Modeling peptide cyclization is critical for the virtual screening of candidate peptides with desirable physical and pharmaceutical properties. This task is challenging because a cyclic peptide often exhibits diverse, ring-shaped conformations, which cannot be well captured by deterministic prediction models derived from linear peptide folding. In this study, we propose MuCO (Multi-stage Conformation Optimization), a generative peptide cyclization method that models the distribution of cyclic peptide conformations conditioned on the corresponding linear peptide. In principle, MuCO decouples the peptide cyclization task into three stages: topology-aware backbone design, generative side-chain packing, and physics-aware all-atom optimization, thereby generating and optimizing conformations of cyclic peptides in a coarse-to-fine manner. This multi-stage framework enables an efficient parallel sampling strategy for conformation generation and allows for rapid exploration of diverse, low-energy conformations. Experiments on the large-scale CPSea dataset demonstrate that MuCO significantly outperforms state-of-the-art methods in consistently in physical stability, structural diversity, secondary structure recovery, and computational efficiency, making it a promising computational tool for exploring and designing cyclic peptides.

On exposure to 1,2-propanediol (1,2-PD), Salmonella enterica serovar Typhimurium LT2 produces 1,2-PD utilization (Pdu) microcompartments (MCPs), nanoscale protein-bound shells that encapsulate metabolic enzymes. MCPs serve as a bioengineering platform to study reaction organization and enhance flux through specific pathways. However, a recently published assay of purified wild-type (WT) MCPs reported metabolic activity that differed markedly from that observed in vivo. Using kinetic modeling, we attribute these discrepancies to in vivo cell growth and to the cytosolic presence of MCP-associated enzymes and promiscuous alcohol dehydrogenases, which are not present in the purified MCPs. Assays of purified MCPs in E. coli lysate, together with an LT2 growth assay in which the native Pdu MCP-associated alcohol dehydrogenase, PduQ, was knocked out, support the conclusion that exogenous Pdu cytosolic enzyme activity can narrow the gap between in vitro and in vivo experiments. Our modeling further suggests that MCP-localized enzymes contribute little to in vivo metabolic flux downstream of PduCDE. We therefore propose a revised in vivo model of WT growth on 1,2-PD in which PduCDE is fully encapsulated, while much of the downstream Pdu activity occurs in the cytosol.

Epidemic and pandemic preparedness with rapid outbreak response rely on timely, trustworthy evidence. Mathematical models are crucial for supporting timely and reliable evidence generation for public health decision-making with models spanning approaches from compartmental and metapopulation models to detailed agent-based simulations. Yet, the accompanying software ecosystem remains fragmented across model types, spatial resolutions, and computational targets, making models harder to compare, extend, and deploy at scale. Here we present MEmilio, a modular, high-performance framework for epidemic simulation that harmonizes the specification and execution of diverse dynamic epidemiological models within a unified and harmonized architecture. MEmilio couples an efficient C++ simulation core with coherent model descriptions and a user-friendly Python interface, enabling workflows that run on laptops as well as high-performance computing systems. Standardized representations of space, demography, and mobility support straightforward adaptations in resolution and population size, facilitating systematic inter-model comparisons and ensemble studies. The framework integrates readily with established tools for uncertainty quantification and parameter inference, supporting a broad range of applications from scenario exploration to calibration. Finally, strict software-engineering practices, including extensive unit and continuous integration testing, promote robustness and minimize the risk of errors as the framework evolves. By unifying implementations across modeling paradigms, MEmilio aims to lower barriers to reuse and generalize models, enable principled comparisons of implicit assumptions, and accelerate the development of novel approaches that strengthen modeling-based outbreak preparedness.

Homologous proteins have similar three-dimensional structures and biological functions that shape their sequences. The resulting coevolution-driven correlations underlie methods from Potts models to AlphaFold, which infer protein structure and function from sequences. Using a minimal model, we show that fluctuating selection strength and the onset of new selection pressures improve coevolution-based inference of structural contacts. Our conclusions extend to realistic synthetic data and to the inference of interaction partners. Out-of-equilibrium noise arising from ubiquitous variations in natural selection thus enhances, rather than hinders, the success of inference from protein sequences.

Mental events are considered to supervene on physical events. A supervenient event does not change without a corresponding change in the underlying subvenient physical events. Since wholes and their parts exhibit the same supervenience-subvenience relations, inter-level causation has been expected to serve as a model for mental causation. We proposed an inter-level causation mechanism to construct a model of consciousness and an agent's self-determination. However, a significant gap exists between this mechanism and cognitive functions. Here, we demonstrate how to integrate the inter-level causation mechanism with the widely known dual-process theories. We assume that the supervenience level is composed of multiple supervenient functions (i.e., neural networks), and we argue that inter-level causation can be achieved by controlling the feedback error defined through changing algebraic expressions combining these functions. Using inter-level causation allows for a dual laws model in which each level possesses its own distinct dynamics. In this framework, the feedback error is determined independently by two processes: (1) the selection of equations combining supervenient functions, and (2) the negative feedback error reduction to satisfy the equations through adjustments of neurons and synapses. We interpret these two independent feedback controls as Type 1 and Type 2 processes in the dual process theories. As a result, theories of consciousness, agency, and dual process theory are unified into a single framework, and the characteristic features of Type 1 and Type 2 processes are naturally derived.

Biological neural networks (BNNs) are increasingly explored for their rich dynamics, parallelism, and adaptive behavior. Beyond understanding their function as a scientific endeavour, a key focus has been using these biological systems as a novel computing substrate. However, BNNs can only function as reliable information-processing systems if inputs are delivered in a temporally and structurally consistent manner. In practice, this requires stimulation with precisely controlled structure, microsecond-scale timing, multi-channel synchronization, and the ability to observe and respond to neural activity in real-time. Existing approaches to interacting with BNNs face a fundamental trade-off: they either depend on low-level hardware mechanisms, imposing prohibitive complexity for rapid iteration, or they sacrifice temporal and structural control, undermining consistency and reproducibility - particularly in closed-loop experiments. The Cortical Labs Application Programming Interface (CL API) enables real-time, sub-millisecond closed-loop interactions with BNNs. Taking a contract-based API design approach, the CL API provides users with precise stimulation semantics, transactional admission, deterministic ordering, and explicit synchronization guarantees. This contract is presented through a declarative Python interface, enabling non-expert programmers to express complex stimulation and closed-loop behavior without managing low-level scheduling or hardware details. Ultimately, the CL API provides an accessible and reproducible foundation for real-time experimentation with BNNs, supporting both fundamental biological research and emerging neurocomputing applications.

The brain interprets visual information through learned regularities, a computation formalized as probabilistic inference under a prior. The visual cortex establishes priors for this inference, some delivered through established top-down connections that inform low-level cortices about statistics represented at higher levels in the cortical hierarchy. While evidence shows that adaptation leads to priors reflecting the structure of natural images, it remains unclear whether similar priors can be flexibly acquired when learning a specific task. To investigate this, we built a generative model of V1 optimized for a simple discrimination task and analyzed it together with large-scale recordings from mice performing an analogous task. In line with recent approaches, we assumed that neuronal activity in V1 corresponds to latent posteriors in the generative model, enabling investigation of task-related priors in neuronal responses. To obtain a flexible test bed, we extended the VAE formalism so that a task can be acquired efficiently by reusing previously learned representations. Task-specific priors learned by this Task-Amortized VAE were used to investigate biases in mice and model when presenting stimuli that violated trained task statistics. Mismatch between learned task statistics and incoming sensory evidence produced signatures of uncertainty in stimulus category in the TAVAE posterior, reflecting properties of bimodal response profiles in V1 recordings. The task-optimized generative model accounted for key characteristics of V1 population activity, including within-day updates to population responses. Our results confirm that flexible task-specific contextual priors can be learned on demand by the visual system and deployed as early as the entry level of visual cortex.

Continuously changing environments have a paramount role in the evolution of cooperative behavior. Previous works have shown that the transitions among different games, as the feedback between behaviors and environments, can promote cooperative behavior significantly. Quantitative analysis, however, is limited to homogeneous populations, while realistic populations in nature are often more complex and highly heterogeneous. We hereby provide an analytical treatment of when the evolution of cooperation can be supported in stochastic games, applying to arbitrary spatial heterogeneity and payoff structure. We highlight that the rule and frequency of game changes can have surprisingly diverse effects on evolutionary outcomes, depending on the governing social dilemmas. While stochastic games favor the evolution of cooperation in donation games, this is not the case for public goods games and snowdrift games. Hence, our framework and model results offer a more subtle insight into the long-standing enigma.

Spiking Neural Networks (SNNs) offer energy-efficient, biologically plausible computation but suffer from non-differentiable spike generation, necessitating reliance on heuristic surrogate gradients. This paper introduces UltraLIF, a principled framework that replaces surrogate gradients with ultradiscretization, a mathematical formalism from tropical geometry providing continuous relaxations of discrete dynamics. The central insight is that the max-plus semiring underlying ultradiscretization naturally models neural threshold dynamics: the log-sum-exp function serves as a differentiable soft-maximum that converges to hard thresholding as a learnable temperature parameter $\eps \to 0$. Two neuron models are derived from distinct dynamical systems: UltraLIF from the LIF ordinary differential equation (temporal dynamics) and UltraDLIF from the diffusion equation modeling gap junction coupling across neuronal populations (spatial dynamics). Both yield fully differentiable SNNs trainable via standard backpropagation with no forward-backward mismatch. Theoretical analysis establishes pointwise convergence to classical LIF dynamics with quantitative error bounds and bounded non-vanishing gradients. Experiments on six benchmarks spanning static images, neuromorphic vision, and audio demonstrate improvements over surrogate gradient baselines, with gains most pronounced in single-timestep ($T{=}1$) settings on neuromorphic and temporal datasets. An optional sparsity penalty enables significant energy reduction while maintaining competitive accuracy.

Accurate prognosis for Glioblastoma (GBM) using deep learning (DL) is hindered by extreme spatial and structural heterogeneity. Moreover, inconsistent MRI acquisition protocols across institutions hinder generalizability of models. Conventional transformer and DL pipelines often fail to capture the multi-scale morphological diversity such as fragmented necrotic cores, infiltrating margins, and disjoint enhancing components leading to scanner-specific artifacts and poor cross-site prognosis. We propose TopoGBM, a learning framework designed to capture heterogeneity-preserved, scanner-robust representations from multi-parametric 3D MRI. Central to our approach is a 3D convolutional autoencoder regularized by a topological regularization that preserves the complex, non-Euclidean invariants of the tumor's manifold within a compressed latent space. By enforcing these topological priors, TopoGBM explicitly models the high-variance structural signatures characteristic of aggressive GBM. Evaluated across heterogeneous cohorts (UPENN, UCSF, RHUH) and external validation on TCGA, TopoGBM achieves better performance (C-index 0.67 test, 0.58 validation), outperforming baselines that degrade under domain shift. Mechanistic interpretability analysis reveals that reconstruction residuals are highly localized to pathologically heterogeneous zones, with tumor-restricted and healthy tissue error significantly low (Test: 0.03, Validation: 0.09). Furthermore, occlusion-based attribution localizes approximately 50% of the prognostic signal to the tumor and the diverse peritumoral microenvironment advocating clinical reliability of the unsupervised learning method. Our findings demonstrate that incorporating topological priors enables the learning of morphology-faithful embeddings that capture tumor heterogeneity while maintaining cross-institutional robustness.

Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as the square root of time. These sublinear fronts preserve an invariant shape, with an effective diffusion constant that diverges at the transition to linear spreading. The model applies to dense cellular aggregates of nonmotile cells consuming a diffusible nutrient. The sublinear spread results from biomass redistribution slowing due to nutrient depletion, a phenomenon supported experimentally but often neglected. Our results provide a potential explanation for the linear rather than quadratic increase of colony area with time, which has been observed for many microbes.

We present a collaboration ring model -- a network of players playing the prisoner's dilemma game and collaborating among the nearest neighbours by forming coalitions. The microscopic stochastic updating of the players' strategies are driven by their innate nature of seeking selfish gains and shared intentionality. Cooperation emerges in such a structured population through non-equilibrium phase transitions driven by propensity of the players to collaborate and by the benefit that a cooperator generates. The robust results are qualitatively independent of number of neighbours and collaborators.

We present scPilot, the first systematic framework to practice omics-native reasoning: a large language model (LLM) converses in natural language while directly inspecting single-cell RNA-seq data and on-demand bioinformatics tools. scPilot converts core single-cell analyses, i.e., cell-type annotation, developmental-trajectory reconstruction, and transcription-factor targeting, into step-by-step reasoning problems that the model must solve, justify, and, when needed, revise with new evidence. To measure progress, we release scBench, a suite of 9 expertly curated datasets and graders that faithfully evaluate the omics-native reasoning capability of scPilot w.r.t various LLMs. Experiments with o1 show that iterative omics-native reasoning lifts average accuracy by 11% for cell-type annotation and Gemini-2.5-Pro cuts trajectory graph-edit distance by 30% versus one-shot prompting, while generating transparent reasoning traces explain marker gene ambiguity and regulatory logic. By grounding LLMs in raw omics data, scPilot enables auditable, interpretable, and diagnostically informative single-cell analyses. Code, data, and package are available at this https URL

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.

The early stages of the collective invasion may occur by single mesenchymal cells or hybrid epithelial-mesenchymal cell groups that detach from cancerous tissue. Tumors may also emit invading protrusions of epithelial cells, which could be led (or not) by a basal cell. Here we devise a fractional step cellular Potts model comprising passive and active cells able to describe these different types of collective invasion before cells start proliferating. Durotaxis and active forces have different symmetry properties and are included in different half steps of the fractional step method. Compared with a single step method, fractional step produces more realistic cellular invasion scenarios with little extra computational effort. Biochemical mechanisms that determine how cells acquire their different phenotypes and cellular proliferation will be incorporated to the model in future publications.

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.

Spoken language is often, if not always, understood in a context formed by the identity of the speaker. For example, we can easily make sense of an utterance such as "I'm going to have a manicure this weekend" or "The first time I got pregnant I had a hard time" when spoken by a woman, but it would be harder to understand when it is spoken by a man. Previous ERP studies have shown mixed results regarding the neurophysiological responses to such speaker-content mismatches, with some reporting an N400 effect and others a P600 effect. In an EEG experiment involving 64 participants, we used social and biological mismatches as test cases to demonstrate how these distinct ERP patterns reflect different aspects of rational inference. We showed that when the mismatch involves social stereotypes (e.g., men getting a manicure), listeners can arrive at a "literal" interpretation by integrating the content with their social knowledge, though this integration requires additional effort due to stereotype violations-resulting in an N400 effect. In contrast, when the mismatch involves biological knowledge (e.g., men getting pregnant), a "literal" interpretation becomes highly implausible or impossible, leading listeners to treat the input as potentially containing errors and engage in correction processes-resulting in a P600 effect. Supporting this rational inference framework, we found that the social N400 effect decreased as a function of the listener's personality trait of openness (as more open-minded individuals maintain more flexible social expectations), while the biological P600 effect remained robust (as biological constraints are recognized regardless of individual personalities). Our findings help to reconcile empirical inconsistencies and reveal how rational inference shapes speaker-contextualized language comprehension.

We develop a neurogeometric model for the arm area of motor cortex, which encodes complex motor primitives, ranging from simple movement features like movement direction, to short hand trajectories, termed fragments, and ultimately to more complex patterns known as neural states (Georgopoulos, Hatsopoulos, Kadmon-Harpaz et al). Based on the sub-riemannian framework introduced in 2023, we model the space of fragments as a set of short curves defined by kinematic parameters. We then introduce a geometric kernel that serves as a model for cortical connectivity and use it in a differential equation to describe cortical activity. By applying a grouping algorithm to this cortical activity model, we successfully recover the neural states observed in Kadmon-Harpaz et al, which were based on measured cortical activity. This confirms that the choice of kinematic variables and the distance metric used here are sufficient to explain the phenomena of neural state formation. The modularity of our model reflects the brain's hierarchical structure, where initial groupings in the kinematic space $\mathcal{M}$ lead to more abstract representations. This approach mimics how the brain processes stimuli at different scales, extracting both local and global properties.

Chemical language models (CLMs) are increasingly used for molecular design and property prediction. Because these models learn from textual encodings of molecules, differences in how such encodings are generated may affect their behavior. In cheminformatics, the term canonical SMILES implies a single standardized notation, yet different toolkits define distinct canonicalization rules, yielding multiple canonical strings for the same molecule. To examine how this variability arises and why it matters, we surveyed 264 CLM papers in PubMed and found that about half did not specify their canonicalization procedure, limiting transparency and reproducibility. Using a molecular translation framework, we show that when multiple valid notations are mixed or left undocumented, inconsistent notations distort latent representations and, in some benchmarks, can spuriously inflate predictive accuracy, a phenomenon we term notation-level confounding. These findings demonstrate how subtle differences in SMILES generation can mislead CLMs and highlight the importance of explicitly reporting preprocessing tools and settings.

Foundation models are transforming neuroscience but are often prohibitively large, data-hungry, and difficult to deploy. Here, we introduce BrainSymphony, a lightweight and parameter-efficient foundation model with plug-and-play integration of fMRI time series and diffusion-derived structural connectivity, allowing unimodal or multimodal training and deployment without architectural changes while requiring substantially less data compared to the state-of-the-art. The model processes fMRI time series through parallel spatial and temporal transformer streams, distilled into compact embeddings by a Perceiver module, while a novel signed graph transformer encodes anatomical connectivity from diffusion MRI. These complementary representations are then combined through an adaptive fusion mechanism. Despite its compact design, BrainSymphony consistently outperforms larger models on benchmarks spanning prediction, classification, and unsupervised network discovery. Highlighting the model's generalizability and interpretability, attention maps reveal drug-induced context-dependent reorganization of cortical hierarchies in an independent psilocybin neuroimaging dataset. BrainSymphony delivers accessible, interpretable, and clinically meaningful results and demonstrates that architecturally informed, multimodal models can surpass much larger counterparts and advance applications of AI in neuroscience.

Integration and analysis of multi-omics data provide valuable insights for improving cancer subtype classification. However, such data are inherently heterogeneous, high-dimensional, and exhibit complex intra- and inter-modality dependencies. Graph neural networks (GNNs) offer a principled framework for modeling these structures, but existing approaches often rely on prior knowledge or predefined similarity networks that produce undirected or unweighted graphs and fail to capture task-specific directionality and interaction strength. Interpretability at both the modality and feature levels also remains limited. To address these challenges, we propose TF-DWGNet, a novel Graph Neural Network framework that combines tree-based Directed Weighted graph construction with Tensor Fusion for multiclass cancer subtype classification. TF-DWGNet introduces two key innovations: (i) a supervised tree-based strategy that constructs directed, weighted graphs tailored to each omics modality, and (ii) a tensor fusion mechanism that captures unimodal, bimodal, and trimodal interactions using low-rank decomposition for computational efficiency. Experiments on three real-world cancer datasets demonstrate that TF-DWGNet consistently outperforms state-of-the-art baselines across multiple metrics and statistical tests. In addition, the model provides biologically meaningful insights through modality-level contribution scores and ranked feature importance. These results highlight that TF-DWGNet is an effective and interpretable solution for multi-omics integration in cancer research.

Synthetic molecular communication (MC) in the cardiovascular system is a key enabler for many envisioned medical applications inside the human body, such as targeted drug delivery, early disease detection, and continuous health monitoring. The design of synthetic MC systems for such applications requires suitable models for the signaling molecule propagation through complex vessel networks (VNs). Existing theoretical models offer limited analytical tractability and lack closed-form solutions, making the analysis of realistic large-scale VNs either infeasible or not insightful. To overcome these limitations, in this paper, we propose a novel closed-form physical model, termed mixture of inverse Gaussians for hemodynamic transport (MIGHT), for the advection-diffusion-driven transport of signaling molecules through complex VNs. The model represents the received molecule flux as a weighted sum of inverse Gaussian distributions, parameterized by the physical properties of the underlying VN. We show that MIGHT is capable of accurately representing the transport dynamics of signaling molecules in large-scale VNs ranging from simple single-input single-output (SISO) to complex multiple-input multiple-output (MIMO) network topologies. The accuracy of the proposed model is validated by comparison to the results from an existing convolution-based model and numerical finite-element simulations, with all finite-element simulation data available on Zenodo. Furthermore, we investigate three applications of the model, namely the reduction of SISO-VNs to obtain simplified representations preserving the essential transport dynamics, the identification and analysis of network regions that are most important for molecule transport in MIMO-VNs comprising multiple transmitters and multiple receivers, and the estimation of representative SISO-VNs that can reproduce the received signal of an unknown SISO-VN.

Fluid-structure interaction (FSI) simulation of biological systems presents significant computational challenges, particularly for applications involving large structural deformations and contact mechanics, such as heart valve dynamics. Traditional ALE methods encounter fundamental difficulties with such problems due to mesh distortion, motivating immersed techniques. This work presents a novel open-source immersed FSI framework that strategically couples two mature finite element libraries: MFEM, a GPU-ready and scalable library with state-of-the-art parallel performance developed at LLNL, and FEBio, a nonlinear finite element solver with sophisticated solid mechanics capabilities designed for biomechanics applications developed at the University of Utah and Columbia University. This coupling creates a unique synergy wherein the fluid solver leverages MFEM's distributed-memory parallelization and pathway to GPU acceleration, while the immersed solid exploits FEBio's comprehensive suite of hyperelastic and viscoelastic constitutive models and advanced solid mechanics modeling targeted for biomechanics applications. FSI coupling is achieved using a fictitious domain methodology with variational multiscale stabilization for enhanced accuracy on under-resolved grids expected with unfitted meshes used in immersed FSI. A fully implicit, monolithic scheme provides robust coupling for strongly coupled FSI characteristic of cardiovascular applications. The framework's modular architecture facilitates straightforward extension to additional physics and element technologies. Several test problems are considered to demonstrate the capabilities of the proposed framework, including a 3D semilunar heart valve simulation. This platform addresses a critical need for open-source immersed FSI software combining advanced biomechanics modeling with high-performance computing infrastructure.

Multi-state structured population models, including integral projection models (IPMs) and age-structured McKendrick equations, link individual life histories to population growth and composition, yet the demographic meaning of their dominant eigenstructure can be difficult to interpret. A main goal of this paper is to derive interpretable demographic indicators for multi-state heterogeneity -- in particular expected generation numbers, which act as an effective genealogical memory length (in generations) of the ancestry-weighted contributions driving growth -- together with type reproduction numbers and generation intervals, directly from life-history transition kernels. To this end we develop a determinant-free genealogical framework based on a reference-point operator, a rank-one construction at the kernel level that singles out a biologically chosen reference state and organizes lineages by their contributions relative to that state. This yields stable distributions and reproductive values as convergent series of iterated kernels, and leads to an Euler--Lotka-like characteristic equation expressed by reference-point moments. The resulting expansion admits a closed combinatorial form via ordinary partial Bell polynomials, providing a direct bridge from transition kernels to genealogical quantities. We extend the approach to multi-state McKendrick equations and show how these indicators quantify how population scale and composition are determined by ancestry-weighted initial-state information. The framework avoids restrictive Hilbert--Schmidt assumptions and clarifies how temporal memory and multi-type heterogeneity emerge from cross-generational accumulation, yielding a unified and interpretable route from transition kernels to multi-state demographic indicators.

How do social animals make effective decisions in the absence of a leader? While coordination can improve accuracy, it also introduces delays as information propagates through the group. In changing environments, these delays can outweigh the benefits of globally coordinated decisions, even when local interactions remain tightly organized. This raises a key question: how can groups implement efficient collective decision-making without central coordination? We address this question using a collective foraging model in which individuals share information and rewards, but each must choose whether to bear the cost of exploring or to remain idle. We show that decentralized collectives can match the performance of centrally controlled groups through a division of labor: a small, heterogeneous subset explores even when expected rewards are negative, acquiring information to enable future foraging, while a coordinated majority forages only when expected rewards are positive. Information redundancy causes the optimal number of explorers to grow sublinearly with group size, so that larger groups need proportionally fewer explorers. The heterogeneity of the group is maximized at intermediate ecological pressures, but optimal groups are homogeneous when costs or fluctuations are extreme. Crucially, these group-level policies do not require central coordination, emerging instead from agents following simple threshold-based decision rules. We thus demonstrate a mechanism through which leaderless collectives can make effective decisions under uncertainty and show how ecological pressures can drive changes in the distribution of strategies employed by the group.

Function diversity, the range of tasks individuals perform, and specialization, the distribution of function abundances, are fundamental to complex adaptive systems. In the absence of overarching principles, these properties have appeared domain-specific. Here, we introduce an empirical framework and a mathematical model for the diversification and specialization of functions across disparate systems, including bacteria, federal agencies, universities, corporations, and cities. We find that the number of functions grows sublinearly with system size, with exponents from 0.35 to 0.57, consistent with Heaps' Law. In contrast, cities exhibit logarithmic scaling. To explain these empirical findings, we generalize the Yule-Simon model by introducing two key parameters: a diversification parameter that characterizes how existing functions inhibit the creation of new ones, and a specialization parameter that describes how a function's attractiveness depends on its abundance. Our model enables cross-system comparisons, from microorganisms to metropolitan areas. The analysis suggests that what drives the creation of new functions depends on the system's goals and structure: federal agencies tend to ensure comprehensive coverage of necessary functions; cities tend to slow the creation of new occupations as existing ones expand; and cells occupy an intermediate position. Once functions are introduced, their growth follows a remarkably universal pattern across all systems.

Single-cell RNA sequencing (scRNA-seq) enables high-resolution analysis of cellular heterogeneity, but its complexity, which is marked by high dimensionality, sparsity, and batch effects, which poses major computational challenges. Transformer-based models have made significant advances in this domain but are often limited by their quadratic complexity and suboptimal handling of long-range dependencies. In this work, we introduce GeneMamba, a scalable and efficient foundation model for single-cell transcriptomics built on state space modeling. Leveraging the Bi-Mamba architecture, GeneMamba captures bidirectional gene context with linear-time complexity, offering substantial computational gains over transformer baselines. The model is pretrained on nearly 30 million cells and incorporates biologically informed objectives, including pathway-aware contrastive loss and rank-based gene encoding. We evaluate GeneMamba across diverse tasks, including multi-batch integration, cell type annotation, and gene-gene correlation, demonstrating strong performance, interpretability, and robustness. These results position GeneMamba as a practical and powerful alternative to transformer-based methods, advancing the development of biologically grounded, scalable tools for large-scale single-cell data analysis.

Analysis of learned representations has a blind spot: it focuses on $similarity$, measuring how closely embeddings align with external references, but similarity reveals only what is represented, not whether that structure is robust. We introduce $geometric$ $stability$, a distinct dimension that quantifies how reliably representational geometry holds under perturbation, and present $Shesha$, a framework for measuring it. Across 2,463 configurations in seven domains, we show that stability and similarity are empirically uncorrelated ($\rho \approx 0.01$) and mechanistically distinct: similarity metrics collapse after removing the top principal components, while stability retains sensitivity to fine-grained manifold structure. This distinction yields actionable insights: for safety monitoring, stability acts as a functional geometric canary, detecting structural drift nearly 2$\times$ more sensitively than CKA while filtering out the non-functional noise that triggers false alarms in rigid distance metrics; for controllability, supervised stability predicts linear steerability ($\rho = 0.89$-$0.96$); for model selection, stability dissociates from transferability, revealing a geometric tax that transfer optimization incurs. Beyond machine learning, stability predicts CRISPR perturbation coherence and neural-behavioral coupling. By quantifying $how$ $reliably$ systems maintain structure, geometric stability provides a necessary complement to similarity for auditing representations across biological and computational systems.