This paper proposes an unsupervised workflow to pseudo-label extracellular spikes from human brain slice MEA recordings into two putative cell types: pyramidal cells and interneurons. Here, the raw data from the data acquisition system is used and processed. The pipeline for pre-processing includes bandpass filtering, threshold--based spike detection, frame alignment and normalization. In the ML workflow, dimensionality reduction (PCA, t-SNE, UMAP), clustering (GMM, k-means). To achieve an online system, template matching and OSort under varying curation strictness is also considered. All pipelines are evaluated by different cluster quality with within-cluster Pearson correlation, Silhouette score, and Calinski-Harabasz index. Applying stricter curation improves separation at some cost to inclusivity.

Physiological tremor of the upper limb is a sensitive neuromuscular indicator that may be modulated by cognitive load and competitive stress, yet its behaviour in real esports conditions remains uncharacterised. We measured wrist accelerometer-based tremor in 16 healthy adult male StarCraft~2 players across two tournament days, computing log power spectral density ($log(PSD)$) and dominant frequency in four bands (2--4, 8--14, 10--20, and 1--25Hz) and comparing them to published population norms using linear mixed models. Players deviated significantly from the reference in all bands: $log(PSD)$ was elevated at 2--4~Hz and substantially reduced at higher frequencies (Cohen's $d = 1.6$--$2.3$), suggesting long-term neuromuscular adaptation to the fine-motor demands of esports. Tremor indicators declined systematically over the tournament day. Contrary to the fatigue-related increases typical of traditional motor tasks. Neither game outcome nor actions per minute significantly predicted post-game tremor. These findings suggest physiological tremor may reflect a generalised psychophysiological adaptation to competitive esports rather than being a short-term performance predictor.

We study how to recover candidate circadian-clock regulators of pituitary hormone genes that are important for women's health but do not show a clear 24-hour rhythm in bulk tissue, aiming to nominate clock-linked regulatory targets that could inform future chronopharmacologic and chronotherapeutic strategies. We propose \textbf{rwMagLap}, which builds a graph on rhythmic backbone genes. For each edge, we combine 24-hour fit quality with peak-time phase, represented as a complex unit-circle value, yielding a Hermitian adjacency matrix and a magnetic Laplacian. We insert arrhythmic hormone genes, treated as anchors, by a reliability-weighted nearest-neighbor projection. The projected anchor-neighbor weights are pooled into a soft teleport distribution, and complex personalized PageRank then ranks rhythmic backbone genes by the magnitude of their PageRank scores. In pituitary data, we find that all 11 women's-health anchors are arrhythmic. Even so, we find that the top-50 list is $7.95\times$ enriched for the 13-gene KEGG circadian set (7 of the 8 set genes in the 454-gene backbone; corrected Benjamini-Hochberg (BH) $p_{\mathrm{BH}}=4\times10^{-6}$) and $4.54\times$ enriched for the 111-gene Reactome set (8 of 16 genes; $p_{\mathrm{BH}}=1.6\times10^{-4}$), while a phase-blind real-valued baseline recovers none. We recover candidates through reliability weighting and phase-aware seeding rather than through magnetic propagation. The magnetic phase adds a different capability: it represents temporal order. On pituitary backbone, the magnetic embedding recovers measured peak-time order of connected pituitary genes with accuracy $0.971$, while $q{=}0$, i.e., no magnetic charge, is at chance.

DNA methylation (DNAm) serves as one of the most robust molecular biomarkers of biological aging. While conventional epigenetic clocks accurately predict chronological age from high-dimensional CpG profiles, they treat aging as a static regression task, meaning they can only output a single score rather than simulating how an entire profile continuously changes over time. To reconstruct these continuous dynamics, we frame lifelong human epigenetic aging as a trajectory inference problem across discrete age snapshots derived from widely available cross-sectional data. We introduce a two-stage computational pipeline: first, an age-regularized Variational Autoencoder (VAE) maps high-dimensional CpG profiles onto a chronologically ordered latent manifold while preserving a generative decoder bridge back to the original methylation space. Second, we model the continuous movement across this latent space via Regularized Unbalanced Optimal Transport (RUOT) that unifies deterministic drift, random diffusion, and non-conservative mass changes. By resolving this RUOT formulation using the DeepRUOT framework, our model fluidly accommodates population-level density shifts like survivorship bias and cellular attrition without requiring rigid biological priors. Evaluated on a large-scale, 80-year pan-tissue dataset, our model demonstrates robust distribution interpolation and uncovers a prominent late-life surge in the learned growth field that mathematically captures the variance expansion driven by stochastic epigenetic drift. Finally, by decoding continuous latent paths back to individual CpG sites, we reconstruct and empirically verify distinct biological aging archetypes, offering a rigorous, generative paradigm for simulating human molecular aging.

Phylogenetic trees are rooted trees with branch lengths that record genetic divergence or elapsed time, and quantifying differences between them is central to a wide range of evolutionary and epidemiological analyses. Graph-polynomial encodings of rooted trees provide an accurate, interpretable, and computationally efficient way to compare tree shapes, but existing polynomial encodings must be paired with auxiliary structures to study rooted trees with branch lengths. We introduce a bivariate polynomial encoding that incorporates branch lengths directly into a recursive computation from the leaf vertices to the root vertex of a tree. We prove that, for rooted trees with branch lengths and no vertices of degree two, which include all standard phylogenetic trees, two trees have the same polynomial if and only if their underlying unlabeled trees are isomorphic and the branch lengths of corresponding edges are equal. We apply the polynomial encoding to three published HIV-1 phylogenies sampled in different epidemiological settings and show that it accurately separates the three datasets based on their tree topologies and branch lengths, outperforming previous polynomial-based approaches for analyzing rooted trees with branch lengths.

The Moran process with selection and recurrent mutation is a classical model in population genetics, yet how the placement of selection within the update rule shapes the stationary distribution has received little attention. We study a finite, well-mixed haploid population of constant size $n$ with $m$ labeled alleles, parent-independent mutation, and allele-specific fitnesses. Within this common framework we compare three Moran update kernels that differ only in the stage at which selection acts: during reproduction, when the offspring copies one of two sampled parents (Scheme~I); through fitness-biased mate choice, followed by neutral copying (Scheme~II); and at death, so that fitter individuals are less likely to be replaced (Scheme~III). Although all three favor fitter alleles, they define different Markov chains. For two alleles, each scheme reduces to a birth-death chain and admits an exact stationary law, but the three laws differ. For $m\ge 3$, the placement of selection becomes decisive: Schemes~I and~II are generally nonreversible when fitnesses are unequal, so no detailed-balance product form exists, whereas Scheme~III remains reversible for every $m$ and has a closed stationary distribution -- a Dirichlet-multinomial core modified by an explicit fitness factor. We further show that all three mechanisms can act simultaneously in the two-allele case without losing exact solvability, and we derive weak-selection expansions that make explicit how small fitness differences tilt the neutral beta-binomial and Dirichlet-multinomial benchmarks. Together, these results clarify when neutral stationary structure survives the introduction of selection and when multiallelic Moran dynamics become genuinely nonreversible

Magnesium ions are essential for RNA structure but difficult to model due to slow binding kinetics and experimental limitations. We present an enhanced-sampling strategy that accelerates Mg$^{2+}$ inner-shell binding by orders of magnitude, enabling quantitative exploration of ion-binding motifs in a large ribozyme. The method combines a barrier-flattening bias with Hamiltonian replica exchange to efficiently sample multiple equivalent binding sites, and builds on an approach that achieved top performance in the CASP16 blind assessment of RNA solvation structure. Using cryo-electron microscopy maps for validation, we introduce a local analysis framework that infers the population of individual binding motifs from their agreement with experimental density, enabling site-by-site validation. We find that insufficient sampling of inner-shell binding leads to significantly poorer agreement with experiment, whereas force fields predicting different inner/outer binding equilibria remain largely indistinguishable at the current experimental resolution. These results highlight the dominant role of sampling in modelling divalent ion binding and provide a general strategy for integrating simulations with experimental data in complex biomolecular systems.

Root-mean-square deviation (RMSD) is the standard metric of structural comparison in molecular dynamics (MD) simulations. In its conventional form, RMSD assigns equal weight to all atoms regardless of mobility. Hence, flexible loops and disordered regions can dominate a global RMSD, while the rigid functional core contributes negligibly to the overall metric. To address this issue, we introduce the Bayes-optimal RMSD (BRMSD), which optimizes per-atom weights jointly with structural averages by maximizing a Bayesian posterior. In a trade-off between low RMSD and weight uniformity, a position-fluctuation parameter $\sigma$ controls the transition from classical RMSD ($\sigma \to \infty$) to a progressive focus on a rigid core ($\sigma \to 0$). The BRMSD framework supports analysis modules for structural alignment, focused alignment onto a user-specified domain, trajectory smoothing, soft $K$-means conformational clustering, and rigid-domain identification. These modules are implemented in the open-source Python package BRMSD (this https URL) and benchmarked on two MD systems, the endoplasmic reticulum translocon-associated protein SND3 and the phosphotransferase adenylate kinase.

Many biological processes are governed by complex dynamical mechanisms that remain incompletely understood despite increasing volumes of experimental data. Biologically-informed neural networks (BINNs) seek to address this challenge by embedding mechanistic differential equations into neural network training, enabling interpretable constitutive operators to be recovered directly from sparse and noisy observations. However, reliable operator recovery depends sensitively on network architecture, optimisation strategy, and data informativeness. Here, we present a systematic empirical study of how these factors influence mechanistic inference using BINNs applied to canonical one-dimensional advection-diffusion-reaction partial differential equation models. Across a suite of benchmark problems, we investigate how network expressivity, learning rate, loss weighting, and batch size influence optimisation behaviour and operator recovery. We show that successful mechanistic inference depends on balancing competing objectives rather than maximising any single aspect of the model or optimisation. Moderately expressive architectures outperform overly complex networks, intermediate learning rates improve optimisation stability, balanced data and PDE losses are essential for accurate operator recovery, and intermediate batch sizes provide the best compromise between computational efficiency and reproducibility. We further identify practical diagnostics for recognising common failure modes, including over-fitting, unstable optimisation, and poor mechanistic recovery when the ground truth is unavailable. Together, these findings provide evidence-based guidelines for deploying BINNs as credible tools for biological model discovery.

Large language models (LLMs) demonstrate remarkable reasoning capabilities, yet their stateless architecture fundamentally limits deployment in long-horizon research workflows requiring multi-session continuity and quantitative rigor. Here we present Ensemble QSP, a multi-agent framework featuring a three-layer hierarchical memory architecture that keeps injected context bounded and constant in project duration (mid-term project state: median 301 tokens, max 4,050, across 104 runs) by capping each state category and evicting completed work, enabling continuous autonomous operation without context degradation. The system orchestrates five specialist worker agents under domain-expert principal investigators, enforcing physical constraints through physics-based checklists and structured-domain knowledge. Comprehensive benchmarking demonstrates robust autonomous pharmacokinetic-pharmacodynamic model selection without human intervention, consistent result quality across both lower-cost and frontier LLMs, improved PK parameter recovery relative to single-agent baselines, and stable model selection across linguistically diverse prompts of the same task. Feature-level ablation across physiologically based pharmacokinetic (PBPK) models spanning a broad complexity range shows that PI-agent oversight improves debugging efficiency while preserving final accuracy across conditions. The architecture is structurally domain-agnostic, adding a new scientific domain requires only a new PI agent configuration.

Ramkrishna, Kompala, and Tsao proposed the cybernetic model of microbial growth, in which cells allocate enzyme synthesis resources according to a matching rule that mimics rational decision-making. The matching rule was later shown to be optimal under general assumptions about the underlying return-on-investment structure, yet the specific objective the cell maximizes, and the constraints bounding that choice, were never written down as an explicit economic decision. Here we supply that missing decision, recasting cybernetic enzyme-synthesis control as a consumer choice problem from microeconomic theory: the cell allocates a limited proteome budget among competing catabolic enzymes as a linear program (LP), maximizing a linear growth utility subject to a linear proteome budget constraint. Because the utility is linear, the LP's solution is geometric: whenever the iso-utility line's slope differs from the budget constraint's, the optimum is a corner, and the entire proteome budget is allocated to the enzyme for the single most profitable substrate. Corner solutions correspond to diauxic growth, and sequential substrate consumption follows from the choice of corner rather than a distinct regulatory mechanism. Only when the two slopes coincide does the optimum spread across the entire budget line instead of concentrating at a single corner; this degenerate case underlies simultaneous substrate use. Using only parameters estimated independently from single-substrate experiments, the LP-derived cybernetic variables reproduced the diauxic and triauxic batch growth of Klebsiella oxytoca on glucose-xylose and glucose-xylose-lactose mixtures, achieving a fit comparable to the classical matching law. Thus, sequential substrate use is the generic outcome of growth-maximizing specialization under perfect substitutability, and co-utilization is the degenerate case of equal profitability.

Recent Vision-Language Models capture increasingly complex aspects of human cognition. Here we ask whether this alignment extends to reward valuation, which we assess in a mechanistic framework built on clinical tests that were developed to evaluate anhedonia and motivational deficits in major depressive disorder. In the brain, anhedonia is frequently linked to dysregulation in the Nucleus Accumbens (NAc) and the broader dopaminergic reward system. While neuroimaging has localized these deficits, establishing a causal link between NAc activity and specific behavioral symptoms remains a challenge. We use these ideas from neuroscience to functionally identify reward-anticipatory units in vision language models, and test their causal role via targeted perturbations. Perturbing NAc-selective units induces behavioral effects that mirror human anhedonia: the model shifts toward low-effort, low-reward options in effort-based decision-making tasks. Crucially, our results reflect a specific deficit in reward valuation and anticipation rather than a loss of task capability: the perturbed model maintains baseline performance when reward-based choice is removed. This induced vulnerability further aligns with clinical anhedonia and motivation scales, including DARS and MAP-SR. Taken together, these results reveal reward valuation circuits in AI models that parallel those in humans.

Brain age -- the age inferred from a physiological recording -- is an emerging biomarker whose deviation from chronological age tracks neurological and psychiatric burden, and EEG is an attractive substrate for it because it is cheap, portable, and temporally rich. Yet EEG brain-age models must contend with cross-site montage heterogeneity, small labelled cohorts, and dominant subject-level non-stationarity, and few EEG foundation models have been shown to deliver competitive age regression across the full pediatric-to-older-adult range in which such a biomarker would actually be deployed. We introduce STST-JEPA, a self-supervised transformer for resting-state and task EEG, pretrained on 47,703 sessions spanning ages 5-81 from the this http URL and Healthy Brain Network (HBN) corpora. The model combines a latent-prediction objective - predicting masked-token representations against an EMA-of-tokenizer target - with an auxiliary signal-reconstruction term, applied to 30-second multi-channel windows under spatiotemporal block masks. A lightweight attentive probe trained on frozen pretrained embeddings achieves a best held-out-validation mean absolute error of 3.06 years (r = 0.924) for age regression on 3,367 sessions, against a predict-the-mean baseline of approximately 10 years MAE. With light task-specific fine-tuning of the model's final layers, the same pretrained encoder achieves rank-1 placements - with the model's native 30-second windows - on the public NeuralBench x this http URL EEG leaderboard for sex classification (balanced accuracy 0.911), age prediction (r = 0.749), and psychopathology composite regression (r = 0.215). We further show that the model's age-prediction residual is negatively correlated with cognitive efficiency over several tasks we examined.

Continuum descriptions of epithelial tissue mechanics can replace expensive individual-based simulations with tractable macroscopic models, yet the link between cell-scale forces and tissue-scale transport remains poorly understood. We show that dimensionality controls this link: long-time mechanical relaxation rates reveal generalized porous-media-type nonlinear transport phenomena, $D(\rho)\propto\rho^\gamma$. Exponents in nonlinear diffusivities are fixed by microscopic mechanics and dimensionality, providing a novel physical mechanism for emergent macroscopic transport phenomena.

Large-scale combinatorial optimization remains demanding for classical heuristics, particularly when dense Quadratic Unconstrained Binary Optimization (QUBO) formulations induce large memory footprints, high CPU utilization, and long execution times. While near-term quantum processors cannot yet deliver unconditional quantum advantage, hybrid architectures can provide practical value by reducing the resource burden. This paper presents a resource-efficiency study of Hybrid Quantum Neighborhood Selection (HQNS), a framework that decomposes large dense QUBO instances into bounded-width quantum subproblems via stochastic frontier selection. We evaluate HQNS on the Maximum Diversity Subset Selection Problem (MDSSP), focusing on the trade-off between solution quality retention and resource consumption. Benchmarks up to N=1000 candidates show that HQNS preserves 99.9908% of the mean diversity score of an 11-restart parallel Simulated Annealing baseline, while reducing wall-clock time by 94.91%, peak CPU utilization by 64.68%, and peak memory usage by 88.61%. The QPU execution time remains bounded within a 6-7 second envelope across scales, indicating that the quantum component is decoupled from the global QUBO dimension when the frontier size is fixed. These results suggest that HQNS provides a resource-aware pathway for deploying hybrid quantum optimization in practical large-scale settings, serving as an efficient architecture for incorporating near-term quantum processors into classical optimization pipelines.

In this work, we reviewed different approaches in mathematical modeling of biologically plausible neural systems. Models are characterized and classified based on their common features and special use cases. In addition to spiking models, different types of discrete and continuous analogs are considered to accurately simulate biological processes, including membrane potential dynamics. The models under investigation include neurons and various components encountered in neural systems and affected the dynamics. The selection of specific approaches was driven by their prevalence and innovative perspectives in order to enhance the relevance of the presented information.

We present Hamiltonian Replica Exchange Transition Interface Sampling (HRETIS), a path sampling framework designed to efficiently sample rare events in systems with complex potential energy landscapes. HRETIS introduces a helper potential within a Hamiltonian replica exchange scheme, which enhances exploration of path space when the underlying potential is not well suited for conventional path sampling approaches. This is particularly advantageous for systems exhibiting multiple pathways separated by orthogonal barriers such as in drug (un)binding, where standard algorithms often show slow convergence since they become trapped within specific pathways. By exchanging Hamiltonians between the path ensembles, HRETIS overcomes these limitations and increases the decorrelation between subsequent paths in the Monte Carlo chain. We demonstrate that HRETIS provides robust and accurate kinetics in several systems, including coarse-grained simulations of amino acid permeation through a dipalmitoylphosphatidylcholine (DPPC) membrane. Moreover, HRETIS is found to improve sampling efficiency and convergence, illustrating its potential as a powerful tool for rare event sampling in complex molecular systems.

Harmful pesticide effects exceeding specific protection goals (SPG) may go undetected in underpowered experimental designs. Regulatory honeybee field studies have consistently failed to reach the statistical power required under European Food Safety Authority (EFSA) guidance, which may have caused approval of high-risk substances. Therefore, EFSA advised a shift from testing the null hypothesis of 'no effect' to equivalence testing. Under this approach, a pesticide is classified as 'low risk' if the null hypothesis that its effect exceeds the SPG can be rejected. For honeybees, the recommended SPG is a colony size reduction below 10%. Critics have argued that this framework requires excessive site replication to demonstrate pesticide safety and proposed an alternative equivalence test defining treatment effects relative to the lower bound of the 90%-control-group confidence interval. Using simulations mimicking a regulatory honeybee field study, we show that although the two equivalence tests share the same trade-off between false 'low-risk' and false 'high-risk' classifications, only EFSA's original recommendation reliably identifies pesticides with effects > SPG at alpha = 0.2. Our results show that increasing site replication beyond the current practice is unavoidable for a reliable regulatory assessment. However, for pesticides with effect sizes of 5% or less, site requirements remain lower than those implied by the power requirement of the former EFSA guidance. Moreover, covariate adjustment through a model term or balanced colony allocation using anticlustering randomisation can reduce site requirements without losing power and thus save costs. Finally, we provide guidance and R functions for anticlustering randomisation and equivalence testing for pesticide risk assessment.

Chiral patterns have been observed in various processes from swirling bacterial colonies to tissue morphogenesis and cytoskeletal organization, yet the physical mechanisms underlying chiral cell motion remain poorly understood. Motivated by experiments demonstrating directional bias in the circular motion of confined cells, we use the tools of dynamical systems analysis with computer simulations to identify minimal intrinsic and extrinsic mechanisms capable of generating persistent biased migration. The dynamical systems framework reveals a common organizing principle: directional bias emerges through changes in the stability and/or basins of attraction of the clockwise and counter-clockwise motility states. We find four distinct routes to such bias. First, intrinsic torque in a polarized cytoskeleton can be spatially integrated to produce biased circular motion. Second, anisotropic cell-substrate friction can generate directional preference when reduced friction along the polarity axis is coupled to a directional offset. Third, a chiral wall-alignment response can also produce a persistent directional preference. Finally, substrate patterns that break mirror symmetry, such as dextral or sinistral ridges and troughs, can likewise bias rotational direction. Together, these mechanisms yield distinct, testable predictions and suggest a unifying lens for experimental interrogation of cellular chirality and the design of synthetic systems with programmable chiral motion.

Bacterial chemotactic sensing converts noisy chemical signals into running and tumbling. We analyze the static sensing limits of mixed Tar/Tsr chemoreceptor clusters in individual \textit{Escherichia coli} cells using a heterogeneous Monod-Wyman-Changeux (MWC) model. Across a seven-dimensional parameter sweep, we compute three sensing-performance metrics -- channel capacity, dynamic range, and effective Hill coefficient -- in the limit that the cells are constantly in such low concentrations of chemoattractant that they need not adapt to new baseline chemoattractant concentration levels. What results are upper bounds on a more complicated trajectory mutual information rate, a quantitative understanding of the tight connection between channel capacity and dynamic range, and the finding that in this regime channel capacity is well described by a closed-form ceiling depending only on the receptor's baseline activity, which every wild-type and mutant strain in our sample achieves to within a few percent. In more realistic scenarios, adaptation plays a larger role and the exact temporal dynamics of chemoattractant concentrations seen by bacteria as they swim. This manuscript thus points to the importance of mapping out naturalistic chemoattractant concentration statistics in the wild as has been done for natural scene statistics.

Microbial keratitis requires rapid pathogen identification to guide treatment, but culture- and PCR-based diagnostics are slow and resource-intensive. We developed a triple-phase multimodal framework for bacterial-versus-fungal keratitis classification using slit-lamp photographs acquired under blue-light, sclerotic-scatter, and white-light illumination, together with clinical metadata. The model combines cross-modality contrastive learning, modality-specific fine-tuning, and feature-level multimodal ensemble learning for patient-level prediction. We evaluated the framework on a multicenter dataset of 1,645 patients and 17,158 images from India and the United States. The model achieved 85.84% accuracy, 84.46% average F1-score, and 0.885 AUC. Site-specific evaluation showed that pooled results were overly optimistic, whereas resampling- and balance-based re-evaluation provided a more realistic assessment of cross-site generalization. Under all settings, our framework remained the top-performing approach. The code is available at this https URL and dataset access will be provided subject to University of Michigan data-sharing clearance.

This paper presents a hybrid modeling approach that couples an Agent-Based Model (ABM) with a partial differential equation (PDE) model in an epidemic setting to simulate the spatial spread of infectious diseases using a compartmental structure with seven health states. The goal is to reduce the computational complexity of a full-ABM by introducing a coupled ABM-PDE model that offers significantly faster simulations while maintaining comparable accuracy. Our results demonstrate that the hybrid model not only reduces the overall simulation runtime (defined as the number of runs required for stable results multiplied by the duration of a single run) but also achieves smaller errors across both 25% and 100% population samples. The coupling mechanism ensures consistency at the model interface: agents crossing from the ABM into the PDE domain are removed and represented as density contributions, while surplus density in the PDE domain is used to generate agents with plausible trajectories derived from mobile phone data. We evaluate the hybrid model using real-world mobility and infection data for the Berlin-Brandenburg region in Germany, showing that it captures the core epidemiological dynamics while enabling efficient large-scale simulations. These results demonstrate that the proposed ABM-PDE framework provides a robust and computationally efficient alternative to full-scale agent-based simulations, making it suitable for realistic epidemic modeling and scenario analysis.

Quantifying the irreversibility and dissipation of non-equilibrium processes is crucial to understanding their behavior, assessing their possible capabilities, and characterizing their efficiency. We introduce a physical quantity that quantifies the irreversibility of stochastic Langevin systems from the observation of individual molecules' displacements. Categorizing these displacements into a few groups based on their initial and final position allows us to measure irreversibility precisely without the need to know the forces and magnitude of the fluctuations acting on the system. For short times, our model-free estimate of irreversibility is related to entropy production by a conditional fluctuation theorem. For short times and in general for stationary protocols, our estimate provides a lower bound to the average entropy production. We validate the method on single-molecule force spectroscopy experiments of proteins subject to force ramps. We show that irreversibility is sensitive to detailed features of the energy landscape underlying the protein folding dynamics and suggest how our methods can be employed to unveil key properties of protein folding processes.

Vesicle-mediated secretion of ions or molecules is a central mechanism of cellular communication, for example in processes such as neurotransmission or hormone release. These events are inherently stochastic: vesicle fusions lead to bursts of variable sizes, releasing discrete packets of transmitters that are subsequently cleared or degraded. The dynamics are intrinsically time-directed due to the interplay of spontaneous bursts and continuous degradation. Using generating functions and a recursion relation, we derive an exact solution for the full time-dependent probability distribution of a general batch arrival degradation model. This framework also enables a full analysis of first-passage times to a concentration threshold representing downstream activation. We show that activation kinetics are not determined by mean dynamics alone, but depend sensitively on the temporal statistics of arrival events, batch-size variability, and degradation. In particular, different arrival processes with identical mean rates can lead to qualitatively distinct first passage behavior, reflecting the role of time-asymmetric fluctuations. We also discuss extensions incorporating vesicle depletion. Our results provide a transparent link between stochastic release dynamics and activation timing in vesicle-mediated signaling.

Tau positron emission tomography (PET) is widely used for the in vivo characterization of disease stage and progression in Alzheimer's disease (AD). With the adoption of multiple tau PET tracers including AV-1451, PI-2620, MK-6240 with different binding behaviors in various large-scale studies, there is a great need of effective harmonization methods to enable the cross-tracer integration of tau PET datasets. While previous methods such as CenTauR were proposed to standardize scalar tau PET measures, they are limited in accounting for the heterogeneity of tau pathology. In this work, we propose Feynman-Kac Reweighted Schrödinger Bridge Matching (FKRSBM), a surface-based framework for cross-tracer tau PET harmonization. FKRSBM learns a direct stochastic transport between tracer domains using Schrödinger Bridge matching, avoiding the Gaussian-prior routing used in diffusion-based translation. To promote biologically consistent transport, FKRSBM introduces an endpoint penalty favoring bridge pairings with matched tau-pathology status and implements it through a Feynman-Kac reweighted endpoint proposal. To preserve cortical organization, FKRSBM uses a spherical convolutional network for vertex-level harmonization on cortical surface meshes. In our experiments, we demonstrate our method by harmonizing Tau PET images acquired with the AV-1451 (n=1480) and PI-2620 (n=2458) tracers from two large-scale datasets. Compared to previous methods including ComBat, CycleGAN, Diffusion Model(DF), and unregularized Schrödinger Bridge Model(DSBM), the proposed FKRSBM method outperforms these baselines in subgroup-level alignment, tau-positivity consistency, and diagnostic classification while preserving subject-specific cortical topography of tau pathology. The code is available at: this https URL.

Predicting biomolecular properties from limited labeled data is a central bottleneck in protein engineering and small-molecule design. As strong pretrained encoders now supply rich fixed-length representations, the difficulty has shifted from representation learning to building a data-efficient predictor for the few-shot regime. Tabular foundation models such as TabPFN and TabICL are unlikely candidates for this role: they are in-context learners pretrained on synthetic tables drawn from random causal graphs, a generative prior with no obvious correspondence to the processes that produce protein sequences or molecular graphs. That this tabular, causal inductive bias should transfer to biomolecular data at all is counter-intuitive, yet we find it does. Treating each method as a predictor-representation pair, we evaluate across two domains. We find that on protein fitness regression tasks these in-context learning models coupled with ESM Cambrian representations achieve or exceed state-of-the-art results on ProteinGym, and outperform task-specific supervised regressors on a diverse esterase catalytic activity dataset. For small-molecule classification with ECFP/RDKit descriptors, no single predictor-representation pairing dominates across TDC ADMET, MoleculeNet, FS-Mol, and DrugOOD, but they are competitive with the existing task-specific state-of-the-art. Crucially, on both protein and small-molecule few-shot tasks, these predictor-representation pairs offer strong performance. We conclude that tabular foundation models can be strong biomolecular predictors, but only when coupled with expressive representations.