Papers

Approximate solutions are found for Feller-like neutral multi-type branching diffusions $\big{(}\mathbf{X}(t)\big{)}_{t \in \mathbb{R}_{\ge 0}}$ in the limit of small mutation rates. The method employed involves solving approximations to the Laplace transformed forward Kolmogorov equation by integrating along characteristics. To leading order in the scale $\theta$ of the overall mutation rate the super-critical diffusion is found to collapse onto a line density aligned with the stationary left eigenvector of the rate matrix following a rapid change of behaviour at a critical time $t_{\rm c}$, which has a weak logarithmic dependence on $\theta$. First order in $\theta$ approximations to the density and moments of $\mathbf{X}(t)$ are also determined. The first-order approximation corresponds to allowing at most one mutation in the coalescent tree of a sample and is valid for $t < t_{\rm c}$ in the supercritical case, and more generally for the critical and sub-critical cases.

Groups of individuals can solve collective problems more accurately than any single member, by aggregating their opinions. Recent theoretical work has identified individual-level reward schemes that allow uninformed individuals to evolve collective intelligence from the bottom up, through social learning. Yet these results are restricted to linear prediction problems and simple averaging, while the decision tasks that real groups confront are often non-linear, and the institutions that aggregate opinions are seldom single-layer averages: districts elect representatives who in turn vote on policy, referees advise editors who decide on publication. Here we develop a framework for the evolution of collective intelligence in multi-layer voting populations, where individuals observe limited information and groups recursively aggregate their opinions by majority rule. We prove that single-layer voting cannot solve non-linear classification problems under any individual reward scheme. We then identify a "marginal feedback" payoff structure, which rewards individuals only when their opinion is pivotal in their group, and at every layer above them. This reward scheme induces a layered population to evolve accurate collective solutions to complex, non-linear decision tasks through individual-level peer imitation alone. The collective behavior that emerges is equivalent to a multi-layer perceptron in machine learning. Our results provide a naturalistic account of hierarchical institutions, in which the outsize importance of swing voters is the incentive that sustains collective accuracy; and they identify the credit-assignment rule in machine learning as not just an engineered solution but a natural evolutionary outcome.

Human health is a continuous, dynamic trajectory shaped by the cumulative interplay of biological processes, clinical events, behaviors and environmental exposures across the life course. Unifying the full breadth of lifelong health information, including longitudinal records, genetic variation, molecular profiles and environmental histories, is essential for whole-person modeling and remains a major challenge. We introduce LifeLong Digital Twin, a unified, event-driven modeling paradigm that organizes Life Events into daily Health States and accumulates them into Lifelong Health Context. An accompanying Agent Harness incorporates multimodal evidence beyond the language model's textual context. We evaluate four language models across 25 disease endpoints on three tasks: Disease Trajectory Forecasting, Disease Risk Ranking and Multi-horizon Disease Prediction. The approach yields marked gains over the reference condition: model-averaged F1 increases by 22.0% for disease identification in trajectory forecasting and 18.3% for five-year disease outcomes; thyroid-disease F1 reaches 0.669. The framework provides a foundation for whole-person digital twins and research on personalized lifelong disease prevention.

Multiple epidemic waves are often taken as evidence that simple compartmental models are structurally inadequate. Yet the key question is not whether a simple model can reproduce multiple peaks, but how much time-varying structure is minimally required to preserve observed epidemic-wave patterns and what can legitimately be inferred from such a representation. Using the susceptible-infectious-removed (SIR) model, we develop a framework for peak-preserving dynamic parsimony linking dynamical systems, inverse problems, statistical inference, and infectious-disease modeling. We establish exact multi-wave representability under time-varying transmission, characterize conditions for epidemic peaks and resurgence, and show the incidence-only non-identifiability of time-varying transmission and removal rates. Our main methodological contribution is minimal peak-preserving complexity (MPPC): the smallest dimension of a positive time-varying transmission function whose posterior-predictive trajectories preserve salient features, including peak count, timing, height, trough depth, and whole-curve agreement. We estimate MPPC using peak-aware approximate Bayesian computation and evaluate it through six reproducible stress tests, a Philippine COVID-19 reported-case proof of concept, and short-term future-knot projection. Across diverse data-generating mechanisms, low-dimensional time-varying SIR models can preserve aggregate epidemic-wave topology with modest dynamic complexity. However, accurate trajectory compression does not imply recovery of the underlying mechanism or reliable long-term counterfactual prediction. The framework therefore separates four often-conflated questions: representability, minimal dynamic complexity, mechanistic identifiability, and projection validity, providing a basis for parsimonious modeling of complex epidemic trajectories.

The Nine-Hole Peg Test (9-HPT) is a widely used clinical measure of manual dexterity in multiple sclerosis (MS), but its primary outcome, task completion time, provides limited information about the visuomotor mechanisms contributing to impaired performance. Instrumented approaches can provide richer kinematic information but often require modifications to the task or physical instrumentation that may alter natural hand-object interaction. We developed a multimodal computer-vision pipeline that enables synchronized analysis of gaze, hand kinematics, and object state during an unmodified 9-HPT. Gaze was recorded using Pupil Labs Invisible glasses, three-dimensional hand landmarks were reconstructed using WiLoR, and a custom YOLO26x-seg model detected and tracked the pegboard, holes, pegs, and collection bin. Eye-tracking, hand, and object data were temporally synchronized at the video-frame level and spatially registered to a common pegboard-centered coordinate system using frame-specific projective transformations. The pipeline further integrated hole-state transitions, hand-zone classification, and fingertip kinematics to identify PICK and PLACE events and segment hand transport and stationary phases, while fixation and saccade labels were derived from the eye-tracking system. Automated detections were visually reviewed and corrected when necessary. The resulting framework provides synchronized, event-resolved measures of gaze behavior, hand movement, object interaction, and eye-hand coordination while preserving standardized 9-HPT administration. This approach extends the 9-HPT beyond completion time and provides a reproducible platform for investigating the visuomotor mechanisms underlying dexterity impairment in MS and other neurological disorders.

Large-scale EEG foundation models have demonstrated promising transferability across neurological disorders, but often require millions of parameters and substantial computational resources. In this paper, we present the Universal Semantic EEG Foundation Model (USE-FM), a lightweight EEG foundation model that learns transferable neural representations through self-supervised signal reconstruction on the Temple University Hospital EEG Corpus (TUEG). After pretraining, the encoder is frozen and evaluated on two clinically distinct downstream tasks, abnormal EEG detection (TUAB) and epileptic seizure recognition (TUEP), using a unified frozen-transfer protocol against recent EEG foundation models, including LUNA-Base and CBraMod. With only 1.46 million parameters, approximately one-fifth the size of existing models, USE-FM achieves competitive overall performance, including strong sensitivity and F1-score on TUEP (SEN $75.00 \pm 14.14$, F1 $70.37 \pm 4.01$), while maintaining competitive performance on TUAB (AUC $85.24 \pm 5.61$). Beyond downstream classification, latent representation analysis using $k$-means clustering together with PCA and t-SNE demonstrates that USE-FM learns organized semantic EEG representations comparable to substantially larger foundation models. These results suggest that large-scale self-supervised pretraining enables lightweight architectures to learn transferable semantic EEG representations, providing a computationally efficient foundation for cross-disorder analysis and future clinical decision support in neurological disorders.

How the brain groups image elements into coherent objects in natural scenes remains unclear. Existing models for grouping in biological vision rely on simplified stimuli with explicit boundaries and cannot explain human behavior in naturalistic settings. We propose a mechanistic framework in which recurrent interactions propagate enhanced neuronal activity within and between cortical areas. The framework links computational principles, neural circuitry and perceptual psychology. Local boundary signals govern early grouping, whereas later stages integrate top-down feedback carrying information about object identity, grouping features across internal edges into coherent object representations. We instantiated this framework as a brain-inspired recurrent neural network trained to group features in natural images. The network learned to propagate enhanced activity across a cued object's representation, mirroring the brain's perceptual grouping mechanisms. The network's dynamics also predicted human reaction times. The framework links cortical dynamics to human vision and generates testable predictions for neuro-physiological and psychophysical experiments.

Identifying kinetic parameters and conserved quantities that support multistationarity and multistability remains challenging in chemical reaction network analysis. Structural theory provides existence and exclusion results, but does not always yield explicit, interpretable descriptions of the corresponding parameter regimes. We present a computational and machine-learning framework for discovering and characterizing parameter regimes with numerical evidence of multistationarity and multistability in mass-action systems. We refer to these numerically detected behaviors as approximate multistationarity and approximate multistability. The framework combines Latin hypercube sampling, adaptive sampling, and interpretable surrogate modeling. Logistic-regression and neural-network surrogates are trained separately on accumulated detection labels and independently guide later sampling toward regions with high scores for approximate multistationarity or multistability. Boundary refinement targets transitions between detected and undetected numerical classes. Buckingham–Pi groups are then used with CN2 rule induction to obtain interpretable empirical descriptions of detected regimes. Illustrative networks yield rules consistent with known multistationarity conditions, while the Schlögl model demonstrates adaptive enrichment of multistationarity detections. In the hybrid histidine kinase model and the sequential dual phosphorylation cycle, adaptive sampling substantially increased the number of parameter - total pairs with detected multistability relative to global sampling under equal sampling budgets. The framework complements analytical chemical reaction network theory by providing efficient, parameter-resolved discovery and characterization of multistationary and multistable regimes.

Despite milk being a global dietary staple, the molecular basis of its health-relevant bioactivity and the factors governing fine-scale compositional variation remain poorly understood. Here, we present an integrated seven-layer omics characterization of 60 US retail milk samples from ten geographic regions, combining genomics, transcriptomics, peptidomics, proteomics, lipidomics, metabolomics, and glycomics on the same samples. We also organized the identified and quantified compounds into the Dairy Molecule Database (DMD), a web-accessible resource for linking milk compound concentrations with SNPs, miRNAs, and product-level factors to support future milk quality optimization. In total, we identified 6,714 compounds and quantified 5,288 with absolute concentrations, including 5,220 compounds not previously available with absolute concentration estimates in existing milk compound databases. These profiles enabled bioactivity efficacy estimation and association analyses of factors linked to milk compound variation. We tested 54 computationally predicted antimicrobial candidate peptides; 35 showed activity and 6 had IC50 values below 256 {\mu}g/mL against A. baumannii, an ESKAPE pathogen. We further identified associations between downstream bioactive compound concentrations or estimated bioactivity efficacy and product-level factors, including purchase region, purchase ambient temperature, and packaging opacity, as well as SNPs, estimated Jersey breed proportion, and miRNA abundance. Overall, bioactivity efficacy profiles were associated with purchase region, selected SNPs, Jersey breed proportion, and selected miRNAs. These findings suggest that selective breeding and supply-chain optimization could help improve the bioactive quality of commercial milk.

Destructive single-cell measurements provide unpaired population snapshots rather than observations of the same cells across conditions. Local cell states and transition requests may also be insufficient to distinguish responses across source populations. We introduce TempoBridge, a common source-conditioned transport formulation for temporal, genetic, and chemical population transitions. Source cells initialize latent transport and provide a fixed empirical population summary. The velocity field receives this summary alongside the evolving cell state, flow time, and a structured transition descriptor. Minibatch optimal transport (OT) supplies couplings only for conditional flow-matching training paths; inference requires neither target expression nor OT computation. On held-out donors, TempoBridge achieves an Energy distance of 0.129 versus 0.144 for scGen. Genetic mean-expression $L_2$ error is 2.261 versus 3.156 for scGPT-scratch under Seen 2/2. On held-out compounds, condition-averaged drug-effect correlation is 0.598 versus 0.561 for the CellFlow adapter. Temporal ablations show higher mean distributional error after removing source context, replacing optimal transport with random pairing, or replacing flow matching with static residual regression. Together, these results demonstrate the predictive utility of a common source-conditioned transport formulation across held-out donors, gene combinations, and compounds.

Near-perfect classification of small clinical datasets can hinge on preprocessing, data leakage, missing-data handling, and the evaluation sample. We reproduced a published chronic kidney disease (CKD) classification study on the UCI CKD dataset (400 records, 24 predictors) under explicit leakage controls. A stratified 70:30 development-holdout partition was fixed before any learned preprocessing; imputation, encoding, scaling, supervised feature selection, and PCA were fitted only within training folds. Nine classifiers, three feature representations, and three missing-data strategies were compared by 5x3 repeated stratified cross-validation and ranked on training cross-validation only (ties reported); a frozen set of finalists was evaluated once on the holdout (discrimination, calibration, Brier score), treated as a locked historical internal sample. Ablation, grouped SHAP values, three further seeds, and post hoc sensitivity analyses examined robustness. The top-ranked selected-feature pipeline (KNN imputation, Extra Trees) reached a repeated cross-validation accuracy of 0.9869 and a holdout accuracy of 0.9833 (exact 95% interval 0.9411-0.9980). PCA (27 components, 95.96% of variance) gave only a marginal, seed-dependent advantage over interpretable original-feature representations, and several pipelines were statistically indistinguishable. Nested resampling of the selection procedure gave an outer accuracy of 0.9845, 0.0095 below the top-ranked pipeline on the same folds; missingness indicators alone yielded a ROC area of 0.85-0.88, and removing renal, urinary, and hematologic fields cut accuracy to 0.89. High internal performance persisted after leakage controls but appears driven largely by clinically proximal laboratory and urinalysis variables and CKD-associated missingness; it is not clinical validation, and external, prospective evaluation remains necessary.

Genomic language models can write synthetic DNA that carries no record of its origin. A generation-time watermark could provide a provenance signal, if a verifier can detect it using only the DNA sequence, a key, and published detector settings, without knowing where the generated region starts, which strand it lies on, or how it was divided into six-base tokens. We embed the SynthID tournament watermark in two genomic language models, Carbon and GENERator-v2. The verifier searches both strands, every start position, and four window lengths, and corrects its decision for the whole search. In a detection cohort of 1,544 held-out prompts, it found all 3,088 marked sequences per model, unedited and after one substituted, inserted, or deleted base. For ordinary sequences, the one-sided 95% upper confidence bound on the false-positive rate was at most 0.850%; one bound for the wrong-key control reached 1.015% (Carbon, after a deletion). In a development cohort, neither model showed a detectable change in likelihood or in predefined sequence measures. Under random edits placed without reference to the detector, detection stayed complete or nearly complete up to a 2% per-base edit rate. These results show statistical detection, not biological function, secret-key security, or robustness to an editor who sees the detector.

This paper develops a one-dimensional model for a mobile viral component propagating through a spatially distributed susceptible population. Random viral motion produces diffusion, whereas a response to the relative gradient of susceptible density generates directed transport. The existence of a positive entire traveling wave is proved when directed transport dominates diffusion, and the limiting case of equal transport and diffusion coefficients is constructed separately. A dimensionless transformation then converts the remaining equation into a logistic equation and supplies closed-form profiles. These formulas identify the unique viral maximum and the far-field behavior. A conservative implicit-explicit finite-difference method provides an independent numerical check. Diffusion is evaluated at the new time level, the gradient-driven flux explicitly at cell interfaces, and susceptible depletion pointwise. Exact traveling-wave values specify the initial data and time-dependent Dirichlet conditions at both endpoints. Thus, the computation tests preservation and translation of the analytical profiles. A calculation with eight hundred spatial subintervals reproduces the localized viral band and the monotone susceptible front. The largest uniform errors are approximately $1.70\cdot10^{-2}$ for viral density and $2.22\cdot10^{-3}$ for susceptible density. The numerical results corroborate the analytical construction and show that the conservative discretization captures the proposed propagation mechanism.

In computational neuroscience, task-trained recurrent neural networks (RNNs) are commonly used as a testbed for exploring the space of recurrent circuit solutions compatible with a particular function. However, these networks are subject to inductive biases that may be misaligned with those of biological circuits, which operate under various efficiency and robustness constraints. Here, using a minimal stimulus recall task, we systematically characterize how the solution space of recurrent neural networks is shaped by the desiderata of weight efficiency, activity efficiency, and robustness to noise. We show that weight efficient solutions exhibit a low-rank bias that aligns with the inductive biases of task-trained networks and favors dynamical motifs involving slow, persistent dynamics, whereas activity efficiency encourages high-rank solutions that rely on transient amplification. Moreover, we find that activity efficient solutions exhibit a strong dissociation between high-variance modes of activity and those that causally influence network output. Unlike in static feedforward settings, we demonstrate that noise robustness and activity efficiency are generally in opposition, rather than synergistic. Using these findings, we propose a normative account of misaligned coding phenomena recently identified in premotor cortex.

Neuroscience treats the brain as a control hierarchy, with cortical systems governing subcortical mechanisms. We argue that this mistakes a configuration for an architecture. Local asymmetries of influence are real, but control is relational and process-specific; because neural elements constrain one another across concurrent processes, relations can form cycles that resist a stable ranking. Evidence from learned action, cortico-cerebellar and thalamocortical loops, and defensive behavior shows that control changes with practice, task phase, urgency, viability demands, and affordances. Hierarchical order therefore characterizes time-bounded configurations, whereas heterarchy characterizes the architecture's repertoire across occasions. We propose a spectrum of control indexed by dynamical decoupling: how far behavior can depend on history, internal state, and anticipated consequences. The account yields experimentally testable predictions.

Genome-wide association studies (GWAS) have greatly advanced the discovery of genetic variants underlying complex traits and diseases. Yet in heterogeneous populations, existing GWAS strategies typically either pool all individuals under an assumption of population homogeneity or perform meta-analysis across predefined subgroups, both of which are limited when latent genetic heterogeneity attenuates subgroup-specific effects and masks true associations or subgroup labels are imprecise. Here we present UCALM, a unified unsupervised framework that infers genetically homogeneous subgroups directly from the data and integrates subgroup-specific GWAS with a novel layered meta-analysis method to capture both shared and subgroup-specific association signals. Through extensive simulations and analyses of large-scale human and livestock cohorts, including the UK Biobank ($n \approx 487{,}000$) and a heterogeneous pig cohort ($n \approx 85{,}000$), we demonstrate that UCALM substantially alleviated the mean genomic inflation across 24 UK Biobank traits to 1.17 compared with 1.43 for GLM and 1.37 for LDAK-KVIK, and further revealed 74 loci in the pig cohort that were previously obscured by conventional approaches. Our results establish a robust and broadly applicable strategy for association mapping in structured populations and improve the resolution of genetic signals across diverse species.

Multiple sclerosis (MS) can impair upper-extremity function through motor, sensory, cognitive, and visual deficits. Although the Nine-Hole Peg Test (9-HPT) is widely used to assess dexterity, completion time alone provides limited insight into the eye-hand coordination underlying performance. We characterized 9-HPT performance in nine people with MS (PwMS) and nine healthy controls using simultaneous eye tracking, markerless hand tracking, and object detection. Each peg cycle was divided into transport, manipulation and insertion, and return-to-bin phases. PwMS had longer overall completion times. Transport was prolonged with the non-dominant hand, manipulation was prolonged with the dominant hand, and return-to-bin duration was longer with both hands, representing the largest phase difference. PwMS also made approximately one additional fixation per peg and showed greater variability in gaze landing position during dominant-hand performance. Saccadic amplitude and mean placement error did not differ significantly between groups, and gaze generally preceded hand movement in both groups. These exploratory findings suggest that MS-related slowing is concentrated in phases requiring precise manipulation and transition to the next peg. Multimodal assessment of the 9-HPT can reveal coordination deficits not captured by completion time alone.

Most arousal-based brain-computer interfaces (BCIs) use EEG to decode cognitive state. But arousal is an autonomic process. We examined if peripheral physiological signals give a better decode of task-related arousal. We used a public dataset from a difficult boundary-avoidance flight task. In this task, participants received EEG-based BCI neurofeedback, sham feedback, or no feedback. We trained a multimodal deep learning decoder on heart rate, heart rate variability (HRV), respiration, electrodermal activity, and pupil diameter. We compared it with an EEG-only decoder and with the original filter-bank common spatial pattern (FBCSP) decoder. All analyses were offline. The peripheral decoder had a within-subject AUC of 93.0%. The EEG-only decoder had 85.2% and the FBCSP decoder had 79.8%. Only the peripheral decoder showed the Yerkes-Dodson inverted-U relation between decoded arousal and performance. The feedback conditions did not change the arousal trajectories. Thus, the BCI benefit possibly comes from regulation at critical moments in the task, not from a continuous shift. We calculated a time-varying optimal arousal trajectory from control trials. Per-trial deviations from this trajectory predicted performance (r = -0.28 to -0.24, p < 0.01). Baseline HRV and gamma power changed the arousal-performance curve of each subject. We used these values to divide subjects into arousal-sensitive and arousal-tolerant groups. Control bands specific to each group increased trial separation (Cohen's d from 1.21 to 1.32 and from 0.85 to 1.10). These results show that peripheral signals are better than EEG for continuous arousal decoding. They also give a specification for individualized closed-loop arousal regulation. A prospective study must test this specification, for example with personalized transcutaneous vagus nerve stimulation.

A mutant gene that appears in a finite population will, in the long run, either disappear from it or become fixed, so that all members of the population will carry a copy of the mutant gene. Determining the fixation probability of a mutant gene is thus a prerequisite for modeling evolutionary dynamics in finite populations. Within the diffusion theory framework, the mutant's competition with the wild-type genes is described by the closed-form solution of a one-dimensional backward Kolmogorov equation for the mutant fixation probability, derived by Motoo Kimura in 1962. However, in asexual populations the rate of adaptation and the relative importance of alternative evolutionary pathways are shaped by clonal interference - the competition between several lineages arising from distinct beneficial or deleterious mutations. Quantitative descriptions of clonal interference require computing fixation probabilities in populations where multiple alleles are present simultaneously - a formidable mathematical problem which amounts to solving a multi-dimensional backward Kolmogorov equation. Here, we employ fluctuation theorems (a set of exact equalities in non-equilibrium statistical mechanics) in order to re-derive Kimura's fixation probability formula. When extended to multi-allele systems, fluctuation theorems provide a constraint which must be satisfied by any valid set of fixation probabilities. Moreover, we present a recursive analytical solution of the multi-allele fixation probability problem. We use our formalism to study the fate of a novel beneficial mutation in a clonal interference scenario, discovering substantial deviations between our exact treatment and the mean-field approximation in which the target mutation competes with a single effective genotype. Our formalism can be used to replace both explicit simulations and approximate analytical results in models of asexual evolution.

Victor Lamme's Recurrent Processing Theory (RPT) proposes that the feedforward sweep (FFS) can extract and categorize visual features unconsciously, while conscious vision emerges through recurrent processing and feedback interactions across representational levels. The Motivated Emotional Mind (MEM) model, developed by Wiesław L. Galus and Janusz A. Starzyk, retains this core principle but embeds it in an embodied architecture integrating multilayer networks, semi-hierarchical semblions, receptors, effectors, allostasis, emotional valuation, and memory-based sensory reconstruction. This article examines the substantive but limited relationship between RPT and MEM. While RPT explains the role of recurrence in perceptual organization and the transition to conscious vision, MEM addresses the content of recurrent processing, its grounding in receptor activity and bodily states, its interaction with memory and action, and the possible role of reconstructed sensory representations in phenomenal experience. Particular emphasis is placed on secondary perception: the top-down reconstruction of sensory and interoceptive maps through which memories, mental imagery, dreams, hallucinations, feelings, and observed scenarios acquire experiential form. MEM thus associates phenomenality not merely with recurrent activity or reportability, but with the reconstruction of modality-specific, receptor-grounded sensory and bodily content. The article also presents the mathematical model of MEM, formalizing re-entrant processing, representational competition, allostasis, affect, curiosity, procedural gaps, and action selection. We conclude that MEM can be viewed as an embodied and motivational extension of RPT. However, its distinctive claims, particularly the sufficiency of secondary perception for phenomenality and the proposed microstructure of semblions, remain hypotheses requiring causal testing.

Non-monotonic steady state response curves can readily arise from an incoherent feedforward loop (IFFL), which has also been conjectured to be a necessary mechanism. In a previous work, we showed this conjecture to be false for systems where the control parameter directly influences only one state variable. Here, we extend this result to arbitrary systems. We show that a stable non-monotonic response requires either an IFFL or a combination of positive and negative feedback loops. Finally, we apply our theoretical findings to three network-structured biological contexts: signaling pathways, gene regulation, and ecological consumer-resource models. For the first two contexts, we identify necessary motifs for non-monotonic responses, while for consumer-resource models, we provide an alternative proof of the Competitive Exclusion Principle.

The Izhikevich model is a computationally efficient neuron model that can exhibit a wide range of firing patterns observed in the brain. However, it is a discontinuous dynamical system, which means the methods for applying weakly coupled oscillator theory developed for continuous dynamical systems cannot be applied. Therefore, the collective behaviour of coupled Izhikevich model has not been fully studied. To our knowledge, we carry out the first computation of the phase model for an Izhikevich neuronal model with chemical synapses. Using the phase model we study the existence and stability of phase-locking states and how these vary with parameters. Moreover, we find an interesting connection between the stability of anti-phase states of the phase model and the bifurcation behaviour of the uncoupled Izhikevich model itself. The accuracy of the prediction of the phase model is supported by simulations of two weakly coupled Izhikevich neurons.

Mathematical invariants provide complementary representations of molecular structure, but their predictive utility can vary across datasets and prediction tasks. For a new dataset, appropriate construction of invariant representations from algebraic topology, differential geometry, topological spectral theory, and commutative algebra is a challenging task, particularly when evaluating multiple representations is computationally expensive. We develop a Mathematical Agentic Model (MathAgent) to automatically optimize invariant representations in molecular property prediction. The framework combines dataset-aware representation design, low-cost candidate screening, and progressive evaluation. Language-model reasoning supports task interpretation, strategy proposal, and workflow coordination, while scientific computations and numerical decisions are carried out by deterministic tools. We evaluate MathAgent on protein–ligand binding-affinity and quantitative toxicity prediction tasks. Different datasets favor different combinations of mathematical invariants, demonstrating the need for dataset-adaptive representation selection rather than a fixed universal representation. Objective-conditioned executions further show that the framework can adjust its evaluation strategy according to user-specified goals. MathAgent therefore provides a systematic, evidence-driven, and traceable approach for optimizing mathematical invariant representations and reducing reliance on manual configuration and/or experimentation in molecular property prediction.

Motivated by a real-life problem, namely, inferring genomic regions affected by selection, we studied some properties of a two-step method that performs this task based on the FST. This approach exhibits computational simplicity as an appealing feature. Step one involves fitting a conjugate Bayesian model to find point estimates of FST and selecting the markers to be considered in step two, where they are grouped using such estimates. Subjective priors are frequently used in this problem and large hyperparameters may be encountered; hence, there is interest in addressing their impact. Preliminary analyses suggested that, the number of markers selected in step one tends to zero when the hyperparameters have the same value and tend to infinity, or are different but tend to infinity and their difference tends to zero. Thus, we studied how hyperparameters affect the posterior mean, variance, and predictive density of allele frequencies, and the posterior distribution of FST, formally. Moreover, an empirical approach based on simulated and real data was performed. Our main findings are summarized in two theorems that set the asymptotic behavior of the method, providing a foundation to understand the aforementioned phenomena. As to the empirical studies, the groups created in the second step, the estimated posterior means and the number of selected markers showed high sensitivity to hyperparameters. Albeit the mathematical intractability of the posterior distribution of FST, our results revealed asymptotic properties explaining two features of the method that lacked a formal elucidation.

Autoregressive transformers remain comparatively weak for protein sequence and structure generation. We study the role of target representation: amino acid tokens encode residue identities without explicit contextual semantics, while backbone coordinates require a discrete representation in our framework. We introduce two learned latent protein languages. Protein Latent Language (PLL) maps sequences to a 4,096-state contextual alphabet built on a frozen ESM-2 encoder, with one token per residue. Structure Latent Language (SLL) adapts GCP-VQVAE Lite with auxiliary sequence and confidence supervision while retaining decoding to backbone coordinates. We separately pretrain autoregressive transformer models on PLL and SLL tokens using next-token prediction, yielding PLLM and SLLM. Under matched downstream sequence training, PLLM has a fitted compute-scaling exponent of 0.038 versus 0.020 for the amino acid autoregressive model. In unconditional sequence generation, PLLM reduces the fraction of samples below a heuristic 1.5-bit residue-composition entropy threshold by 54% relative to the amino acid model across sampling temperatures. For sequence-to-structure prediction, replacing the original GCP-VQVAE Lite tokenizer with SLL reduces best validation perplexity by 34% under matched training. For long proteins, latent-token sampling is approximately 1,000 times faster than MSA-based AlphaFold2 in our measurements. In backbone generation, SLLM compares favorably with other generative models on diversity and novelty. We also observe early signs that using SLLM's internal token confidence for inference-time sampling can improve sequence-to-structure prediction quality beyond a single decoded sample. These results position learned latent protein languages as a promising substrate for autoregressive transformer scaling and inference-time sampling in protein generation.

Let $\cP_{\ell,k}$ be the set of rooted binary phylogenetic networks with $\ell$ labelled leaves, $k$ reticulations and no parallel edges. We write $|\cP_{\ell,k}|=W_k(\ell)+D_k(\ell)$, where the weighted count $W_k(\ell)$ adds the inverse orders of the leaf-fixing automorphism groups and the defect $D_k(\ell)$ collects the remainder. The weighted count satisfies, for every $k$, a recursion over the source layers of the tree-component structure that involves neither a list of component graphs nor any distinction between symmetric and asymmetric configurations, and its exponential generating function is a Laurent polynomial in $\sqrt{1-2x}$. Automorphism groups of networks are $2$-groups, elementary abelian for $k\le5$ but not in general. For $k\le5$ the defect is the weighted count of networks with a distinguished involution, which obeys an extension of the same recursion. An exact symbolic evaluation of the two recursions yields $|\cP_{\ell,k}|$ in closed form for $k\le5$, the case $k=5$ being new; it reproduces the published counts for $k\le4$ and corrects a coefficient in a published generating function for $k=3$. For every $k$, uniformly over explicit ranges of $k$, we prove that the non-tree-child networks are a fraction $2k(k-1)/\ell$ of the tree-child networks to leading order, which gives the third term of the asymptotic expansion of $|\cP_{\ell,k}|$. We also prove that reticulation-visible networks exceed tree-child networks by the fraction $k(k-1)/\ell$, and that a uniformly random network in $\cP_{\ell,k}$ has a nontrivial automorphism with probability $k(k-1)/(4\ell^3)$ to leading order.

A leading explanation for why humans cooperate with strangers is indirect reciprocity: when conduct is observed, individuals earn good reputations by cooperating with the deserving. Previous research has identified many "moral systems" that sustain cooperation through indirect reciprocity - each pairing a strategy for how to act with a norm for how to judge others - yet what makes them succeed, and whether that success generalizes beyond the donation game, has remained unclear. Here we evaluate all 1,048,576 moral systems whose norms condition on both players' reputations and actions, across every two-player social dilemma. We find that every highly stable, cooperative system pairs a "discriminating" strategy - one that cooperates with the good and defects against the bad when in good standing - with a "consistent" norm that deems good exactly those who act as the strategy prescribes. Such systems "practice what they preach" and preach what they practice. In the limit of small errors, only one strategy paired with a consistent norm remains stable across all social dilemmas: the "contrite discriminator", which cooperates to make amends when its standing is bad. Our results unify decades of research on indirect reciprocity, revealing moral consistency as the common ingredient of every stable, cooperative moral system.

Real-world outpatient oncology notes contain specialised terminology, tumour staging expressions, treatment names, toxicity descriptions, and institution-specific de-identification markers that may not be represented efficiently by general biomedical or adjacent clinical language models. We developed and evaluated oncology-specific BERT-style encoders using a governed UK outpatient oncology corpus comprising 290,026 notes from 21,564 patients treated for lung and head-and-neck cancer. We compared RadBERT and PathologyBERT with two local strategies: OncoNote-RadBERT, produced by continued masked language model pretraining, and OncoNoteBERT, trained from scratch with an oncology WordPiece tokenizer. Models were evaluated using masked language modelling loss and perplexity on the validation set, tokenizer fragmentation metrics, clinical term tokenisation, masked-token probes, and exploratory representation analysis. Both external encoders fit the oncology corpus poorly in zero-shot evaluation (perplexity 113.04 for RadBERT; 2035.03 for PathologyBERT), while continued pretraining produced the strongest fit (2.10 for OncoNote-RadBERT). OncoNoteBERT achieved perplexity 2.83 but produced the most efficient tokenisation, with lower subword fertility and shorter normalised sequence length. It also returned a clinically acceptable prediction for 12 of 13 masked-token probes, compared with 7 of 13 for OncoNote-RadBERT. This divergence between corpus-level fit and masked-token performance was partly attributable to tokenizer fragmentation rather than learned semantics alone. Both locally developed models represented the institutional placeholder as a single learnable token. These findings show that continued adaptation and bespoke tokenisation provide complementary benefits, and that representation-layer design matters before adjacent-domain encoders are applied to oncology NLP.

Similarity scores are often offered as evidence that a model shares structure with the brain or across languages. We ask what such a score reads when that structure is removed, or when the instrument measuring it does not work, in two settings. Across seventeen languages, a grammaticality probe transfers worse between more distant languages (r = -0.66). But the probe's own accuracy falls along the same axis and is at chance in four languages, four of the five most distant. Dropping them halves the explained variance, and because it also narrows the range of distances, the design cannot say how much of the gradient is the instrument. Counting the 272 language pairs as independent gives p = 0.0006 for a steering effect that is null when the seventeen languages are the unit (p = 0.155). In brain alignment, a training objective raises a language model's similarity to fMRI responses from 0.10 to 0.34 (reliability ceiling 0.54), yet targets with the brain correspondence destroyed still reach 0.31. A shuffled target scores about k/n against the real one, for rank k and n sentences, a baseline that can be computed before any model is trained. Both interventions work, yet we detect no distance-graded steering effect and no syntactic benefit from alignment. Before reading a correspondence score, measure how much of it survives without the correspondence.

Ribonucleic acid (RNA) functions through conformational changes that are not fully captured by static structures. However, large-scale standardized RNA dynamics data remain limited, and existing approaches typically treat trajectory generation and dynamics understanding as separate objectives. Here, we introduce RNADynBench, a standardized RNA molecular dynamics (MD) benchmark with 2585 quality-controlled 100-ns all-atom trajectories and leakage-controlled splits. Building on RNADynBench, we develop RNADynNet, a unified model for RNA dynamics learning that uses a shared backbone for both trajectory generation and dynamics fingerprint extraction from a single conformer. It combines coordinate denoising, single-frame-to-trajectory alignment, and physical grounding to connect all-atom trajectory generation with dynamics representation learning. Physical grounding improves both generated dynamics and the physical information recoverable from these fingerprints. Across both test sets, including the high-flexibility challenge set, the generated trajectories achieve RMSF correlations of 0.875 and 0.766, while single-conformer predictions show comparable agreement with MD-derived dynamics. RNADynBench and RNADynNet together establish a benchmark and unified modeling framework for generating and understanding RNA dynamics.