Recent advances in machine learning and large-scale biological data collections have revived the prospect of building a virtual cell, a computational model of cellular behavior that could accelerate biological discovery. One of the most compelling promises of this vision is the ability to perform in silico phenotypic screens, in which a model predicts the effects of cellular perturbations in unseen biological contexts. This task combines heterogeneous textual inputs with diverse phenotypic outputs, making it particularly well-suited to LLMs and agentic systems. Yet, no standard benchmark currently exists for this task, as existing efforts focus on narrower molecular readouts that are only indirectly aligned with the phenotypic endpoints driving many real-world drug discovery workflows. In this work, we present AssayBench, a benchmark for phenotypic screen prediction, built from 1,920 publicly available CRISPR screens spanning five broad classes of cellular phenotypes. We formulate the screen prediction task as a gene rank prediction for each screen and introduce the adjusted nDCG, a continuous metric for comparing performance across heterogeneous assays. Our extensive evaluation shows that existing methods remain far from empirically estimated performance ceilings and zero-shot generalist LLMs outperform biology-specific LLMs and trainable baselines. Optimization techniques such as fine-tuning, ensembling, and prompt optimization can further improve LLM performance on this task. Overall, AssayBench offers a practical testbed for measuring progress toward in silico phenotypic screening and, more broadly, virtual cell models.

We investigate infectious disease spreading on scale-free networks using a heterogeneous mean-field approach applied to the susceptible-infected-susceptible model, incorporating a mitigation factor. Individual heterogeneity is incorporated through a power-law distribution, while a mitigation factor accounts for behavioral responses and external effects that effectively reduce transmission from infected individuals. This mechanism, inspired by Malthus-Verhulst-type constraints, introduces a nonlinear saturation effect that encodes self-limiting dynamics in a tractable way. Analytical results are supported by stochastic simulations. We find that the mitigation factor induces a nontrivial behavior in the probability that a link points to an infected node, which develops a maximum at finite infection rates. In contrast, the overall prevalence remains a monotonically increasing function of the transmission rate. Additionally, the mitigation mechanism leads to an inversion in the dependence of epidemic observables on the degree exponent at sufficiently high transmission rates. While in the standard model smaller exponents yield higher endemic prevalence, in the modified model this trend reverses, with larger exponents producing higher prevalence and increased infection probability along network links.

One of the classical results of mathematical population genetics states that the frequency of a beneficial mutant's offspring, on its way to fixation in a large population, looks like a logistic curve. A logarithmic scaling (both in height and time) of these selective sweep curves leads (in the case of strong selection) to a tent-like shape in the large population limit: First the logarithmic frequency of the mutant increases linearly from 0 to 1, then that of the former resident decreases from 1 to 0. For moderate selection the logarithmic frequencies develop (in the large population limit) a jump at the beginning/the end of the sweep, which takes the shape of the tent into that of a house. Our main result (proved for the Moran model) assesses the regularity of this convergence in the large population limit: It is uniform in the house's roof (phases of linear growth and decline) and "Skorokhod $M_1$" in the house's walls (closely around the jumps). Apart from interest in its own right, we anticipate that this result and the proof techniques will be instrumental for extending the description of clonal interference by Poissonian interacting trajectories (as it was done in Hermann et al. (2024) for strong selection) also to moderate selection.

Complex microbial habitats see the spatial competition of different clonal bacterial populations that switch between different phenotypes. Here, we determine the effect of this subpopulation structure on the invasion of one species by another in a minimal model of two competing species: one species switches, both stochastically and in response to its competitor, to a persister phenotype resilient to competition. Surprisingly, our combined analytical and numerical results show that this phenotypic switching has no effect on the speed of the travelling wave by which the competitors invade the first population. Conversely, we discover that phenotypic switching can speed up the wave by which this population invades their competitors. Our results thus suggest, counterintuitively, that bacterial persistence can be an offensive, rather than defensive ecological strategy.

The cerebellum and cerebral cortex form tightly coupled circuits thought to support flexible and efficient temporal processing. How this interaction shapes cortical learning dynamics, and whether such heterogeneous modularity can benefit artificial systems, remains unclear. Here, we augment a recurrent neural network (RNN) with a cerebellar-inspired feedforward module and evaluate the resulting architecture on temporal tasks of varying difficulty. The cortico-cerebellar RNN (CB-RNN) learns faster and reaches higher maximum performance than parameter-matched fully recurrent baselines across a variety of regimes. Crucially, freezing the recurrent core after minimal training and delegating subsequent learning to the cerebellar module preserves superior learning efficiency, suggesting the cerebellar module is a primary driver of efficiency and that the cortical network can largely function as a fixed reservoir. Our results suggest that heterogeneous modular architectures can act as a powerful structural inductive bias in neural systems.

Adaptive behavior requires the brain to transition between distinct contexts while maintaining representations of prior experience. The ability to reconfigure neural representations without erasing previously acquired knowledge is central to learning in dynamic environments, yet the neural mechanisms that support this balance remain unclear. Understanding these mechanisms is also critical for addressing catastrophic forgetting in artificial systems designed for lifelong learning. Here, we identify joint sparse coding and temporal dynamics in both the mouse medial prefrontal cortex (mPFC) and computational networks as mechanisms that help preserve prior representations during context transitions. Specifically, sparsity in context-dependent representations reduces cross-context interference, whereas temporal dynamics within the network activity further enhance context separability across time. Strikingly, networks endowed with both properties, such as spiking neural networks, exhibit improved retention during lifelong learning without auxiliary heuristics. These findings establish joint sparse coding and temporal dynamics as a core mechanism supporting flexible context reconfiguration in lifelong learning and, through their activity constraining nature, as an energy-efficient architectural principle for stable adaptation. Together, they provide a mechanistic framework for understanding how the brain preserves prior knowledge while flexibly adapting to new contexts.

Phylogenetic networks provide a framework for representing evolutionary histories involving reticulate events such as hybridization or horizontal gene transfer. A central problem is to infer such networks from local structural information. In this paper, we study network inference from least common ancestor (LCA) constraints, which specify relative ancestral relationships between pairs of taxa. While previous work has characterized when a set of required LCA constraints can be realized by a phylogenetic network, practical applications may also involve constraints that must be explicitly avoided, for example due to biological prior knowledge. We therefore consider the realization problem for pairs $(R,F)$, where $R$ is a set of required LCA-constraints and $F$ is a set of forbidden ones. Since there are several natural ways to formalize what it means for a network to avoid a forbidden LCA-constraint, we study three such variants. For each of them, we characterize exactly when there exists a phylogenetic network that realizes all constraints in $R$ while avoiding all constraints in $F$ in the respective sense. Based on these characterizations, we derive polynomial-time algorithms that decide the existence of such networks and construct one whenever it exists.

The present study evaluated the effectiveness of transcranial alternating current stimulation (tACS) treating patients with post-stroke anomia using a picture-naming task and a Single-Case Experimental Design (SCED). A right-handed 38-year-old woman with a left-hemisphere stroke and a left-handed 54-year-old man with a right-hemisphere stroke underwent an eight-week treatment program. Specifically, they participated in a picture-naming task three times a week, alternating between sessions with and without tACS stimulation every two weeks. Electroencephalography (EEG) measurements were taken at the end of each two-week period, and behavioral data were collected before, during and after the treatment. EEG and behavioral assessments were also conducted at one- and three-month follow-ups. Picture-naming performance was significantly faster during tACS sessions compared to sessions without tACS. By the end of the intervention, both participants demonstrated improved accuracy and speed, with positive effects also observed in behavioral measures. EEG analysis showed that post-treatment brain activity resembled that of healthy individuals performing similar tasks. Patients' improvements in picture-naming and behavioral tests showed that the positive effects remained stable even after three months. Thus, preliminary data suggest that tACS might be a promising intervention for anomia, with lasting effects. Large-scale studies are needed to confirm these findings.

Microbial adaptation to extreme stress, such as starvation, antimicrobial exposure, or freezing often reveals fundamental trade-offs between survival and proliferation. Understanding how populations navigate these trade-offs in fluctuating environments remains a central challenge. We develop a quantitative model to investigate the adaptation of populations of yeast (Saccharomyces cerevisiae) subjected to cycles of growth and extreme freeze-thaw stress, focusing on the role of quiescence as a mediator of survival. Our model links key life-history traits: growth rate, lag time, quiescence probability, and stress survival, to a single underlying phenotype, motivated by the role of intracellular trehalose in the adaptation of yeast to freeze-thaw stress. Through stochastic population simulations and analytical calculation of the long-term growth rate, we identify the evolutionary attractors of the system. We find that the strength of the growth-survival trade-off depends critically on environmental parameters, such as the duration of the growth phase. Crucially, our analysis reveals that populations optimized for growth-stress cycles can often maintain viability alongside growth-optimized populations even in the absence of stress. This demonstrates that underlying physiological trade-offs do not necessarily translate into fitness trade-offs at the population level, providing general insights into the complex interplay between environmental fluctuations, physiological constraints, and evolutionary dynamics.

Risk stratification is a key tool in clinical decision-making, yet current approaches often fail to translate sophisticated survival analysis into actionable clinical criteria. We present a novel method for unsupervised machine learning that directly optimizes for survival heterogeneity across patient clusters through a differentiable adaptation of the multivariate logrank statistic. Unlike most existing methods that rely on proxy metrics, our approach represents novel methodology for training any neural network architecture on any data modality to identify prognostically distinct patient groups. We thoroughly evaluate the method in simulation experiments and demonstrate its utility in practice by applying it to two distinct cancer types: analyzing laboratory parameters from multiple myeloma patients and computed tomography images from non-small cell lung cancer patients, identifying prognostically distinct patient subgroups with significantly different survival outcomes in both cases. Post-hoc explainability analyses uncover clinically meaningful features determining the group assignments which align well with established risk factors and thus lend strong weight to the methods utility. This pan-cancer, model-agnostic approach represents a valuable advancement in clinical risk stratification, enabling the discovery of novel prognostic signatures across diverse data types while providing interpretable results that promise to complement treatment personalization and clinical decision-making in oncology and beyond.

Transformer-based models have demonstrated remarkable reasoning abilities, but the mechanisms underlying relational reasoning remain poorly understood. We investigate how transformers perform \textit{transitive inference}, a classic relational reasoning behavior from psychology which elicits inference about indirectly related items (e.g., if $A > B$ and $B > C$, then $A > C$). We compare in-weights learning (IWL) and in-context learning (ICL) behaviors and mechanisms on these tasks, and fine profoundly different patterns of generalization. IWL models learn a linear embedding, which leads to transitive inference as well as other behavioral effects present in humans and animals. ICL models, in contrast, are capable of learning to generalize transitively, but only do so when it is necessitated by the training data, otherwise learning a match-and-copy strategy. Interestingly, pre-training ICL models on in-context linear regression tasks that provide them with a latent linear representation is sufficient to make the ICL behaviors and internal representations qualitatively and quantitatively more like IWL. In order to test whether the same inference patterns are present across in large language models, we leverage a congruency paradigm which allows us to differentially probe IWL and ICL generalization patterns without access to their training data. We indeed see IWL reasoning leads to more transitive generalization than ICL. Moreover, we find that prompting the ICL models to use a linear mental map led to increased transitive inference over different geometric prompts. Together, these results reveal that both the training regime and the geometric structure of induced representations critically determine transformers capacity for transitive inference.

De novo molecule generation allows the search for more drug-like hits across a vast chemical space. However, lead optimization is still required, and the process of optimizing molecular structures faces the challenge of balancing structural novelty with pharmacological properties. This study introduces the Deep Genetic Molecular Modification Algorithm (DGMM), which brings structure modification to the level of medicinal chemists. A discrete variational autoencoder (D-VAE) is used in DGMM to encode molecules as quantization code, mol-gene, which incorporates deep learning into genetic algorithms for flexible structural optimization. The mol-gene allows for the discovery of pharmacologically similar but structurally distinct compounds, and reveals the trade-offs of structural optimization in drug discovery. We demonstrate the effectiveness of the DGMM in several applications.

Multimodal models that jointly reason over protein sequences, structures, and function annotations within a unified representation hold immense potential for integrating multimodal data and generating new proteins with designed functional properties. To utilize transformer architectures, such models require a tokenizer that converts protein structure from continuous atomic coordinates into discrete representations suitable for scalable multimodal training. The quality of such models are fundamentally upper bounded by the fidelity and expressiveness of the underlying tokenized structure. However, existing tokenizers prioritize reconstruction over generative abilities. To address these gaps, we introduce Yeti, a simple and compact protein structure tokenizer based on lookup free quantization and trained end to end with a flow matching objective for multimodal learning. Compared to existing models, Yeti generally achieves the best codebook utilization and token diversity, and second best reconstruction accuracy (with 10x fewer parameters than ESM3) on diverse datasets. To validate Yeti's generative capability, we trained a compact multimodal model jointly over its structure tokens and amino acid sequence entirely from scratch, with no pretrained initialization. The resulting multimodal model generates plausible structures under unconditional cogeneration of protein sequence and structures, achieving comparable results to 10x larger models. Together, these results demonstrate that Yeti is a compact and expressive protein structure tokenizer suitable for training multimodal models that cogenerates highly plausible sequences and structures.

Protein function is often controlled by ligands that bias the direction of state transitions, such as agonists and antagonists, rather than stabilizing a single conformation. This is especially important for clinically relevant G protein-coupled receptors (GPCRs), where therapeutic efficacy depends on functional directionality. Structure-based design methods optimize binding to static conformations and cannot represent non-reversible, directional effects or systematically distinguish agonist from antagonist behavior. To address this gap, we introduce Transition-Directed Discrete Diffusion for Allosteric Binder Design (TD3B), a sequence-based generative framework that designs binders with specified agonist or antagonist behavior via a directional transition control objective. TD3B combines a target-aware Direction Oracle, a soft binding-affinity gate, and amortized fine-tuning of a pre-trained discrete diffusion model, enabling targeted agonist and antagonist generation decoupled from binding affinity and unattainable by equilibrium-based or inference-only guidance baselines. The code and checkpoints are available at https://huggingface.co/ChatterjeeLab/TD3B.

Spike-based encodings are sparse and energy-efficient, but have largely been formulated probabilistically, disconnected from most signal processing literature. We recast spike encoders as time-causal wavelet frames with quantitative bandwidths and reconstruction error bounds. The proposed wavelets preserve the sparsity and locality of spiking representations, with reconstruction up to spike quantization and time discretization. We demonstrate reconstruction on ECG and audio datasets, achieving a normalized RMSE comparable to continuous wavelet transforms. The spiking wavelets map directly to neuromorphic hardware.

Multi-nucleated cells exist in all domains of life, ranging from animals, plants and fungi to single-celled organisms such as the slime mold Physarum polycephalum. The large cell size, in the case of Physarum reaching centimeters and more, challenges the coordination of nuclei activity as signals need to cross large distances. In search for a mechanism for fast long-ranged communication among nuclei, we quantify nuclei dynamics and cytoplasmic flows in Physarum's tubular network. We observe nuclei in two interchangeable, dynamic states: mobile, flowing within the cytoplasmic shuttle flow, or trapped in the tube's porous cell cortex. As we find nuclei to accumulate at the tube's inner fluid-porous interface we theoretically explore and confirm, with physiological parameters, that slowing down of mobile nuclei during flow is sufficient for diffusible signal exchange between mobile and trapped nuclei. We analytically derive that communication akin to pigeon-post with mobile nuclei serving as pigeons shuttling between trapped nuclei acting as waypoints, gives rise to signaling velocities that account for the rapid intracellular reorganization observed in Physarum. Since signal transfer by flow-transported nuclei outcompetes the mere diffusion of signals encoded in cytosolic proteins, pigeon-post communication surpasses alternative signaling mechanisms, even diffusive relay signaling up to twenty-fold in velocity. The key ingredients of pigeon-post communication, namely alternating flows and waypoints, exist in other multi-nucleated cells and may also be generalized beyond intracellular signaling.

In Bayesian phylogenetics, our goal is to estimate the posterior distribution over phylogenetic trees. Markov chain Monte Carlo methods are widely used to approximate the phylogenetic posterior distributions. For large-scale sequence data, repeated evaluation of the likelihood function incurs a high computational cost. In this article, we propose a machine-learning algorithm with over 35 topological and branch-length features to predict the changes in the likelihood function caused by tree moves (\eg,~eSPR, stNNI) used in standard MCMC approaches. This algorithm is then used to design a delayed acceptance MCMC kernel, which utilized the predicted surrogate function for preliminary rejection, to accelerate tree space searches. Furthermore, we integrate our proposed MCMC kernel into the sequential Monte Carlo sampler framework. We validate the proposed delayed-acceptance sequential Monte Carlo approach (DA-SMC) on simulation and real data sets. Our delayed acceptance kernel can maintain robust estimation while reduces the number of likelihood evaluations significantly, yielding substantial computational time savings. We develop a Python package that is available at https://github.com/wentYu/DAphyloSMC.

Adults vary greatly in how effectively they learn a new language, but the signals driving the learning processes and individual differences remain unclear. Over seven days, we tracked behavioral learning and collected fMRI data from 102 adults as they learned an artificial language with corrective feedback. We trained matched transformer models with prediction, feedback, or combined objectives and compared their internal representations to brain activity. Representations derived from the prediction-focused model accounted for the largest share of unique neural variance at the group level, despite the human task being feedback-based. Throughout model training, both objectives showed a shift in brain-model alignment from sensory to higher-order language and associative networks, indicating abstraction processing. Conversely, neural patterns related to the feedback model were most useful for predicting individual generalization outcomes on Day 7. These findings support a multi-signal model of adult language learning, in which prediction shapes a common neural learning architecture across learners, whereas feedback-related mechanisms better explain individual differences over time.

The reasoning gap between large and compact vision-language models (VLMs) limits the deployment of medical AI on portable clinical devices. Compact VLMs of 2--4B parameters can run on resource-constrained hardware but lack the multi-step reasoning capacity needed for interpretable clinical decision support. Existing knowledge distillation methods transfer answers without the reasoning process behind them. Medical visual question answering (VQA) serves as a testbed for this problem, as it requires models to integrate visual evidence with clinical knowledge through structured reasoning chains. We introduce LiteMedCoT-VL, a pipeline that transfers chain-of-thought reasoning from a 235B teacher model to 2B student models through LoRA-based fine-tuning on explanation-enriched training data. All inference is conducted without image captions by default, simulating the clinical scenario in which a physician interprets a medical image directly without an accompanying radiology report. On the PMC-VQA benchmark, LiteMedCoT-VL achieves 64.9% accuracy, exceeding the zero-shot Qwen3-VL-4B baseline of 53.9% by 11.0 percentage points and outperforming all published baselines. This result indicates that a 2B model with reasoning distillation can match or exceed models with twice the parameters. Visual grounding analysis shows that the model relies on image content rather than exploiting textual priors. Our code is publicly available at https://anonymous.4open.science/r/LiteMedCoT-VL.

Evolutionary computation has long promised to deliver both high-performance optimization tools as well as rigorous scientific simulations of Darwinian evolution. However, modern algorithms frequently abandon evolutionary fidelity for physics-inspired heuristics or superficial biological metaphors. This paper derives a suite of advanced gradient-based optimization algorithms directly from evolutionary first principles. We introduce Darwinian Lineage Simulations (DLS) to prove that, in an asexual context, Fisher's and Wright's historically opposed views of evolution are actually formally equivalent; One can partition Fisher's deterministically-evolving total population into Wright's randomly-drifting sub-populations. We prove that proper bookkeeping requires introducing a specific kind of structured noise (the DLS noise relation). Crucially, any bookkeeping choices which satisfy this relation will yield a faithful simulation of evolution. Using this vast representational freedom, we prove that a broad family of battle-tested optimization algorithms are already perfectly compatible with evolutionary dynamics. These include: Stochastic Gradient Descent as well as many regularizations/approximations of Newton's method and Natural Gradient Descent. By simply adding DLS noise (i.e., evolutionarily faithful genetic drift), these algorithms become scientifically valid in silico simulations of Darwinian evolution. Finally, we demonstrate that even the state-of-the-art Adam optimizer can be brought into evolutionary compliance through a minor mathematical surgery.

Background: Autism spectrum disorder (ASD) is characterized by significant clinical and biological heterogeneity. Conventional group-mean analyses of eye movements often mask individual atypicalities, potentially overlooking critical pathological signatures. This study aimed to identify idiosyncratic oculomotor patterns in ASD using an "outlier analysis" of smooth pursuit eye movement (SPEM). Methods: We recorded SPEM during a slow Lissajous pursuit task in 18 adults with ASD and 39 typically developed (TD) individuals. To quantify individual deviations, we derived an "outlier score" based on the Mahalanobis distance. This score was calculated from a feature vector, optimized via Principal Component Analysis (PCA), comprising the temporal lag ($Δ$t) and the spatial deviation ($Δ$s). An outlier was statistically defined as a score exceeding $\sqrt{10}$ (approximately 3.16$σ$) relative to the TD normative distribution. Results: While the TD group exhibited a low outlier rate of 5.1%, the ASD group demonstrated a significantly higher prevalence of 38.9% (7/18) (binomial P = 0.0034). Furthermore, the mean outlier score was significantly elevated in the ASD group (3.00 $\pm$ 2.62) compared to the TD group (1.52 $\pm$ 0.80; P = 0.002). Notably, these extreme deviations were captured even when conventional mean-based comparisons showed limited sensitivity. Conclusions: Our outlier analysis successfully visualized the high degree of idiosyncratic atypicality in ASD oculomotor control. By shifting the focus from group averages to individual deviations, this approach provides a sensitive metric for capturing the inherent heterogeneity of ASD, offering a potential baseline for identifying clinical subtypes.

In this paper, we introduce gonosomic algebras to algebraically translate the phenomenon of genetic sterility. Gonosomic algebras extend the concept of gonosomal algebras used as algebraic model of genetic phenomena related to sex-determination and sex-linked gene transmission by allowing genetic sterility to be taken into account. Conditions under which gonosomic algebras are not gonosomal and several algebraic constructions of gonosomic algebras are given. To each gonosomic algebra, an evolution operator noted W is associated that gives the state of the offspring population at the birth stage. Next from W we define the operator V which gives the frequency distribution of genetic types. We show that the various stability notions of equilibrium points are preserved by passing from W to V .

High-resolution neural datasets enable foundation models for the next generation of brain-computer interfaces and neurological treatments. The community requires rigorous benchmarks to discriminate between competing modeling approaches, yet no standardized evaluation frameworks exist for intracranial EEG (iEEG) recordings. To address this gap, we present Neuroprobe: a suite of decoding tasks for studying multi-modal language processing in the brain. Unlike scalp EEG, intracranial EEG requires invasive surgery to implant electrodes that record neural activity directly from the brain with minimal signal distortion. Neuroprobe is built on the BrainTreebank dataset, which consists of over 40 hours of iEEG recordings from 10 human subjects performing a naturalistic movie viewing task. Neuroprobe serves two critical functions. First, it is a source from which neuroscience insights can be drawn. The high temporal and spatial resolution of the labeled iEEG allows researchers to systematically determine when and where computations for each aspect of language processing occur in the brain by measuring the decodability of each feature across time and all electrode locations. Using Neuroprobe, we visualize how information flows from key language and audio processing sites in the superior temporal gyrus to sites in the prefrontal cortex. We also demonstrate the time evolution of processing from simple auditory features (e.g., pitch and volume) to more complex language features (e.g., part of speech) in a purely data-driven manner. Second, as the field moves toward neural foundation models trained on large-scale datasets, Neuroprobe provides a rigorous framework for comparing competing architectures and training protocols. We make the code for Neuroprobe openly available, aiming to enable rapid progress in the field of iEEG foundation models. Public leaderboard: https://neuroprobe.dev/

Proper regulation of cell signaling and gene expression is crucial for maintaining cellular function, development, and adaptation to environmental changes. Reaction dynamics in cell populations is often noisy because of (i) inherent stochasticity of intracellular biochemical reactions (``intrinsic noise'') and (ii) heterogeneity of cellular states across different cells that are influenced by external factors (``extrinsic noise''). In this work, we introduce an extrinsic-noise-driven neural stochastic differential equation (END-nSDE) framework that utilizes the Wasserstein distance to accurately reconstruct SDEs from trajectory data from a heterogeneous population of cells (extrinsic noise). We demonstrate the effectiveness of our approach using both simulated and experimental data from three different systems in cell biology: (i) circadian rhythms, (ii) RPA-DNA binding dynamics, and (iii) NF$κ$B signaling process. Our END-nSDE reconstruction method can model how cellular heterogeneity (extrinsic noise) modulates reaction dynamics in the presence of intrinsic noise. It also outperforms existing time-series analysis methods such as recurrent neural networks (RNNs) and long short-term memory networks (LSTMs). By inferring cellular heterogeneities from data, our END-nSDE reconstruction method can reproduce noisy dynamics observed in experiments. In summary, the reconstruction method we propose offers a useful surrogate modeling approach for complex biophysical processes, where high-fidelity mechanistic models may be impractical.

Formulating quantitative and predictive models for tissue development requires consideration of the complex, stochastic gene expression dynamics, its regulation via cell-to-cell interactions, and cell proliferation. Including all of these processes into a practical mathematical framework requires complex expressions that are difficult to interpret and apply. We construct a simple theory that incorporates intracellular stochastic gene expression dynamics, signaling chemicals that influence these dynamics and mediate cell-cell interactions, and cell proliferation and its accompanying differentiation. Cellular states (genetic and epigenetic) are described by a Waddington vector field that allows for non-gradient dynamics (cycles, entropy production, loss of detailed balance) which is precluded in Waddington potential landscape representations of gene expression dynamics. We define an epigenetic fitness landscape that describes the proliferation of different cell types, and elucidate how this fitness landscape is related to Waddington's vector field. We illustrate the applicability of our framework by analyzing two model systems: an interacting two-gene differentiation process and a spatiotemporal organism model inspired by planaria.

The dataset collected at the Cape Rodney-Okakari Point Marine (CR-OPM) reserve on the North Island of New Zealand is rather unique. It describes the cyclic time evolution of a rocky intertidal community, with the relative abundances of the various coastal species that have been meticulously monitored for more than 20 years. Past theoretical studies, anchored on a deterministic description, required invoking ad hoc mechanisms to reproduce the observed dynamical paths. Following a maximum likelihood approach to interpolate individual stochastic trajectories, we here propose quasi-cycles as an alternative and simpler mechanism to explain the oscillations observed in the population numbers of the ecosystem. From a general standpoint, we also show that it is possible to return conclusive evidence on the existence of stochastic quasi-cycles, without resorting to global fitting strategies which necessitate handling a large collection of independent replicas of the dynamics, a possibility that is often precluded in real life applications.

Over recent decades, neuroimaging tools, particularly electroencephalography (EEG), have revolutionized our understanding of the brain and its functions. EEG is extensively used in traditional brain-computer interface (BCI) systems due to its low cost, non-invasiveness, and high temporal resolution. This makes it invaluable for identifying different brain states relevant to both medical and non-medical applications. Although this practice is widely recognized, current methods are mainly confined to lab or clinical environments because they rely on data from multiple EEG electrodes covering the entire head. Nonetheless, a significant advancement for these applications would be their adaptation for "real-world" use, using portable devices with a single-channel. In this study, we tackle this challenge through two distinct strategies: the first approach involves training models with data from multiple channels and then testing new trials on data from a single channel individually. The second method focuses on training with data from a single channel and then testing the performances of the models on data from all the other channels individually. To efficiently classify cognitive tasks from EEG data, we propose Convolutional Neural Networks (CNNs) with only a few parameters and fast learnable spectral-temporal features. We demonstrated the feasibility of these approaches on EEG data recorded during mental arithmetic and motor imagery tasks from three datasets. We achieved the highest accuracies of 100%, 91.55% and 73.45% in binary and 3-class classification on specific channels across three datasets. This study can contribute to the development of single-channel BCI and provides a robust EEG biomarker for brain states classification.

We derive from first principles a three-dimensional theory of self-propelled particle swarming in a viscous fluid environment. Our model predicts emergent collective behavior that depends critically on fluid opacity, mechanism of self-propulsion, and type of particle-particle interaction. In "clear fluids" swimmers have full knowledge of their surroundings and can adjust their velocities with respect to the lab frame, while in "opaque fluids," they control their velocities only in relation to the local fluid flow. We also show that "social" interactions that affect only a particle's propensity to swim towards or away from neighbors induces a flow field that is qualitatively different from the long-ranged flow fields generated by direct "physical" interactions. The latter can be short-ranged but lead to much longer-ranged fluid-mediated hydrodynamic forces, effectively amplifying the range over which particles interact. These different fluid flows conspire to profoundly affect swarm morphology, kinetically stabilizing or destabilizing swarm configurations that would arise in the absence of fluid. Depending upon the overall interaction potential, the mechanism of swimming (e.g., pushers or pullers), and the degree of fluid opaqueness, we discover a number of new collective three-dimensional patterns including flocks with prolate or oblate shapes, recirculating peloton-like structures, and jet-like fluid flows that entrain particles mediating their escape from the center of mill-like structures. Our results reveal how the interplay among general physical elements influence fluid-mediated interactions and the self-organization, mobility, and stability of new three-dimensional swarms and suggest how they might be used to kinetically control their collective behavior.

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but they are structurally unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using e.g., the Bellman-Harris equation, do not resolve a population's age-structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the Logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an ageing population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a BBGKY-like hierarchy. However, explicit solutions are derived in two simple limits and compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.

Applications of first passage times in stochastic processes arise across a wide range of length and time scales in biological settings. After an initial technical overview, we survey representative applications and their corresponding models. Within models that are effectively Markovian, we discuss canonical examples of first passage problems spanning applications to molecular dissociation and self-assembly, molecular search, transcription and translation, neuronal spiking, cellular mutation and disease, and organismic evolution and population dynamics. In this last application, a simple model for stem-cell ageing is presented and some results derived. Various approximation methods and the physical and mathematical subtleties that arise in the chosen applications are also discussed.