuracy by 5% and runs at 2.7 times t... | The standard method in literature for instance segmentation is to build a two-stage pipeline (He et al., 2017). First, objects are detected and highlighted using bounding boxes. Then, a semantic segmentation model processes the areas of the detected boxes to produce objects masks. This approach suffers from various dra... | Various applications such as (Tang et al., 2017) and (Ali et al., 2018) require prediction of oriented bounding boxes. Such method requires an additional regression operation to be performed to predict the angle of the box. Conventional oriented boxes methods suffer from angle encoding problem. For practical implementa... | Two-stage instance segmentation methods usually deal with the problem as a detection task followed by segmentation, they detect the bounding boxes of the objects in the first stage, and a binary segmentation is performed for each bounding box in the second stage. Mask R-CNN (He et al., 2017), which is an extension for ... | C |
We study the classical problem of nonparametric dependence detection through a novel perspective of binary expansion. The novel insights from the extension of the Euler formula and the binary expansion approximation of uniformity (BEAUTY) shed lights on the unification of important tests into the novel framework of the... | To facilitate the analysis of large datasets, some desirable attributes of distribution-free tests of independence include (a) a robust high power against a wide range of alternatives, (b) a clear interpretation of the form of dependency upon rejection, and (c) a computationally efficient algorithm. An example of recen... | Two important special cases of goodness-of-fit tests are the test of uniformity and the test of independence. The test of uniformity can be formulated as | When U1subscript𝑈1U_{1}italic_U start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT and U2subscript𝑈2U_{2}italic_U start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT are Unif[−1,1]Unif11\text{Unif}[-1,1]Unif [ - 1 , 1 ] distributed, the binary expansion up to depth D𝐷Ditalic_D effectively leads to a discretization of [−1,1]2superscript11... | Our study on powerful nonparametric tests of uniformity can be further extended and generalized to many directions. For example, extensions to general goodness-of-fit tests and two-sample tests can be investigated through the BEAST approach. Recent papers in these directions include Brown and Zhang (2023); Zhao et al. ... | D |
Large Model Approaches often have deeper architectures and more parameters, allowing them to capture complex features and patterns. Popular approaches can include segmenting point clouds with large image models (such as SAM [79], [188]) and natural language models like ChatGPT. The advanced capabilities of large models... | Generalization and Robustness: Models trained on specific datasets may not generalize well to different types of 3D data, such as those acquired from different sensors or environments. Developing robust models that perform well across various domains remains a challenge. Besides, Variations in object shapes, sizes, and... | Transfer Learning involves leveraging pre-trained models to improve performance on specific tasks, where the models are generally trained on large, often unrelated datasets [192], [234]. In the context of 3D segmentation, transfer learning can significantly enhance accuracy performance and address challenges related to... | Meta-Learning trains models to adapt rapidly to new, unseen data with minimal additional training [231]. By optimizing the learning process and leveraging prior knowledge from various tasks, meta-learning enhances a model’s ability to generalize, perform well with few examples, and transfer knowledge across different t... | Given the differences in domain knowledge required for semantic, instance, and part segmentation tasks in 3D segmentation, this paper reviews the deep learning techniques for each of these three segmentation tasks separately. | C |
Let us remark how bizarre this theorem appears from a cryptographer’s point of view. If 𝖡𝖰𝖯=𝖰𝖬𝖠𝖡𝖰𝖯𝖰𝖬𝖠\mathsf{BQP}=\mathsf{QMA}sansserif_BQP = sansserif_QMA, then no computationally-secure classical cryptographic primitives exist, because such primitives can be broken in 𝖭𝖯𝖭𝖯\mathsf{NP}sansserif_NP, whic... | We use the following definitions of pseudorandom quantum states (PRSs) and pseudorandom unitaries (PRUs), which were introduced by Ji, Liu, and Song [JLS18]. | Ji, Liu, and Song [JLS18] define a pseudorandom state (PRS) ensemble as a keyed family of quantum states {|φk⟩}k∈{0,1}κsubscriptketsubscript𝜑𝑘𝑘superscript01𝜅\{|\varphi_{k}\rangle\}_{k\in\{0,1\}^{\kappa}}{ | italic_φ start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT ⟩ } start_POSTSUBSCRIPT italic_k ∈ { 0 , 1 } start_PO... | Several applications of pseudorandom states and unitaries are known. PRSs and PRUs are useful in quantum algorithms: in computational applications that require approximations to the Haar measure, PRSs and PRUs can be much more efficient than t𝑡titalic_t-designs, which are information-theoretic approximations to the Ha... | Theorem 2 thus provides a negative answer (in the quantum black box setting) to a question of Ji, Liu, and Song [JLS18] that asks if quantum-secure one-way functions are necessary for pseudorandom states. | D |
Numerical experiments on G-set are performed in Section 4. Concluding remarks are given in Section 5. | It should be pointed out that both MOH and CirCut are originally designed for the maxcut problem (1.3) and this work modifies them to generate approximate reference solutions for the anti-Cheeger cut problem (1.2). The descriptions for MOH and CirCut are presented in Appendix A and Appendix B, respectively. | That is, the anti-Cheeger cut problem (1.5) and the maxcut problem (1.6) are fully treated on equal terms by CIA2. | It should be pointed out that both MOH and CirCut are originally designed for the maxcut problem (1.3) and we have to modify them to produce approximate reference solutions for the anti-Cheeger cut problem (1.2) in this work. The interested readers may find more details on MOH and CirCut for the anti-Cheeger cut in App... | The similarity between the anti-Cheeger cut problem (1.5) and the maxcut problem (1.6), which shares a common numerator I(𝒙)𝐼𝒙I(\mbox{\boldmath$x$})italic_I ( bold_italic_x ) for the cut values, | A |
−μ⋅Mt⋅y⊺<0⋅𝜇superscript𝑀𝑡superscript𝑦⊺0-\mu\cdot M^{t}\cdot y^{\intercal}<0- italic_μ ⋅ italic_M start_POSTSUPERSCRIPT italic_t end_POSTSUPERSCRIPT ⋅ italic_y start_POSTSUPERSCRIPT ⊺ end_POSTSUPERSCRIPT < 0 if and only if μ⋅Mt⋅z⊺>1⋅𝜇superscript𝑀𝑡superscript𝑧⊺1\mu\cdot M^{t}\cdot z^{\intercal}>1italic_μ ⋅ italic... | This is where the value of w𝑤witalic_w is important. The result holds if y=z−e𝑦𝑧𝑒y=z-eitalic_y = italic_z - italic_e, | where w⊺superscript𝑤⊺w^{\intercal}italic_w start_POSTSUPERSCRIPT ⊺ end_POSTSUPERSCRIPT is the transpose of w𝑤witalic_w, and | and we just need to show that y=z−e𝑦𝑧𝑒y=z-eitalic_y = italic_z - italic_e satisfies Equations (3.2.2), namely that | In this way, we obtain the main result of this section: an approximation of the value with | A |
The models are implemented with PyTorch and trained/tested on one NVIDIA GTX 1080 Ti graphic card. The experimental settings are kept the same across all experiments for fair comparisons. | Following the mainstream evaluation of SR models [18], we present our model performance with self-ensemble [26], which forms the model ‘KASR+’ | Interestingly, from these tables, we can verify that models with self-ensemble (‘KASR+’ models) are able to boost performance for both PSNR and SSIM, but not for LPIPS. This can be because the self-ensemble operation performs a pixel-level ensemble that may not effectively increase the perceptual quality of the images. | In the experiments, comparisons between the proposed model with existing SR models are performed. In the ablation study, the effectiveness of each component is validated. Also, we examine the effectiveness of the proposed KASR framework combined with multiple mainstream super-resolution models on two real-world dataset... | By default, the model labelled as ‘KASR’ in the experiments below consists of our proposed KASR paired with the EDSR model [18]. | A |
5: if mod(k,τ1)=0mod𝑘subscript𝜏10\mathrm{mod}\left(k,\tau_{1}\right)=0roman_mod ( italic_k , italic_τ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ) = 0 then | 3: for each client node i∈𝒞𝑖𝒞i\in\mathcal{C}italic_i ∈ caligraphic_C in parallel do | We consider an edge-assisted federated learning system as shown in Fig. 1, which consists of C𝐶Citalic_C client nodes (denoted as set 𝒞𝒞\mathcal{C}caligraphic_C) and D𝐷Ditalic_D edge servers (denoted as set 𝒟𝒟\mathcal{D}caligraphic_D). Each client node is associated with an edge server according to some pre-defin... | FEEL [7]: This is a conventional edge-assisted FL scheme, where an edge server randomly schedules five client nodes at each iteration due to the limited number of wireless channels. Note that this is consistent with the number of accessible client nodes for each edge server in SD-FEEL. | 6: for each edge server d∈𝒟𝑑𝒟d\in\mathcal{D}italic_d ∈ caligraphic_D in parallel do | D |
We keep the logic minimal. In [19], more conceivable principles of agency and ability are discussed, and many are rejected. However, any sensible principle (e.g., exploiting the set-theoretical relationships between the acting entities) can find its way into a formalization of a more precise particular domain. | to acknowledge the special character of a group without members, any ability of the empty group is rejected. This is stipulated by the formula ¬can∅ϕsubscriptcanitalic-ϕ\lnot\textsc{can}_{\emptyset}\phi¬ can start_POSTSUBSCRIPT ∅ end_POSTSUBSCRIPT italic_ϕ which is adopted as an axiom. | That is, in what follows, for any formula φ𝜑\varphiitalic_φ, we adopt φ𝜑\varphiitalic_φ as an axiom of an extension of the logic lbda by stating ⊢φprovesabsent𝜑\vdash\varphi⊢ italic_φ. | infer an ability to ϕitalic-ϕ\phiitalic_ϕ from an occurrence of ϕitalic-ϕ\phiitalic_ϕ-ing, this is of little significance since we cannot reason about what will become of the ability in the | We now present the temporalisation of the static core logic of being deemed able with the until-since logic. | B |
Also, analyzing the market capitalization of 264 coins, we find out that 140 (71%) coins are below the $20 million of market capitalization, with 44 (22%) below $1 million. | Instead, Bread is a low market cap cryptocurrency with higher volatility. This means that this asset is more prone to quick market oscillations as well as market manipulations. | Also, analyzing the market capitalization of 264 coins, we find out that 140 (71%) coins are below the $20 million of market capitalization, with 44 (22%) below $1 million. | In particular, the median market capitalization of the cryptocurrencies for exchange is $25,574,192 for Binance, $2,619,703 for YoBit, $2,512,627 for BitTrex, and $144,373 for Cryptopia. | The market capitalization of targeted coins is low, considering that the first asset with less than $20 million is at the 616th616𝑡ℎ616th616 italic_t italic_h position of the cryptocurrency ranking by market capitalization333According to CoinMarketCap data retrieved on February 18, 2021. Typically, Binance is the ma... | D |
M≥D,t+1⊆M≥D,tsuperscriptsubscript𝑀𝐷𝑡1superscriptsubscript𝑀𝐷𝑡M_{\geq}^{\mathit{D},t+1}\subseteq M_{\geq}^{\mathit{D},t}italic_M start_POSTSUBSCRIPT ≥ end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_D , italic_t + 1 end_POSTSUPERSCRIPT ⊆ italic_M start_POSTSUBSCRIPT ≥ end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_D... | Since problem 𝒫𝒫\mathcal{P}caligraphic_P meets the respectful decisions criterion | Problem 𝒫𝒫\mathcal{P}caligraphic_P meets the respectful decisions criterion (with | Problem 𝒫𝒫\mathcal{P}caligraphic_P meets the respectful decisions criterion (with | Since problem 𝒫𝒫\mathcal{P}caligraphic_P meets the respectful decisions criterion | A |
We propose Regularised Ising MIMO (RI-MIMO), which is based on the proposed RI formulation, and show that it is asymptotically optimal and can achieve near-optimal performance, in the relevant BER regime (an uncoded BER of 10−3superscript10310^{-3}10 start_POSTSUPERSCRIPT - 3 end_POSTSUPERSCRIPT-10−6superscript10610^{-... | In this section, we propose the RI-MIMO detector, based on our novel regularised Ising formulation of maximum-likelihood MIMO receiver, which mitigates the error floor problem. We use a single auxiliary spin variable to transform the Ising problem into a form compatible with CIMs. We finally propose TRIM, a novel tree ... | We see from Fig 11(left) that RI-MIMO and TRIM allows us to operate using aggressive modulations and coding schemes and hence achieve much better performance. In particular RI-MIMO achieves around 2.5×\times× more throughput in low-SNR regime (≈7.5dBabsent7.5𝑑𝐵\approx 7.5dB≈ 7.5 italic_d italic_B) and 2×\times× mor... | We further evolve RI-MIMO into Tree search with RI-MIMO (TRIM) that allows us to achieve better performance when the complexity of the underlying MIMO detection problem increases with higher-order modulations. | We start comparing the optimal decoder (the Sphere Decoder) and the linear MMSE decoder against RI-MIMO and the unregularized ML-MIMO using as a test case BPSK 16×\times×16. This case will represent a baseline for our benchmarks and their sophistication. Note that a trivial way to remove the error floor is to take the ... | C |
The actual channel, the BS measurements, and the precoding are time-varying in general. Thus, we have access to the input data (features) and training outputs (labels) sequentially. Older data samples tend to become irrelevant. | The proposed online deep learning model performs the mapping from the SINR measurements to the optimal MCS. The most significant advantage is achieved on the rises and falls of the SINR quality because ODL is more adaptive to the instant SINR than OLLA and instantly converges to the optimal MCS. The following Fig. 8 sh... | Compared with Q-learning, the main difference in our ODL approach is the use of a binary logarithmic loss function (log-loss) instead of Q-learning Temporal-Difference (TD)-Loss [15]. This way, we move to the binary classification problem instead of maximizing the delayed rewards (a) and modeling the influence on the s... | The novelty of our work is in the proposed scheme of online deep learning with a new optimization target. On the one hand, it is simpler and more effective than the existing Q-learning approach ([10, 11]) to the AMC problem. On the one hand, it outperforms the basic OLLA approach because of the better utilization of th... | Observations (a) and (b) motivate the use of the traditional deep learning approach rather than Q-learning. We consider acknowledgment prediction as a binary classification problem and use the scheme (2) to select the optimal MCS. Observation c) motivates the use of the online approach. | D |
Instead, hard bounding functions (so to speak, 100% confidence intervals) are sufficiently competitive with those 99% confidence intervals already at the second (m=2𝑚2m=2italic_m = 2) or third (m=3𝑚3m=3italic_m = 3) iteration. | Before closing this section, let us stress again that the proposed framework has been constructed for quite a large class of multidimensional stochastic differential equations with jumps, based on the previous developments (Sections 3.1, 3.2, 3.3 and 3.4) alone, without coming into the present subsection (Section 3.5),... | The aim of the present work is to establish recursive representations for a large class of stochastic differential equations with jumps. | The underlying class is large enough to accommodate the multivariate time-inhomogeneous dynamics, even in the absence of uniform ellipticity. | Let us, last but not least, remind that the proposed framework is general enough to accommodate quite a large class of multidimensional inhomogeneous stochastic differential equations with jumps and, particularly, does not require the drift and diffusion coefficients to be as smooth as in existing univariate exact simu... | D |
For k⩾1𝑘1k\geqslant 1italic_k ⩾ 1 and r⩾0𝑟0r\geqslant 0italic_r ⩾ 0, let f1(k,r):=f(k,h)assignsubscript𝑓1𝑘𝑟𝑓𝑘ℎf_{1}(k,r):=f(k,h)italic_f start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ( italic_k , italic_r ) := italic_f ( italic_k , italic_h ), where f𝑓fitalic_f is the function from Theorem 10. | Next, let us show that every vortex V∈𝒲𝑉𝒲V\in\mathcal{W}italic_V ∈ caligraphic_W must be bipartite. | It suffices to show that c+(F)⩾cW(S{1,2})superscript𝑐𝐹subscript𝑐𝑊subscript𝑆12c^{+}(F)\geqslant c_{W}(S_{\{1,2\}})italic_c start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT ( italic_F ) ⩾ italic_c start_POSTSUBSCRIPT italic_W end_POSTSUBSCRIPT ( italic_S start_POSTSUBSCRIPT { 1 , 2 } end_POSTSUBSCRIPT ) holds since the... | Let us show that the theorem holds with this choice of f1subscript𝑓1f_{1}italic_f start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT. | It suffices to show that c+(F)⩾cW(S{3})superscript𝑐𝐹subscript𝑐𝑊subscript𝑆3c^{+}(F)\geqslant c_{W}(S_{\{3\}})italic_c start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT ( italic_F ) ⩾ italic_c start_POSTSUBSCRIPT italic_W end_POSTSUBSCRIPT ( italic_S start_POSTSUBSCRIPT { 3 } end_POSTSUBSCRIPT ) holds since then we obta... | C |
{2}^{2}\leq\frac{R_{0}^{2}}{2}.italic_f ( over^ start_ARG italic_x end_ARG start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT ) - italic_f ( italic_x start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT ) ≤ divide start_ARG italic_μ italic_R start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG st... | Upper bound for ③. We derive the upper bound for ③ using the same technique as for ①. First of all, we notice that the summands in ③ are conditionally unbiased: | Upper bound for ③. We derive the upper bound for ③ using the same technique as for ①. First of all, we notice that the summands in ③ are conditionally unbiased: | From mathematical induction and the union bound for probability events, it follows that the inequalities | From mathematical induction and the union bound for probability events, it follows that inequalities | D |
\draw(10,10) node[lab] (b1) 1; \draw(30,10) node[lab] (b3) 0; \draw(40,10) node[lab] (b4) 1; | \draw(10,20) node[lab] (v2) v2subscript𝑣2v_{2}italic_v start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT; | \draw(10,10) node[lab] (b1) 1; \draw(30,10) node[lab] (b3) 0; \draw(40,10) node[lab] (b4) 1; | \draw(10,50) node[lab] (f1) 1; \draw(30,50) node[lab] (f3) 0; \draw(40,50) node[lab] (f4) 1; | \draw(20,30) node[lab] (d2) 1; \draw(30,30) node[lab] (d3) 1; \draw(50,30) node[lab] (d5) 0; | D |
Embedded methods select features during parameter optimisation by manipulating the objective function, such as Lasso [18] or the structure of a model, such as CART [19]. | Unlike wrapper and embedded methods, filter methods do not involve model training, which makes them faster than the other two methods. | The classification results show that the filter methods generally have worse classification performance but higher computational speed than the embedded methods and the wrapper methods. | These eight methods cover three types of feature selection methods, namely filter, wrapper, and embedded methods. | Feature selection methods can generally be categorised into filter, wrapper, and embedded methods [1]. | A |
The authors declare that they have no known competing financial interests or personal relationships that could have | The authors declare that they have no known competing financial interests or personal relationships that could have | Figure 4: (a), (b) and (c), (d) are the mean correlations between weight and two properties (length and diversity) of paths on Cora and Citeseer respectively. In (b) and (d), to remove the influence of length, the path length is fixed on 10. Y-axis denotes the average weight of the corresponding paths. | This work was supported in part by National Key Research and Development Program of China (No. 2020YFB2103402), Shenzhen Science and Technology Program (No. JCYJ20230807115959041), and the open project of Sichuan Provincial Key Laboratory of Philosophy and Social Science for Language Intelligence in Special Education (... | To analyze how the properties of paths influence weight scores, we draw the correlations between weight scores and two properties of paths, i.e., length and diversity, on Figure 4. Length is defined as the number of nodes in a path; Diversity is defined as the number of different categories of labeled node in a path. F... | C |
Hessian at the optimum is ρ1−ρdρ1−ρ2subscript𝜌1subscript𝜌𝑑subscript𝜌1subscript𝜌2\frac{\rho_{1}-\rho_{d}}{\rho_{1}-\rho_{2}}divide start_ARG italic_ρ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_ρ start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT end_ARG start_ARG italic_ρ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT -... | The bound on the condition number in Theorem 18 decomposes two components: the first, κ𝐅𝐃𝐀⋆superscriptsubscript𝜅𝐅𝐃𝐀⋆\kappa_{{\bf FDA}}^{\star}italic_κ start_POSTSUBSCRIPT bold_FDA end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ⋆ end_POSTSUPERSCRIPT, | The condition number bound from Corollary 19 decomposes to two components: the first | The following theorem provides a bound on the condition number of the Riemannian | The condition number bound from Corollary 10 decomposes into two components: the first | B |
2DPASS [72] enhances the representation learning of 3D semantic segmentation network by distilling multi-modal knowledge to single point cloud modality. In this way, 2DPASS can use LiDAR-only input in test-time. However, the model performance is unsatisfactory under the scene with sparser point clouds (e.g., A2D2 with ... | To better understand the benefits of PMF, we visualize the predictions of PMF on the benchmark data sets. From Figure 8, compared with Cylinder3D, PMF achieves better performance at the boundary of objects. For example, as shown in Figure 8 (d), the truck segmented by PMF has a more complete shape. More critically, PMF... | In this work, we have proposed a perception-aware multi-sensor fusion scheme for 3D LiDAR semantic segmentation. Unlike existing methods that conduct feature fusion in the LiDAR coordinate system, we project the point clouds to the camera coordinate system to enable a collaborative fusion of the perceptual features fro... | Besides, unlike existing methods that perform feature fusion in the LiDAR domain, PMF [82] exploits a collaborative fusion of multimodal data in camera coordinates. In this work, we further extend PMF to improve its efficiency and performance. | In multi-sensor fusion methods, fusing multimodal data from different sensors is an important problem. Existing fusion-based methods [47, 64] mainly lift the dense 2D image features to the 3D LiDAR coordinates using spherical projection [50] and conduct feature fusion in the sparse LiDAR domain. However, these methods ... | C |
The embeddability problem has been largely considered in the special case where the input 2-complex is (homeomorphic to) a surface. This problem is already NP-hard [39], and the existing algorithms that are fixed-parameter tractable in the genus are notoriously complicated; we review them now. | Mohar [28] has given an algorithm for embedding graphs on a fixed surface that takes linear time in the input graph, for every fixed surface. This algorithm is very technical and relies on several other articles. The dependence on the genus is not made explicit, but seems to be doubly exponential [20]. | General graph minor theory provides an algorithm for the same purpose. The graph minor theorem by Robertson and Seymour [35] implies that, for every fixed surface 𝒮𝒮\mathscr{S}script_S, there is a finite list of graphs 𝒪𝒮subscript𝒪𝒮\cal O_{\mathscr{S}}caligraphic_O start_POSTSUBSCRIPT script_S end_POSTSUBSCRIPT s... | Kawarabayashi, Mohar, and Reed, in an extended abstract [20], have given a simpler linear-time algorithm for this problem, with a singly-exponential dependence in the genus, but not all details are presented, which makes the approach hard to check [22, p. 3657, footnote]. | In this paper, we describe an algorithm for deciding the embeddability of graphs into topological spaces that are, in a sense, as general as possible: two-dimensional simplicial complexes (or 2-complexes for brevity), which are made from vertices, edges, and triangles glued together. (We remark that every graph is embe... | A |
Given that S(μ)𝑆𝜇S(\mu)italic_S ( italic_μ ) is a Laurent polynomial, the proof about | ∥S(μ)∥−1superscriptdelimited-∥∥𝑆𝜇1\lVert S(\mu)\rVert^{-1}∥ italic_S ( italic_μ ) ∥ start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT is identical to [nosh:15, Lemma | ∥S(μ)−1Q(μ)∥delimited-∥∥𝑆superscript𝜇1𝑄𝜇\displaystyle\lVert S(\mu)^{-1}Q(\mu)\rVert∥ italic_S ( italic_μ ) start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT italic_Q ( italic_μ ) ∥ | upper bound for ∥S(μ)−1Q(μ)∥delimited-∥∥𝑆superscript𝜇1𝑄𝜇\lVert S(\mu)^{-1}Q(\mu)\rVert∥ italic_S ( italic_μ ) start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT italic_Q ( italic_μ ) ∥ is equal to 1111. | ≤∥S(μ)−1∥∥Q(μ)∥absentdelimited-∥∥𝑆superscript𝜇1delimited-∥∥𝑄𝜇\displaystyle\leq\lVert S(\mu)^{-1}\rVert\lVert Q(\mu)\rVert≤ ∥ italic_S ( italic_μ ) start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT ∥ ∥ italic_Q ( italic_μ ) ∥ | A |
Streufert 2023 specifies an arbitrary pentaform game and shows [a] that the piece-form collection partitions the pentaform and [b] that this piece-form partition is coarser than the pentaform’s slice partition. Thus it can use Corollary 4.2(b) to show that each piece form is a pentaform. On this foundation the paper is... | In the opposite direction, Section 4.2 defines a “block” to be a quintuple set which satisfies all but one of the axioms. Then it essentially shows that the union of a “separated” collection of blocks is itself a block (Proposition 4.4), and that the union of an expanding sequence of pentaforms is itself a pentaform (P... | For example, equation (10) shows that the pentaform Q2superscript𝑄2Q^{2}italic_Q start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT (Figure 2.2 or 3.2) has information-set situations, while equation (9) shows that the pentaform Q3superscript𝑄3\smash{Q^{3}}italic_Q start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT (Figure 2.3 or 3... | This Section 4.2 shows how to construct pentaforms as unions of “blocks”.212121This Section 4.2 is related to the ongoing work of Ghani, Kupke, Lambert, and Nordvall Forsberg 2018; Bolt, Hedges, and Zahn 2023; and Capucci, Ghani, Ledent, and Nordvall Forsberg 2022. Both that literature and this Section 4.2 seek to syst... | Finally, a “pentaform game” is constructed by combining a pentaform with utility functions.333This paper does not formally consider probability. If a game has a finite number of nodes, mixed strategies and expected utilities can be derived by standard means (for example, Myerson 1991, Chapter 4). Meanwhile, if there ar... | C |
2Ω(n)superscript2Ω𝑛2^{\Omega(n)}2 start_POSTSUPERSCRIPT roman_Ω ( italic_n ) end_POSTSUPERSCRIPT | 2Ω(n)superscript2Ω𝑛2^{\Omega(n)}2 start_POSTSUPERSCRIPT roman_Ω ( italic_n ) end_POSTSUPERSCRIPT | 2Ω(n)superscript2Ω𝑛2^{\Omega(n)}2 start_POSTSUPERSCRIPT roman_Ω ( italic_n ) end_POSTSUPERSCRIPT | 2Ω(n)superscript2Ω𝑛2^{\Omega(n)}2 start_POSTSUPERSCRIPT roman_Ω ( italic_n ) end_POSTSUPERSCRIPT | 2Ω(n)superscript2Ω𝑛2^{\Omega(n)}2 start_POSTSUPERSCRIPT roman_Ω ( italic_n ) end_POSTSUPERSCRIPT | A |
The Winograd Schema Challenge (WSC) [51] is proposed as an alternative to the Turing Test [63], focusing on a machine’s ability to resolve referential ambiguities that are trivial for humans but challenging for AI. A Winograd schema consists of a pair of sentences that differ by only one or two words, leading to a refe... | While naive physics commonsense knowledge is generally universal across human societies, intuitive psychology commonsense can vary depending on linguistic or cultural backgrounds, particularly regarding daily activities, social behaviors, and norms. Some existing studies have incorporated multilingual settings when dev... | COPA (Choice Of Plausible Alternatives) [52] is a benchmark that involves causal inference between events. The dataset comprises 1,000 examples, each presenting an event followed by a question asking the model to select the correct cause or effect from two options. Triangle-COPA [64] is a variation of COPA, containing ... | HeadlineCause [80] is a dataset designed to detect implicit causal relations between pairs of news headlines, addressing the challenges in existing datasets that focus predominantly on either commonsense causal reasoning or explicit causal relations. Comprising over 5,000 headline pairs in English and 9,000 in Russian,... | Social IQa [50] is a large-scale benchmark for evaluating and improving NLP models’ social and emotional intelligence through commonsense reasoning about social interactions. It includes 38,000 multiple-choice questions designed to challenge models in understanding motivations, emotional reactions, and outcomes of ever... | B |
We quantify how many projections are needed to achieve a certain accuracy in a general case (Theorem 6). | Considering the simplicity of the thresholding after random projection classification method, Occam’s razor principle suggests that such a classifier should be used for any training dataset that can be well classified after a random projection, as one expects the resulting classifier to generalize well. The first part ... | where dVCsubscript𝑑𝑉𝐶d_{VC}italic_d start_POSTSUBSCRIPT italic_V italic_C end_POSTSUBSCRIPT is the VC dimension of the class ℱℱ\mathcal{F}caligraphic_F. In this section we prove a similar result for the generalization gap of the method of thresholding after random projection where we roughly speaking replace the VC... | In Section 5 we also include an example of a classification problem where the number of random projections needed for obtaining a classifier with high accuracy is small. | In general, according to Formula 21, the number of projections n𝑛nitalic_n needed for achieving a high classification accuracy could be very large, | C |
The results obtained by the Lagrange multiplier method and our new method are shown in Tables 1 and 2, respectively. | Numerical solutions obtained by the new method achieve optimal convergence rate of 2222nd order under the L2superscript𝐿2L^{2}italic_L start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT norm inside the domain. | The testing results for the Lagrange multiplier method and the new method are shown in Tables 3 and 4, respectively. The numerical solutions obtained by the new method again achieve optimal convergence rate of 2222nd order under the L2superscript𝐿2L^{2}italic_L start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT norm inside t... | When the Lagrange multiplier method is used, the L2superscript𝐿2L^{2}italic_L start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT error convergence rate is not optimal, although the numerical solutions still converge. | Theoretical analysis and numerical experiments show that our proposed method achieves optimal convergence rate under both L2superscript𝐿2L^{2}italic_L start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT norm and H1superscript𝐻1H^{1}italic_H start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT semi-norm. | A |
An enumeration problem is the task of listing a set of elements without redundancies. It is an important and old class of problems: the Baguenaudier game [32] from the 19191919th century can be seen as the problem of enumerating integers in Gray code order. Ruskey even reports [38] on thousand-year-old methods to list ... | In this paper, we complemented our algorithms with lower bounds in a model of computation where the underlying enumeration algorithm is accessed in a blackbox fashion. We have shown that no regularization scheme can achieve a worst case delay that is linear in the real amortized delay. Moreover, we show that if one wan... | The main specificity of enumeration problems is that the size of the enumerated set is typically exponential in the size of the input. | On particular consequence of Theorem 13 is that one cannot use regularization schemes to prove that classes DelayP\polysuperscriptDelayP\poly\mathrm{DelayP}^{\poly}roman_DelayP start_POSTSUPERSCRIPT end_POSTSUPERSCRIPT and AmDelayP\polysuperscriptAmDelayP\poly\mathrm{AmDelayP}^{\poly}roman_AmDelayP start_POSTSUPERSCRIP... | For most problems, the set to enumerate is too large, or may not be needed in its entirety. It is then desirable to efficiently generate a part of the set for statistical analysis or on the fly processing. In this case, a more relevant measure of the complexity and hence of the quality of the enumeration algorithm is i... | B |
We may assume that ξ𝜉\xiitalic_ξ is the smallest leaf in the subtree of T𝑇Titalic_T rooted at ξ|2jevaluated-at𝜉2𝑗\xi|_{2j}italic_ξ | start_POSTSUBSCRIPT 2 italic_j end_POSTSUBSCRIPT. | If ξ′superscript𝜉′\xi^{\prime}italic_ξ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT does not exist, then return ⊤top\top⊤. | Otherwise, we can set it to the smallest leaf of the next subtree rooted at that depth using Tighten (we return ⊤top\top⊤ if this next subtree does not exist). | Otherwise, we can set it to the smallest leaf of the next subtree rooted at that depth using Tighten (we return ⊤top\top⊤ if this next subtree does not exist). | Otherwise, it is the smallest leaf of the next subtree rooted at that depth, which can be obtained via Tighten. | B |
_{1}\leq\mathcal{O}(\varepsilon).∥ italic_ρ start_POSTSUBSCRIPT italic_L italic_L start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT italic_Y italic_Y start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT italic_M end_POSTSUBSCRIPT - italic_U start_POSTSUBSCRIPT italic_k / 4 end_POSTSUBSCRIPT ⊗ italic_ρ start_POSTSUBSCRIPT italic_L sta... | As stated before, the main conceptual hurdle in extending the analysis from [CGL20] to the quantum case, lies in finding the proper framework in which we can express the correlations that arise from quantum side information. | Very little is known about the security of non-malleable extractors against quantum side information. The initial challenge lies in defining a non-malleable extractor with quantum side information, as we need to provide security with updated quantum side information when the adversary modifies (E,S)→(E′,S′)→𝐸𝑆supersc... | In this scenario, we require that the output remains nearly independent given the quantum side information and any of the tampered outputs. For example, in the seeded case (see Definition 21): | In this section, we define and prove the quantum security of 2222-source non-malleable extractor. As specified before, the parameters in our construction are set similarly in line with the construction of [CGL20] considering the use of quantum secure seeded extractors in the alternating extraction. The following parame... | A |
\operatorname{dist}(\cdot,P\cup\partial B)\right\|_{L_{\gamma}(B)}^{\alpha}.∥ italic_f - ∑ start_POSTSUBSCRIPT italic_x ∈ italic_P end_POSTSUBSCRIPT italic_f ( italic_x ) italic_u start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT ∥ start_POSTSUBSCRIPT italic_L start_POSTSUBSCRIPT italic_q end_POSTSUBSCRIPT ( italic_B ) en... | if this quantity exists and is finite. It is independent of the choice of the coordinates x𝑥xitalic_x. | and the desired convergence nan→a→𝑛subscript𝑎𝑛𝑎na_{n}\to aitalic_n italic_a start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT → italic_a follows. This completes the proof of (14) and thus of Theorem 3. | The first property is proven precisely this way in [18] and thus we turn to the second property. | This definition of the integral is independent of the atlas and the partition of unity. | C |
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