Costly cooperation and costly signaling are both difficult to reconcile with simple fitness maximization, yet both are common in biological and social systems. We study a model in which agents emit costly signals and condition their actions on the signals they observe. Across the Prisoner's Dilemma (PD), Snowdrift (SD), and Stag Hunt (SH) games, we ask when this coevolutionary process can sustain cooperation and how it changes across well-mixed populations, spatial lattices, and fluctuating strategic environments. The simulations show that signals are selected less by their raw production costs than by the cooperative responses they currently elicit. In well-mixed populations, the mechanism sustains partial cooperation in PD and SD and drives near-complete cooperation in SH. On lattices, cooperation is strengthened further by local assortment. A reduced mean-field analysis explains why average population feedback is already sufficient in SD and SH, but not in the PD. To account for the PD dynamics, the reduced theory must include transient correlations associated with rare signals, inheritance, or spatial clustering. Our results therefore delineate a class of settings in which costly signals persist because they transiently organize cooperative responses and thereby reshape the effective strategic environment.

Deep neural networks trained with different architectures, objectives, and datasets have been reported to converge on similar visual representations. However, what remains unknown is which visual properties models actually converge on and which factors may underlie this convergence. To address this, we decompose the object similarity structure of 162 diverse vision models into a small set of non-negative dimensions. To determine universal versus model-specific dimensions, we then estimate how often each dimension reappears across models. In contrast to model-specific dimensions, universal dimensions are more interpretable and more strongly driven by conceptual image properties, indicating the relevance of interpretability and semantic content as implicit factors driving universality across models. Differences in architecture, objective function, training data, model size, and model performance do not explain the emergence of universal dimensions. However, models with more universal dimensions also better predict macaque IT activity and human similarity judgments, suggesting that universality reflects representations relevant to biological vision. These findings have important implications for understanding the emergent representations underlying deep neural network models and their alignment with biological vision.

RNA viruses form genetically diverse populations structured as mutant spectra, or quasispecies, whose internal organization influences their evolutionary and adaptive dynamics. While genetic diversity has been extensively characterized, the structural organization of viral populations in sequence space remains less explored. Here, we compare genotype network architectures in two RNA viruses with markedly different evolutionary contexts: bacteriophage $Qβ$ evolving in controlled laboratory conditions and SARS-CoV-2 evolving within infected human hosts. Using deep sequencing data, we reconstruct the genotype network of mutationally coupled variants within viral populations and analyze their topological properties. Despite large differences in genome size, mutation rate, and ecological setting, both viruses exhibit a common organization: a highly abundant central haplotype surrounded by layers of variants of diminishing abundance as Hamming distance to the central haplotype increases. All reconstructed networks share qualitative and quantitative topological features, displaying a hierarchical structure. The robust organization of both populations under multiple conditions suggests that RNA viruses may share a common genotype network architecture governed by fundamental properties of sequence space and the generic mechanisms of replication and mutation. Genotype networks provide a unifying framework to describe viral population structure beyond conventional diversity measures and, by revealing how local constraints shape mutational search, offers insights into the predictability of viral evolution.

The increasing availability of experimental data has intensified interest in calibrating stochastic models, raising fundamental questions about parameter identifiability. Structural identifiability determines whether parameters can be uniquely recovered from idealised, noise-free data, a prerequisite to allow for parameter estimation. However, existing methods to assess structural identifiability are not generally applicable to stochastic processes. We develop a methodology to analyse structural identifiability for a class of spatio-temporal stochastic processes. We investigate how identifiability depends on the type of available data, distinguishing between single-particle trajectories and total particle density measurements. For trajectory data, we use the individual-based model description that explicitly represents single-particle dynamics. For population-level data, we derive a partial differential equation model representation, that describes the evolution of total particle density, and apply a differential algebra approach, common to ordinary differential equations analysis. We further introduce a novel method to study the initial condition, based on characteristic equations to construct a Taylor expansion of the density evolution, enabling identification of additional identifiable parameter combinations. We apply our methodology to a model, and show it is identifiable with trajectory data but only locally identifiable with density data, and demonstrate the critical role of initial conditions in the identifiability analysis.

Endocrine-disrupting chemicals (EDCs) threaten human health, ecosystems, and biodiversity by interfering with hormonal signaling pathways conserved across vertebrates. Traditional in vivo assays are costly and time-consuming, limiting their capacity to screen the growing number of chemicals. To address this, we developed a deep learning-based QSAR model to predict estrogen receptor (ER) binding molecules. Using a curated dataset of 224 compounds and 2,944 molecular descriptors and fingerprints, a deep neural network (DNN) incorporating dropout and batch normalization was trained and validated. The model achieved training and test accuracies of 96.65% and 91.30%, respectively, with an ROC-AUC of 0.81, a precision of 0.82, and a recall of 0.88 for the active class. Molecular docking against estrogen receptor (PDB ID: 5TOA) confirmed that several predicted compounds exhibited binding comparable to Estradiol, sharing key interactions. This model enables rapid screening of potential EDCs, supporting efficient chemical risk assessment and contributing to biodiversity conservation by identifying compounds that may disrupt reproduction and population stability in humans and wildlife.

Multilayer networks are widely used across biology to represent systems in which complex networks vary across space, time, or interaction types. However, interactive visualization tools remain limited. We present MiRA (Multilayer Interactive Rendering Application), a browser-based, installation-free web application for visualizing biological multilayer networks. MiRA offers seven complementary visualization modes and interactive features that enable researchers to visually navigate the high complexity of multilayer networks for research and education.

Qualitative models provide crucial instruments for modelling complex biological systems. While advances in automated reasoning and symbolic encodings have enabled rigorous inference of these models from data, the process remains highly fragile. First, biological measurement errors inevitably propagate into formal model specifications. Second, when a specification becomes unsatisfiable, distinguishing between fundamental design flaws and minor technical errors is notoriously difficult. This uncertainty often leads to under-specification, as it is unclear which observations are still ``safe'' to incorporate. To overcome these challenges, we introduce a robust inference method based on weighted MaxSMT. By encoding uncertain biological observations as weighted soft constraints, our approach enables the solver to identify a model best reflecting the observations, even with some conflicting constraints. Our method allows for Boolean and multi-valued variable domains, alongside observations derived from discretisation (level constraints) and differential expression (ordering constraints). We show our approach can be used to successfully infer neural cell differentiation models from prior-knowledge networks with 200--1300 genes using ordering constraints on all included genes.

The study of shapes is one of the most fundamental problems in life sciences. Although numerous methods have been developed for the morphometry of planar biological shapes over the past several decades, most of them focus solely on either the outer silhouettes or the interior features of the shapes without capturing the coupling between them. Moreover, many existing shape mapping techniques are limited to establishing correspondence between planar structures without further allowing for the quantitative analysis or modelling of shape changes. In this work, we introduce FDA-QC, a novel planar morphometry method that combines functional shape data analysis (FDA) techniques and quasi-conformal (QC) mappings, taking both the boundary and interior of the planar shapes into consideration. Specifically, closed planar curves are represented by their square-root velocity functions and registered by elastic matching in the function space. The induced boundary correspondence is then extended to the entire planar domains by a quasi-conformal map, optionally with landmark constraints. Moreover, the proposed FDA-QC method can naturally lead to a unified framework for shape morphing and shape variation quantification. We apply the FDA-QC method to various leaf and insect wing datasets, and the experimental results show that the proposed combined approach captures morphological variation more effectively than purely boundary-based or interior-based descriptions. Altogether, our work paves a new way for understanding the growth and form of planar biological shapes.

Causal inference in continuous-time sequential decision problems is challenged by hidden confounders. We show that, in latent state-space models with time-varying interventions, observability of the latent dynamics from observed data is necessary for identifying dynamic treatment effects, linking control-theoretic observability to causal identifiability, even when hidden confounders affect both treatments and outcomes. We derive a continuous-time adjustment formula expressing potential outcome distributions under treatment trajectories via the measurement model, latent dynamics, and the filtering distribution over latent states given observed histories. We propose Observable Neural ODEs (ObsNODEs), Neural ODE models in observable normal form for causal forecasting. ObsNODEs learn continuous-time dynamics with states reconstructible from observations, enabling outcome prediction under alternative treatment paths. Experiments on synthetic cancer data, semi-synthetic data based on MIMIC-IV, and real-world sepsis data show strong performance over recent sequence models.

The two-thirds power law of human motor control ($v \propto κ^{-1/3}$) is geometrically equivalent to constant equi-affine speed. In classical differential geometry, however, the equi-affine metric is not a tensor: it depends on acceleration, which does not transform covariantly under arbitrary coordinate changes. To recover tensorial behavior, one must either restrict the symmetry group to the affine group or introduce an affine connection -- sacrificing full diffeomorphism covariance. This article proposes a different geometric setting. We equip the Euclidean plane with the "wire diffeology', the smooth structure generated by all smooth curves. In this diffeological space, the equi-affine metric becomes a true covariant $3$-tensor under the **full** diffeomorphism group -- no restriction of symmetries, no additional structure required. The construction is motivated by a simple fact: the motor cortex traces curves, not two-dimensional patches. Accordingly, curves are taken as primitive, echoing the motor control literature in which movements are built from a repertoire of elementary building blocks -- motor primitives. The wire plane offers a geometric formalization of this idea in which the two-thirds power law emerges as a fully covariant invariant.

Network topology excels at structural predictions but fails to capture functional semantics encoded in biomedical literature. We present RAG-GNN, an end-to-end trainable retrieval-augmented graph neural network framework that integrates GNN representations with dynamically retrieved literature-derived knowledge through a jointly optimized retrieval projection, gated fusion mechanism, and contrastive alignment. In a cancer signaling case study (379 proteins, 3,498 interactions, 14 functional categories), RAG-GNN improves functional clustering from silhouette $= -0.237 \pm 0.065$ (GNN-only) to $-0.144 \pm 0.066$, a consistent improvement of $+0.093 \pm 0.022$ across 10 random seeds, while the learned retrieval achieves mean precision@10 $= 0.242$, a 152\% improvement over the random baseline ($0.096$). Heuristic information decomposition with bootstrap confidence intervals reveals that topology and retrieval encode overwhelmingly shared information (95.6\%), with retrieval improving both intra-cluster cohesion (silhouette) and cluster agreement (ARI $+0.021 \pm 0.015$). Counterfactual experiments confirm that adversarial, absent, and random retrieval all degrade performance, validating that the gated fusion mechanism depends on document content. Benchmarking against eight established embedding methods demonstrates task-specific complementarity: topology-focused methods achieve strong link prediction, while retrieval augmentation consistently improves functional clustering within the controlled GNN-only ablation. DDR1 subnetwork analysis provides confirmatory validation consistent with established synthetic lethality relationships. These results establish that topology-only and retrieval-augmented approaches serve complementary purposes for precision medicine applications.

Humans systematically misrepresent probability in a stereotyped inverse-S pattern. It has been documented for decades, but its origin remains unexplained. We propose a Bayesian encoding-decoding account in which probabilities are represented by noisy internal signals and decoded by Bayes-risk minimization. For bounded probability stimuli, we show that distortion decomposes into boundary regression, likelihood repulsion, and prior attraction, yielding a key prediction: the classic inverse-S-shaped weighting pattern implies a U-shaped allocation of encoding precision with greater sensitivity near 0 and 1. Across judgment of relative frequency, lottery pricing, and risky choice, this U-shape is recovered from data without imposing any functional form on the encoding, and our framework outperforms deterministic weighting functions, bounded log-odds models, uniform-encoding Bayesian accounts, and matched efficient-coding models on held-out data. In a new dot probability estimation experiment with bimodal stimulus statistics, the recovered prior tracks the new distribution while the recovered encoding remains U-shaped. Together, these results identify the inverse-S-shaped probability weighting function as the joint product of a stable U-shaped encoding and a flexible prior, integrated by optimal Bayesian decoding.

We study the mixing time of a Susceptible--Infected--Susceptible (SIS) model on graphs with external sources of infection, which we refer to as the noisy SIS model. Under suitable assumptions on the parameters of the dynamics, we show that the mixing time is of the order $Θ(n\log n)$ with respect to the number of vertices $n$. We further investigate the model on random graph families, including Erd{ö}s--R{é}nyi graphs, random regular multigraphs, and Galton--Watson trees. By identifying high-probability structural properties of these graphs and conditioning on typical realizations, we prove that the mixing time remains of order $Θ(n\log n)$ with high probability.

Characterizing the local voltage distribution within nanophysiological domains, driven by ionic currents through membrane channels, is crucial for studying cellular activity in modern biophysics, yet it presents significant experimental and theoretical challenges. Theoretically, the complexity arises from the difficulty of solving electro-diffusion equations in three-dimensional domains. Currently, there are no methods available for obtaining asymptotic computations or approximated solutions of nonlinear equations, and numerically, it is challenging to explore solutions across both small and large spatial scales. In this work, we develop a method to solve the Poisson-Nernst-Planck equations with ionic currents entering and exiting through two narrow, circular window channels located on the boundary. The inflow through the first window is composed of a single cation, while the outflow maintains a constant ionic density satisfying local electro-neutrality conditions. Employing regular expansions and Green's function representations, we derive the ionic profiles and voltage drops in both small and large charge regimes. We explore how local surface curvature and window channels size influence voltage dynamics and validate our theoretical predictions through numerical simulations, assessing the accuracy of our asymptotic computations. These novel relationships between current, voltage, concentrations and geometry can enhance the characterization of physiological behaviors of nanodomains.

Biological neural networks (BNNs) have been established as a powerful and adaptive substrate that offer the potential for incredibly energy and data efficient information processing with distinct learning mechanisms. Yet a core challenge to utilizing BNN for neurocomputation is determining the optimal encoding and decoding mechanisms between the traditional silicon computing interface and the living biology. Here, we propose an Embodied Neurocomputation framework as a systems-level approach to this multi-variable optimization encoding/decoding problem. We operationalize this approach through the first large-scale parameter optimization of encoding configurations for a BNN agent performing closed-loop navigation along an odor-style gradient in a simulated grid-world. Despite the relative simplicity of the task, the biological interactions gave rise to a massive multi-combinatorial search space for optimal parameters. By considering how the components of the system are interconnected and parameterized, we evaluated approximately 1,300 parameter combinations, over 4,000 hours of real-time agent-environment interactions, to identify 12 configurations that consistently demonstrated learning across multiple episodes. These configurations achieved significantly higher task performances than optimized silicon-based DQN agents under the same interaction budget. These findings represent an initial step toward robust and scalable goal-oriented learning using BNNs. Our framework establishes a foundation for applying task-driven neurocomputing and supports the development of field-wide benchmarks. In the long term, this work supports the development of hybrid bio-silicon architectures capable of efficient, adaptive and real-time computation, including the potential for robotic control applications.

Modern SMILES-based chemical language models obtain strong MoleculeNet performance by treating SMILES as generic text and compensating with multi-million-molecule self-supervised pretraining. We ask: when a domain carries structural priors as rich as chemistry's, does it warrant a domain-native transformer rather than a generic one rescued by scale? We answer affirmatively with \textbf{GM-Net} (Geometric Measure Network), a transformer family in which every module is replaced by a sphere-native counterpart, and instantiate it as \textbf{Chem-GMNet}. Three blocks follow: SH-Embedding (tokens as learnable directions on $S^{k-1}$ lifted through a Gegenbauer feature map); DualSKA (a per-head fusion of a linear-time gated Sphere-Flow recurrence whose persistent state we prove is the truncated multipole expansion of the input distribution, and a softmax Sphere-Kernel branch over the same Schoenberg-valid kernel); and SH-FFN (sphere projection $\to$ Gegenbauer lift $\to$ moment readout). On canonical DeepChem scaffold splits, against same-shape ChemBERTa-2 baselines under the chemberta3-faithful protocol: (i) random-initialised, Chem-GMNet wins on 7 of 10 MoleculeNet endpoints at $\sim\!35\%$ fewer parameters; (ii) pretrained on the same 10M-SMILES ZINC corpus as ChemBERTa-2 MLM-10M, it matches or beats the public release on 6 of 8 shared endpoints (5/7 excluding a known ClinTox release anomaly). A $(k,L)$ ablation shows that increasing the sphere dimension from $k\!=\!8$ to $k\!=\!10$ at fixed $L\!=\!3$ lowers ESOL RMSE to $0.938$ at scratch, beating pretrained ChemBERTa-2 MLM-10M on this endpoint without any pretraining at all.

Across metazoans, early embryos exhibit a strikingly conserved slowing down of their cell duplication speed, despite widely varying developmental paces and underlying molecular mechanisms. Here we show that this common behavior arises because early development unfolds along a biochemical rather than a chronological timescale, resulting from the coupling of finite maternal resource consumption to the Michaelis-Menten-like kinetics governing the rates of the biochemical reactions involved in cell duplication. This leads to a hyperbolic growth of the Cell Cycle Length (CCL), approaching a mathematical singularity, which would correspond to developmental arrest. Data from a wide range of organisms -- cnidarians, nematodes, arthropods, molluscs, echinoderms, tunicates, amphibians, and fish -- collapse on a single curve, quantitatively capturing not only a universal CCL dynamical behaviour, but also key hallmarks of early metazoan development, including cell-number temporal evolution, the dependency of CCL on cell size, and, remarkably, gastrulation timing at the predicted singularity. Crucially, experimental modulation of resource availability and consumption rates validate the model and further demonstrate that a source of heterochrony in early development is an altered biochemical timescale of resource depletion. Overall, this work reveals resource consumption rates as a fundamental mechanism driving developmental timing in early embryogenesis across species.

The orientation of cell division is a major determinant of three-dimensional plant morphogenesis. Whether and how a simple division orientation rule explains the establishment of symmetric body plans is a fundamental question. Testing such hypotheses is facilitated by a modeling framework that combines realistic three-dimensional cell mechanics, irreversible cell-wall growth, and a deformable tissue geometry. We recently introduced such a framework, a 3D mechano-geometric multicellular model of apical stem cell-driven morphogenesis. Here we document how the model is built from physiological and computational perspectives. We describe the triangulated thin-shell representation of cells, the treatment of turgor pressure, cell-wall elasticity and strain-driven wall growth, the cell-division algorithm together with its two pluggable division-rule implementations, and the remeshing operations that keep the triangulation well-conditioned as cells grow, divide, and deform. The aim of this paper is to make the present model accessible and customizable to experimental plant biologists.

Biological systems perform complex multi-step processes in a reproducible way despite underlying stochasticity. The standard explanation is micromanagement by molecular machinery that recognizes and corrects specific errors. Here we study conditioning, a qualitatively different strategy in which attempts failing a coarse criterion are destroyed and do not leave a physical record. The surviving, i.e., conditioned, ensemble is narrower and therefore more ordered. We model conditioning through stochastic resets in a ''socks-before-shoes'' model of a growing population, where $n$ actions must be completed in any order to replicate and any replication attempt not finished by a threshold time is discarded. We find that resets impose hierarchical temporal ordering of the $n$ actions without microscopic control over which action happens when. When disorder carries a sufficient time penalty, this ordering is free: the fastest-growing population is automatically the most ordered, with no direct selection for order required. Save points, at which verified progress is preserved across resets, allow conditioning to scale to complex multi-step processes. Conditioning provides a minimal route to reliable behavior, requiring only a clock rather than molecular machinery that recognizes specific errors. For the right class of processes, it pays for itself.

Closed-loop brain-computer interfaces often require both a forecast of upcoming neural population activity and a readout of the animal's behavioral state. A single Mamba forecaster, trained only on next-step spike counts at Neuropixels scale, can deliver both in one forward pass. A lightweight per-session linear head reading the model's predicted rates decodes behavior better than the same linear classifier reading the raw spike counts, under matched temporal context. We test on the Steinmetz visual-discrimination benchmark, which spans 39 sessions, roughly 27,000 neurons, and 1,994 held-out trials. Across three training seeds, Mamba's predicted rates decode mouse choice at 75.7$\pm$0.2% trial vote, roughly 2.3 times chance level, and stimulus side at 66.1$\pm$0.6%, about twice chance. Compared to a matched 500 ms-context linear decoder on the raw spike counts, Mamba wins at trial vote by 4-6 pp on response and 4-6 pp on stimulus side. A session-start calibration block of about 100-150 trials brings the readout within 1-2 pp of asymptote, and the full pipeline fits inside the 50 ms bin budget on workstation-class GPUs typical of tethered chronic Neuropixels recordings.

Neural population models, which predict the joint firing of many simultaneously recorded neurons forward in time, are typically evaluated by a single aggregate Pearson correlation $r$ between predicted and actual spike counts, a number that masks critical structure. We argue that how we evaluate spike forecasting matters as much as what we build, and introduce SpikeProphecy, the first large-scale benchmark for causal, autoregressive spike-count forecasting on real electrophysiology recordings. Our core contribution is a population metric decomposition that separates aggregate performance into temporal fidelity, spatial pattern accuracy, and magnitude-invariant alignment. The decomposition surfaces aspects of the underlying data that an aggregate scalar collapses together. We apply the protocol to 105 Neuropixels sessions (Steinmetz 2019 + IBL Repeated Site; ~89,800 neurons) with seven architecture baselines spanning four structural families: four SSMs (three diagonal and one non-diagonal), a Transformer, an LSTM, and a spiking network. The decomposition surfaces a brain-region predictability ranking that reproduces across all seven baselines and survives ANCOVA correction for firing-statistics constraints (region $ΔR^2 = 0.018$ above the firing-statistics covariates). It also exposes a sub-Poisson evaluation floor where rigorous metrics combine with genuine biophysical constraints on regular spike trains, and yields a negative result on KL-on-output-rates distillation for ANN-to-SNN transfer in this Poisson count domain.

Pertussis booster vaccination produces immune responses that vary widely across individuals in both peak magnitude and long-term durability. These two phases are governed by partly distinct biological compartments:peak reflects acute B-cell activation and antibody secretion, while durability reflects the establishment of long-term humoral memory. Yet most computational models target only one, missing the full boost-and-wane trajectory. Jointly predicting both is non-trivial because the two endpoints are biologically dissociated rather than redundant; samples are small, modalities are heterogeneous with structured missingness, and the two tasks rely on different measurement windows. We propose a multi-task contrastive multimodal fusion architecture combining frozen TabPFN-v2 per-modality encoders, a dual-label supervised contrastive loss that treats two subjects as a positive pair if they agree on the Task 1 label or the Task 2 label, modality dropout calibrated to empirical missingness, and missingness-masked attention fusion. Applied to a curated subset of the CMI-PB pertussis booster dataset (n = 158 subjects, four modalities, 44.9% with at least one modality missing; Spearman r = -0.58 between peak and durability, n = 96), the model achieves test AUROC 0.797 (95% CI [0.621, 0.948]) for peak response and 0.755 (95% CI [0.519, 0.945]) for durability, with both significant under joint label permutation (N = 1000; p = 0.002 and p = 0.045). Across logistic regression, XGBoost, and MLP baselines on raw features and on TabPFN embeddings, the proposed model is the only one whose 95% CIs lie above chance on both tasks simultaneously. Per-modality contribution analyses recover task-specific modality contributions consistent with the underlying immunology: peak prediction is carried by cytokine signatures, while durability is carried by baseline antibody features.

Coarse-grained (CG) molecular dynamics enables simulations of atomic systems such as biomolecules at timescales inaccessible to all-atom (AA) methods, but existing CG neural potentials trained via force matching capture only the gradient of the free-energy surface, leaving its curvature unconstrained. We introduce a framework that augments force matching with stochastic Hessian-vector product (HVP) matching, instilling second-order curvature information into CG potentials without constructing the full Hessian. We derive a decomposition of the target CG Hessian into a model-independent projected AA Hessian, precomputed once before training, and a model-dependent covariance correction computed online at negligible cost. We construct an unbiased stochastic estimator of the Hessian-matching objective by using random probe vectors. We evaluate our method by comparing against force matching on a benchmark of nine fast-folding proteins unseen during training. HVP matching outperforms plain force matching on 8 of 9 proteins on slow-mode metrics, with reductions of up to 85% in the Kullback--Leibler divergence between the CG and reference distributions along the slowest collective mode of the largest protein. Our results demonstrate that higher-order physical supervision is a practical path to more accurate and transferable CG potentials for biomolecular simulation.

Individual contributions to the spread of an epidemic vary widely due to an individual's location in a social network and their intrinsic ability to spread or contract diseases. While the effect of heterogeneous population structure and infection rates is well-understood, less studied is the impact of population-level covariance between susceptibility and transmissibility, despite empirical evidence showing that both susceptibility and transmission vary across individuals. We introduce a mathematical modeling framework incorporating population subgroups, each with its own joint distribution of susceptibility and transmissibility. We apply this framework to the susceptible-infected-recovered (SIR) model to examine the effect of community structure and degree heterogeneity. We derive analytical expressions for the basic reproduction number, which, when reduced, corroborates prior results and validate these results with numerical simulations. We pair these estimates with simulations exploring first, the temporal dynamics of this model with the homogeneous SIR model, and second, implications for effective social intervention. This analysis provides a foundation for future studies exploring the interplay between structural and dynamical heterogeneity in infectious disease transmission.

Rich feature learning in tasks that unfold over time often requires the model to pass through bifurcations, constituting qualitative changes in the underlying model dynamics. We develop a local theory of gradient descent near these transitions through the empirical state-space neural tangent kernel (sNTK). Our central finding is that bifurcations both dominate and simplify learning dynamics: near bifurcations, we can reduce sNTK to a rank-one operator corresponding to learning in a classical normal form system, providing an analytically tractable description of the local learning geometry, even for high-dimensional recurrent systems. Concretely, we give a procedure for decomposing sNTK into bifurcation-relevant and residual channels, showing that near commonly codimension-1 bifurcations the relevant channel is a rank-one operator that is highly amplified. This amplification causes the bifurcation channel to dominate the full sNTK. Thus, bifurcations locally warp the learning landscape, funneling gradient descent into a few critical dynamical directions and making the nearby kernel and loss geometry predictable from classical normal forms. We illustrate this in a student-teacher recurrent neural network: the first learned bifurcation coincides with a sharp collapse in sNTK effective rank and the emergence of a dominant parameter direction whose restricted sNTK closely matches the landscape predicted by the scalar pitchfork normal form. Finally, we show that low-rank natural gradient methods resolve the resulting learning instability near bifurcations with very little overhead over SGD.

The ability to predict the future is of great value for biological and artificial cognitive systems alike. However, successfully predicting the future typically requires maintaining a memory of the recent past. It is currently unclear how biological or artificial spiking neural networks can learn to maintain past sensory information to help predict the future. Here we propose Predictive Coding Light+ (PCL+), a spiking neural network architecture for unsupervised sequence processing that learns recurrent excitatory connections with delays to enable short-term retention of information. We show that the PCL+ network reproduces classic findings on sequence learning in visual cortex. Furthermore, it learns to ``fill in'' missing input in a challenging gesture recognition task. Overall, our work shows how spiking neural networks can learn recurrent excitatory connections with delays to maintain a record of the recent past and successfully predict the future.

RSNet is an open-source R package that provides a resampling-based framework for robust and interpretable network inference, designed to address the limited-sample-size challenges common in high-dimensional data. It supports both the estimation of partial correlation networks modeled as Gaussian networks and conditional Gaussian Bayesian networks for mixed data types that combine continuous and discrete variables. The framework incorporates multiple resampling strategies, including bootstrap, subsampling, and cluster-based approaches, to accommodate both independent and correlated observations. To enhance interpretability, RSNet integrates graphlet-based topology analysis that captures higher-order connectivity and edge sign information, enabling single-node and subnetwork-level insights. Notably, RSNet is the first R package to efficiently construct signed graphlet degree vector matrices (GDVMs) in near-constant time for sparse networks, providing scalable analysis of higher-order network structure. Collectively, RSNet offers a versatile tool for statistically reliable and interpretable network inference in high-dimensional data.

High-dimensional point cloud data arise across many scientific domains, especially single-cell biology. The shapes or topologies of these datasets determine the types of information that can be extracted. For example, clustered data supports cell-type identification, trajectory structures support transition analysis, and archetypal structures capture continua of cellular behaviors. Existing analysis pipelines often assume a specific shape. The standard Seurat pipeline combines UMAP visualization with Louvain clustering and therefore assumes clustered data, while tools such as Monocle and SPADE assume tree-like structures, and flow-based models such as MIOFlow and Conditional Flow Matching target trajectories. Choosing which pipeline to apply is therefore often left to bioinformaticians who visually inspect datasets before selecting an analysis strategy. With the rise of agentic AI scientists, automating shape detection is increasingly important for selecting downstream analysis pipelines. To address this problem, we introduce scShapeBench, a benchmark dataset for shape detection containing both synthetic and expert-annotated single-cell datasets. Synthetic datasets are sampled from ground-truth skeleton graphs with controlled variance. Real single-cell datasets are curated from diverse sources and annotated by experts into four categories: clusters, single trajectory, multi-branching, and archetypal. We additionally introduce scReebTower, a baseline method that uses diffusion geometry to extract Reeb graphs and connect visualization with pipeline selection. We provide topology-aware evaluation metrics and compare scReebTower against PAGA and Mapper on synthetic and real data. Our results indicate that scReebTower outperforms existing baselines. Overall, our contributions span benchmarks, evaluation metrics, and a baseline for automated shape detection in single-cell data.

Protein language models (pLMs) have emerged as powerful predictors of protein structure and function. However, the computational circuits underlying their predictions remain poorly understood. Recent mechanistic interpretability methods decompose pLM representations into interpretable features, but they treat each layer independently and thus fail to capture cross-layer computation, limiting their ability to approximate the full model. We introduce ProtoMech, a framework for discovering computational circuits in pLMs using cross-layer transcoders that learn sparse latent representations jointly across layers to capture the model's full computational circuitry. Applied to the pLM ESM2, ProtoMech recovers 82-89% of the original performance on protein family classification and function prediction tasks. ProtoMech then identifies compressed circuits that use <1% of the latent space while retaining up to 79% of model accuracy, revealing correspondence with structural and functional motifs, including binding, signaling, and stability. Steering along these circuits enables high-fitness protein design, surpassing baseline methods in more than 70% of cases. These results establish ProtoMech as a principled framework for protein circuit tracing.

Chemical Language Models (CLMs) pre-trained on large scale molecular data are widely used for molecular property prediction. However, the common belief that increasing training resources such as model size, dataset size, and training compute improves both pretraining loss and downstream task performance has not been systematically validated in the chemical domain. In this work, we evaluate this assumption by pretraining CLMs while scaling training resources and measuring transfer performance across diverse molecular property prediction (MPP) tasks. We find that while pretraining loss consistently decreases with increased training resources, downstream task performance shows limited improvement. Moreover, alternative metrics based on the Hessian or loss landscape also fail to estimate downstream performance in CLMs. We further identify conditions under which downstream performance saturates or degrades despite continued improvements in pretraining metrics, and analyze the underlying task dependent failure modes through parameter space visualizations. These results expose a gap between pretraining based evaluation and downstream performance, and emphasize the need for model selection and evaluation strategies that explicitly account for downstream task characteristics.