Daily Papers

Predicting the intermediate trajectories between an initial and target distribution is a central problem in generative modeling. Existing approaches, such as flow matching and Schr\"odinger Bridge Matching, effectively learn mappings between two distributions by modeling a single stochastic path. However, these methods are inherently limited to unimodal transitions and cannot capture branched or divergent evolution from a common origin to multiple distinct outcomes. To address this, we introduce Branched Schr\"odinger Bridge Matching (BranchSBM), a novel framework that learns branched Schr\"odinger bridges. BranchSBM parameterizes multiple time-dependent velocity fields and growth processes, enabling the representation of population-level divergence into multiple terminal distributions. We show that BranchSBM is not only more expressive but also essential for tasks involving multi-path surface navigation, modeling cell fate bifurcations from homogeneous progenitor states, and simulating diverging cellular responses to perturbations.

We propose a transformer architecture and training strategy for tree generation. The architecture processes data at multiple resolutions and has an hourglass shape, with middle layers processing fewer tokens than outer layers. Similar to convolutional networks, we introduce longer range skip connections to completent this multi-resolution approach. The key advantage of this architecture is the faster processing speed and lower memory consumption. We are therefore able to process more complex trees than would be possible with a vanilla transformer architecture. Furthermore, we extend this approach to perform image-to-tree and point-cloud-to-tree conditional generation and to simulate the tree growth processes, generating 4D trees. Empirical results validate our approach in terms of speed, memory consumption, and generation quality.

CONSPECTUS: Two-dimensional (2D) compound materials are promising materials for use in electronics, optoelectronics, flexible devices, etc. because they are ultrathin and cover a wide range of properties. Among all methods to prepare 2D materials, chemical vapor deposition (CVD) is promising because it produces materials with a high quality and reasonable cost. So far, much efforts have been made to produce 2D compound materials with large domain size, controllable number of layers, fast-growth rate, and high quality features, etc. However, due to the complicated growth mechanism like sublimation and diffusion processes of multiple precursors, maintaining the controllability, repeatability, and high quality of CVD grown 2D binary and ternary materials is still a big challenge, which prevents their widespread use. Here, taking 2D transition metal dichalcogenides (TMDCs) as examples, we review current progress and highlight some promising growth strategies for the growth of 2D compound materials. The key technology issues which affect the CVD process, including non-metal precursor, metal precursor, substrate engineering, temperature, and gas flow, are discussed. Also, methods in improving the quality of CVD-grown 2D materials and current understanding on their growth mechanism are highlighted. Finally, challenges and opportunities in this field are proposed. We believe this review will guide the future design of controllable CVD systems for the growth of 2D compound materials with good controllability and high quality, laying the foundations for their potential applications.

We study growth of solid tumors in a partial differential equation model introduced by Hillen et al for the interaction between tumor cells (TCs) and cancer stem cells (CSCs). We find that invasion into the cancer-free state may be separated into two regimes, depending on the death rate of tumor cells. In the first, staged invasion regime, invasion into the cancer-free state is lead by tumor cells, which are then subsequently invaded at a slower speed by cancer stem cells. In the second, TC extinction regime, cancer stem cells directly invade the cancer-free state. Relying on recent results establishing front selection propagation under marginal stability assumptions, we use geometric singular perturbation theory to establish existence and selection properties of front solutions which describe both the primary and secondary invasion processes. With rigorous predictions for the invasion speeds, we are then able to heuristically predict how the total cancer mass as a function of time depends on the TC death rate, finding in some situations a tumor invasion paradox, in which increasing the TC death rate leads to an increase in the total cancer mass. Our methods give a general approach for verifying linear determinacy of spreading speeds of invasion fronts in systems with fast-slow structure.

The rapid growth of artificial intelligence (AI), particularly Large Language Models (LLMs), has raised concerns regarding its global environmental impact that extends beyond greenhouse gas emissions to include consideration of hardware fabrication and end-of-life processes. The opacity from major providers hinders companies' abilities to evaluate their AI-related environmental impacts and achieve net-zero targets. In this paper, we propose a methodology to estimate the environmental impact of a company's AI portfolio, providing actionable insights without necessitating extensive AI and Life-Cycle Assessment (LCA) expertise. Results confirm that large generative AI models consume up to 4600x more energy than traditional models. Our modelling approach, which accounts for increased AI usage, hardware computing efficiency, and changes in electricity mix in line with IPCC scenarios, forecasts AI electricity use up to 2030. Under a high adoption scenario, driven by widespread Generative AI and agents adoption associated to increasingly complex models and frameworks, AI electricity use is projected to rise by a factor of 24.4. Mitigating the environmental impact of Generative AI by 2030 requires coordinated efforts across the AI value chain. Isolated measures in hardware efficiency, model efficiency, or grid improvements alone are insufficient. We advocate for standardized environmental assessment frameworks, greater transparency from the all actors of the value chain and the introduction of a "Return on Environment" metric to align AI development with net-zero goals.

Perovskite solar cells (PSCs) have rapidly emerged as a leading contender in next-generation photovoltaic technologies, owing to their exceptional power conversion efficiencies and advantageous material properties. Despite these advances, challenges such as long-term stability, environmental sustainability, and scalable manufacturing continue to hinder their commercialization. Precursor additive engineering has shown promise in addressing these issues by enhancing both the performance and durability of PSCs. However, the explosive growth of scientific literature and the complex interplay of materials, processes, and device architectures make it increasingly difficult for researchers to efficiently access, organize, and utilize domain knowledge in this rapidly evolving field. To address this gap, we introduce Perovskite-R1, a specialized large language model (LLM) with advanced reasoning capabilities tailored for the discovery and design of PSC precursor additives. By systematically mining and curating 1,232 high-quality scientific publications and integrating a comprehensive library of 33,269 candidate materials, we constructed a domain-specific instruction-tuning dataset using automated question-answer generation and chain-of-thought reasoning. Fine-tuning the QwQ-32B model on this dataset resulted in Perovskite-R1, which can intelligently synthesize literature insights and generate innovative and practical solutions for defect passivation and the selection of precursor additives. Experimental validation of several model-proposed strategies confirms their effectiveness in improving material stability and performance. Our work demonstrates the potential of domain-adapted LLMs in accelerating materials discovery and provides a closed-loop framework for intelligent, data-driven advancements in perovskite photovoltaic research.

A major outstanding challenge in cosmology is the persistent discrepancy between the Hubble constant obtained from early and late universe measurements -- the Hubble tension. Examining cosmological evolution through the lens of information growth within a black hole we show the appearence of two fractal growing processes characterizing the early and late ages. These fractals induce space growth rates of 62.79pm5.59 km/s/Mpc and 70.07pm0.09 km/s/Mpc; close to the current values of the Hubble constants involved in the tension. These results strongly suggest that the Hubble tension is not given by unexpected large-scale structures or multiple, unrelated errors but by innate properties underlying the universe dynamics.

In this work we update the L-Galaxies semi-analytic model (SAM) to better follow the physical processes responsible for the growth of bulges via disc instabilities (leading to pseudo-bulges) and mergers (leading to classical bulges). We address the former by considering the contribution of both stellar and gaseous discs in the stability of the galaxy, and we update the latter by including dissipation of energy in gas-rich mergers. Furthermore, we introduce angular momentum losses during cooling and find that an accurate match to the observed correlation between stellar disc scale length and mass at z ~ 0.0 requires that the gas loses 20% of its initial specific angular momentum to the corresponding dark matter halo during the formation of the cold gas disc. We reproduce the observed trends between the stellar mass and specific angular momentum for both disc- and bulge-dominated galaxies, with the former rotating faster than the latter of the same mass. We conclude that a two-component instability recipe provides a morphologically diverse galaxy sample which matches the observed fractional breakdown of galaxies into different morphological types. This recipe also enables us to obtain an excellent fit to the morphology-mass relation and stellar mass function of different galactic types. Finally, we find that energy dissipation during mergers reduces the merger remnant sizes and allows us to match the observed mass-size relation for bulge-dominated systems.

Developing computer vision-based rice phenotyping techniques is crucial for precision field management and accelerating breeding, thereby continuously advancing rice production. Among phenotyping tasks, distinguishing image components is a key prerequisite for characterizing plant growth and development at the organ scale, enabling deeper insights into eco-physiological processes. However, due to the fine structure of rice organs and complex illumination within the canopy, this task remains highly challenging, underscoring the need for a high-quality training dataset. Such datasets are scarce, both due to a lack of large, representative collections of rice field images and the time-intensive nature of annotation. To address this gap, we established the first comprehensive multi-class rice semantic segmentation dataset, RiceSEG. We gathered nearly 50,000 high-resolution, ground-based images from five major rice-growing countries (China, Japan, India, the Philippines, and Tanzania), encompassing over 6,000 genotypes across all growth stages. From these original images, 3,078 representative samples were selected and annotated with six classes (background, green vegetation, senescent vegetation, panicle, weeds, and duckweed) to form the RiceSEG dataset. Notably, the sub-dataset from China spans all major genotypes and rice-growing environments from the northeast to the south. Both state-of-the-art convolutional neural networks and transformer-based semantic segmentation models were used as baselines. While these models perform reasonably well in segmenting background and green vegetation, they face difficulties during the reproductive stage, when canopy structures are more complex and multiple classes are involved. These findings highlight the importance of our dataset for developing specialized segmentation models for rice and other crops.

Biological nervous systems are created in a fundamentally different way than current artificial neural networks. Despite its impressive results in a variety of different domains, deep learning often requires considerable engineering effort to design high-performing neural architectures. By contrast, biological nervous systems are grown through a dynamic self-organizing process. In this paper, we take initial steps toward neural networks that grow through a developmental process that mirrors key properties of embryonic development in biological organisms. The growth process is guided by another neural network, which we call a Neural Developmental Program (NDP) and which operates through local communication alone. We investigate the role of neural growth on different machine learning benchmarks and different optimization methods (evolutionary training, online RL, offline RL, and supervised learning). Additionally, we highlight future research directions and opportunities enabled by having self-organization driving the growth of neural networks.

We study a discrete model for generalized exchange-driven growth in which the particle exchanged between two clusters is not limited to be of size one. This set of models include as special cases the usual exchange-driven growth system and the coagulation-fragmentation system with binary fragmentation. Under reasonable general condition on the rate coefficients we establish the existence of admissible solutions, meaning solutions that are obtained as appropriate limit of solutions to a finite-dimensional truncation of the infinite-dimensional ODE. For these solutions we prove that, in the class of models we call isolated both the total number of particles and the total mass are conserved, whereas in those models we can non-isolated only the mass is conserved. Additionally, under more restrictive growth conditions for the rate equations we obtain uniqueness of solutions to the initial value problems.

Most deep neural networks are trained under fixed network architectures and require retraining when the architecture changes. If expanding the network's size is needed, it is necessary to retrain from scratch, which is expensive. To avoid this, one can grow from a small network by adding random weights over time to gradually achieve the target network size. However, this naive approach falls short in practice as it brings too much noise to the growing process. Prior work tackled this issue by leveraging the already learned weights and training data for generating new weights through conducting a computationally expensive analysis step. In this paper, we introduce MixtureGrowth, a new approach to growing networks that circumvents the initialization overhead in prior work. Before growing, each layer in our model is generated with a linear combination of parameter templates. Newly grown layer weights are generated by using a new linear combination of existing templates for a layer. On one hand, these templates are already trained for the task, providing a strong initialization. On the other, the new coefficients provide flexibility for the added layer weights to learn something new. We show that our approach boosts top-1 accuracy over the state-of-the-art by 2-2.5% on CIFAR-100 and ImageNet datasets, while achieving comparable performance with fewer FLOPs to a larger network trained from scratch. Code is available at https://github.com/chaudatascience/mixturegrowth.

Acceleration of large language model pre-training is a critical issue in present NLP research. In this paper, we focus on speeding up pre-training by progressively growing from a small Transformer structure to a large one. There are two main research problems related to progressive growth: growth schedule and growth operator. For growth schedule, existing work has explored multi-stage expansion of depth and feedforward layers. However, the impact of each dimension on the schedule's efficiency is still an open question. For growth operator, existing work relies on the initialization of new weights to inherit knowledge, and achieve only non-strict function preservation, limiting further optimization of training dynamics. To address these issues, we propose Masked Structural Growth (MSG), including growth schedules involving all possible dimensions and strictly function-preserving growth operators that is independent of the initialization of new weights. Experiments show that MSG is significantly faster than related work: we achieve a speed-up of 80% for Bert-base and 120% for Bert-large pre-training. Moreover, MSG is able to improve fine-tuning performances at the same time.

Recent observations by the James Webb Space Telescope have revealed massive galaxies at very high redshift (zsimeq 7-15). The question of whether the existence of such galaxies is expected in the corresponding JWST surveys has received a lot of attention, though the answer straddles areas of cosmology and complex astrophysical details of high-redshift galaxy formation. The growth rate of density fluctuations determines the amplitude of overdensities that collapse to form galaxies. Late-time modifications of growth, combined with measurements at both zsim 1 from large-scale structure and zsim 1000 from the cosmic microwave background, affect the predictions for the abundance of first galaxies in the universe. In this paper, we point out that the late-time growth rate of structure affects the statistical significance of high-redshift, high-mass objects very weakly. Consequently, if the existence and abundance of these objects are confirmed to be unexpected, the variations in the late-time growth history are unlikely to explain these anomalies.

The Growth-at-Risk (GaR) framework has garnered attention in recent econometric literature, yet current approaches implicitly assume a constant Pareto exponent. We introduce novel and robust econometrics to estimate the tails of GaR based on a rigorous theoretical framework and establish validity and effectiveness. Simulations demonstrate consistent outperformance relative to existing alternatives in terms of predictive accuracy. We perform a long-term GaR analysis that provides accurate and insightful predictions, effectively capturing financial anomalies better than current methods.

There is a widening recognition that cancer cells are products of complex developmental processes. Carcinogenesis and metastasis formation are increasingly described as systems-level, network phenomena. Here we propose that malignant transformation is a two-phase process, where an initial increase of system plasticity is followed by a decrease of plasticity at late stages of carcinogenesis as a model of cellular learning. We describe the hallmarks of increased system plasticity of early, tumor initiating cells, such as increased noise, entropy, conformational and phenotypic plasticity, physical deformability, cell heterogeneity and network rearrangements. Finally, we argue that the large structural changes of molecular networks during cancer development necessitate a rather different targeting strategy in early and late phase of carcinogenesis. Plastic networks of early phase cancer development need a central hit, while rigid networks of late stage primary tumors or established metastases should be attacked by the network influence strategy, such as by edgetic, multi-target, or allo-network drugs. Cancer stem cells need special diagnosis and targeting, since their dormant and rapidly proliferating forms may have more rigid, or more plastic networks, respectively. The extremely high ability to change their rigidity/plasticity may be a key differentiating hallmark of cancer stem cells. The application of early stage-optimized anti-cancer drugs to late-stage patients may be a reason of many failures in anti-cancer therapies. Our hypotheses presented here underlie the need for patient-specific multi-target therapies applying the correct ratio of central hits and network influences -- in an optimized sequence.

Common-pool resource governance requires users to cooperate and avoid overexploitation, but defection and free-riding often undermine cooperation. We model a human-environmental system that integrates dynamics of resource and users' strategies. The resource follows a logistic function that depends on natural growth rate, carrying capacity, and extraction rates of cooperators and defectors. The users' strategies evolve according to different processes that capture effects of payoff, resource, and noise. We analyze the feedback between resource availability and strategic adaptation, and explores the conditions for the emergence and maintenance of cooperation. We find different processes lead to different regimes of equilibrium solutions and resource levels depending on the parameter configuration and initial conditions. We also show that some processes can enhance the sustainability of the resource by making the users more responsive to the resource scarcity. The paper advances the understanding of human-environmental system and offers insights for resource governance policies and interventions.

A common expectation is that career productivity peaks rather early and then gradually declines with seniority. But whether this holds true is still an open question. Here we investigate the productivity trajectories of almost 8,500 scientists from over fifty disciplines using methods from time series analysis, dimensionality reduction, and network science, showing that there exist six universal productivity patterns in research. Based on clusters of productivity trajectories and network representations where researchers with similar productivity patterns are connected, we identify constant, u-shaped, decreasing, periodic-like, increasing, and canonical productivity patterns, with the latter two describing almost three-fourths of researchers. In fact, we find that canonical curves are the most prevalent, but contrary to expectations, productivity peaks occur much more frequently around mid-career rather than early. These results outline the boundaries of possible career paths in science and caution against the adoption of stereotypes in tenure and funding decisions.

Many cellular processes involve information processing and decision making. We can probe these processes at increasing molecular detail. The analysis of heterogeneous data remains a challenge that requires new ways of thinking about cells in quantitative, predictive, and mechanistic ways. We discuss the role of mathematical models in the context of cell-fate decision making systems across the tree of life. Complex multi-cellular organisms have been a particular focus, but single celled organisms also have to sense and respond to their environment. We center our discussion around the idea of design principles which we can learn from observations and modeling, and exploit in order to (re)-design or guide cellular behavior.

Learning the underlying dynamics of single cells from snapshot data has gained increasing attention in scientific and machine learning research. The destructive measurement technique and cell proliferation/death result in unpaired and unbalanced data between snapshots, making the learning of the underlying dynamics challenging. In this paper, we propose joint Velocity-Growth Flow Matching (VGFM), a novel paradigm that jointly learns state transition and mass growth of single-cell populations via flow matching. VGFM builds an ideal single-cell dynamics containing velocity of state and growth of mass, driven by a presented two-period dynamic understanding of the static semi-relaxed optimal transport, a mathematical tool that seeks the coupling between unpaired and unbalanced data. To enable practical usage, we approximate the ideal dynamics using neural networks, forming our joint velocity and growth matching framework. A distribution fitting loss is also employed in VGFM to further improve the fitting performance for snapshot data. Extensive experimental results on both synthetic and real datasets demonstrate that VGFM can capture the underlying biological dynamics accounting for mass and state variations over time, outperforming existing approaches for single-cell dynamics modeling.

LLMs are computationally expensive to pre-train due to their large scale. Model growth emerges as a promising approach by leveraging smaller models to accelerate the training of larger ones. However, the viability of these model growth methods in efficient LLM pre-training remains underexplored. This work identifies three critical textit{O}bstacles: (O1) lack of comprehensive evaluation, (O2) untested viability for scaling, and (O3) lack of empirical guidelines. To tackle O1, we summarize existing approaches into four atomic growth operators and systematically evaluate them in a standardized LLM pre-training setting. Our findings reveal that a depthwise stacking operator, called G_{stack}, exhibits remarkable acceleration in training, leading to decreased loss and improved overall performance on eight standard NLP benchmarks compared to strong baselines. Motivated by these promising results, we conduct extensive experiments to delve deeper into G_{stack} to address O2 and O3. For O2 (untested scalability), our study shows that G_{stack} is scalable and consistently performs well, with experiments up to 7B LLMs after growth and pre-training LLMs with 750B tokens. For example, compared to a conventionally trained 7B model using 300B tokens, our G_{stack} model converges to the same loss with 194B tokens, resulting in a 54.6\% speedup. We further address O3 (lack of empirical guidelines) by formalizing guidelines to determine growth timing and growth factor for G_{stack}, making it practical in general LLM pre-training. We also provide in-depth discussions and comprehensive ablation studies of G_{stack}. Our code and pre-trained model are available at https://llm-stacking.github.io/{https://llm-stacking.github.io/}.

We introduce a new predator-prey model by replacing the growth and predation constant by a square matrix, and the population density as a population vector. The classical Lotka-Volterra model describes a population that either modulates or converges. Stability analysis of such models have been extensively studied by the works of Merdan (https://doi.org/10.1016/j.chaos.2007.06.062). The new model adds complexity by introducing an age group structure where the population of each age group evolves as prescribed by the Leslie matrix. The added complexity changes the behavior of the model such that the population either displays roughly an exponential growth or decay. We first provide an exact equation that describes a time evolution and use analytic techniques to obtain an approximate growth factor. We also discuss the variants of the Leslie model, i.e., the complex value predator-prey model and the competitive model. We then prove the Last Species Standing theorem that determines the dominant population in the large time limit. The recursive structure of the model denies the application of simple regression. We discuss a machine learning scheme that allows an admissible fit for the population evolution of Paramecium Aurelia and Paramecium Caudatum. Another potential avenue to simplify the computation is to use the machinery of quantum operators. We demonstrate the potential of this approach by computing the Hamiltonian of a simple Leslie system.

We study a model of a branching process subject to selection, modeled by giving each family an individual fitness acting as a branching rate, and mutation, modeled by resampling the fitness of a proportion of offspring in each generation. For two large classes of fitness distributions of Gumbel type we determine the growth of the population, almost surely on survival. We then study the empirical fitness distribution in a simplified model, which is numerically indistinguishable from the original model, and show the emergence of a Gaussian travelling wave.

This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical optimization. It is necessary as well as beneficial to take a robust approach, by applying an optimization method that learns as one goes along, learning from experience as more aspects of the problem are observed. This view of optimization as a process has become prominent in varied fields and has led to some spectacular success in modeling and systems that are now part of our daily lives.

This paper introduces a continuous-time stochastic dynamical framework for understanding how large language models (LLMs) may self-amplify latent biases or toxicity through their own chain-of-thought reasoning. The model posits an instantaneous "severity" variable x(t) in [0,1] evolving under a stochastic differential equation (SDE) with a drift term μ(x) and diffusion σ(x). Crucially, such a process can be consistently analyzed via the Fokker--Planck approach if each incremental step behaves nearly Markovian in severity space. The analysis investigates critical phenomena, showing that certain parameter regimes create phase transitions from subcritical (self-correcting) to supercritical (runaway severity). The paper derives stationary distributions, first-passage times to harmful thresholds, and scaling laws near critical points. Finally, it highlights implications for agents and extended LLM reasoning models: in principle, these equations might serve as a basis for formal verification of whether a model remains stable or propagates bias over repeated inferences.

We introduce a novel score-based diffusion framework named Twigs that incorporates multiple co-evolving flows for enriching conditional generation tasks. Specifically, a central or trunk diffusion process is associated with a primary variable (e.g., graph structure), and additional offshoot or stem processes are dedicated to dependent variables (e.g., graph properties or labels). A new strategy, which we call loop guidance, effectively orchestrates the flow of information between the trunk and the stem processes during sampling. This approach allows us to uncover intricate interactions and dependencies, and unlock new generative capabilities. We provide extensive experiments to demonstrate strong performance gains of the proposed method over contemporary baselines in the context of conditional graph generation, underscoring the potential of Twigs in challenging generative tasks such as inverse molecular design and molecular optimization.

We present a general computational theory of cancer and its developmental dynamics. The theory is based on a theory of the architecture and function of developmental control networks which guide the formation of multicellular organisms. Cancer networks are special cases of developmental control networks. Cancer results from transformations of normal developmental networks. Our theory generates a natural classification of all possible cancers based on their network architecture. Each cancer network has a unique topology and semantics and developmental dynamics that result in distinct clinical tumor phenotypes. We apply this new theory with a series of proof of concept cases for all the basic cancer types. These cases have been computationally modeled, their behavior simulated and mathematically described using a multicellular systems biology approach. There are fascinating correspondences between the dynamic developmental phenotype of computationally modeled {\em in silico} cancers and natural {\em in vivo} cancers. The theory lays the foundation for a new research paradigm for understanding and investigating cancer. The theory of cancer networks implies that new diagnostic methods and new treatments to cure cancer will become possible.

We study long-run progress in artificial intelligence in a quantitative way. Many measures, including traditional ones such as patents and publications, machine learning benchmarks, and a new Aggregate State of the Art in ML (or ASOTA) Index we have constructed from these, show exponential growth at roughly constant rates over long periods. Production of patents and publications doubles every ten years, by contrast with the growth of computing resources driven by Moore's Law, roughly a doubling every two years. We argue that the input of AI researchers is also crucial and its contribution can be objectively estimated. Consequently, we give a simple argument that explains the 5:1 relation between these two rates. We then discuss the application of this argument to different output measures and compare our analyses with predictions based on machine learning scaling laws proposed in existing literature. Our quantitative framework facilitates understanding, predicting, and modulating the development of these important technologies.

This paper details the process of developing the first native large generative language model for the Nordic languages, GPT-SW3. We cover all parts of the development process, from data collection and processing, training configuration and instruction finetuning, to evaluation and considerations for release strategies. We hope that this paper can serve as a guide and reference for other researchers that undertake the development of large generative models for smaller languages.

Interrogating the evolution of biological changes at early stages of life requires longitudinal profiling of molecules, such as DNA methylation, which can be challenging with children. We introduce a probabilistic and longitudinal machine learning framework based on multi-mean Gaussian processes (GPs), accounting for individual and gene correlations across time. This method provides future predictions of DNA methylation status at different individual ages while accounting for uncertainty. Our model is trained on a birth cohort of children with methylation profiled at ages 0-4, and we demonstrated that the status of methylation sites for each child can be accurately predicted at ages 5-7. We show that methylation profiles predicted by multi-mean GPs can be used to estimate other phenotypes, such as epigenetic age, and enable comparison to other health measures of interest. This approach encourages epigenetic studies to move towards longitudinal design for investigating epigenetic changes during development, ageing and disease progression.

Diabetes is a chronic condition, considered one of the civilization diseases, that is characterized by sustained high blood sugar levels. There is no doubt that more and more people is going to suffer from diabetes, hence it is crucial to understand better its biological foundations. The essential processes related to the control of glucose levels in the blood are: glycolysis (process of breaking down of glucose) and glucose synthesis, both taking place in the liver. The glycolysis occurs during feeding and it is stimulated by insulin. On the other hand, the glucose synthesis arises during fasting and it is stimulated by glucagon. In the paper we present a Petri net model of glycolysis and glucose synthesis in the liver. The model is created based on medical literature. Standard Petri nets techniques are used to analyse the properties of the model: traps, reachability graphs, tokens dynamics, deadlocks analysis. The results are described in the paper. Our analysis shows that the model captures the interactions between different enzymes and substances, which is consistent with the biological processes occurring during fasting and feeding. The model constitutes the first element of our long-time goal to create the whole body model of the glucose regulation in a healthy human and a person with diabetes.

Neural networks often exhibit emergent behavior, where qualitatively new capabilities arise from scaling up the amount of parameters, training data, or training steps. One approach to understanding emergence is to find continuous progress measures that underlie the seemingly discontinuous qualitative changes. We argue that progress measures can be found via mechanistic interpretability: reverse-engineering learned behaviors into their individual components. As a case study, we investigate the recently-discovered phenomenon of ``grokking'' exhibited by small transformers trained on modular addition tasks. We fully reverse engineer the algorithm learned by these networks, which uses discrete Fourier transforms and trigonometric identities to convert addition to rotation about a circle. We confirm the algorithm by analyzing the activations and weights and by performing ablations in Fourier space. Based on this understanding, we define progress measures that allow us to study the dynamics of training and split training into three continuous phases: memorization, circuit formation, and cleanup. Our results show that grokking, rather than being a sudden shift, arises from the gradual amplification of structured mechanisms encoded in the weights, followed by the later removal of memorizing components.

We investigate a new dynamical system that describes tumor-host interaction. The equation that describes the untreated tumor growth is based on non-extensive statistical mechanics. Recently, this model has been shown to fit successfully exponential, Gompertz, logistic, and power-law tumor growths. We have been able to include as many hallmarks of cancer as possible. We study also the dynamic response of cancer under therapy. Using our model, we can make predictions about the different outcomes when we change the parameters, and/or the initial conditions. We can determine the importance of different factors to influence tumor growth. We discover synergistic therapeutic effects of different treatments and drugs. Cancer is generally untreatable using conventional monotherapy. We consider conventional therapies, oncogene-targeted therapies, tumor-suppressors gene-targeted therapies, immunotherapies, anti-angiogenesis therapies, virotherapy, among others. We need therapies with the potential to target both tumor cells and the tumors' microenvironment. Drugs that target oncogenes and tumor-suppressor genes can be effective in the treatment of some cancers. However, most tumors do reoccur. We have found that the success of the new therapeutic agents can be seen when used in combination with other cancer-cell-killing therapies. Our results have allowed us to design a combinational therapy that can lead to the complete eradication of cancer.

Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality. For example, extending the inference process with auxiliary variables leads to improved sample quality. While there are many such multivariate diffusions to explore, each new one requires significant model-specific analysis, hindering rapid prototyping and evaluation. In this work, we study Multivariate Diffusion Models (MDMs). For any number of auxiliary variables, we provide a recipe for maximizing a lower-bound on the MDMs likelihood without requiring any model-specific analysis. We then demonstrate how to parameterize the diffusion for a specified target noise distribution; these two points together enable optimizing the inference diffusion process. Optimizing the diffusion expands easy experimentation from just a few well-known processes to an automatic search over all linear diffusions. To demonstrate these ideas, we introduce two new specific diffusions as well as learn a diffusion process on the MNIST, CIFAR10, and ImageNet32 datasets. We show learned MDMs match or surpass bits-per-dims (BPDs) relative to fixed choices of diffusions for a given dataset and model architecture.

We introduce Version 3 (V3) of the gridded near real-time Multi-Source Weighted-Ensemble Precipitation (MSWEP) product -- the first fully global, historical machine learning powered precipitation (P) dataset, developed to meet the growing demand for timely and accurate P estimates amid escalating climate challenges. MSWEP V3 provides hourly data at 0.1^circ resolution from 1979 to the present, continuously updated with a latency of approximately two hours. Development follows a two-stage process. First, baseline P fields are generated using machine learning model stacks that integrate satellite- and (re)analysis-based P and air-temperature products, along with static variables. The models are trained using hourly and daily observations from 15,959 P gauges worldwide. Second, these baseline P fields are corrected using daily and monthly gauge observations from 57,666 and 86,000 stations globally. To assess MSWEP V3's baseline performance, we evaluated 19 (quasi-) global gridded P products -- including both uncorrected and gauge-based products -- using observations from an independent set of 15,958 gauges excluded from the first training stage. The MSWEP V3 baseline achieved a median daily Kling-Gupta Efficiency (KGE) of 0.69, outperforming all evaluated products. Other uncorrected products achieved median daily KGE values of 0.61 (ERA5), 0.46 (IMERG-L V7), 0.38 (GSMaP V8), and 0.31 (CHIRP). Using leave-one-out cross-validation, the daily gauge correction was found to improve the median daily correlation by 0.09, constrained by the already strong baseline performance. We anticipate that MSWEP V3 -- accessible at www.gloh2o.org/mswep -- will enable more reliable monitoring, forecasting, and management of water-related risks in a variable and changing climate.

The quantitative prediction of the intensity of rainfall events (light or heavy) has remained a challenge in Numerical Weather Prediction (NWP) models. For the first time the mean coefficient of diffusional growth rates are calculated using an Eulerian-Lagrangian particle-based small-scale model on in situ airborne measurement data of Cloud Aerosol Interaction and Precipitation Enhancement Experiment (CAIPEEX) during monsoon over Indian sub-continent. The results show that diffusional growth rates varies in the range of 0.00025 - 0.0015(cm/s). The generic problem of the overestimation of light rain in NWP models might be related with the choice of cm in the model. It is also shown from DNS experiment using Eulerian-Lagrangian particle-based small-scale model that the relative dispersion is constrained with average values in the range of ~ 0.2 - 0.37 (~ 0.1- 0.26) in less humid (more humid) conditions. This is in agreement with in situ airborne observation (dispersion ~ 0.36) and previous study over Indian sub-continent. The linear relationship between relative dispersion and cloud droplet number concentration (NC) is obtained from this study using CAIPEEX observation over Indian subcontinent. The dispersion based autoconversion-scheme for Indian region must be useful for the Indian summer monsoon precipitation calculation in the general circulation model. The present study also provide valuable guidance for the parameterization of effective radius, important for radiation scheme.

We present a concise dynamical picture of infant-driven household chaos. The framework has three postulations: recurrent daily chaos, overall entropy growth in household organization, and transient local ordering episodes with switching rules (a volatile Maxwell-demon effect). We illustrate entropy growth with a two-region toy model (organizer vs. play area), where entropy production is nonnegative and long-time behavior is typically play-area dominated. We also model toy diffusion and curiosity-driven behavior, where novelty matters more than punishment in the short term, while gradual learning still occurs.

This study examines the effects of de-globalization trends on international trade networks and their role in improving forecasts for economic growth. Using section-level trade data from nearly 200 countries from 2010 to 2022, we identify significant shifts in the network topology driven by rising trade policy uncertainty. Our analysis highlights key global players through centrality rankings, with the United States, China, and Germany maintaining consistent dominance. Using a horse race of supervised regressors, we find that network topology descriptors evaluated from section-specific trade networks substantially enhance the quality of a country's GDP growth forecast. We also find that non-linear models, such as Random Forest, XGBoost, and LightGBM, outperform traditional linear models used in the economics literature. Using SHAP values to interpret these non-linear model's predictions, we find that about half of most important features originate from the network descriptors, underscoring their vital role in refining forecasts. Moreover, this study emphasizes the significance of recent economic performance, population growth, and the primary sector's influence in shaping economic growth predictions, offering novel insights into the intricacies of economic growth forecasting.

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.

We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models with latent and observed variables. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al., 2021) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approximates the actual conditional model with known likelihood-ratio between the two. The backward filter and the forward change of measure are suitable to be incorporated into a probabilistic programming context because they can be formulated as a set of transformation rules. The guided generative model can be incorporated in different approaches to efficiently sample latent states and parameters conditional on observations. We show applicability in a variety of settings, including Markov chains with discrete state space, interacting particle systems, state space models, branching diffusions and Gamma processes.