Papers

DNA replication requires the coordination of origin firing and fork progression to ensure the entire genome is timely duplicated before cell division. Yet origin firing is stochastic, giving rise to the classical random completion problem of how probabilistic local events can nevertheless ensure reliable genome duplication. Although several biological mechanisms have been proposed to resolve this problem, a quantitative account of how heterogeneous initiation and fork speed govern the persistence of the final unreplicated regions is still lacking. To address this gap, we introduce a population-level kinetic framework that extends KJMA nucleation-and-growth models by tracking unreplicated intervals over size, genomic position and time. We establish well-posedness of the resulting mean-field system and global existence for compatible data. Notably, by introducing a local initiation mass function, we quantify how the density and spatial organisation of origin firing constrain replication completion, yielding novel and sharp upper bounds on both the worst-locus unreplicated fraction and locuswise near-completion time. These results provide a rigorous and computable foundation for mapping vulnerabilities in replication completion and relating persistent unreplicated regions to replication stress and genome instability.

Automated prediction of Enzyme Commission (EC) numbers plays a central role in functional annotation and computational drug discovery. However, standard multi-label machine learning pipelines frequently rely on default decision thresholds (t=0.50), assuming balanced prior distributions across target heads. In this study, we present a systematic empirical diagnostic of uncalibrated fixed decision boundaries operating under severe class imbalance across N = 14,096 annotated compounds categorized into six primary EC classes (EC1-EC6). Our results highlight a pronounced Accuracy Paradox: while the multi-label system achieves a deceivingly high mean accuracy of 77.16%, the macro F1-score (0.3976) and macro recall (0.3872) reveal severe predictive breakdown. Majority target classes suffer from hyper-sensitivity and over-prediction, whereas minority classes exhibit sharp recall decay, culminating in a total decision boundary collapse for EC6 (Recall = 0.00%) despite underlying discriminative power (ROC-AUC = 0.5857). Feature correlation analysis further reveals high linear redundancy among topological indices relative to fingerprint density metrics. Ultimately, this diagnostic study demonstrates that standard point predictions mask critical errors in bioinformatics workflows. We establish target-specific threshold optimization and post-hoc conformal calibration as essential, open-source post-processing safeguards for reliable applied machine learning and deep learning architectures.

Normative age models are trained to predict chronological age in a nominally healthy cohort. Applied to patients, they deviate, and the gap between predicted and chronological age is read as disease risk. Here, we attribute the disease-related effect size of the age gap directly to individual training samples, rather than using a prediction-level loss as the attribution target. For Cohen's $d$, the resulting closed-form influence functional, validated against leave-one-out retraining, ranks training samples by their effect on held-out case-control separation. Across four diseases and two biomarker modalities in UK Biobank, removing the 10% most influential training samples raises held-out disease-related effect size in every seed. It more than doubles the metabolomic-age effect for type-2 diabetes and raises the brain-age effect for multiple sclerosis by roughly a third. Random removal leaves effect size flat even at 50% removal, confirming the gain comes from which samples are removed, not how many. Flagged subjects carry subclinical cardiometabolic burden that diagnosis-based exclusion misses, on markers the model never sees. For type-2 diabetes, where the method gains most, the marker recovered is HbA1c, the standard measure of blood sugar control. We release pyinfluence, our influence-function package, for reproducibility and reuse.

Motor control research involves the study of movement kinematics derived from the positional trajectories that complex motions describe. In natural, unconstrained motions requiring cognitive and memory processes in real time, the temporal speed profiles are not bell-shaped, may have multiple maxima and the peaks distribution is best fit by the continuous gamma family with two parameters, the shape and the scale. As the stochastic processes described by complex motion trajectories are non-stationary, the gamma shape and scale parameters describing them span stochastic trajectories. These points live on a curved surface where Euclidean distance depends on the arbitrary choice of parameterization. We adopt the Fisher-Rao distance (the geodesic length on the gamma manifold) as a coordinate-free metric for movement fluctuation signatures and present a robust numerical solver that converges across the full range of empirically observed parameters. We demonstrate the metric on a tablet-based digitized Trail Making Test in healthy adults, comparing micromovement fluctuations under low and high cognitive load. Load displaced every participant's fluctuation signature but with no shared direction. Instead, participants converged toward a common operating regime, with those farthest from it at baseline moving the most. Cognitive load thus contracts individuality in motor fluctuations rather than shifting the population uniformly.

Critical phenomena are widespread across many disciplines and have recently become a topic of deep interest in the study of biological and artificial neural networks. A distinct signature of criticality is the emergence of avalanches with power-law-distributed sizes and durations. However, empirically estimating the critical exponents remains challenging, and their interpretation is often model-dependent. In this work, we demonstrate how the Fisher Information Metric (FIM), a measure of generalized susceptibility, provides a comprehensive, model-agnostic characterization of the critical region in neural systems. We validate this approach across models of increasing biological complexity, from prototypical branching processes to spiking and whole-brain models, showing that FIM of each model's control parameter reliably tracks the system's degree of criticality. To emulate the study of real-world systems, where the control parameter is unknown, we additionally calculate FIM of the observed branching ratio of neural activity. The resulting FIM peaks where activity growth and decay balance, with the peak sharpening as the system approaches criticality. Hence, FIM peak width and height yield continuous, model-free readouts of proximity to criticality without requiring knowledge of the true control parameter, offering a robust tool for probing criticality in neural systems.

Continuous-time multi-type branching processes are fundamental models for expanding and migrating populations with cancer evolution being a prototypical example. Inferring model parameters, like mutation and growth rates, from time-series count data requires efficient computation of population size distributions. Existing methods are mainly based on large-time or large-number asymptotics, which rely on either restricted initial conditions or simplified interactions between cell types. Here, we introduce two numerical approximations of population size distributions for multi-type branching processes on directed graphs with arbitrary initialization. The first approach combines a saddle-point approximation with numerical integration of the probability generating function. We characterize admissibility and establish conditions for saddle-point existence and uniqueness. For directed acyclic graphs, the second approach provides a large-time small-mutation-rate alternative based on closed-form approximate Laplace transforms and efficient numerical inversion. We benchmark the accuracy and speed of both solutions in simulations, showing substantial improvement over the state-of-the-art large-number approximation and orders of magnitude speedup over Gillespie's stochastic simulation algorithm at matching accuracy. We apply our methods to analyze the relapse dynamics of an acute myeloid leukemia patient, where rapid parameter scans over a six-type patient-specific mutation tree quantify how unobserved remission burden and treatment-altered fitness can explain relapse. Our methods provide computational building blocks for future likelihood-based inference in cancer evolution and other expanding populations.

A common formalization of homeostasis is the free energy principle, a framework that defines a set of desired observation values, or critical states, that the agent should reach or remain close to. Under the free energy principle, an agent should act to maximize the probability of receiving the desired observations. Here we revisit the common approach of solving the problem of maximizing the log probability of the desired observations by maximizing a variational lower bound, the so-called negative free energy. We show that, instead, an approach directly maximizing that probability under the agent's policy is better suited to, and provides a better solution for, the original homeostatic control problem. This is done using hidden Markov model (HMM) control by allowing the policy to act over hidden states or noisy versions thereof while trying to maximize the probability of repeatedly having the desired observations. HMM control largely improves performance over the variational, or free energy, approach. We also show that the optimal policy is strictly deterministic, while the variational approach leads to a stochastic policy approximation. We finally provide a homeostatic reinterpretation of the maximum occupancy principle -a principle proposing that agents ought to maximize the occupancy of action-state path space -by defining homeostatic states as any states that do not immediately entail the termination or death of the agent.

The evolution of DNA sequences can be viewed as stochastic dynamics on a high-dimensional discrete space, but it is unclear when empirical transition biases reduce to an effective energy landscape versus retain irreducible non-equilibrium circulation. Human context-dependent mutation probabilities offer a direct test: every single-nucleotide substitution in a local context has a reverse substitution, so the logarithm of the forward-to-reverse probability ratio defines an antisymmetric field-the human mutation field. We show this field has a dominant gradient component and a smaller but reproducible curl component. Using seven-base human germline substitution probabilities, we infer an effective mutational landscape with a Siamese neural network constrained to predict only energy differences. This model predicts forward-to-reverse log-ratios for held-out mutations with a correlation of about 0.93, close to both an unconstrained predictive reference (0.948) and the empirical reversible ceiling from Hodge projection (about 0.96). Although trained only on mutation probabilities, the inferred landscape largely recovers short-word genomic composition and Chargaff reverse-complement symmetry for sequences up to length four. Deviations from equilibrium structure reveal a small but detectable nonequilibrium component: a residual irreversible circulation violating the Kolmogorov cycle condition for detailed balance, reproducible across African, Asian, and European populations, and strongest in CpG-linked cycles and CpG-transition edges, consistent with methylcytosine deamination. These results give a thermodynamic decomposition of the human mutation field: most mutation bias is organized by a local equilibrium-like energy landscape aligned with genome composition, while the residual circulation points to specific directional mutational mechanisms.

Reservoir computing provides a controlled setting for studying how recurrent network architectureshapes computation: input signals are projected into a high-dimensional state space by a fixed nonlinear dynamical system, and only the readout is trained. However, reservoir performance can be dependent on hyperparameters; this paper asks which recurrent network features support robustness to those parameter changes. We characterize computational performance using memory capacity (MC), truncated single-delay information-processing capacity (IPC), and kernel rank (KR). Generalization across input histories is measured using generalization rank (GR), while hyperparameter robustness is quantified using the coefficient of variation (CV) of each metric across sweeps of target spectral radius, input scaling, leak rate, and neuron bias. To examine the architectural determinants of robustness, we construct perturbations that alter connectivity topology, excitatory/inhibitory sign structure, weight magnitudes, and weight placement while preserving complementary properties. Across these experiments, the C. elegans connectome consistently occupies a relatively low-variance regime. The central result is a performance-robustness tradeoff: architecture variants with higher task-agnostic performance also tend to exhibit greater hyperparameter sensitivity and poorer common-tail generalization. Across the E/I edge balance sweeps and shuffle controls, this tradeoff is closely associated with the raw spectral radius before normalization. Because every perturbed matrix is rescaled to the same target radius, matrices with lower raw spectral radius receive greater global amplification of their recurrent weights. The observed differences among architectures therefore characterize the joint effects of structural variation and architecture-specific global rescaling under spectral-radius normalization.

Infectious diseases may interact by competing for the same hosts or by facilitating subsequent infections. Understanding the dynamics of such multi-pathogen systems, particularly those subject to endemic seasonality and mitigation, is essential for designing robust public health interventions. We propose a three-stage modeling framework to disentangle the interplay between seasonality and behavioral feedback as a way of mitigation. First, we analyze a coupled susceptible-infectious-recovered-susceptible (SIRS) system without external forcing and show that the abrupt transition between the disease-free and endemic equilibria arises from a backward bifurcation-induced first-order phase transition. Second, we independently examine seasonality and behavioral feedback, characterizing where and when oscillatory behavior is induced near critical tipping points. Third, we demonstrate that their combination generates complex multi-annual wave patterns, with high-incidence cycles driven by seasonality and low-incidence intervals driven by behavioral feedback. By mapping stability as a function of seasonal forcing, mitigation strength, and cooperativity, we identify distinct period-doubling cascades with chaotic signatures arising from different mechanisms: the interplay between seasonality and behavior, and inter-pathogen cooperativity with the backward bifurcation it induces. We then analyze how these mechanisms interact across parameter ranges. Altogether, we show that cooperation fundamentally expands the spectrum of possible epidemic patterns, highlighting the importance of considering multi-pathogen interactions in epidemic modeling and control strategies.

We test whether the Kuramoto model quantitatively describes spatial synchronization in regional epidemic waves, using daily COVID-19 incidence for 400 German Kreise (2021–2023) and weekly ILI rates for 12 European countries (ECDC, 2021–2026). Bandpass filtering and Hilbert-transform phase extraction yield high global order parameters ($\langle r\rangle\approx0.87$ for Germany; $\langle r\rangle\approx0.97$ for Europe), yet both are dominated by a common-mode driver rather than pairwise local coupling. Removing the common mode reveals genuine short-range synchronization: an exponentially decaying residual local order with correlation length $\xi=152\pm6$~km in Germany, and a significant neighbor-vs.-non-neighbor contrast (Mann–Whitney $p=0.005$) in the European panel. We interpret this convergent pattern across two diseases and two spatial scales as a universal two-scale structure: a long-range common-mode field superimposed on shorter-range diffusive coupling. Cross-validation against a companion gauge-mediated Doi–Peliti framework shows that district-level effective screening mass $m_R$ is uncorrelated with local~$r$ (null result), the national $(m_R,r)$ phase portrait independently reproduces a previously reported hysteresis loop, and pairwise phase lags quantitatively match fractional-calculus predictions. A frequency–degree correlation provides the structural signature of explosive synchronization; excess synchronization between districts sharing the same Bundesland implicates shared school-holiday calendars and state-level policy as local coupling drivers.

High-resolution volumetric medical imaging is critical for clinical diagnosis, yet acquisition is often limited by scanner hardware, scan time, and for CT, radiation dose. Medical 3D Super-Resolution (Med3DSR) offers a computational alternative, but existing methods commonly rely on per-subject optimization, pretrained priors, or coordinate-based implicit representations, which compromise anatomical fidelity and limit efficiency. To address these limitations, we present MedGSSR, a fully end-to-end feed-forward framework that represents volumes as an explicit 3D Gaussian field for Med3DSR. Unlike coordinate-based implicit functions, our explicit 3D Gaussian representation naturally enhances signal continuity and local high-frequency fidelity. Specifically, MedGSSR explicitly decouples the reconstruction process into coarse-grained structural preservation and fine-grained textural refinement through the proposed Pyramid Anatomical Encoder and a Hierarchical Gaussian Projector. To support arbitrary-scale super-resolution, we introduce sub-voxel Gaussian decomposition and a Differentiable Gaussian Voxelizer that directly queries the continuous 3D intensity field, reducing discretization artifacts. Extensive experiments on MRI and CT benchmarks demonstrate that MedGSSR significantly outperforms state-of-the-art methods. Notably, our framework exhibits robust generalizability across unseen datasets without requiring per-subject optimization, enabling fast inference and high-fidelity volumetric super-resolution in practical clinical settings. Our project webpage, including code, is at https://william2ai.github.io/medgssr

This paper examines the theory of Invariant Structural Learning (ISL), which proposes a non-optimization approach to concept formation. Learning is interpreted as convergence to structural attractors in a hypergraph space, rather than as the minimization of a global loss function. The paper presents the ISL model, including its mathematical formalization, computational verification, and a hypothetical neurobiological interpretation. The mathematical section introduces the formal apparatus of the structural reduction process and proves its finite convergence, the existence and uniqueness of class structural attractors, and the self-organization of attractor maps. The computational section demonstrates the feasibility of the proposed approach on classical image recognition tasks, utilizing the proposed learning mechanism without backpropagation and with extremely small training datasets. Finally, the neurobiological section formulates hypotheses regarding the possible implementation of structural attractors in dendritic trees, neural coding as a projection of internal attractor dynamics, and the development of neural architectures supporting the proposed learning concept. These hypotheses are discussed in the context of modern experimental data in the fields of dendritic computations, synaptic plasticity, and the structural organization of neural circuits. The proposed neurobiological mechanisms are presented as testable hypotheses rather than established biological facts. The results demonstrate the mathematical consistency and computational feasibility of the proposed model, while the neurobiological hypotheses outline potential directions for its experimental verification.

Mosquito-borne diseases such as dengue, Zika, and yellow fever impose a substantial global health burden, motivating genetic control strategies that replace wild mosquito populations with disease-refractory ones. Maternal-effect dominant embryonic arrest (Medea) is a gene drive in which the offspring of a Medea-carrying mother die unless they inherit the Medea allele, producing biased inheritance capable of driving a linked refractory trait to high prevalence. We develop and analyze a continuous-time compartmental model of Medea dynamics in Aedes aegypti that tracks mosquito abundance by life stage and genotype, and that generalizes the drive mechanism to allow both imperfect Medea-killing and imperfect rescue. We characterize the biologically relevant equilibria and derive their local stability conditions, together with genotype-specific reproduction numbers and the basic reproduction number (R0) governing invasion from low frequency. Bifurcation analysis reveals bistability, and hence a release threshold that must be exceeded for Medea to take over, even though R0<1 at baseline. Imperfect killing and imperfect rescue reshape this bifurcation structure in distinct ways: killing leakage governs the invasion threshold, while rescue efficiency governs the composition of the resulting population. Sensitivity analysis identifies the fitness coefficient and killing leakage as the dominant drivers of both threshold and coverage outcomes, with mosquito demographic parameters affecting absolute abundances but not genotype proportions. Simulations of batched release programs inform efficient field deployment and show that reversing an established drive is substantially more costly than achieving forward invasion, though co-releasing both sexes accelerates reversal considerably more than it accelerates invasion.

Motivated by the pulsed control and resulting evolution of harmful biological populations, we develop and analyze an ordinary differential equation model of an n-dimensional stage-structured population undergoing periodic disturbances. The eco-evolutionary model couples both ecological dynamics through life cycle information, and evolutionary dynamics of allele frequency changes. Building off prior work in eco-evolutionary models and theory of linear systems, we show that if a resistant allele is present in the population, the population will always approach full resistance. Furthermore, we establish persistence conditions and show that these depend solely on system dynamics at full resistance. Finally, we demonstrate the utility of this model via an application to the Spotted-Winged Drosophila, an invasive species often treated periodically with insecticides. We use a parameterized model to further understand the complexities of relationships between ecological and evolutionary features of a species and its resistance evolution due to pulsed disturbances.

Elastic buckling has explained shape formation in growing tissues, yet the role of tissue fluidity remains elusive. We derive a minimal fluidized growth-elasticity model as a nonlinear analogue of Maxwell rheology. Analysis of a growing strip reveals a different picture of growth-induced morphogenesis: rather than emerging at a critical stress, symmetry breaking develops continuously during growth. Fluidity regulates stress evolution, the rate of shape-symmetry breaking, and flow patterns, establishing it as an active regulator of morphogenesis beyond its intuitive role in stress relaxation.

We introduce ABLE, a benchmark for evaluating LLM agents' ability to use biological AI models (BAIMs), such as ProteinMPNN and AlphaFold3, in dual-use protein design workflows. ABLE assesses agent performance through a set of tasks spanning structure retrieval, sequence generation, and design validation. We evaluate 15 frontier models and find that seven refuse all tasks, while the remaining models exhibit substantial performance differences. Claude Sonnet 4 and Gemini 3 Pro achieve the highest scores across information retrieval, tool selection, and tool use. We further compare model performance on a subset of tasks against an expert human baseline. Our results suggest that current LLMs can substantially lower barriers to protein design, but remain inconsistent in planning, strategy generation, and integrating biological knowledge with tool use.

We develop a network-structured Bayesian hierarchical model for sparse association mapping between genomic alterations and quantitative treatment-response phenotypes. The framework combines a Gaussian Markov random field prior that borrows strength across pathway-connected genes, a global-local horseshoe prior inducing sparsity, and a conjugate Gibbs sampler requiring no Metropolis-Hastings steps. Though broadly applicable to high-dimensional settings with known predictor networks, we validate it using cancer cell-line drug-sensitivity data. Applied to GDSC2 ($N=951$ cell lines, $G=219$ driver genes, $D=295$ drugs), the model identifies 126 gene-drug associations (0.195% of 64{,}605 pairs), concentrated in EZH2 (45 drugs, all sensitivity-direction, mean effect $-0.911$ $\ln$IC50) and KMT2D (36 drugs, all sensitivity-direction, mean effect $-0.496$ $\ln$IC50). These markers show external support in an independent PRISM screen (1{,}518 compounds), with KMT2D achieving complete directional replication (36/36) and EZH2 partial replication (8/12). Five-fold cross-validated predictive log-likelihood confirms each prior layer's value: the full model outperforms the no-network ablation by $+3{,}109$ log-units per fold and the no-horseshoe ablation by $+14{,}039$ log-units, consistently across folds. Simulations under three scenarios show the full model achieves the highest precision and lowest false-discovery rate throughout, while the network prior improves sensitivity recovery under network-structured signal. A tissue-stratified extension identifies coherent subgroup refinements, including lung-specific EGFR-inhibitor sensitivity and skin-specific BRAF-Dabrafenib sensitivity. These results show the framework identifies sparse, interpretable, externally supported drug-sensitivity markers while enabling principled investigation of tissue-specific departures from shared effects.

Interstitial flow plays a key role in drug delivery, angiogenesis, cancer, and edema. Recent studies have identified connected interstitial pathways that can transport material over long distances. However, the spatial scale of physiological interstitial flow remains unclear: despite the existence of connected pathways, flow may be dominated by nearby vascular filtration or extend over longer distances. Here, we identify organ-scale interstitial flow patterns in the chick yolk sac and elucidate the mechanisms that determine their spatial scale. The yolk sac contains an organ-scale interstitial region that enables large-scale flow patterns to be identified without truncation. Our approach combines experimental imaging with computational modeling of coupled blood and interstitial flow in the whole yolk sac. Scaling analysis identifies a hydraulic conductivity ratio that controls the transition from small-scale to organ-scale flow. In organ-scale patterns, we find interstitial flow speed to be substantially greater than the transvascular flow speed. Mechanistically, the organ-scale patterns arise from the spatial segregation of the leakage and drainage of interstitial fluid from the vessels. These findings have important implications for biological transport by interstitial flow, suggesting that flow-mediated cues may be sensed locally but generated nonlocally.

When there is not enough labeled data to properly train deep learning models, transfer learning can help. We still do not fully understand how effective it is in neuroimaging, especially for Alzheimer's disease research. It is also not clear if these transferred models can work on new datasets without being retrained for each specific task. We evaluate whether a compact, supervised pretrained model can serve as a reusable foundation model for downstream neuroimaging tasks. We freeze the 7.18 million weights of a 3D CNN previously trained for brain-age prediction, and adapt it to each task using Low-Rank Adaptation (LoRA), requiring only ~1% additional trainable parameters. We evaluate generalizability in six experiments. Adapting the model to classify cognitively normal versus Dementia on ADNI gave an AUC of 0.964 on held-out folds (Experiment #1). Applying that adapted model unchanged to OASIS-3, with no retraining, gave an AUC of 0.871 (Experiment #2). Reusing its output logit together with age and a cognitive score distinguished stable from progressing MCI with an AUC of 0.828 (Experiment #3). Adapting the same backbone to predict amyloid positivity from structural MRI gave an AUC of 0.804 (Experiment #4). Finally, the same approach estimated ICV-normalized hippocampal and white matter hypointensity volumes directly from the T1w image, with R^2 of 0.80 and 0.91 respectively, tasks normally addressed with much larger U-Net networks (Experiments #5 and #6). A compact model supervised on brain age can therefore serve as a reusable backbone, adapting to each task with ~1% additional parameters and transferring to an unseen cohort without any training. Our findings suggest that a carefully trained brain age model can serve as an effective foundation model for Alzheimer's related tasks, even under strict data constraints.

Protein-protein interaction (PPI) network alignment combines topological and sequence information to identify conserved modules across species, but global alignment remains challenging: heuristics sacrifice optimality, while exact methods lack scalability. We model the alignment as a weighted maximum common induced subgraph problem and reformulate it through the modular product graph to a minimum-weight vertex cover on the complement, with node weights carrying sequence similarity. To solve this problem, we develop a hybrid framework combining kernelisation, branch-and-bound, and seven Quantum Approximate Optimisation Algorithm (QAOA) formulations. These formulations differ in how the cover constraints are enforced, from penalty terms in the cost Hamiltonian to mixers confined to the feasible subspace. For single round QAOA, we derive closed-form expressions for the expected cost of four circulant mixer variants, enabling performance characterisation without circuit simulation. Applied to synthetic and real-world networks reduced to KEGG pathways, the QAOA formulations achieve high topological conservation on the aligned core while at least maintaining biological conservation comparable to leading classical aligners, at the cost of reduced node coverage. Across selected KEGG pathways, the aligned subnetworks retain disease-associated proteins, preserving biologically relevant information. Cheaper formulations leave more edges uncovered, while enforcing feasibility in the mixer raises circuit depth by one to two orders of magnitude. Together, these results highlight the potential of quantum optimisation for PPI network alignment and the resource trade-offs that will shape its scalability as quantum hardware matures.

The purpose of this work is twofold. In the first part, we consider layered mixed matrices introduced by Murota, relate them to existing notions in combinatorial commutative algebra, and investigate the irreducibility of their determinants. Furthermore, for a layered mixed matrix in combinatorial canonical form, we determine the sparsity structure of its inverse. That is, we characterize which entries of the inverse are nonzero. In the second part, we establish for the first time a formal connection between these algebraic results and the theory of buffering structures for reaction networks developed by Mochizuki and Okada. We identify the lattice of buffering structures with the lattice of order ideals of the block poset of the combinatorial canonical form of the associated layered mixed matrix. This allows us to characterize the reducibility of the symbolic Jacobian determinant as a polynomial in the reaction-rate derivatives, as well as the nonzero sensitivity responses of species concentrations to reaction-rate perturbations.

Tree-child networks are a useful class of binary phylogenetic networks. The Pons–Batle identity (Pons and Batle, Scientific Reports, 2021) states that the number $a_{n,k}$ of tree-child networks with $k$ reticulations on $n$ taxa satisfies \[ a_{n,k}=(n-k+1)a_{n,k-1} +\frac{n(2n+k-3)}{n-k}a_{n-1,k}. \] In this paper, we present a short combinatorial proof of this identity.

We study the population dynamics of a predator-prey system with two types in each species. Within a species, predator or prey, dynamics are described by a neutral competitive Lotka-Volterra model, i.e., birth, death and competition parameters are equal for both types. Additionally, we assume that the intra- and inter-type competition parameters are equal. The predator-prey interaction is defined by a matching-types model where predators of type $i$ exclusively interact with prey of type $i$. The individual-based model is described by a birth-death process with immigration, where immigration reflects mutations between the types of the same species. We completely describe the deterministic dynamics arising as a large population limit of this birth-death process. We find that depending on the parameters, potential equilibria are the coexistence of all four types, coexistence of a non-matching or matching pair of predators and prey, or the extinction of the predator or prey species resulting in a line of two-type equilibria. When mutations are sufficiently rare, then the predator-prey dynamics are described by successive jumps between the different deterministic equilibria on this mutational time scale. These jumps describe eco-evolutionary cycles of repeated prey or predator invasions and declines. When coexistence of all the types is possible, we show that these cycles accumulate on this time scale. Lastly, to prove that after the accumulation point the system converges to the coexistence equilibrium, we consider a slightly modified model with unequal intra- and inter-type competition parameters. This modified setting allows us to conclude that after the accumulation point all four populations remain macroscopic and converge to the coexistence equilibrium.

Inferring cellular dynamics from unpaired single-cell snapshots requires modeling both state transitions and population growth or death. Unbalanced dynamic optimal transport (UDOT) addresses this by penalizing growth along transport paths, making the choice of growth penalty a key way to encode biological priors on proliferation and apoptosis. However, existing UDOT solvers either rely on computationally expensive NeuralODE simulations or depend on analytical solutions of conditional paths, restricting their efficiency solely to quadratic penalties, i.e. Wasserstein-Fisher-Rao (WFR) geodesics. To enable an efficient UDOT solver for general growth penalties, we first show that concave growth penalties lead to degenerate solutions where growth and transport are separated. We then introduce Simulation-free Unbalanced Dynamic Optimal transport (SUDO), a simulation-free framework for UDOT with general non-quadratic convex growth penalties. SUDO learns the conditional paths and transport costs, solves the induced semi-coupling problem, and subsequently leverages unbalanced flow matching to achieve a simulation-free solution. On WFR benchmarks, SUDO matches the accuracy of efficient, analytical solution-driven algorithms while outperforming simulation-based methods in computational speed. Beyond WFR, SUDO supports asymmetric penalties that encode proliferation-dominant priors and produce more plausible trajectories and growth estimates on synthetic and single-cell datasets.

Multi-omic studies increasingly require data to be examined from complementary biological perspectives, yet interactive exploration remains fragmented across modalities and tools. We present VizIt, an open-source framework for multi-view exploration of single-cell and spatial transcriptomic, epigenomic and genetic data. VizIt connects gene-, cell type-, condition-, spatial-, genomic region- and variant-centered views, enabling seamless navigation across biological perspectives. We demonstrate VizIt through the Parkinson's Cell Atlas, a customizable interactive multi-omic resource.

We introduce a fully stochastic, non-Markovian SIRS-type epidemic model that incorporates varying infectivity, waning immunity and a pulse vaccination strategy that may not confer permanent immunity. The model is constructed at the individual level, where each person is characterized by random infectivity and susceptibility functions, and vaccination campaigns occur at the jump times of a Poisson random measure with arbitrary intensity. We rigorously derive the epidemic dynamics as the large-population limit of an interacting stochastic particle system, leading to a system of nonlinear Volterra-type integral equations governing the average susceptibility and total force of infection. We establish a functional law of large numbers(FLLN) for the empirical processes and provide explicit expressions for the limiting compartmental proportions. The long-term behavior of the system is analyzed: we prove that the infection-free solution is globally asymptotically stable when the basic reproduction number falls below a critical threshold, and that the disease persists when this threshold is exceeded. The threshold is given by the harmonic mean of the maximal susceptibility across individuals and generalizes previous results by incorporating vaccination and memory effects. Our framework provides a probabilistically grounded extension of classical deterministic pulse vaccination models and offers new insights into the control of epidemics through scheduled immunization policies.

Chronic wasting disease (CWD) is a fatal prion disease affecting deer, elk, moose, reindeer, muntjac, and other cervids. Because free-ranging cervid populations face environmental variability and randomness, deterministic models may miss important dynamics like stochastic fade-out. We develop a stochastic Susceptible-Infectious-Environmental model using differential equations with reflection to ensure the susceptible class remains non-negative. We examine how environmental variability influences cervid populations as CWD pressure and control measures increase. For the deterministic model, we derive the basic reproduction number as the sum of direct and environmental contributions, showing the endemic phase arises at R0=1. For the stochastic system, we establish local well-posedness, positivity, and the disease-free law. The top Lyapunov exponent for invasion remains unaffected by reflection. We evaluate CWD mitigation using a deep reinforcement learning agent trained with Proximal Policy Optimization in a hybrid action space, comparing hunting, decontamination, and combined strategies. In the deterministic case, hunting alone can control the disease but reduces the population by about 58%, while decontamination requires sustained effort. The combined policy more than doubles the cervid population and nearly eliminates infection and contamination. In the stochastic case, the policy contains the disease in about 80% of runs, with 10% experiencing large outbreaks; effectiveness decreases as noise increases. Across all scenarios, the agent consistently emphasizes environmental decontamination, the key control method.

Breast cancer diagnosis commonly considers individual nuclear morphological characteristics, whereas their joint organization is less frequently evaluated. We developed the Morphological Network Disruption Index (MNDI), a patient-level measure of morphological abnormality relative to a benign reference state. Using the Wisconsin Diagnostic Breast Cancer dataset, ten nuclear characteristics were represented as network nodes, with MNDI summarizing disruption across 45 pairwise feature configurations. Performance was evaluated using repeated stratified five-fold cross-validation. Malignant lesions exhibited substantially higher MNDI than benign lesions (mean: 3.454 vs. 1.165; p = 2.94e-69). MNDI achieved an AUC of 0.941 (95% CI: 0.918-0.961), with 85.9% sensitivity and 91.6% specificity. A classifier using network-derived descriptors achieved an AUC of AUC of 0.928 +/- 0.024. Independent evaluation in the BreaKHis histopathology cohort showed limited discrimination (AUC = 0.538, 95% CI: 0.401-0.668), indicating dependence on the underlying morphological representation. MNDI provides an interpretable framework for quantifying patient-specific morphological disruption, while individual implementations require validation within compatible feature spaces.

Scientific and clinical decision-making depends on evidence from the primary literature, but existing standards for representing that evidence (FHIR Evidence, ECO, SEPIO, and the GA4GH Genomic Knowledge Standards) are oriented toward clinical-trial workflows, evidence codes, or single-variant assertions, and do not capture the fine-grained, domain-specific structure of claims in basic and pre-clinical research. We introduce a semantic model for scientific evidence with three core classes, specialize it for genetics, align it structurally to FHIR Evidence with a SEPIO-anchored credibility decomposition, and attach a compact dimensional vocabulary whose conditional-activation rules are validated by a SHACL schema for the implemented constraints. Using clinical variant interpretation as the driving use case, we evaluate the model through a human-AI annotation pilot over six genetics papers, yielding 28 evidence items and 95 source-anchored assertions, with a workflow that keeps curator-authored reference annotations distinct from AI-drafted annotations. Treating the pilot as a feasibility study rather than a benchmark, we argue that the model is a useful increment toward trustworthy, AI-ready infrastructure for variant interpretation: a reference data model and validation schema for representing genetic evidence.