Papers

This paper provides a complete characterization of the sign of the propagation speed in the symmetric two-species Lotka-Volterra competition-diffusion model under strong competition. The system admits a unique bistable travelling front and the sign of its speed determines which of the two species invades the other. We prove that for every strong competition intensity greater than $1$ and every diffusion ratio $d\neq1$, the travelling front propagates so as to expand the territory occupied by the faster-diffusing species. The front has a zero speed exactly when $d=1$. We also establish the smooth dependence of the wave speed and the travelling front on the model parameters. The main step in the sign characterization is to prove that a monotone standing front cannot exist when the diffusion rates are different. Combined with continuity of the wave speed with respect to the parameters, the species-exchange symmetry of the system, and an explicit travelling front at a particular parameter value, we obtain the sign of the propagation speed throughout the entire parameter region. This establishes the “Unity is not strength” theorem, which was previously known only in restricted parameter regimes.

Identifying and representing object instances such as cells or nuclei is a common task in microscopy image analysis. Established machine learning workflows typically use supervised detection or segmentation followed by feature extraction or classification, which requires manual annotations and treats instance segmentation and cell representation as separate stages. We describe a new unsupervised method for cell instance segmentation and phenotypic classification from unlabeled microscopy images. Our method is based on reconstructing each image using a coarse-to-fine routing pyramid that associates pixels with spatially sparse latent sources. The resulting pixel-to-latent associations yield instance masks, while the source latents encode cell morphology. We demonstrate competitive performance in instance segmentation across diverse cell morphologies and imaging modalities, as well as generative modeling of cellular phenotypes under perturbations. Source code and checkpoints are available at https://github.com/weigertlab/routing-pyramids.

Componentwise weak convergence of signed synaptic kernels does not, by itself, determine the fast-synapse limit of a sparse threshold-reset network. Within a causal event protocol with clamped refractoriness and smooth positive-delay kernels, we construct two families whose excitatory and inhibitory measures converge weakly to $\delta_0$ while their microscopic arrival orders are reversed. A target fires in the excitatory-first family and not in the inhibitory-first family precisely when $x+a-b<\theta\le x+a$. Strict margins preserve this response under perturbations of the target state, aggregate E/I pulse masses, and bounded drift. The macroscopic effect persists on a moderately sparse Dale-compatible random block graph with $q_N\to\infty$ and $q_N/N\to0$. The two systems share their graph and initial data. Along every deterministic joint scale $\varepsilon_N\downarrow0$, their population-averaged firing counts differ by $1/2+o_{L^1}(1)$. A bounded-degree construction and a later probe show that the discrepancy is macroscopic and can persist through reset. Fixed positive-delay kernels with finitely many classes admit a stable regime. Before grazing, typewise-mixing sparse networks converge to a delayed class mean-field system. Directed Erdos-Renyi graphs yield the bound $O_P(\lambda_N^{-1/2}+\|\pi_N-\pi\|_1)$ when $\lambda_N\to\infty$ and $\lambda_N/N\to0$. This separates stable averaging at a fixed delay from singular collapse. In the latter, componentwise weak convergence discards signed arrival-order information needed by the threshold-reset response.

Large language models can describe mechanisms, yet scalable post-training still depends on costly, manually curated biological reasoning traces. Here we show that cellular perturbation atlases can instead become reinforcement-learning environments, where measured gene responses provide computable rewards for biological reasoning. We introduce PertMind, which combines trusted-trajectory supervised initialization with gene-, pathway-, and format-level reinforcement signals. Although trained only on forward perturbation-response prediction, PertMind improves response inference in unseen cellular contexts while retaining general language capabilities. It also transfers, without task-specific post-training, to reverse perturbation identification, double-perturbation reasoning, phenotypic-screen prioritization, and biological-process interpretation. PertMind further generates biological profiles that support competitive gene, cell, and donor representations across multiscale downstream tasks. These results support the hypothesis that reinforcement on experimental endpoints can concentrate reusable biological strategies already accessible to pretrained models. More broadly, perturbation-derived reinforcement learning offers a scalable route for transforming expanding experimental atlases into training environments for general-purpose biological reasoning.

Longitudinal symptom networks encode directed prediction across measurement occasions, but outgoing connectivity does not by itself identify which symptom should be modified, how strongly it should be changed, or how a perturbation would propagate to later symptoms. We introduce tSymPerturb, a temporal extension of SymPerturb for cross-lagged panel networks (CLPNs). The framework separates source-state operators (temporal virtual knockout and knockdown), transition operators (directed edge and source-node communication blocking), and strategy procedures (dosage perturbation, combination analysis and sequence optimisation). For a two-wave linear CLPN, the central propagation identity is $\Delta \mu_2 = B(\mu_1 - \mu_1^*)$, which makes the source time, outcome time and transition operator explicit. The formulation also yields three falsification constraints: dose response is exactly linear under a fixed linear transition model and linear dose map; independent source-state perturbations are additive at the mean level; and genuine treatment order is not identified from a single two-wave transition. In a known 22-node, four-module generating system, analytical temporal-knockout responses agreed with 250,000-draw Monte Carlo estimates within 0.0057 standard deviations. Across 200 independently generated datasets, median Spearman correlation with the population tVPPS ranking increased from 0.76 at n=250 to 0.88 at n=500 and 0.93 at n=1,000; median top-five recovery was 0.60, 0.80 and 0.80, respectively. Multi-wave simulations showed that target profiles can change across propagation horizons despite high overall rank concordance. tSymPerturb therefore converts longitudinal network structure into auditable, time-indexed intervention hypotheses while retaining the distinction between prediction and causal treatment effects.

Lifelong learning requires acquiring new knowledge without erasing the old. Yet neural population codes for familiar stimuli and behaviors change over days and weeks. This coexistence of stable memory and changing internal codes may depend on how a learning system prevents forgetting. We therefore tested whether different continual-learning mechanisms produce distinct patterns of representational drift. We trained convolutional networks on sequential image classification tasks and recurrent networks on sequences of cognitive tasks, tracking fixed probe representations across learning. Experience replay preserved earlier tasks in both architectures while representations drifted progressively with the number of intervening tasks. Drift was structured: later visual-processing stages and recurrent units' temporal tuning were especially labile, whereas coarse class organization and task-relevant temporal structure persisted. In contrast, algorithm that strongly anchored weights nearly froze representations. Directly anchoring an old representation during replay likewise suppressed drift and impaired acquisition of subsequent tasks. Together, these results link representational drift to the stability–plasticity trade-off: its magnitude is shaped by the mechanism that protects old knowledge, and suppressing it can restrict future learning. Drift may therefore provide an observable signature of the constraints that enable continual learning in brains and machines.

In clinical motor imagery brain-computer interface (MI-BCI) decoding, cross-day transferability and online operation remain two critical challenges. Hypergraphs can improve transferability by capturing higher-order sample relationships, yet existing hypergraph-based methods for online emotion recognition neglect the cross-day benefits of Riemannian geometry widely adopted in EEG transfer learning. To bridge this gap, we propose the Multi-feature Riemannian Hypergraph (MRieHy), a framework tailored for online test-time adaptation in MI-BCI decoding that leverages Riemannian geometry to strengthen cross-day transferability. MRieHy first computes Riemannian means of covariance matrices from cross-day training data to align multi-day distributions. It then constructs a hypergraph over covariance matrices using Riemannian distance, complemented by a second hypergraph over deep features built with cosine similarity. The two hypergraphs are fused via adaptively learned combination weights, jointly optimized with the label projection matrices. During online testing, MRieHy maintains a first-in-first-out buffer of recent samples, performs Riemannian alignment on the buffered data, and decodes with the learned hypergraph. Extensive experiments on a private four-class ECoG dataset and two public four-class EEG datasets validate that MRieHy achieves notable performance gains over state-of-the-art baselines.

Born in London in 1953 and raised in Australia, Phil Bourne spent over four decades in science moving across scales: from crystal structures to the world's premier structural biology database; from scientific journals to national data policy; from molecules to institutions. The International Society for Computational Biology (ISCB) chose Phil to receive its 2026 Outstanding Service Award (Wiper, 2026). He passed away on 8 March 2026, in Charlottesville, Virginia, before he could receive it. This piece is in memory of Phil, who most recently served as the Founding Stephenson Dean of the University of Virginia's School of Data Science and as a Professor of Biomedical Engineering$\unicode{x2013}$and who was, over the course of his career, a steadfast builder of Computational Biology and Bioinformatics, of Open Science and Data Science. A tribute site, https://philbourne.muchloved.com, invites those who knew Phil to share memories, photos, and reflections.

What happens when you teach an LLM-based agent the scientific method? Motivation: Scientific discovery emerges from cycles of hypothesis, implementation, empirical testing, and feedback. Can this process be automated? We approach automated algorithm design through the lens of the scientific method, where an LLM-based agent goes through each step of the process in an ordered, iterative fashion. Results: We present The Little Scientist, a framework in which a "Scientist agent" works inside an evaluation environment that benchmarks its code and returns structured per-instance diagnostics. When the Scientist plateaus at a local optimum, a "Kuhn agent" injects a paradigm-shifting conjecture paired with a cross-disciplinary inspiration, forcing exploration of a different region of the LLM's latent space. We demonstrate the framework on two problems that require fundamentally different modes of discovery. For protein fitness prediction, the Scientist discovered Delta V, an ensemble calibration strategy that ranks first on the ProteinGym DMS Substitutions Zero-Shot leaderboard across all five official evaluation metrics, exceeding the #2 model (VenusREM) by +0.033 mean Spearman correlation across 217 DMS assays. For DNA motif discovery, the Scientist wrote an algorithm from scratch–DALE (Dual-seed Algorithm for Latent Enumeration)–that outperforms STREME (the default in the MEME Suite) across 132 ENCODE transcription factors (mean AUROC 0.842 vs. 0.803, Wilcoxon p < 10^{-6}) while running 11x faster. This demonstrates that the framework can produce genuinely novel algorithms, not just optimize existing components. Together, these results show that an LLM agent stepping through the scientific method can discover both new algorithms and new ensemble strategies that outperform prior solutions. The entire research program consumed 704M tokens on a single virtual machine with no GPUs

Global workspace theory explains conscious access as the broadcasting of selected information to the rest of the network, but it lacks a formal criterion for identifying the mechanism that enables this access. We propose that a global workspace is a mediator, namely, a subnetwork that receives activity from distributed systems, transforms it through internal modes, and returns differentiated effects to the broader network. We formalize this claim as the Global Mediation Workspace (GMW), a control-theoretic formulation in which a candidate subnetwork is treated as an open system embedded in the remainder of the network. In this framework, reachability characterizes how the remainder can drive the candidate, observability characterizes how candidate states affect the remainder, and a boundary Hankel operator identifies the internal modes linking the two directions. The resulting signature quantifies mediation capacity, input-output alignment, effective dimensionality, and routed source-target breadth, each of which characterizes different components of global workspace. In synthetic benchmarks, we tested whether the signature can distinguish a planted differentiated mediator from dense hubs, one-sided receivers or broadcasters, and a split read/write aggregate with no common internal route. A nonlinear extension characterizes mediation through trajectory-conditioned differential operators, finite-amplitude response profiles, and state-dependent coalitions. As a preliminary application, we estimated the signature from ECoG recordings in four macaques under ketamine anesthesia. We found that input-output alignment was reduced during unconsciousness whereas potential capacity was increased. The GMW thus provides a formal and testable criterion for locating candidate global workspaces in neural recordings and for asking which aspects of mediation is crucial for conscious access.

Characterising electrophysiological properties of cardiac tissue efficiently and accurately from spatially sparse intracardiac measurements is clinically important for localising ablation targets and improving arrhythmia treatment. We developed a graph neural network-based framework trained on synthetic electrogram signals on 2D flat surfaces to identify areas of interest in the context of cardiac ablation for premature ventricular complexes (PVCs). Our method achieved an average precision of 0.96, 0.97, and 0.95 for the detection of single-patch fibrosis, rapid depolarisation and high excitability, respectively. The trained model can then be applied to 2D curved surfaces with few-shot fine-tuning, demonstrating its generalisation capability. Future work will develop this framework further for clinical use in PVC ablation.

The population structure of an inbred population of 781 people on Norfolk Island in the Pacific, 318 of which are descendants of the original Mutineers of the Bounty, is analyzed phenotypically using shape from stereo retinal fundus photographs. Three-dimensional optic nerve head (ONH) shape is reconstructed from stereo pairs by a multi-scale stereo matching algorithm. Using deep neural network, the shape of ONH, which is under genetic control, is decomposed into a set of hierarchical features through self-taught learning. Features captured at different levels are selected according to their discriminant power in identifying the two populations. The prediction accuracy is evaluated with stratified cross validation. Given the selected feature set, individuals are grouped into k hierarchical clusters and cluster membership fractions are determined for k=2,3,4,5,6,7. Population structure analysis on the basis of phenotypes through image analysis allows heritability and linkage analysis, including founder effects from English and Polynesian ancestors, potentially leading to new genetic risk factors for glaucoma and other ONH-related eye diseases.

Background. Artificial-intelligence design tools now plan genome-scale edits, and agentic systems execute those plans with progressively less human oversight. Biosecurity controls are limited to two points: refusal guardrails at the foundation model and sequence-identity screening at the synthesiser. The design stage between them, where the plan is specified, remains governed by recommendations rather than any deployed system. Results. We present BioFirewall, a rule-governed middleware that intercepts a genome-writing plan and returns allow, flag-for-review, or refuse across five hazard axes native to genome writing: cargo, locus, edit type, germline and scale, with cited evidence, a signed design passport, a tamper-evident audit log, and tiered access. On a de-circularised benchmark of safe proxies scored against independent oracles, a function-aware cargo classifier reached a true-positive rate of 0.72 (95% CI 0.43 to 0.89) at a 1% false-positive rate, whereas frontier and open language-model judges did not screen the same sequences reliably. Under prompt injection, the open-weight judges flipped their blocking verdict to allow in 3 and 5 of 6 trials per channel, while the deterministic screen remained invariant. None of 288 legitimate plans from three templates was refused, yielding a certified 95% upper bound of 0.0103 on the false-refuse rate, and a session monitor intercepted cross-call decomposition attacks. On a held-out gene set, the locus axis was enriched for drivers of in vivo insertional oncogenesis (AUROC 0.605; odds ratio 3.34). Conclusions. Design-stage governance is achievable in practice. BioFirewall is released as open source with a pre-registered, open-data-reproducible benchmark.

Background. Language-model agents are widely used in biology, but they report quantities without a verifiable source and pose unmanaged biosecurity risks. Genome writing sharpens both: a write plan must specify a location, writer enzyme, cargo, and delivery vehicle, all quantitative and interdependent, so without an integrated tool layer, the agent must supply them. We introduce PEN-STACK, an open tool layer that supplies them with guaranteed provenance. Results. PEN-STACK provides ten genome-writing design stages as twenty-two scope-aware tools, accessible via a software development kit, a Model Context Protocol server, and a Representational State Transfer interface, under a type-enforced invariant: every quantity must originate from a validated tool. Without tools, three model families fabricated 90.8% to 98.8% of the 240 required quantities under a naive prompt; coaching left a residual of 0 to 4, with no model certified at zero. Driving the tools, the same models fabricated nothing on a four-goal audit. A pre-emission biosecurity screen matched expert labels on all eight designs. The expression-robustness axis validated at exact-site resolution (\rho = 0.571, n = 1,506) but not at the coarser resolution served by default (\rho \approx 0.16), which returns a machine-readable downgrade flag. Eight of ten pre-registered claims did not pass, each flagged as machine-readable. Conclusions. On this evidence, grounding, not prompting or model scale, removes fabrication, and grounding requires a substrate; the grounded arm, a four-goal audit, warrants replication at the 240-field scale. PEN-STACK provides that substrate as open, importable code for agentic genome-engineering systems.

Anticipated synchronization (AS), in which the receiver leads the sender and the phase lag is negative, can emerge in unidirectionally coupled dynamical systems when the receiver has faster internal dynamics than the sender. In cortical-like population models, AS and bistability between AS and delayed synchronization (DS) have been reported mainly in unidirectional motifs and have been proposed as possible explanations for phase relations observed in electrophysiological recordings. Because cortical areas are often connected bidirectionally, it is important to understand how excitatory feedback from the receiver to the sender affects the emergence and persistence of anticipatory synchronization and phase-bistable regimes. Here, we investigate the effect of the excitatory feedback on the phase relations between two cortical-like neuronal populations. We show that AS and phase bistability are not restricted to strictly unidirectional architectures, but remain robust in the presence of reciprocal coupling. In addition, we find that the transition from AS to DS can occur through different routes within the same motif, either via a bistable regime or via zero-lag synchronization, depending on the inhibitory coupling. More generally, the model exhibits a rich repertoire of phase relations, including: positive, negative, and zero-lag phase-lockings, as well as phase bistability, and phase-drift regimes. These results are consistent with the diversity of phase relations reported in electrophysiological experiments and suggest that fixed structural connectivity may support rapid reconfiguration of functional dynamics without requiring structural rewiring.

In this study, we develop a novel integrated framework that links the impact response with cellular dynamics using a live-neuron cell-integrated biomechanical full-body surrogate model. The impact event is simulated by allowing the surrogate model to fall from controlled seated release angles of 30-degree, 60-degree, and 90-degree. Three vertically stacked cell-culture Petri dishes, each containing live SH-SY5Y neuroblastoma cells, were placed inside the head of a commercially available surrogate model. The dynamic response of the impact event was evaluated using acceleration measurements from six accelerometers, comprising three sensors mounted on the head surface and three embedded in series with the cell stacks, along with kinematic measurements of the fall and deformation of the head model. In parallel, an OpenSim-based modified musculoskeletal model was used to simulate the fall experiment. We found that variation in contact stiffness produced the largest change in the predicted head acceleration in the simulation. When the cellular response and the measured accelerations are compared, oxidative stress and cell viability showed trends consistent with the regional acceleration and angle of fall. At the 90-degree fall, where median peak linear accelerations ranged from 170-258g, and the maximum headform deformation was approximately 9.4 mm, oxidative stress increased to approximately twice that of the control sample. We also quantified the cellular drift of SH-SY5Y cells, which is focal in nature for the 90-degree impact condition. The corresponding fall scenarios were also simulated in OpenSim and a preliminary calibration relationship was developed to compare the kinematic responses of the physical surrogate and musculoskeletal model. Finally, the framework provides a basis for relating experimental surrogate measurements to human head-neck response during impact.

Large language models (LLMs) are increasingly proposed for healthcare decision support, but their evaluations still reward single-answer accuracy rather than reasoning about interventions, mechanisms, harms, evidence, and uncertainty. We propose a reproducible, graph-centered evaluation framework for intervention-oriented LLM behavior in healthcare and stress-test it in a cardiovascular pilot. The framework has four components: (i) a domain causal knowledge graph in which assertions are first-class, provenance-preserving nodes with stable identifiers; (ii) a scenario-conditioned subgraph extraction step that, given any clinical scenario, retrieves the relevant reified-assertion subgraph; (iii) four controlled grounding conditions that vary how the retrieved subgraph is composed into the model's context (ungrounded C1, knowledge-graph C2, causal-graph C3, integrated C4); and (iv) an automated scoring pipeline, anchored on assertion identifiers, that computes intervention accuracy, and other evaluation measures on a single pass. To test the framework, we built a category-balanced scenario generator across eight reasoning failure modes and instantiated it on a cardiovascular graph. The metric panel discriminates conditions along interpretable, non-redundant axes: C4 obtains the strongest causal edge F1 (0.838), adverse-effect F1 (0.833), evidence accuracy (0.738), and unsupported claim rate (0.114), while C1 obtains the highest raw intervention accuracy (0.948) with no measurable causal or evidential grounding.

Classical mathematical oncology employs deterministic mean-field models predicting that sufficiently high chemotherapy doses drive tumor density to zero. We show that this apparent cure is an artifact of neglecting demographic fluctuations. We construct a nonequilibrium stochastic PK-PD field theory combining a two-compartment pharmacokinetic model with a stochastic tumor-immune sector in the Doi-Peliti formalism, then map it to coupled multiplicative Langevin equations via the Martin-Siggia-Rose/Janssen-De Dominicis approach. In immune-depleted sanctuary sites, the dynamics reduce to a time-dependent Feller diffusion whose Fokker-Planck equation yields an analytical survival functional: demographic noise implies a strictly nonzero relapse probability for tumor micro-clusters under high-dose chemotherapy. Standard bolus administration acts as a nonselective annihilation process, driving immune fields into an absorbing state and creating a spatially immune-depleted vacuum that enables fluctuation-induced relapse – Stochastic Pharmacokinetic Escape. We derive quantitative conditions under which metronomic dosing and adjuvant immunotherapy suppress this stochastic window of vulnerability. A model-agnostic analysis of 1461 longitudinal patient records shows that the majority of evaluable lesions exhibit a nadir followed by measurable regrowth rather than monotonic elimination; fitting the model's drift functional to these trajectories reproduces this pattern quantitatively, and a direct test of the predicted demographic-noise scaling law reveals size-dependent noise largest at the smallest observed tumor volumes, consistent with the proposed mechanism.

Growth is a fundamental process in living systems. Although the stress-deformation response of growing materials is often described as either purely elastic or purely viscous, many biological tissues, from biofilms to tumors, exhibit both elastic and viscous behavior. Here, we show that this viscoelastic response can crucially control the mechanics of proliferating matter when the growth rate becomes comparable to the rate of stress relaxation. Focusing first on the prototypical case of a growing elastic beam, we find that the dynamics are governed by a single dimensionless parameter, $g \tau$, where $g$ is the growth rate and $\tau$ is the viscoelastic relaxation time. While the limits $g \tau \to 0$ and $g \tau \to \infty$ recover purely viscous and purely elastic behavior, respectively, the intermediate regime is not merely a smooth crossover between them. Instead, qualitatively new dynamics emerge at $g \tau \sim 1$, including rapid transitions between metastable states that occur in neither limiting regime. We then develop a general, growth-compatible theoretical framework in which unconstrained growth is intrinsically stress-free, extending the analysis to other prototypical geometries and enabling simulations of more realistic growing biological materials. Within this framework, sharp mechanical transitions arise when stress generated by exponential growth accumulates faster than it can be dissipated by viscoelastic relaxation.

The concept of valuing evolutionary history has a long tradition and was formalized by several research groups in the early 1990s, each aiming to capture the products of evolution more comprehensively than species richness alone. Preserving the "Tree of Life" has since become a central, if sometimes contested, goal in conservation biology. Faith's phylogenetic diversity (PD), defined as the sum of the edge lengths of a rooted tree connecting a set of focal entities, is the most widely used metric in this context and underpins an extensive methodological framework. This framework includes widely used species-specific indices such as EDGE, as well as approaches that quantify expected species-specific contributions to PD such as EDGE2. This chapter focuses on the development of this framework of phylogeny-based conservation metrics. We review the development of species-specific indices, highlighting their strengths and limitations, and trace their progression from simple formulations to game-theoretic approaches and more abstract generalizations. We also discuss how these indices are applied in conservation practice, with particular emphasis on the EDGE framework. We further discuss the relationship between the edge lengths of a phylogeny and the evolutionary features they are intended to represent. Finally, we highlight recent advances in the field and identify areas for future research.

As large language model (LLM) agents are increasingly adopted in scientific research, external knowledge bases, knowledge graphs, and long-term memory have improved information retrieval and task continuity. However, most structured knowledge systems remain node-centric, representing files, concepts, results, and judgments as nodes and relations in a graph. While suitable for personal knowledge management, such structures often depend on individual organizational practices, limiting knowledge sharing, integration, and reorganization across users. This paper presents Valhalla, a layered knowledge-state and service-governance framework for long-term scientific knowledge work. Valhalla replaces flat graphs with layered encapsulation and stable semantic boundaries through a five-layer File-Resource-Entity-Relationship-Graph (FREG) model. File and Resource preserve source identity and provenance, Entity represents knowledge objects, Relationship captures semantic judgments, and Graph provides task-oriented knowledge views, enabling knowledge states from different researchers to be exchanged and reorganized under a unified structure. We further introduce a Router-Contract-Workflow service-governance architecture, inspired by the microkernel paradigm, to constrain how language models access, modify, and extend knowledge states while maintaining structural consistency and auditable operational boundaries. We implement a Valhalla prototype and validate knowledge ingestion, cross-member integration, and scientific writing support through an antibody-design review task comprising 26 paper resources, 80 knowledge entities, and 92 semantic relations. Rather than proposing a new knowledge-extraction algorithm, Valhalla offers a paradigm for organizing collaborative scientific knowledge, transforming individualized knowledge structures into transferable and reorganizable shared knowledge states.

This work investigates the class of SIR/SEIR models and their extension to an ODE-based SVEIR system, whose parameters are calibrated and validated using real influenza outbreak data. The theoretical part establishes existence and uniqueness of solutions for the SVEIR model via the Picard-Lindelof theorem and analyzes invariance of the admissible region. To describe spatiotemporal infection spread in an urban setting, a diffusion-chemotaxis extension of the SIR framework is formulated as a PDE system; an additional term is introduced to represent fear/avoidance effects in the system dynamics. A numerical workflow is proposed, including grid discretization, Neumann boundary conditions enforced by mirror extension, a semi-implicit IMEX time-stepping scheme, and sparse linear solves; computational correctness is monitored, in particular, by checking conservation of the total population.

Oscillatory neuronal networks exhibit complex collective responses to external perturbations that depend on both the intrinsic network dynamics and the timing of stimulation. Although phase response curves (PRCs) have become a standard tool for characterizing these responses, phase resetting alone provides an incomplete description of how transient perturbations reshape collective activity. Here, we investigate the dynamics of a balanced excitatory-inhibitory network of exponential integrate-and-fire (EIF) neurons subjected to phase-targeted current pulses. By jointly analyzing the network phase response curve (nPRC), network amplitude response curve (nARC), and changes in the population synchrony, we establish a framework for characterizing collective network responses in terms of phase, amplitude, and synchronization. We show that identical stimulation pulses can either enhance, suppress, or leave network synchronization unchanged depending solely on their phase within the oscillation cycle, revealing distinct synchronizing and desynchronizing windows. The nARC further identifies robust phase intervals that maximize suppression of oscillatory activity and provide optimal targets for repeated stimulation. Successive perturbations progressively desynchronize the network activity while continuously reshaping the phase, amplitude, and synchrony response landscapes, driving the network toward a modified dynamical state without altering the optimal stimulation phase. These cumulative effects remain robust across stimulation intensities, inhibitory synaptic time constants, and independent network realizations. Our results demonstrate that phase, amplitude, and synchronization represent complementary dynamical dimensions of oscillatory neuronal networks and provide general principles for the state-dependent control of collective dynamics through phase-targeted perturbations.

Synaptic delays are fundamental determinants of neuronal communication and can profoundly influence the emergence and stability of cortical oscillations. Although their role in shaping network synchronization is well established, how synaptic delays regulate the collective response of neuronal populations to transient perturbations remains poorly understood. Here, we investigate the effects of synaptic delays on the phase and amplitude responses of oscillatory activity in a conductance-based excitatory-inhibitory spiking network operating in the pyramidal-interneuron gamma (PING) regime. By systematically varying the synaptic delay and applying brief external perturbations to the excitatory population, inhibitory population, or the entire network, we computed network phase response curves (nPRCs) and network amplitude response curves (nARCs) to quantify changes in oscillation timing and population coherence. Increasing synaptic delay slowed network oscillations while enhancing population synchrony, demonstrating a trade-off between oscillation frequency and coherence. Excitatory perturbations produced relatively robust phase responses across delays but exhibited a pronounced delay-dependent reduction in amplitude enhancement. In contrast, inhibitory perturbations generated substantially stronger delay-dependent modulation of both phase resetting and amplitude suppression, whereas whole-network stimulation combined features of both excitatory and inhibitory responses. Taken toghether, these findings identify synaptic delay as a key parameter governing the balance between phase resetting and amplitude modulation and provide a computational framework for understanding delay-dependent control of oscillatory brain networks.

Heart rate and respiration rate are crucial vital signs. We present CORAL to address challenges in automating continuous vital sign monitoring 1) in-hospital across broader populations (age, disease states), 2) at-home in telehealth and wellbeing applications (noise, placement), and 3) across data modalities (ECG, PPG, SCG, BioZ, etc.). We re-introduce Short-Time Autocorrelation Functions (STACFs) to introduce the correloform - a highly interpretable 2D signal transformation for tracking periodicity over time - and define CORAL as a generic analytical framework for robust rate estimation of quasi-periodic signals. We rigorously benchmark CORAL to show ubiquitous application in biosignals via capabilities arising by mathematical construction rather than domain-specific engineering, including rate estimation, resilient noise handling, automatic channel selection, and signal quality indication. CORAL achieves excellent instantaneous noninvasive fetal HR agreement in FECGSYNDB (F1 = 0.999) and ADFECGDB (F1 = 1.000). With difficult NICU neonates, CORAL estimates RR from wearable BioZ at r = 0.858 against breath-interval RR from simultaneous wired Philips impedance. CORAL SCG HR on CEBS achieves r = 0.990 and in free-living activity r = 0.970 when compared against commercial ECG. Without QRS detection, CORAL's instantaneous HR agrees with Pan-Tompkins and NeuroKit2 detectors as closely as they agree with each other (MIMIC-IV ICU ECG r = 0.87 to each vs. 0.88 between them). CORAL's HR standard deviation correlates strongly with interval-based HRV SDNN, even from mechanical SCG (CEBS r = 0.733) and across an ICU ECG cohort (r = 0.768).

Solitary animals face a tradeoff when detecting threats: faster detection means accepting more false alarms. We show that groups can manage this tradeoff better by treating an undisturbed neighbor as evidence against a threat, becoming both faster and more accurate than lone individuals. Modeling each animal as a noisy evidence-accumulator that flees when its belief crosses a threshold, we find that a neighbor's flight signals danger while its stillness signals safety. A naive responder reacts only to flights and inflates false alarms as the group grows; a Bayesian responder weighs both, approximated by a single social discounting rate that interpolates between these limits. This yields closed-form expressions for group performance, including cascade branching ratios that stay strongly subcritical in safety and turn supercritical under threat, so the rate at which an animal discounts a threat while its neighbors stay still can be inferred from behavior alone, and it sets a ceiling on how many neighbors an animal can attend before discounting alone can no longer hold its false-alarm rate. Wild sulphur molly shoals under bird attack are best described by discounting rates well above what individually Bayesian updating supplies over any neighborhood they could plausibly attend, and the same model, at the inferred value, predicts a false-alarm rate that stays constant as shoals grow.

Low-rank matrix decompositions can uncover patterns and structure in data and have a number of different applications across many disciplines. Extensions to "joint" low-rank decompositions have been proposed to link datasets from different modalities. While these methods enable the discovery of common patterns across modalities, they require that all the multimodal data share one or more dimensions. We propose a new analysis method, PathFinder, that enables co-analysis of datasets that do not necessarily all share a dimension. The key insight is that as long as pairs or subgroups of matrices do share some dimension, and that there are one or more paths that link across the data matrices, a global joint decomposition can be sought out. This enables the joint estimation of common patterns across different modalities, species, or scales, where a one-to-one mapping across all data along some dimension is not necessarily available. We show that PathFinder is a general umbrella under which many matrix decomposition methods fall as special cases. It can be used to discover common patterns across disparate datasets and to make predictions for missing data or modalities.

We introduce MultiStructRNA, a unified Python toolkit for RNA secondary structure prediction, ensemble analysis, and visualization. Although RNA secondary structure is central to RNA biology and therapeutic design, practical adoption is often hindered by fragmented tooling, incompatible input and output formats, and limited visualization support. MultiStructRNA addresses these challenges through a single high-level API that orchestrates multiple prediction algorithms, harmonizes results into a consistent schema, and provides reproducible, ensemble-aware metrics through an object model suited to both interactive notebooks and production pipelines. MultiStructRNA enables seamless switching between prediction methods without requiring workflow changes and supports both in-notebook and exportable visualizations. Designed for scalability, it supports high-throughput analyses and simplifies comparison across methods while standardizing downstream feature extraction. The current release also includes optional agent-readable workflow recipes that document dependency setup, backend-adapter conventions, SHAPE-data reconciliation, structure interpretation, and comparative sequence analyses. By integrating diverse RNA secondary structure packages within a common framework, MultiStructRNA streamlines structure analysis and facilitates its use in RNA design, optimization, and machine learning workflows.

We present a parameter-free episodic evaluation of nearest-centroid classification of elephant vocalisations on fixed pretrained embeddings, for the Elephant Voices (EV) and Linguistic Data Consortium (LDC) datasets. We ask not which embedding yields the best classifier trained on all labelled data, but how the simplest classifier performs as the number of exemplars per class varies. There are no learnable parameters, because each class is modelled as the mean of its support embeddings and each query is assigned to the nearest centroid under squared Euclidean distance. Evaluation covers the fixed Perch (ver. 1), Perch (ver. 2) and HuBERT (base, layer 2) embeddings, alongside mel frequency cepstral coefficient (MFCC) features, $N$-way $k$-shot, under the same stratified $K$-fold cross-validation protocol as the trained classifiers. None of these embedding models was trained to distinguish elephant call types. On the smaller EV dataset the centroid classifier is markedly data-efficient. Using Perch (ver. 1) or Perch (ver. 2) embeddings it overtakes in mean average precision (mAP) the fully-trained logistic regression (LR) baseline from one or two exemplars and the recurrent baseline from two. Over the reduced set of call types on which the strongly-supervised end-to-end baseline was trained, the centroid classifier using Perch (ver. 2) embeddings overtakes that baseline in mAP as well, from two exemplars. On the larger LDC dataset the recurrent baselines retain their advantage for all considered values of $k$. Only LR is overtaken, and only in mAP. Nearest-centroid classification is therefore preferable precisely when exemplars are few and the fixed embedding already separates the call types.

Whole Slide Image (WSI) analysis has been widely studied for cancer diagnosis. Conventionally, a gigapixel WSI is divided into small patches and processed by Multiple Instance Learning (MIL) models. However, existing MIL models typically process all patches, many of which contain redundant or non-informative tissue patterns. Although recent approaches have focused on instance selection to identify discriminative patches and reduce redundancy, these selection modules still require additional training. In this work, we propose Test-Time Instance Selection (TTIS), a training-free, plug-and-play framework that selects compact yet representative patches during inference. TTIS further incorporates a multi-view ensemble strategy to integrate distinct facets of tissue morphology, enhancing robustness. Importantly, TTIS can be seamlessly integrated into existing MIL models without retraining or architectural changes, enabling flexible deployment. Extensive evaluations across multiple benchmarks demonstrate that our approach improves or matches baseline MIL performance across a range of classification and subtyping tasks. Our implementation code is available at https://github.com/QuIIL/TTIS