Objective: Algorithmic fairness is essential for equitable and trustworthy machine learning in healthcare. Most fairness tools emphasize single-axis demographic comparisons and may miss compounded disparities affecting intersectional populations. This study introduces Fairlogue, a toolkit designed to operationalize intersectional fairness assessment in observational and counterfactual contexts within clinical settings. Methods: Fairlogue is a Python-based toolkit composed of three components: 1) an observational framework extending demographic parity, equalized odds, and equal opportunity difference to intersectional populations; 2) a counterfactual framework evaluating fairness under treatment-based contexts; and 3) a generalized counterfactual framework assessing fairness under interventions on intersectional group membership. The toolkit was evaluated using electronic health record data from the All of Us Controlled Tier V8 dataset in a glaucoma surgery prediction task using logistic regression with race and gender as protected attributes. Results: Observational analysis identified substantial intersectional disparities despite moderate model performance (AUROC = 0.709; accuracy = 0.651). Intersectional evaluation revealed larger fairness gaps than single-axis analyses, including demographic parity differences of 0.20 and equalized odds true positive and false positive rate gaps of 0.33 and 0.15, respectively. Counterfactual analysis using permutation-based null distributions produced unfairness ("u-value") estimates near zero, suggesting observed disparities were consistent with chance after conditioning on covariates. Conclusion: Fairlogue provides a modular toolkit integrating observational and counterfactual methods for quantifying and evaluating intersectional bias in clinical machine learning workflows.

Balanced spiking networks can transition between silent, asynchronous-irregular, and oscillatory states depending on interacting synaptic and temporal time scales, while their joint parameter structure remains incompletely characterized. In this work, we systematically map how postsynaptic decay (τs), conduction delay (d), and plasticity rate (λp) jointly shape oscillatory regimes in recurrent leaky integrate-and-fire networks. By combining Brian2 simulations across the (τs, d, λp) space with a coarse Hopf-reference boundary, we construct regime maps that directly visualize SIL-AI-OSC transitions and corresponding spectral prominence landscapes. The mapped results show that increasing λp expands oscillatory regions toward shorter τs and moderate-to-long delays, while prominence maps identify parameter regions with the strongest rhythmic coherence. Representative control experiments further connect this global landscape to local rhythm-forming mechanisms, showing that STDP freezing weakens rhythmic coherence whereas delay jitter enhances it with minimal change in mean firing rate. As a result, these findings provide a useful reference for operating-point selection, synchrony modulation studies, and future biologically grounded spiking-network modeling within similar balanced-network settings.

A method that reconstructs protein residue networks using suitable node selection and edge recovery policies produced numerical observations that correlate strongly (Pearson's correlation coefficient < -0.83) with published folding rates for 52 two-state folders and 21 multi-state folders; correlations are also strong at the fold-family level. These results were obtained serendipitously with the ND model, which was introduced previously, but is here extended with policies that dictate actions according to feature states. This result points to the importance of both the starting search point and the prevailing condition (random seed) for the quick success of policy search by a simple hill-climber. The two conditions, suitable policies and random seed, which (evidenced by the strong correlation statistic) setup a conducive environment for modelling protein folding within ND, could be compared to appropriate physiological conditions required by proteins to fold naturally. Of interest is an examination of the sequence of restored edges for potential as plausible protein folding pathways. Towards this end, trajectory data is collected for analysis and further model evaluation and development.

Scalar variability -- the finding that representational noise scales proportionally with magnitude, producing a constant coefficient of variation -- is a hallmark of biological magnitude systems. We tested whether transformer language models exhibit this property by analysing the dispersion of hidden-state representations across carrier sentences for 26 numerical magnitudes in three 7-8B parameter models (Llama-3-8B-Instruct, Mistral-7B-Instruct-v0.3, Llama-3-8B-Base; data from Cacioli, 2026). We found the opposite: representational variability decreased with magnitude along the magnitude axis (scaling exponent alpha approx -0.19; 0/16 primary layers with alpha > 0, all three models). The negative sign was consistent in full-dimensional space (alpha approx -0.04) and after sentence-identity correction (alpha approx -0.007). The anti-scalar pattern was 3-5x stronger along the magnitude axis than orthogonal dimensions, and corpus frequency strongly predicted per-magnitude variability (rho = .84). These results demonstrate that distributional learning alone is insufficient to produce scalar variability: transformers reproduce log-compressive magnitude geometry but not the constant-CV noise signature observed in biological systems.

Multimodal deep learning models that fuse whole-slide histopathology images with genomic data have achieved strong discriminative performance for cancer survival prediction, as measured by the concordance index. Yet whether the survival probabilities derived from these models - either directly from native outputs or via standard post-hoc reconstruction - are calibrated remains largely unexamined. We conduct, to our knowledge, the first systematic fold-level 1-calibration audit of multimodal WSI-genomics survival architectures, evaluating native discrete-time survival outputs (Experiment A: 3 models on TCGA-BRCA) and Breslow-reconstructed survival curves from scalar risk scores (Experiment B: 11 architectures across 5 TCGA cancer types). In Experiment A, all three models fail 1-calibration on a majority of folds (12 of 15 fold-level tests reject after Benjamini-Hochberg correction). Across the full 290 fold-level tests, 166 reject the null of correct calibration at the median event time after Benjamini-Hochberg correction (FDR = 0.05). MCAT achieves C-index 0.817 on GBMLGG yet fails 1-calibration on all five folds. Gating-based fusion is associated with better calibration; bilinear and concatenation fusion are not. Post-hoc Platt scaling reduces miscalibration at the evaluated horizon (e.g., MCAT: 5/5 folds failing to 2/5) without affecting discrimination. The concordance index alone is insufficient for evaluating survival models intended for clinical use.

Foundation models for biology and physics optimize predictive accuracy, but their internal representations systematically fail to preserve the continuous geometry of the systems they model. We identify the root cause: the Geometric Alignment Tax, an intrinsic cost of forcing continuous manifolds through discrete categorical bottlenecks. Controlled ablations on synthetic dynamical systems demonstrate that replacing cross-entropy with a continuous head on an identical encoder reduces geometric distortion by up to 8.5x, while learned codebooks exhibit a non-monotonic double bind where finer quantization worsens geometry despite improving reconstruction. Under continuous objectives, three architectures differ by 1.3x; under discrete tokenization, they diverge by 3,000x. Evaluating 14 biological foundation models with rate-distortion theory and MINE, we identify three failure regimes: Local-Global Decoupling, Representational Compression, and Geometric Vacuity. A controlled experiment confirms that Evo 2's reverse-complement robustness on real DNA reflects conserved sequence composition, not learned symmetry. No model achieves simultaneously low distortion, high mutual information, and global coherence.

Continual learning in artificial neural networks is fundamentally limited by the stability--plasticity dilemma: systems that retain prior knowledge tend to resist acquiring new knowledge, and vice versa. Existing approaches, most notably elastic weight consolidation~(EWC), address this empirically without a physical account of why plasticity eventually collapses as tasks accumulate. Separately, the distinction between sudden insight and gradual skill acquisition through repetitive practice has lacked a unified theoretical description. Here, we show that both problems admit a common resolution within non-equilibrium statistical physics. We model the state of a learning system as a particle evolving under Langevin dynamics on a double-well energy landscape, with the noise amplitude governed by a time-dependent effective temperature $T(t)$. The probability density obeys a Fokker--Planck equation, and transitions between metastable states are governed by the Kramers escape rate $k = (ω_0ω_b/2π)\,e^{-ΔE/T}$. We make two contributions. First, we identify the EWC penalty term as an energy barrier whose height grows linearly with the number of accumulated tasks, yielding an exponential collapse of the transition rate predicted analytically and confirmed numerically. Second, we show that insight and repetitive learning correspond to two qualitatively distinct temperature protocols within the same Fokker--Planck equation: insight events produce transient spikes in $T(t)$ that drive rapid barrier crossing, whereas repetitive practice operates at a modestly elevated but fixed temperature, achieving transitions through sustained stochastic diffusion. These results establish a physically grounded framework for understanding plasticity and its failure in continual learning systems, and suggest principled design criteria for adaptive noise schedules in artificial intelligence.

We introduce a filtration-based framework for studying when and why adding taxa improves phylodynamic inference, by constructing a natural ordering of observed tips and applying sequential Bayesian analysis to the resulting filtration. We decompose the expected variance reduction on taxa addition into learning, mismatch, and covariance components, classify estimands into learning classes based on the pathwise behaviour of the mismatch, and show that for absorbing estimands an oracle who knows the latent absorption status obtains event-wise learning guarantees unavailable to the analyst. The gap between oracle and analyst is irreducible assumptions that are likely to hold for many real phylodynamic estimands, establishing a fundamental limit on what sequence data alone can reveal about the latent genealogy.

Effective representations of protein sequences are widely recognized as a cornerstone of machine learning-based protein design. Yet, protein bioengineering poses unique challenges for sequence representation, as experimental datasets typically feature few mutations, which are either sparsely distributed across the entire sequence or densely concentrated within localized regions. This limits the ability of sequence-level representations to extract functionally meaningful signals. In addition, comprehensive comparative studies remain scarce, despite their crucial role in clarifying which representations best encode relevant information and ultimately support superior predictive performance. In this study, we systematically evaluate multiple ProtBERT and ESM2 embedding variants as sequence representations, using the adeno-associated virus capsid as a case study and prototypical example of bioengineering, where functional optimization is targeted through highly localized sequence variation within an otherwise large protein. Our results reveal that, prior to fine-tuning, amino acid-level embeddings outperform sequence-level representations in supervised predictive tasks, whereas the latter tend to be more effective in unsupervised settings. However, optimal performance is only achieved when embeddings are fine-tuned with task-specific labels, with sequence-level representations providing the best performance. Moreover, our findings indicate that the extent of sequence variation required to produce notable shifts in sequence representations exceeds what is typically explored in bioengineering studies, showing the need for fine-tuning in datasets characterized by sparse or highly localized mutations.

Proteins underpin most biological function, and the ability to design them with tailored structures and properties is central to advances in biotechnology. Diffusion-based generative models have emerged as powerful tools for protein design, but steering them toward proteins with specified properties remains challenging. The Feynman-Kac (FK) framework provides a principled way to guide diffusion models using user-defined rewards. In this paper, we enable FK-based steering of RFdiffusion through the development of guiding potentials that leverage ProteinMPNN and structural relaxation to guide the diffusion process towards desired properties. We show that steering can be used to consistently improve predicted interface energetics and increase binder designability by $89.5\%$. Together, these results establish that diffusion-based protein design can be effectively steered toward arbitrary, non-differentiable objectives, providing a model-independent framework for controllable protein generation.

We develop a framework for non-Markovian, well-mixed SIR and SIS models beyond mean field, utilizing the continuous-time random walk formalism. Using a gamma distribution for the infection and recovery inter-event times as a test case, we derive asymptotical late-time master equations with effective memory kernels and obtain analytical predictions for the final outbreak size distribution in the SIR model, and quasistationary distribution and disease lifetime in the SIS model. We show that varying the width of the inter-event time distribution can greatly alter the outbreak size distribution or the disease lifetime. We also show that rescaled Markovian models may fail to capture fluctuations in the non-Markovian case. Overall, our analysis, confirmed against numerical simulations, paves the way for studying large deviations in structured populations on degree-heterogeneous networks

It is still challenging for computer vision to imitate human color perception, e.g., color constancy, which is a fundamental perceptual ability in humans to perceive, interpret and interact with their surroundings. Among others, the anchoring theory provides impressive insights for human lightness perception, yet the specific anchoring rules underlying color constancy have remained contentious for decades. In this work, we introduced a novel computational theory - gray-anchoring (GA) theory - to explain how the early stage of visual system contributes to color constancy and demonstrate how our GA rule applies to the chromatic domain by identifying gray surfaces within complex scenes. Furthermore, we also demonstrate the potential neural implementation of gray-anchoring by quantitatively analyzing the computational flows of concentric double-opponent (DO) cells in V1. The simulational results show that the concentric DO cells have the ability to identify gray surfaces within color-biased scenes and these gray surfaces can then be used by the higher-level cortices to easily estimate the illuminant. This finding offers not only a clear functional explanation of the concentric DO receptive fields of this cell type in the visual system but also an effective and efficient solution to computational color constancy for computer vision.

Connectome-constrained neural networks are often evaluated against sparse random controls and then interpreted as evidence that biological graph topology improves learning efficiency. We revisit that claim in a controlled flyvis-based study using a Drosophila connectome, a naive self-loop-matched random graph, and a degree-preserving rewired null. Under weak controls, in which both models were recovered from a connectome-trained checkpoint and the null matched only global graph counts, the connectome appeared substantially better in early loss, mean activity, and runtime. That picture changed under stricter controls. Training both graphs from a shared random initialization removed the early loss advantage, and replacing the naive null by a degree-preserving null removed the apparent activity advantage. A five-sample degree-preserving ensemble and a pre-training activity-scale diagnostic further strengthened this revised interpretation. We also report a descriptive mechanism analysis of the earlier weak-control comparison, but we treat it as behavioral characterization rather than proof of causal superiority. We show that previously reported topology advantages in connectome-constrained neural networks can arise from initialization and null-model confounds, and largely disappear under fair from-scratch initialization and degree-preserving controls.

Background music shapes attention, affect, and approach behavior in commercial environments, yet the neural plausibility of AI-generated music for such settings remains poorly characterized. We present an in-silico pilot study that combines Wubble, a generative music system, with TRIBE v2, a publicly released whole-brain encoding model, to estimate cortical response profiles for prompt-conditioned retail music. Five fully instrumental tracks were generated to span low-to-high arousal, sparse-to-dense arrangement, and neutral-to-positive valence prompts, then analyzed with audio-only TRIBE v2 inference on loudness-normalized waveforms. Analysis focused on fsaverage5 cortical predictions summarized over auditory, superior temporal, temporo-parietal, and inferior frontal HCP parcels. The fast bright major-pop condition produced the largest whole-cortex mean activation (0.0402), the strongest prefrontal ROI composite response (0.0704), and the highest parcel means in IFJa (0.1102), IFJp (0.0995), A5 (0.0188), and area 45 (0.0015). Pairwise spatial correlations ranged from 0.787 to 0.974, indicating that prompt variation modulated predicted cortical states rather than yielding a single undifferentiated response profile. Predicted cortical surface maps further revealed visually distinct spatial organization between low-arousal and high-arousal conditions. These results support a cautious claim of cortical neurological plausibility: prompt-conditioned AI music can systematically shift predicted auditory-temporal-prefrontal patterns relevant to salience and valuation. Although the study does not establish subcortical reward engagement or consumer behavior, it provides a reproducible framework for neural pre-screening and pre-optimization of commercial music generation against biologically informed cortical proxies.

Dementia affects over 55 million people worldwide, yet whether distinct domains of physical fitness independently protect against neurodegeneration through shared or divergent biological mechanisms remains unknown. Using the UK Biobank (n = 51,517; 12-year follow-up), we integrated epidemiological, proteomic, and neuroimaging analyses to systematically characterize the multidimensional fitness-dementia relationship. Higher handgrip strength, cardiorespiratory fitness, and pulmonary function were each independently associated with reduced dementia risk (HRs 0.50, 0.62, and 0.73, respectively, for highest vs. lowest tertiles), with stronger associations in women and younger individuals. Plasma proteomic profiling revealed domain-specific molecular signatures--neurofilament light chain predominating for muscular and cardiorespiratory fitness, and inflammatory mediators including GDF15 for pulmonary function--with 22-40 proteins per domain independently predicting dementia, converging on neuroinflammatory and neurovascular pathways. Brain MRI analyses identified hippocampal volume as a significant structural mediator (proportion mediated: 3.7-10.1%), indicating structural preservation as one of multiple mechanistic pathways. Population attributable fraction analyses estimated that suboptimal fitness may account for approximately 26% of dementia cases. These findings reveal that multidimensional physical fitness shapes dementia risk through distinct yet converging neuroinflammatory, neurovascular, and structural brain mechanisms, with implications for life-course prevention.

Generating molecular dynamics (MD) trajectories using deep generative models has attracted increasing attention, yet remains inherently challenging due to the limited availability of MD data and the complexities involved in modeling high-dimensional MD distributions. To overcome these challenges, we propose a novel framework that leverages structure pretraining for MD trajectory generation. Specifically, we first train a diffusion-based structure generation model on a large-scale conformer dataset, on top of which we introduce an interpolator module trained on MD trajectory data, designed to enforce temporal consistency among generated structures. Our approach effectively harnesses abundant structural data to mitigate the scarcity of MD trajectory data and effectively decomposes the intricate MD modeling task into two manageable subproblems: structural generation and temporal alignment. We comprehensively evaluate our method on the QM9 and DRUGS small-molecule datasets across unconditional generation, forward simulation, and interpolation tasks, and further extend our framework and analysis to tetrapeptide and protein monomer systems. Experimental results confirm that our approach excels in generating chemically realistic MD trajectories, as evidenced by remarkable improvements of accuracy in geometric, dynamical, and energetic measurements.

Stochastic chemical reaction networks (SRNs) in cellular systems are commonly modeled as continuous-time Markov chains (CTMCs) describing the dynamics of molecular copy numbers. The exact evaluation of transient copy number statistics is, however, often hindered by a non-closed hierarchy of moment equations. In this paper, we propose a method for computing theoretically guaranteed upper and lower bounds on transient moments based on the Kolmogorov's backward equation, which provides a dual representation of the CME, the governing equation for the probability distribution of the CTMC. This dual formulation avoids the moment closure problem by shifting the source of infinite dimensionality to the dependence on the initial state. We show that, this dual formulation, combined with the monotonicity of the CTMC generator, leads to a finite-dimensional linear time-invariant system that provides bounds on transient moments. The resulting system enables efficient evaluation of moment bounds across multiple initial conditions by simple inner-product operations without recomputing the bounding system. Further, for certain classes of SRNs, the bounding ODEs admit explicit construction from the reaction model, providing a systematic and constructive framework for computing provable bounds.

Moment dynamics in stochastic chemical kinetics often involve an infinite chain of coupled equations, where lower-order moments depend on higher-order ones, making them analytically intractable. Moment bounding via semidefinite programming provides guaranteed upper and lower bounds on stationary moments. However, this formulation suffers from the rapidly growing size of semidefinite constraints due to the combinatorial growth of moments with the number of molecular species. In this paper, we propose a sparsity-exploiting matrix decomposition method for semidefinite constraints in stationary moment bounding problems to reduce the computational cost of the resulting semidefinite programs. Specifically, we characterize the sparsity structure of moment equations, where each reaction involves only a subset of variables determined by its reactants, and exploit this structure to decompose the semidefinite constraints into smaller ones. We demonstrate that the resulting formulation reduces the computational cost of the optimization problem while providing practically useful bounds.

Spatial transcriptomics (ST) enables gene expression mapping within anatomical context but remains costly and low-throughput. Hematoxylin and eosin (H\&E) staining offers rich morphology yet lacks molecular resolution. We present \textbf{\ours} (\textbf{S}patial \textbf{T}ranscriptomics and hist\textbf{O}logy \textbf{R}epresentation \textbf{M}odel), a foundation model trained on 1.2 million spatially resolved transcriptomic profiles with matched histology across 18 organs. Using a hierarchical architecture integrating morphological features, gene expression, and spatial context, STORM bridges imaging and omics through robust molecular--morphological representations. STORM enhances spatial domain discovery, producing biologically coherent tissue maps, and outperforms existing methods in predicting spatial gene expression from H\&E images across 11 tumor types. The model is platform-agnostic, performing consistently across Visium, Xenium, Visium HD, and CosMx. Applied to 23 independent cohorts comprising 7,245 patients, STORM significantly improves immunotherapy response prediction and prognostication over established biomarkers, providing a scalable framework for spatially informed discovery and clinical precision medicine.

Repeated interactions are ubiquitous and known to promote social behaviour. While research often focuses on cooperation in the Prisoner's Dilemma, experimental evidence suggests repeated interactions also foster fairness. This study addresses a gap in the literature by theoretically modelling the evolution of fairness within a repeated mini-ultimatum game. Specifically, we construct a repeated-game framework where offerers and accepters interact using reactive strategies. We then investigate whether fair reactive strategy pairs are resilient against unfair mutants in a two-species population. By analyzing short-term evolutionary stability via the concept of two-species evolutionary stable strategy, we identify a critical effective game length: below this value, fairness is promoted by offerers and accepters who comply with their partner's past actions. Above this critical value, fairness is maintained by `complier' offerers and fair accepters. We also show that specific reactive strategies effectively facilitate the emergence and sustenance of fairness in long-term mutation-selection dynamics. To this end, we develop a two-population stochastic dynamics model -- a generalization of classical adaptive dynamics -- that accounts for finite population sizes and non-local mutants in the reactive strategy space.

Voltage-gated ion channels are essential for propagating signals in neurons. Each channel senses the local membrane potential created by nearby ions. Fluctuations in these ions introduce two fundamental noise sources: (i) shot noise, from the discreteness of ionic charge, and (ii) Johnson-Nyquist noise, from long-wavelength thermal fluctuations of the electric field. We show that, for an individual channel, shot noise dominates and sets an intrinsic limit to voltage sensing. On the $10$ $μ$s timescales relevant to channel gating, this limit corresponds to an accuracy of about $10$ mV -- close to measured channel sensitivities. When signals from many channels are aggregated, Johnson-Nyquist noise eventually overtakes shot noise and bounds the total information that can be sensed from the environment. This transition occurs at an ion channel density of $< 1$ channel/$μ$m$^2$ for slow signals and around $10^2-10^4$ channels/$μ$m$^2$ for signals with $10$ $μ$s timescales, both of which are within the range of experimentally-measured densities for somas and axon initial segments, respectively. These results provide design principles for single-channel architecture and collective sensing and suggest that neuronal computation is ultimately constrained by thermal fluctuations.

Creative thinking is a fundamental aspect of human cognition, and divergent thinking-the capacity to generate novel and varied ideas-is widely regarded as its core generative engine. Large language models (LLMs) have recently demonstrated impressive performance on divergent thinking tests and prior work has shown that models with higher task performance tend to be more aligned to human brain activity. However, existing brain-LLM alignment studies have focused on passive, non-creative tasks. Here, we explore brain alignment during creative thinking using fMRI data from 170 participants performing the Alternate Uses Task (AUT). We extract representations from LLMs varying in size (270M-72B) and measure alignment to brain responses via Representational Similarity Analysis (RSA), targeting the creativity-related default mode and frontoparietal networks. We find that brain-LLM alignment scales with model size (default mode network only) and idea originality (both networks), with effects strongest early in the creative process. We further show that post-training objectives shape alignment in functionally selective ways: a creativity-optimized \texttt{Llama-3.1-8B-Instruct} preserves alignment with high-creativity neural responses while reducing alignment with low-creativity ones; a human behavior fine-tuned model elevates alignment with both; and a reasoning-trained variant shows the opposite pattern, suggesting chain-of-thought training steers representations away from creative neural geometry toward analytical processing. These results demonstrate that post-training objectives selectively reshape LLM representations relative to the neural geometry of human creative thought.

The modeling of bio-molecular system across molecular scales remains a central challenge in scientific research. Large language models (LLMs) are increasingly applied to bio-molecular discovery, yet systematic evaluation across multi-scale biological problems and rigorous assessment of their tool-augmented capabilities remain limited. We reveal a systematic gap between LLM performance and mechanistic understanding through the proposed cross-scale bio-molecular benchmark: BioMol-LLM-Bench, a unified framework comprising 26 downstream tasks that covers 4 distinct difficulty levels, and computational tools are integrated for a more comprehensive evaluation. Evaluation on 13 representative models reveals 4 main findings: chain-of-thought data provides limited benefit and may even reduce performance on biological tasks; hybrid mamba-attention architectures are more effective for long bio-molecular sequences; supervised fine-tuning improves specialization at the cost of generalization; and current LLMs perform well on classification tasks but remain weak on challenging regression tasks. Together, these findings provide practical guidance for future LLM-based modeling of molecular systems.

We develop a unified spectral framework for finite ultrametric phylogenetic trees, grounding the analysis of phylogenetic structure in operator theory and stochastic dynamics in the finite setting. For a given finite ultrametric measure space $(X,d,m)$, we introduce the ultrametric Laplacian $L_X$ as the generator of a continuous time Markov chain with transition rate $q(x,y)=k(d(x,y))m(y)$. We establish its complete spectral theory, obtaining explicit closed-form eigenvalues and an eigenbasis supported on the clades of the tree. For phylogenetic applications, we associate to any ultrametric phylogenetic tree $\mathcal{T}$ a canonical operator $L_{\mathcal{T}}$, the ultrametric phylogenetic Laplacian, whose jump rates encode the temporal structure of evolutionary divergence. We show that the geometry and topology of the tree are explicitly encoded in the spectrum and eigenvectors of $L_{\mathcal{T}}$: eigenvalues aggregate branch lengths weighted by clade mass along ancestral paths, while eigenvectors are supported on the clades, with one eigenspace attached to each internal node. From this we derive three main contributions: a spectral reconstruction theorem with linear complexity $O(|X|)$; a rigorous geometric interpretation of the spectral gaps of $L_{\mathcal{T}}$ as detectors of distinct evolutionary modes, validated on an empirical primate phylogeny; an eigenmode decomposition of biological traits that resolves trait variance into contributions from individual splits of the phylogeny; and a closed-form centrality index for continuous-time Markov chains on ultrametric spaces, which we propose as a mathematically grounded measure of evolutionary distinctiveness. All results are exact and biologically interpretable, and are supported by numerical experiments on empirical primate data.

Under-ice blooms in the Arctic can develop rapidly under conditions where conventional early warning signals based on critical slowing down fail due to strong noise or limited observational records. We analyze noise-induced transitions in a temperature phytoplankton stochastic differential equation model exhibiting bistability between background and bloom states. The committor function defines a stochastic separatrix as its 1/2-isocommittor, and the normal width of the associated transition layer yields a geometric indicator via arc-length averaging. Under systematic variation of noise intensity, this indicator scales linearly with noise strength, while the logarithm of the mean first passage time follows the Freidlin-Wentzell asymptotic law. Eliminating the noise parameter produces an affine scaling between the logarithmic transition time and the inverse square of the geometric indicator. The relation is robust under variations in discretization, neighborhood definition, and diffusion structure, and holds in the weak noise regime where the transition-layer width scales linearly with noise strength. Unlike variance or lag-one autocorrelation, the geometric indicator remains well defined when rapid transitions preclude reliable time-series estimation. These results provide a geometrically interpretable precursor of bloom onset that may support model-based ecological monitoring in high-variability Arctic systems.

A critical visual computation is to construct global scene properties from activities of early visual cortical neurons which have small receptive fields. Such a computation is enabled by contextual influences, through which a neuron's response to visual inputs is influenced by contextual inputs outside its classical receptive fields. Accordingly, neurons can signal global properties including visual saliencies and figure-ground relationships. Many believe that intracortical axons conduct signals too slowly to bring the contextual information from receptive fields of other neurons. A popular opinion is that much of the contextual influences arise from feedback from higher visual areas whose neurons have larger receptive fields. This paper re-examines pre-existing data to reveal these unexpected findings: the conduction speed of V1 intracortical axons increases approximately linearly with the conduction distance, and is sufficiently high for conveying the contextual influences. Recognizing the importance of intracortical contribution to critical visual computations should enable fresh progress in answering long-standing questions.

Epiboly, during which a tissue closes around the surface of the egg, pervades animal development. This epithelial gap closure involves cell intercalations at the edge of the gap. Here, inspired by serosa closure in the beetle Tribolium, we study the interplay between these plastic cell rearrangements and the elasticity of the tissue in a minimal continuum model of the closure of a circular gap bounded by a contractile actomyosin cable. We discover two different closure mechanisms at the tissue scale depending on the energy barrier $E_\text{b}$ to and the energy $ΔE$ released by intercalation: If $E_\text{b}\ggΔE$, cells intercalate into the gap to close it. For a fluidised tissue in which $E_\text{b}\llΔE$, however, cells deintercalate from the boundary into the bulk of the tissue, and we reveal an emergent mechanical role of inhomogeneities of the actomyosin cable. Our work thus explains the mechanical role of tissue fluidisation in Tribolium serosa closure and processes of epiboly and wound healing more generally.

Across development, the morphology of fluid-filled lumina enclosed by epithelial tissues arises from an interplay of lumen pressure, mechanics of the cell cortex, and cell-cell adhesion. Here, we explore the mechanical basis for the control of this interplay using the shape space of MDCK cysts and the instability of their apical surfaces under tight junction perturbations [Mukenhirn et al., Dev. Cell 59, 2886 (2024)]. We discover that the cysts respond to these perturbations by significantly modulating their lateral and basal tensions, in addition to the known modulations of pressure and apical belt tension. We develop a mean-field three-dimensional vertex model of these cysts that reproduces the experimental shape instability quantitatively. This reveals that the observed increase of lateral contractility is a cellular response that counters the instability. Our work thus shows how regulation of the mechanics of all cell surfaces conspires to control lumen morphology.

Complex spatial structure, with partially isolated subpopulations, and environment heterogeneity, such as gradients in nutrients, oxygen, and drugs, both shape the evolution of natural populations. We investigate the impact of environment heterogeneity on mutant fixation in spatially structured populations with demes on the nodes of a graph. When migrations between demes are frequent, we find that environment heterogeneity can amplify natural selection and simultaneously accelerate mutant fixation and extinction, thereby fostering the quick fixation of beneficial mutants. We demonstrate this effect in the star graph, and more strongly in the line graph. We show that amplification requires mutants to have a stronger fitness advantage in demes with stronger migration outflow, and that this condition allows amplification in more general graphs. As a baseline, we consider circulation graphs, where migration inflow and outflow are equal in each deme. In this case, environment heterogeneity has no impact to first order, but increases the fixation probability of beneficial mutants to second order. Finally, when migrations between demes are rare, we show that environment heterogeneity can also foster amplification of selection, by allowing demes with sufficient mutant advantage to become refugia for mutants.

When substrate-constrained covariance flow on the Bures--Wasserstein manifold reaches the Williamson boundary, single-mode compression saturates and further admissible covariance evolution is forced into the cross-mode complement. This paper derives how that substrate boundary transition becomes experimentally visible in an embedded spin probe in the living human brain. We formulate a boundary-conditioned transfer theorem: when the substrate enters the deep boundary regime in a coupled mode, the boundary-selected cross-mode continuation of substrate covariance flow enters the reduced spin dynamics as a nonzero inter-spin correlation block. The spin probe does not inherit the substrate boundary as a state; it detects the boundary indirectly through the transferred cross-mode sector of the reduced dynamics. To leading order, this transfer is selective: it acts through an additive cross-diffusion channel while leaving conventional single-mode NMR observables such as \(T_1\), \(T_2\), linewidths, and the ordinary single-quantum response dominated by the thermal background. Projecting the induced spin cross-mode structure into the two-spin algebra, we argue that the experimentally relevant dominant recipient is the double-quantum SU(1,1) pair sector rather than the compact zero-quantum SU(2) exchange sector. We then derive the coherence-transfer pathway through which this double-quantum pair coherence is converted into a detectable signal by the \(45^\circ\)--gradient--\(45^\circ\) readout block.