Antibodies play a central role in the immune response by specifically recognizing and neutralizing antigens, and therapeutic antibodies have become major drugs for cancer and autoimmune diseases. However, their discovery still relies on extensive in vitro screening, and accurate computational modeling of antibody structures and antibody-antigen interactions can prioritize candidates, reduce experimental burden, and accelerate rational design. Despite recent advances in high-accuracy protein and complex prediction, a persistent performance gap remains for antibody-related tasks compared with general protein-protein interactions, limiting downstream design. This thesis investigates why antibody-related tasks are harder and proposes improvements along two complementary directions. First, we investigate protein language model (PLM)-based methods for antibody and antibody-antigen structure prediction. Using embeddings from multiple PLMs, our approach achieves the best CDR-H3 accuracy among compared PLM-based methods on antibody monomer prediction. Extending it to complex prediction does not generalize: without co-evolutionary signals between antibody and antigen, single-sequence PLM representations do not reliably identify binding interfaces. Second, we develop two MSA-based interventions for antibody-antigen complex prediction: MSA refinement, which combines CDR-focused filtering with depth recovery from a larger sequence database, and convergence-aware recycling, which selects a stable intermediate recycle state for final diffusion sampling. Together, these interventions provide consistent gains over the AlphaFold3 baseline on a held-out antibody-antigen test set. Because the methods modify MSA construction and recycling behavior rather than model parameters, they apply without retraining or weight access.

The Shigesada-Kawasaki-Teramoto (SKT) model has become a classical modelling framework for studying spatial segregation and cross-diffusion-driven pattern formation in competing populations. This model assumes phenotypic homogeneity, but phenotypic variability persists within any population and can strongly influence both ecological and evolutionary dynamics. In this paper, we present a generalised phenotype-structured formulation of the SKT model that accounts for phenotypic variability. In this formulation, the competing populations are continuously structured across some phenotype state spaces. Population members move and compete in phenotype-dependent ways, and can also switch between different phenotype states. First we show how a form of the classical SKT model, wherein parameters are written in terms of continuous weighted averages of the phenotype-dependent functions of the generalised structured model, with weights given by the phenotype distributions of the two populations, can be obtained in the quasi-invariant regime of fast phenotype switching. Then, still assuming fast phenotype switching and extending classical Turing-like linear and weakly nonlinear analyses, we explore the conditions for the emergence of spatial patterns, identify a Turing-type bifurcation threshold leading to pattern formation, and investigate the nature of such a bifurcation (super- or sub-critical) as well as the stability of the patterned state. The results obtained make it possible to draw connections between phenotype-dependent model functions and the emergence of population-scale aggregate spatial dynamics, showing in particular how phenotype distributions can act as effective control parameters for Turing instability and pattern selection. These findings are complemented by numerical simulations, which validate the formal asymptotics and confirm the predictions of the pattern formation analyses.

A novel two-phase molecule inference framework, mol-infer, has recently been developed to infer chemical graphs with prescribed abstract structures and desired property values through mixed integer linear programming (MILP) under the two-layered model, with guaranteed optimality and exactness relative to the given learned prediction function and structural constraints. In this study, we extend this framework to copolymers by introducing a simple feature representation, called the mixing vector (MV) model. In the proposed model, a copolymer feature vector is represented as a convex combination of MILP-tractable monomer descriptors weighted by the mixing ratio of the constituent monomers. This representation does not require explicit sequence-class information and is therefore naturally compatible with MILP-based inverse design. Under this model, we construct prediction functions for several copolymer property datasets using artificial neural networks, reduced quadratic multiple linear regression, and random forests. The proposed representation achieves practically useful predictive performance across multiple physicochemical property datasets; in particular, the best test R^2 score exceeds 0.7 for nine of the ten datasets and exceeds 0.9 for six datasets. We also formulate a multi-monomer inverse-design problem under the MV representation with a prescribed mixing ratio and show that the resulting MILP instances remain tractable, even for three-monomer settings. Finally, we perform an external consistency check by re-evaluating the inferred candidates and comparing the re-computed property values with those predicted by the learned model. Overall, the proposed framework gives a tractable first step toward model-level exact inverse design of copolymers under the two-layered model.

In transcriptomics, gene-set-aware factorization methods such as the Pathway Level Information Extractor (PLIER) are most effective when trained on large, heterogeneous expression compendia. Yet, many clinically relevant cohorts cannot be pooled into a single dataset due to privacy and governance constraints. We present FPLIER, a federated extension of PLIER that enables distributed training across multiple data holders while incorporating publicly available datasets. Through secure aggregation, FPLIER produces training updates algebraically equivalent to those of a centralized pooled-data approach while keeping expression data local. We evaluate FPLIER across multiple scenarios in two simulated consortia (from the K-CLIER and MultiPLIER studies) and demonstrate stable convergence. We further conduct a systematic analysis of membership inference attacks targeting both intermediate training statistics and the released model. Our results show that privacy risk is governed by the rank of the training expression matrix. Incorporating public data or reducing data dimensionality increases this rank, moving the system toward a full-rank regime in which training and non-training samples become indistinguishable to the attacker, and membership-inference performance approaches random guessing.

The study of brain morphology changes in normal individuals may capture aspects of functionally-relevant brain aging not fully indicated by gross volumetry. Despite the important role of subcortical brain structures in cognition, the associations between their morphological trajectories and cognitive changes in aging have not been documented. We use neuroimaging, demographic, and cognitive data from a large longitudinal study of cognitive aging, the Lothian Birth Cohort 1936, to explore shape changes in subcortical brain structures of community-dwelling individuals across their 8th decade of life. We investigate the association of these changes with cognitive aging using ANCOVA and mixed linear model analyses. Subcortical shape changes were heterogeneous, with varied atrophy patterns across whole period. The hippocampus and the ventral DC experienced varied morphological deformations (from its baseline point) different in left and right hemispheres, while the thalami and globus pallidi shapes, for example, experienced a more uniform volume contraction, nearly symmetrical throughout different timelines. Changes in general cognition were mainly associated with inwards and outwards vertex displacements between the time-points.

We study the temporal dynamics of the first two empirical moments of Brownian traits on phylogenetic trees. For a fixed tree, we characterize the distributions of their empirical mean and empirical variance across all lineages extant at any given time. In particular, we show that the variance of the empirical mean and the expected empirical variance are piecewise linear between diversification events. For lineage-homogeneous random trees, both the variance of the empirical mean and the expected empirical variance can be expressed in terms of the expected age of the most recent common ancestor (MRCA) of a uniformly sampled pair of extant lineages. In this representation, the expected MRCA age enters the two quantities with opposite signs, pointing to a structural opposition between the variance of the empirical mean and the expected empirical variance. For generalized birth-death processes with time-dependent speciation and extinction rates, we derive an explicit formula for the distribution of the MRCA age of a uniformly sampled pair of extant lineages. This yields integral expressions, at any time, for both the variance of the empirical mean and the expected empirical variance. In the constant-rate birth-death case, we further obtain closed-form expressions for the expected empirical variance and describe its asymptotic behavior in the supercritical, critical and subcritical regimes.

Parameter inference and state estimation in stochastic and partially observed biological systems remain major problems in mathematical biology. In this work, we introduce a two-dimensional lattice graph model for the spread of infectious diseases. Estimating states and parameters in graph-based stochastic epidemic systems is particularly challenging because of randomness and incomplete observations. To address these issues, we propose a particle filter based data assimilation framework for the sequential estimation of both model states and unknown parameters. Two methodologies are developed: one based on the number of infected agents and another based on partial spatial location's information of infected agents on a two-dimensional lattice. The performance of the two methods are firstly analyzed and validated using synthetic data, and the first method is then applied to influenza data collected from different prefectures in Japan between July 2024 and December 2025. One-week-ahead forecasting simulations are also performed using current weekly data. The findings highlight the effectiveness of the proposed PF framework for real-time epidemic monitoring, forecasting, and adaptive public health decision-making.

We extend the ``Brownian bees'' model of Berestycki et al. (2021, 2022) to cooperative reproduction, $kA\to(k{+}1)A$, of a population of $N$ symmetric random walkers with removal, at each birth event, of the particle farthest from the origin. Working in the limit $N\to\infty$, we formulate a hydrodynamic free-boundary problem for this model. Using this formalism, we determine steady state population densities for all~$k$ and prove their linear stability for $k\le 2$ and instability for $k\ge 4$. In the marginal case $k=3$, there is a whole continuous family of steady states at a single, critical ratio of the reproduction and diffusion rates. Above criticality the population undergoes an asymptotically self-similar finite-time collapse to the origin. Below the criticality the population spreads diffusively, but the reproduction remains quantitatively relevant. For $k\ge 4$, the unstable steady state separates regimes of a finite-time collapse and a diffusive spreading. Here the collapse dynamics is asymptotically self-similar, and the population density exhibits a scale separation requiring a matched-asymptotic description. Our analytical predictions are confirmed by numerical solutions of the hydrodynamic free-boundary problem and by Monte Carlo simulations of the original microscopic model.

Recent progress in diverse intelligence has shown simple learning capacities below the organism level - single cells and even molecular networks. However, there are still many knowledge gaps around learning capacity above the organism level, and about memory implemented purely by dynamical interactions without explicit memory media. We demonstrate that minimal ecological dynamics (in silico) are sufficient for several kinds of learning, assayed as changes in both, magnitude of response, and of recovery time. Systematic exploration of over 220,000 parameter combinations in a simulated classic predator-prey model revealed that, when perturbed by stimuli, recovery time exhibits habituation, sensitization, and a form of discrete number learning in a scale-invariant manner. Robustness analysis revealed that habituation and sensitization persist under stochastic perturbations, while discrete number learning is disrupted even at low noise levels. Dimensionality reduction revealed that the incidence of learning capacity is primarily determined by ecological interaction strengths. Clear, unique clustering patterns in parameter space allow high prediction accuracy for novel parameter combinations that enable learning. Response magnitude revealed a striking asymmetry: 90.6% of parameter combinations exhibited recovery time sensitization paired with habituation of response magnitude, while the opposite pattern was extremely rare. These findings highlight a set of phenomena at the intersection of ecology, basal cognition, and mathematics with many implications for a wide range of systems describable by similar kinds of equations. These properties provide numerous efforts in biology and engineering with a substrate that has considerable, pre-patterned, propensity for learning, which ultimately arises from mathematics, not depending on the details of physics or biology.

Large language models (LLMs) exhibit remarkable flexibility: they can adapt to novel tasks from in-context examples without any parameter updates, a capability known as in-context learning (ICL). Prior work on synthetic tasks has shown that ICL can implement specific algorithms, demonstrating architectural competence, and mechanistic analyses have identified key circuits that support this behavior. However, because in-context computation -- regardless of its algorithmic form -- relies on transformations in high-dimensional representation space, it remains unclear how the geometry of that space shapes ICL effectiveness. Motivated by the neuroscience view of classification as the untangling of neural representations, we hypothesize that ICL depends on the successful online untangling of task-relevant representations. To test this idea, we study how LLMs classify in-context examples whose labels are defined by the model's own internal representations with known structure. We show that ICL performance correlates systematically with the representational structure of the underlying classification task and that successful ICL is accompanied by geometric reorganization that increases online separability. We further find that LLM behavior is well described by a prototype-like algorithm that integrates evidence while reshaping representations to support classification. These findings offer a geometric account of ICL in pretrained LLMs, establish representational geometry as a mechanistic constraint on ICL, and quantify the gap between what pretrained representations afford and what in-context learning can exploit.

Drug discovery is a lengthy and resource-intensive process composed of multiple stages. Among these stages, lead optimization plays a critical role in transforming early hit compounds into viable drug candidates. This stage requires improving ADMET-related properties through subtle structural refinement while preserving key molecular substructures responsible for binding affinity to disease targets. Recent advances in artificial intelligence have shown promise in accelerating various aspects of drug discovery; however, most existing approaches to lead optimization rely on one-step molecular optimization, which fail to account for the long-term consequences of sequential design decisions. To address this limitation, we propose TRACE, a trajectory-aware, LLM-reasoning agent for molecular lead optimization that formulates tool selection as a sequential decision-making problem over action trajectories. Given a lead molecule and an optimization objective, TRACE makes trajectory-aware decisions over molecular optimization tools, enabling forward-looking refinement under structural constraints. Experiments on multiple ADMET optimization tasks show that our agent achieves higher optimization success, larger property improvements, and higher validity, while preserving molecular similarity compared to baseline models.

Protein homology search underlies function annotation, structure prediction, and evolutionary analysis, but remains challenging in the "twilight zone," where global sequence similarity is weak and classical alignment methods lose sensitivity. Protein language models provide context-aware representations that could improve alignment sensitivity in this regime. However, prior protein embedding-based retrieval pipelines often pool these representations into a single vector, potentially obscuring local motifs, domains, or conserved residues that reveal remote homology. We introduce ProtoCol, a model which represents proteins as sets of residue embeddings and uses ColBERT-style late interaction to test whether residue-level comparison improves homolog retrieval. ProtoCol encodes proteins independently, keeps candidate representations pre-computable, and scores candidates with MaxSim over residue embeddings. On SCOPe superfamily and Pfam clan benchmarks, ProtoCol outperforms sequence-composition, alignment-based, pooled PLM, and trained single-vector baselines, supporting late interaction as an effective retrieval layer for remote homology search.

Protein structure classification (PSC) uses supervised learning to predict a protein's CATH/SCOP(e) class from the protein's sequence or 3D structural feature(s). We already modeled 3D structures as (static) protein structure networks (PSNs), demonstrating the competitiveness of PSN-based features to sequence or direct (i.e. non-network) 3D structural features in the PSC task. More recently, we demonstrated the power of features extracted from dynamic PSNs over features extracted from static PSNs (and thus by transitivity over sequence and direct 3D structural features) in the same task. That dynamic PSN approach used traditional machine learning (ML), combining manual (pre-engineered) features with an off-the-shelf classifier. Here, we evaluate whether automatic deep learning (DL) from the dynamic PSNs yields improvements. Our evaluation on 72 datasets spanning ~44,000 CATH- or SCOPe-labeled dynamic PSNs reveals that in terms of PSC accuracy, traditional ML and DL are (close to) tied for a large majority of the datasets, while DL is on average 10+ times slower. We are the first to evaluate traditional ML vs. DL in the dynamic PSN-based PSC task.

Understanding how cortical activity represents natural whole-body behaviors in primates remains challenging. Limited by the diversity of movements and inaccessibility of large-scale neural representation of whole-body kinematics, previous motor decoding studies focused on constrained tasks and limited limb movements. Here, we present a neural-behavioral recording and modeling framework for freely moving monkeys, combining large-scale epidural cortical signals from distributed sensory- and motor-related areas with synchronized multi-view motion capture through a custom-made data collection platform. We reconstructed whole-body monkey kinematics and learned a compact behavior prior using an autoregressive encoder-decoder model. Conditioned on neural signals, the model decoded accurate and realistic whole-body movement without explicit physical constraints. Our results provide a novel proof-of-concept approach for decoding natural whole-body movements in primates using large-scale intracranial neural activity.

We investigate group-level synchronization between oscillator groups induced by common noise in the absence of inter-group coupling. Each group receives a common noise shared by all its oscillators and independent local noise inputs to individual oscillators. The same common noise is applied to all groups. The system is studied with both identical and nonidentical oscillators, and with and without intra-group coupling. In the nonidentical case, natural frequencies are drawn from the same distribution for both groups, making them statistically equivalent. Through numerical simulations of this system, we find that the degree of synchronization within each group, measured by the absolute value of a complex Kuramoto order parameter, typically shows significant temporal fluctuations. Importantly, the complex order parameters representing the collective oscillations of the groups synchronize when the groups are driven by the same common noise. By deriving a phase density evolution mapping, we analytically explain how this group-level synchronization is achieved in the absence of intra-group coupling.

Decoding visual content from fMRI signals recorded while a person views images, and specifically answering questions about the seen images, is a long-standing challenge. While significant progress has been made in recent years in visual question answering (VQA) from fMRI, performance remains limited. Moreover, although recent models can make increasingly accurate predictions, they have rarely been used as tools for understanding the structure of visual representations in the brain. We present Brain-IT-VQA, a framework for visual question answering from fMRI. Building on the Brain Interaction Transformer (Brain-IT), our method decodes language tokens from brain activity and integrates them with a language model to answer visual questions. Our model substantially outperforms previous fMRI-based captioning and VQA approaches. We further introduce NSD-VQA, a new dataset and benchmark for visual question answering from fMRI. Unlike existing image-fMRI VQA datasets, which typically provide only a few broad and weakly controlled questions per image, NSD-VQA provides on average 20 question-answer pairs per image across 20 controlled question categories that disentangle multiple levels of visual understanding. This enables more reliable and interpretable evaluation despite limited fMRI test data. Together, Brain-IT-VQA and NSD-VQA provide both a strong predictive framework and a tool for studying brain representations. Using this benchmark, we quantify which forms of visual and semantic information can be reliably decoded from fMRI responses to natural images. We further analyze the contributions of different brain regions across question types.

Continuous brain-computer interfaces (BCIs) that decode motion trajectories from imagined movement offer intuitive motor control, yet how feedback modality and longitudinal training shape neural representations and decoding performance remains poorly understood. We present the first systematic investigation of embodied virtual reality (VR) feedback during real-time 3D virtual limb control driven by motor imagery, across ten longitudinal sessions in ten participants. Performance was evaluated using three strategies: actual online performance (Fixed Decoder Generalisation, FDG), periodic retraining (Sequential Adaptive Training, SAT), and within-session upper-bound estimation (Within-Session Reconstruction, WSR). A CNN-LSTM decoder achieved within-session imagined movement correlations of r = 0.762 under VR and r = 0.672 under screen feedback. VR significantly outperformed screen feedback across all strategies and movement dimensions (improvements of 8.9-13.0%, all p <= 0.002, d = 1.42-2.05). This advantage persisted under fixed decoders without retraining, demonstrating that embodied VR feedback elicits inherently more decodable and generalisable neural representations. Linear mixed-effects modelling confirmed robust main effects of feedback modality and movement axis with no interaction. Neurophysiologically, VR produced stronger sensorimotor-parietal desynchronisation and enhanced motor-frontal functional connectivity, with pervasive anterior insula engagement across all frequency bands and increased superior parietal lobule coupling, paralleling patterns associated with real movement execution. These findings establish embodied spatial feedback as a key design principle for next-generation continuous BCIs targeting intuitive motor control and neurorehabilitation.

Earlier detection of pancreatic cancer is key to enabling wider access to curative treatment and reducing cancer deaths; however, screening is presently not viable. Latent indicators of pathology are evident in an individual's disease and blood test trajectories and may predict the development of pancreatic cancer. Longitudinal sequences of coded diagnoses and blood test values accrued by patients throughout their clinical interactions were used to train a custom Transformer-based neural network with a multi-head attention mechanism to predict risk of pancreatic cancer with a multi-year lead time and risk-stratify populations for targeted screening. The cohort comprised 6,017 adults with pancreatic cancer and 177,081 controls (overall median age 75, 45% female) with median 12 years (interquartile range 6.9-16.2) of medical history prior to pancreatic cancer diagnosis. External validation via leave-one-site-out, out-of-sample testing predicting pancreatic cancer 1-, 2-, and 3-years prior to diagnosis demonstrated mean area under the receiver operating characteristic of 0.837 (95% confidence interval 0.827-0.848), 0.797 (95% confidence interval 0.782-0.813), and 0.760 (95% confidence interval 0.745-0.776), respectively. Estimated pancreatic cancer risks were well-calibrated (calibration plot slope 1.08, intercept of -0.077; Brier score 0.025), and a Bayesian population pancreatic cancer prevalence update allows estimated cancer risk outputs to be transportable across settings. At testing, a screening threshold of >3.3% risk of pancreatic cancer in 1-year offered a diagnostic odds ratio of 18.2. Our work therefore lays the foundation for a first population-level digital enrichment tool to widen access to curative-intent management of pancreatic cancer.

Projection neurons in the dorsal horn relay nociceptive input to supraspinal centers. During central sensitization, a subset of them switches from tonic firing to plateau potentials with sustained afterdischarges, a change that requires intrinsic bistability between a resting and a spiking state. Voltage-gated L-type calcium (CaL) channels can produce bistability, but reach physiological resting states only when paired with voltage-gated potassium channels, most of which simultaneously shrink the bistability window. How robust, physiological bistability arises has therefore remained unclear. Using a minimal conductance-based model, we show that inward rectifier potassium (Kir) channels enlarge the bistability window when combined with CaL channels, while M-type potassium (KM) channels slightly reduce it. Within the parameter region where bistability is both robust and physiological, both channel types can sustain bistability, but the CaL+Kir combination produces a substantially larger window and is more robust to noise and intrinsic variability. This window-enlarging effect traces to a shape feature of the outward Kir steady-state current: like the CaL current, it has a region of negative differential conductance around the spike threshold, a feature absent from KM and from most other voltage-gated potassium currents. Bifurcation analysis further shows that the two pairs support qualitatively distinct excitability: plateau-generating bistability for CaL+Kir and resonator-like dynamics for CaL+KM. These conclusions hold in a two-compartment model of deep projection neurons with realistic ion channel complements, and identify the CaL+Kir pair as a candidate intrinsic mechanism for central sensitization.

Mental rotation -- the ability to compare objects seen from different viewpoints -- is a fundamental example of mental simulation and spatial world modeling in humans. Here we propose a mechanistic model of human mental rotation, leveraging recent advances in deep, equivariant, and neuro-symbolic learning. Our model consists of three stacked components: (1) an equivariant neural encoder, producing 3D spatial representations of objects from images, (2) a neuro-symbolic object encoder, deriving symbolic objects descriptions from these spatial representations, and (3) a neural decision agent, comparing these symbolic descriptions to prescribe rotation simulations in 3D latent space via a recurrent pathway. Our model design is guided by the existing experimental literature on mental rotation, which we complemented with experiments in VR where participants could at times manipulate the objects to compare. Our model captures well the performance, response times and behavior of participants in our and others' experiments, and through ablation studies we demonstrate the necessity of each component. Our work adds to a recent collection of deep neural models of human spatial reasoning, further demonstrating the potency of integrating deep, equivariant, and symbolic representations to model the human mind.

Estimating brain age (BA) from T1-weighted magnetic resonance images (MRIs) provides a powerful framework for quantifying anatomical brain aging. Whereas global BA (GBA) summarizes overall brain health, local BA (LBA) provides cortically specific patterns of aging at the subject level. Although previous studies have examined anatomical contributors to GBA, to our knowledge, no framework has been established to estimate LBA using cortical morphology. To address this gap, we introduce a graph neural network (GNN) that uses morphometric features$\unicode{x2013}$cortical thickness, surface area, curvature, gray/white matter intensity ratio (GWR), sulcal depth$\unicode{x2013}$to estimate LBA across the cortical surface at high spatial resolution (mean inter-vertex distance = 1.37 mm). Trained on cortical surface meshes extracted from the MRIs of cognitively normal (CN) adults (N = 14,423), our model achieves lower mean absolute error (MAE) than the existing state-of-the-art while identifying more biologically plausible patterns of aging in Alzheimer's disease (AD) on the ADNI dataset. Association cortices emerge as primary sites of morphometric aging in CNs, whereas mild cognitive impairment is characterized by widespread aging that is pronounced in the parahippocampal gyrus. AD subjects demonstrate significant aging across the entire cortex, particularly within medial temporal regions and associated cortical networks. Feature ablation highlights curvature and GWR as preferentially sensitive to AD pathology. Regional LBA gaps are significantly associated with neuropsychological measures of AD-related cognitive impairment, linking cortical aging patterns to clinical outcomes. These results demonstrate that GNN-based modeling of cortical morphometry enables biologically interpretable mapping of local brain aging with greater interpretability than prior work.

D-peptide binders targeting L-proteins have promising therapeutic potential. Despite rapid advances in machine learning-based target-conditioned peptide design, generating D-peptide binders remains largely unexplored. In this work, we show that by injecting axial features to $E(3)$-equivariant (polar) vector features, it is feasible to achieve cross-chirality generalization from homo-chiral (L--L) training data to hetero-chiral (D--L) design tasks. By implementing this method within a latent diffusion model, we achieved D-peptide binder design that not only outperforms existing tools in \textit{in silico} benchmarks, but also demonstrates efficacy in wet-lab validation. To our knowledge, our approach represents the first wet-lab validated generative AI for the \textit{de novo} design of D-peptide binders, offering new perspectives on handling chirality in protein design. Codes are available at this https URL .

When competing species grow into new territory, the population is dominated by descendants of successful ancestors at the expansion front. Successful ancestry depends on both the reproductive advantage (fitness), as well as ability and opportunity to colonize new domains. We present a model that integrates both elements by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (KPZ equation). Macroscopic manifestations of these equations are distinct growth morphologies controlled by expansion rates, competitive abilities, or spatial anisotropy. In some cases the ability to expand in space may overcome reproductive advantage in colonizing new territory. When new traits appear with accumulating mutations, we find that variations in fitness in range expansion may be described by the Tracy--Widom distribution.

Single-cell trajectory inference from destructive time-course snapshots is fundamentally ill-posed: neither cross-time cell correspondences nor continuous trajectories are observed, so the snapshot distributions alone do not uniquely determine the underlying dynamics. Existing optimal transport and flow-based methods typically couple cells by Euclidean proximity at observed clock times, which can misalign trajectories when development is asynchronous and cells sampled at the same experimental time occupy different latent pseudotime stages. We propose PACE, a trajectory inference framework that recovers geometry-consistent continuous transport dynamics from destructive time-course snapshots through three coupled components. First, PACE constructs a state- and time-dependent anisotropic Riemannian metric that assigns low transport cost along locally supported tangent directions while penalizing normal velocity components. Second, it alternates between refining cross-time couplings under the induced path-action cost and fitting endpoint-preserving neural bridges between adjacent snapshots. Third, it distills the learned bridge dynamics into a global continuous-time velocity field over cellular states. Across seven controlled and biological datasets covering nine held-out reconstruction experiments, PACE achieves the strongest overall reconstruction performance, reducing MMD, Wasserstein-1 distance, and Wasserstein-2 distance by 23.7% on average relative to the strongest competing baseline. PACE also improves RNA-velocity alignment by 15.4% on an embryoid body differentiation benchmark, without requiring explicit cell pairing, lineage tracing, or RNA-velocity supervision during training. Code is available at this https URL.

Large language model (LLM) serving creates environmental impacts beyond carbon and water, including ecosystem damage through biodiversity-related pathways. We present BIRDS, a framework for Biodiversity Impact of Request-Driven LLM Serving. BIRDS defines request-level functional units, quantifies operational and embodied biodiversity impact, and introduces Quality-Normalized Biodiversity Impact (QNBI) to jointly analyze ecological impact and response quality. Across diverse workloads, models, GPUs, and regions, BIRDS reveals that biodiversity impact accumulates at scale and exposes actionable quality-aware serving tradeoffs.

Previous research has proven that the set of maps implemented by neural networks with a ReLU activation function is identical to the set of piecewise linear continuous maps. Furthermore, such networks induce a hyperplane arrangement splitting the input domain of the network into convex polyhedra $G_J$ over which a network $\Phi$ operates in an affine manner. In this work, we leverage these properties to define an equivalence relation $\sim_\Phi$ on top of an input dataset, which defines a quotient space that can be split into two sets related to the local rank of $\Phi_J$ and the intersections $\cap \text{Im}\Phi_{J_i}$. We refer to the latter as the \textit{overlap decomposition} $\mathcal{O}_\Phi$ and prove that if the intersections between each polyhedron and an input manifold are convex, the homology groups of neural representations are isomorphic to quotient homology groups $H_k(\Phi(\mathcal{M})) \simeq H_k(\mathcal{M}/\mathcal{O}_\Phi)$. This lets us intrinsically calculate the Betti numbers of neural representations without the choice of an external metric. We develop methods to numerically compute the overlap decomposition through linear programming and a union-find algorithm. Using this framework, we perform several experiments on toy datasets showing that, compared to standard persistent homology, our overlap homology-based computation of Betti numbers tracks purely topological rather than geometric features. Finally, we study the evolution of the overlap decomposition during training on several classification problems and discuss some shortcomings of our method.

Generative models frequently suffer miscalibration, wherein statistics of the sampling distribution, such as the fraction of generations in a given class, deviate from desired values. We frame calibration as a constrained optimization problem and seek the closest model in Kullback-Leibler divergence satisfying a calibration constraint. To address the intractability of imposing these constraints exactly, we introduce two surrogate objectives for fine-tuning: (1) the relax loss, which replaces the constraint with a miscalibration penalty, and (2) the reward loss, which converts calibration into a reward fine-tuning problem. We demonstrate that these approaches substantially reduce calibration error across hundreds of simultaneous constraints and models with up to nine billion parameters, spanning applications in protein design, image generation, and language modeling.

Foundation models have revolutionized various fields such as natural language processing (NLP) and computer vision (CV). While efforts have been made to transfer the success of the foundation models in general AI domains to biology, existing works focus on directly adopting the existing foundation model architectures from general machine learning domains without a systematic design considering the unique physicochemical and structural properties of each biological data modality. This leads to suboptimal performance, as these repurposed architectures struggle to capture the long-range dependencies, sparse information, and complex underlying ``grammars'' inherent to biological data. To address this gap, we introduce BioArc, a novel framework designed to move beyond intuition-driven architecture design towards principled, automated architecture discovery for biological foundation models. Leveraging Neural Architecture Search (NAS), BioArc systematically explores a vast architecture design space, evaluating architectures across multiple biological modalities while rigorously analyzing the interplay between architecture, tokenization, and training strategies. This large-scale analysis identifies novel, high-performance architectures, allowing us to distill a set of empirical design principles to guide future model development. Furthermore, to make the best of this set of discovered principled architectures, we propose and compare several architecture prediction methods that effectively and efficiently predict optimal architectures for new biological tasks. Overall, our work provides a foundational resource and a principled methodology to guide the creation of the next generation of task-specific and foundation models for biology.

Changing environmental conditions can significantly affect the dynamics of disease spread. These changes may arise naturally or result from human interventions; in the latter case, lockdown measures that lead to abrupt but temporary reductions in transmission rates are used to combat disease spread. Yet, the impact of these measures on rare events in heterogeneous populations remains understudied. Here, we analyze the susceptible-infected-susceptible (SIS) model in a stochastic setting where disease extinction -- a sudden clearance of the infection -- occurs via a rare, large fluctuation. We use a semiclassical approximation and numerical simulations on heterogeneous assortative networks, with degree-degree correlations between neighboring nodes, to show how the extinction risk of the disease depends on the lockdown's duration and magnitude, and on the network topology.

Why does the mammalian vascular tree maintain a conserved branching exponent $\alpha^* \approx 2.72$ across a $10^7$-fold range in body mass, despite a fundamental shift from viscous to wave-dominated transport? We prove this universality cannot emerge from local optimization: any junction-level coupling of incommensurable costs requires scale-dependent fine-tuning varying by $O(10^2$--$10^3)$ across the hierarchy. Real networks resolve this through structural heterogeneity, and vascular geometry emerges as a scale-free attractor of a network-level minimax principle. Grounding the fitness penalty in ATP stoichiometry, we prove a Topological Rigidity theorem: the optimal branching exponent depends only on dimensionless structural parameters $(G, N, p, \alpha_w)$, independent of all metabolic quantities. A self-consistency condition on the viscous--inertial energy partition yields a dual-threshold framework with $\mathrm{Wo}_c^{\mathrm{fluid}} = \sqrt{3}$ and $\mathrm{Wo}_c^{\mathrm{wave}} = 3/\sqrt{2}$. The symmetric model yields $\alpha^*_{\mathrm{model}} \approx 2.626$, in agreement with mammals near the allometric transition; morphometric heterogeneities shift large-mammal values toward $2.72$. The framework explains developmental stability of cardiovascular networks as a consequence of architecture being decoupled from biochemistry.

A central puzzle for the behavioural sciences and for human-facing artificial intelligence is the persistence of within-person variability. The same individual, presented with the same observable input, produces different outcomes on different occasions, and different individuals produce divergent outcomes that no observable covariate fully predicts. We argue that this variability belongs in the dynamic latent state of the person, and that human outcomes are controllable in a precise and operational sense through interventions that target the state and its weighting at the moment a decision is being formed. We define a state as the time-indexed weighting vector over the dimensions that govern how an individual's biology, physiology, and neuropsychology process the next event into a decision and an outcome. The relationship between state, decision, and outcome is causal rather than correlational. The weighting vector is dynamic at sub-daily timescales. The conscious channel through which outcomes are reportable is a narrow attentional bottleneck whose contents are themselves state-dependent. Taken together, these claims imply that the outcome of a given event is controllable, conditionally, on the state-trajectory at the time of intervention. We motivate the framework with six strands of established evidence (causal inference, predictive processing, allostasis, attentional bottleneck, chronobiology, computational psychiatry) and a 24-month observational base from a deployed behavioural platform spanning more than 200,000 consented users across four occupational personas (research period 2023 to 2026). We derive seven testable predictions, list six operational requirements for state-aware systems, and discuss implications for digital health, education, AI personalisation, and personal agency.