The baboon (Papio) is an invaluable resource within nonhuman primate research, having the advantage of being a cercopithecoid (Old World monkey) with one of the largest brains among non-hominid primates. In order to facilitate comparative developmental neuroscience research, we present the BABACOOL (BAby Brain Atlas COnstruction for Optimized Labeled segmentation) approach for creating multi-modal developmental atlases, which we used to produce BaBa21, a population-based longitudinal developmental baboon template. BaBa21 is a spatio-temporal template that consists of structural (T1- and T2-weighted) images and tissue probability maps from a population of 21 baboons (Papio anubis) scanned at 4 timepoints beginning from about 2 weeks after birth and continuing to sexual maturity (5 years). Further, his study offers a fully automatic method for generating a template at any intermediate age for future age-specific group studies. This resource is made available to provide a normalization target for baboon data across the lifespan, including intermediate timepoints, and moreover facilitate neuroimaging research in baboons, comparative research with humans and nonhuman primate species for which developmental templates are available (e.g., macaques).

Genetic testing reports coding variants far faster than they can be interpreted, and placing a variant in its biophysical context, the domain it perturbs, whether its residue is buried or exposed, whether it lies near a disulfide bond or a predicted binding pocket increasingly requires projecting it onto a three dimensional protein model. The Genomics 2 Proteins (G2P) portal unifies the gene-to-structure identifier chain with a dense, residue indexed annotation table, but its visualization layer presumes a desktop browser and is awkward at the bedside, in the classroom, or in the field, where a phone or tablet is often the only device. We present G2P Explorer, a native iOS framework that consumes the public G2P REST API on device, parses its seventy one column tab separated feature tables without loss of fidelity, and presents the result through six interlinked modules sharing a single observable view model. Beyond porting, it contributes a SwiftUI Canvas multi-track sequence renderer, an on device reconstruction of the portal's unavailable isoform alignment route, a bidirectional Swift JavaScript structural bridge that absorbs the AlphaFold model file versioning scheme, and a fault tolerant ingestion layer that parses semi structured free text and distinguishes absent annotations from zero. Each searched protein is cached on device after the first fetch, so it reopens instantly and works offline, and the embedded structural view is drawn in a reduced form suited to a small screen. Across six proteins spanning 189-1{,}863 residues, the framework sustains interactive frame times (3.1-16.6\,ms) and modest memory (16-72\,MB). G2P Explorer is an open, reproducible mobile companion to the G2P portal for hypothesis generation, teaching, and on the go variant interpretation.

Background: Dynamic programming in biological sequence analysis computes probabilities or partition functions by summing over exponentially many latent paths, alignments, derivation trees, or RNA secondary structures. Their backward and outside quantities are used model-specifically, but the relation between differential sensitivities and exact finite sequence changes is rarely stated in a common framework. Methods: We represent hidden Markov models, affine-gap alignment ensembles, stochastic context-free grammars, and RNA secondary-structure ensembles as sum--product dynamic programs, defining backward and outside quantities as adjoints of forward or inside variables and sequence changes as finite replacements of sequence-dependent local factors. Results: Posterior item marginals are normalized inside--outside products, local-event posteriors additionally include the local factor and child inside terms, and expected feature counts are logarithmic derivatives of the partition function. For HMMs, ordinary SCFGs, and single-position substitutions in affine-gap alignment, the partition function is multi-affine in position-specific factor groups, so a one-site change is recovered exactly from first-derivative coefficients and multisite changes from mixed derivatives. In nearest-neighbor RNA models a substitution alters overlapping loop, stacking, and multiloop factors and boundary contexts, so exact mutation effects instead require context-dependent inside--outside recombination, as in the Rchange algorithm. Numerical experiments reproduce brute-force recomputation to machine precision. Conclusions: The framework identifies when derivatives give exact finite sequence effects and when broader recombination is required, providing a unified basis for posterior marginals, expected counts, parameter sensitivity, mutation analysis, and sequence design.

Dimensionality reduction has proven powerful for identifying neural manifolds, which are low-dimensional structures underlying high-dimensional neural activity. These low-dimensional representations have improved the interpretability of population-level coding. Yet whether such low-dimensional representations are biologically relevant and confer functional advantages in learning systems, or merely reflect neuron-level activity, remains contested in neuroscience. We show that an explicit information bottleneck forcing a recurrent neural network to learn a low-dimensional representation is necessary for rotational and out-of-distribution generalisation in a time-series prediction task. Using information-theoretic measures of causal emergence, we characterise the dynamics of this representation across the memorisation-to-generalisation transition, finding a non-monotonic trajectory which shows an initial decrease, a minimum, and a subsequent rise to a maximum, even as prediction loss falls monotonically. This trajectory scales with task complexity, and the magnitude of emergent structure reliably predicts generalisation performance. Analysis of CA1 hippocampal activity in mice learning an alternating maze task reveals analogous non-monotonic emergence dynamics that track behavioural performance. Together, these findings indicate that the ability of neural networks to learn compact, distributed and emergent representations confers a functional advantage for generalisation, supporting a causal role for learned representations in cognition.

We model human motor cortex during a wrist-extension BCI task as a port-Hamiltonian system (pHS): a conservative interconnection (gyroscopic coupling between neural phasors) plus a dissipative port (power-law energy decay driven by a GNN surrogate). A metriplectic integrator evolves the phasor state; a Fluctuation--Dissipation-consistent noise channel produces stochastic trajectories at body temperature. Training on \FitTrainN\ real EEG cycles (PhysioNet EEGMMIDB, 3 held-out subjects) reaches a test MSE of \FitTestMSE\ and passes three scale-free criticality rungs: near-critical branching ratio ($\sigma\approx1$), $1/f$ power-law spectrum, and long-range DFA correlations. The model generates closed-loop neuromodulation signals that restore phase-locking in silico when applied to de-synchronised inputs, suggesting a path toward structure-preserving BCI decoders.

Energy landscapes provide a common framework for describing learning, embryonic development, and collective dynamics. Although such landscapes may evolve over time, their dynamics are typically prescribed externally rather than generated by the system itself. Here we get inspiration from biology to introduce sandscapes : self-modifying landscapes in which the motions of interacting agents continuously reshape the landscape that governs their own trajectories. We derive sandscapes from a minimal model of interacting Hopfield units, where the basins of each attractor are modulated by their occupancies. Sandscapes spontaneously generate sequential symmetry breaking and differentiation trees, with local branching described by coupled Ising dynamics. We then drive the dynamics of sandscapes (using local proliferation common in biology) and leverage catastrophe theory to show that sandscapes self-organize toward flip bifurcations, suggesting a generic mechanism for the emergence of ubiquitous binary cell-fate decisions. We further demonstrate that sandscapes can act as generative models of developmental trajectories : starting from terminal states alone, we reconstruct realistic hematopoietic differentiation trees with multiple layers of intermediate progenitor states. More broadly, our results identify sandscapes as a general principle of adaptive dynamics, explaining how feedback between agents and landscapes produces branching, criticality, and self-organization across learning and biology.

Decoding brain activity is useful for characterizing brain processes and understanding the functional architecture underlying cognition. However, the inter-individual variability in brain response patterns limits the development of decoders that generalize across individuals. A solution to this challenge is functional alignment: aligning functional data across individuals before training population-level decoders. The core issue is to strike the balance between aligning functional features and preserving the anatomical structure, while maintaining computational efficiency. We introduce a new functional alignment method for fMRI, SpectralOT, that embeds cortical geometry into Laplace-Beltrami eigenmodes along functional data to regularize the alignment.

Tumor evolution is shaped by cell division, cell death, competition, and constraints imposed by the local microenvironment. Because these dynamics are usually not observed directly, phylogenetic trees inferred from somatic variation in sampled tumor cells can provide an indirect record of the population history that produced the sample. In this paper, we examine whether the distribution of inferred internal branching times exhibits signatures that depend on the underlying tumor growth regime. Specifically, we study the distribution of internal branching times in continuous-time birth-death models of tumor evolution. Exponentially growing populations exhibit a unimodal distribution of internal branching times, with the mode located near the root. In contrast, logistic growth, which models expansion constrained by carrying capacity, yields a substantially more intricate genealogical structure: the distribution of branching times undergoes a systematic transition as the time elapsed since tumor initiation increases. Specifically, this progression shifts from an expansion-dominated phase, through an intermediate early-recent bimodal phase, to a final recent-dominated phase. Extensive simulations of reconstructed tumor genealogies support these theoretical findings.

These are lecture notes for an advanced topics course in the master's programme at Bonn University. It aims to give a concise review of some of the work that has been done around the topic of adaptive dynamics from a rigorous stochastic point of view over the last 25 years and to make this area accessible to students with a good knowledge of probability in general, and the theory of Markov processes in particular. Our emphasis is on the issue of emerging scaling limits, where scaling parameters are time, population size, mutation rates, and mutation step size. These allow to exhibit within a fairly simple class of models a variety of biologically relevant phenomena. These notes are organised in three parts. Part 1 presents some historical background as well as the mathematical setting and main tools. Part 2 is the core of the notes and discusses the various scaling regimes and scaling limits. Part 3 looks at some extensions on the basic model, notably diploid models, phenotypic plasticity, and effects of environmental changes over time.

Depth of anesthesia is a complex but important vital state to analyze during a surgery or other procedure. One parameter to estimate this state is the bispectral index (BIS), a value ranging from 0 to 100 with a target of 40 to 60 for a stable state during surgery, which is based on the electroencephalogram (EEG). Despite its widespread clinical use, the BIS remains the subject of ongoing discussion as the exact algorithm underlying the BIS is not publicly disclosed, motivating the search for alternative EEG-based indices. In this publication, two entropy-based EEG measures, Permutation Entropy (PeEn) and Entropy of Difference (EoD) are investigated as potential alternatives to replace the BIS for anesthesia monitoring. Both measures quantify the complexity and irregularity of EEG signals and have previously been proposed as indicators of changes in consciousness and anesthetic depth. Their performance is evaluated by comparing with the simulated BIS values generated using the pharmacokinetic/pharmacodynamic (PK/PD) models, proposed by Marsh, Schnider and Eleveld. For each model, the root mean squared error (RMSE) between the simulated BIS and the recorded BIS, PeEn, or EoD is calculated, respectively. Statistical analysis using the Wilcoxon rank-sum test reveal no significant differences between the median RMSE values of the simulated BIS, PeEn, and EoD across the investigated PK/PD models. These results suggest that PeEn and EoD provide performance comparable to that of the simulated BIS, indicating that they may represent promising EEG-based indicators for monitoring depth of anesthesia.

Accurate diagnostic classification and disease-severity prediction for Alzheimer's disease are hampered by the incompleteness and heterogeneity of real-world clinical data. Left unaddressed, these barriers prevent reliable disease modelling and hinder effective clinical evaluation. Conventional imputation strategies introduce systematic bias, distort inter-feature relationships, and yield overconfident predictions, limitations especially consequential in diagnostic settings. Here, we propose NITROGEN, an imputation-free transformer that jointly models within-patient feature dependencies and between-patient relational structure through masked and intersample attention, enabling robust multimodal learning directly from partially observed records. We trained NITROGEN on ADNI (N=7858 scans), and evaluated it on two independent cohorts: OASIS-3 (N=2675 scans) and AIBL (N=1286 scans). Across cohorts and diagnostic and cognitive score prediction tasks, NITROGEN showed robust calibration and uncertainty quantification advantages over tree-based ensemble methods, while maintaining competitive discriminative performance. Cross-cohort and cross-method analyses identified cortical thickness in the temporal pole, age, and APOE genotype as important, though not individually sufficient, features for AD classification. We further introduced a modality-aware uncertainty adjustment that augments predictive uncertainty proportionally to the importance of absent modalities, enabling calibrated confidence when diagnostic information is unavailable. Together, our results show that imputation-free attention learning preserved meaningful discrimination under cohort shift, revealing expected degradation on more distributionally different cohorts, and demonstrate that evaluating models along calibration, interpretability, and cross-cohort reliability, not accuracy alone, is essential for clinical deployment.

DNA methylation can function as a toxic alkylation reaction exploited by chemotherapeutic agents to induce cancer cell death. However, finely tuned DNA methylation plays a fundamental role in cellular physiology, particularly in the epigenetic regulation of gene expression. Once thought to act solely as a repressor of gene transcription, its functional role has since been elucidated as genomic locus-specific and deeply connected with other epigenetic factors. Following the clinical approval of DNA methyltransferase inhibitors, such as Azacitidine and Decitabine, for the treatment of haematological malignancies, considerable efforts have been devoted to developing pharmacological tools that modulate epigenetic DNA methylation. However, the lack of gene selectivity in these agents limits their therapeutic efficacy and increases off-target toxicity. Moreover, the non-gene-selective nature of current DNA methylation-targeting molecules fails to meet the standards required to discern the nuanced roles of DNA methylation across diverse pathophysiological contexts and genomic loci, particularly in an era where next-generation sequencing and omics technologies enable hi ghresolution epigenetic analyses. In this review, we examine the mechanisms and roles of DNA methylation in epigenetic regulation, evaluate the current landscape of DNA methylation modulators, from traditional DNMT inhibitors to cutting-edge CRISPR-dCas9 fusion systems and protein-protein interaction disruptors, and discuss their clinical relevance. Finally, we emphasise the need for precise, locus-specific tools to advance both cancer research and therapeutic strategies.

Cancer progression is driven by the ability of cells with identical driver mutations to adopt biologically distinct adaptive phenotypes. Yet the population dynamics implied by intratumour phenotypic heterogeneity is poorly understood. Melanoma, a highly aggressive skin cancer, represents an excellent model to explore phenotype-switching, in part because phenotypic identity is conferred by melanocyte-associated transcription factor (MITF) activity. Here we develop and analyse a multiscale phenotype-structured PDE model for melanoma cell populations in the epidermis, progressing from subcellular MITF dynamics to well-mixed and radially resolved population models. Numerical solutions revealed that the model admits three distinct and stable long-term population behaviours: a slow-growing melanoma of proliferative cells and non-cycling, differentiated cells without invasive potential; a faster-propagating melanoma with an invasive core; and a rapidly growing melanoma with oscillatory core dynamics. More broadly, the analysis also highlights that phenotype reversibility by individual cells does not imply reversibility of phenotype distributions at the population scale. Hence, properties at the single-cell level (e.g., reversibility of invasive capacity) must be extrapolated with caution to populations with coupled cell dynamics. These findings further the understanding of melanoma population dynamics and cell plasticity more generally.

Intramolecular electron transport in biological systems is typically described as a diffusive hopping process, according to the semi-classical rate theories of Marcus and Hopfield combined with classical Pauli-type master equations. However, the possibility that non-trivial quantum mechanical effects could play a functional role in the transport dynamics in certain biomolecular processes has attracted increasing attention. Here, we extend the quantum mechanical model of open system dynamics by the Lindblad equation to a key biological component, the long chains of redox centers based on iron-sulfur clusters or heme groups that are widespread in many biological organisms, where they realize the cellular respiration. This approach allows to explore a wide range of physical parameters, showing key features of electron transport in these multi-domain protein structures. We pay particular attention to heat and entropy transfer between the electrons and the protein bath, which constitutes a benchmark of physical realism for the models. Electron currents, average transfer times and relative efficiency of the transport process are also explicitly characterized.

When is a material system a candidate for life at all? We argue that this question is prior to behavior, functional architecture, or computational capacity, and that at root it is one of physical admissibility. We develop a framework in which minimal autonomy, taken in the interactivist sense of normativity grounded in self-maintaining far-from-equilibrium organization, corresponds to a distinct non-equilibrium phase of matter, and we take complex plasmas, a physical and non-biological system, as its in-materio exemplar. We formalize a diagnostic phase-space whose criteria (sustained free-energy throughput, organizational closure, active information maintenance, and regulated noise sensitivity) constitute necessary conditions for life-attribution. We instantiate the diagnostics across contrasting systems and fix the boundaries of the phase space via Bénard convection as a driven baseline lacking closure, and a digital self-replicating soup that carries measured informational heredity while its physical closure remains a structural zero. We demonstrate that plasmas satisfy every admissibility condition for minimal physical autonomy while carrying none of the informational heredity that open-ended evolution requires, sharpening the distinction between physical admissibility and biological sufficiency, and bounding downstream questions of machine sentience.

Large-scale, multi-subject widefield calcium imaging provides unprecedented access to brain-wide cortical dynamics. However, the high dimensionality, complex spatiotemporal structure, and substantial task-irrelevant activity in widefield recordings have largely restricted modeling efforts to single-session analyses, limiting scalability and generalization. While multi-subject pretrained models have been explored for some neural modalities, multi-subject models for widefield calcium imaging have not yet been demonstrated; further, subject-invariant zero-shot behavior decoding remains elusive for multi-subject models across neural modalities more broadly. As a first step toward foundation modeling of widefield data, we introduce WiCAT, a multi-subject model that leverages self-supervised pretraining to both outperform single-session models and enable zero-shot behavior decoding on unseen subjects. WiCAT introduces an atlas-grounded tokenization scheme without session-specific components and learns globally shared spatiotemporal representations. Across multiple widefield datasets, the pretrained model supports lightweight downstream decoding, transfers across subjects, tasks, and datasets, and outperforms baseline models. Notably, the model also achieves robust zero-shot continuous behavior decoding and left-out brain region reconstruction on unseen subjects.

Automatically retrieving videos from large camera-trap datasets remains challenging. Text-to-Video retrieval (TVR) methods based on large video-language models (VLMs) have potential to retrieve events of interest by describing them with simple text queries. However, current methods often lack spatiotemporal understanding and do not generalize well to ecological data. In this work, we introduce Prompting-MammAlps, the first camera-trap TVR benchmark, and propose a fine-grained and interpretable TVR method. Specifically, we trained a vision transformer to perform spatiotemporal action localization, and convert its output to structured text, describing each video. Independently, ethology-inspired queries are processed by a Large-Language Model (LLM) based coding agent to parse the structured text per video and retrieve videos accordingly. We harnessed the LLM to use functions from a custom parsing library to minimize the risk of LLM hallucinations and to improve method interpretability. This retrieval approach applied on the Prompting-MammAlps benchmark achieved a set-based F1-score of 34\% on a test set of 135 ecologically-relevant queries and 775 candidate videos. In comparison the best zero-shot VLM achieved a F1-score of 18\%, while also lacking interpretability. Project page: this https URL

Macrocyclic peptides are an increasingly important therapeutic modality, but existing computational methods for modeling their structures and properties are limited in scope and do not generalize well across the synthetically accessible chemical space. In this work, we introduce Vilya-1, a deep learning model that addresses two central challenges in macrocycle design: sampling biologically relevant conformations across arbitrary chemistries and predicting key developability properties such as membrane permeability. Vilya-1 operates on a uniform all-atom representation and is trained on heterogeneous structural datasets spanning diverse topologies and chemical classes. Across a broad set of macrocycles composed of canonical and non-canonical residues, Vilya-1 substantially improves geometric accuracy relative to physics-based methods, co-folding networks, and deep-learning conformer generators, while maintaining broad chemical coverage that extends to small molecules. Vilya-1 also supports generative applications, enabling the design of novel macrocycles with tailored chemical, structural, and property profiles. Together, these capabilities establish Vilya-1 as a foundation model for accelerating the development of next-generation macrocycle therapeutics.

Brain-computer interfaces (BCIs) are a class of diverse hardware modalities, associated software, and connected devices which are widely used in a variety of fields, including neurosurgery, biomedical data analysis, and neuroimaging. Recent years have seen rapid advancements in BCI technology, and neurotechnology more broadly, with the first devices now passing clinical trials, early examples of consumer hardware entering the market, and many variants of consumer and medical hardware with increasingly extensive capabilities being developed rapidly. However, research and development in security for BCIs--known as neurosecurity--lags significantly behind the capabilities of BCIs themselves. In an effort to address as many vulnerabilities as feasible immediately, in this paper we review the current state of the art in neurosecurity, thoroughly survey the breadth and complexity of both firmly established and highly probable security threats to BCI systems, and provide recommendations of existing methods from cybersecurity, hardware security, and machine learning which can immediately be applied to address some of these gaps in neurosecurity.

Enzymatic catalysis can generate nonequilibrium fluctuations, but how these couple to tracer motion at larger length scales depends on physical context. Here, we investigate colloidal tracers in two configurations: passive particles dispersed in an enzymatically active solution, and enzyme-decorated particles where catalysis occurs directly at the tracer surface. We combine differential dynamic microscopy (DDM), which probes ensemble-averaged long-time diffusion, with optical tweezer (OT) measurements of short-time force fluctuations, and compare several complementary metrics for quantifying activity-induced enhancement. For 1 $\mu$m tracers, we observe activity-induced enhancements in both configurations, with the strongest effects for enzyme-decorated particles, which exhibit enhanced diffusion and increased non-thermal force fluctuations. For 200 nm tracers, enhancements are more subtle and method-dependent: DDM detects modest increases in diffusion for bare particles, while corresponding signatures are not resolved by the OT. These results demonstrate that enzymatic activity can be transduced from molecular to microscale motion and forces, but that the apparent magnitude and detectability of enhancement depend strongly on tracer size, localization of activity, the timescales probed by the measurement, and the metric used to quantify enhancement. More broadly, understanding how enzyme activity modifies transport and fluctuations across scales is important for interpreting nonequilibrium dynamics in active soft matter, intracellular transport, and chemically crowded biological environments.

Molecular property models are commonly evaluated by holding out Bemis--Murcko scaffolds, yet a scaffold identifier is only one notion of chemical unfamiliarity. We introduce a label-free structural-frontier split that reserves the sparsest and most physicochemically remote scaffold groups, and evaluate it on six public experimental or curated ADMET tasks. Against a 70/10/20 scaffold control with identical acyclic grouping, the frontier inflates equally weighted primary error with a taskwise median of 87.0\% and a skew-sensitive mean of 130.3\% (descriptive task/seed bootstrap interval, 52.1--246.0\%). The mean falls to 75.9\% once BBB is removed; that endpoint is the one whose score ranking inverts at the frontier. A message-passing graph-network control still shows a large gap (mean 82.8\% over four tasks) and does not invert, so a low-capacity head does not explain the effect. We also test Multi-View Frontier Risk Extrapolation (\method), a count-adjusted tail-risk penalty over four molecular views, and treat it as a falsifiable probe. It changes normalized frontier error by only 0.16\% relative to empirical risk minimization for the perceptron head (interval, $-0.43$--0.84\%) and by $-1.9$\% for the graph network; three fixed robust-penalty controls are likewise inconclusive. Against the published Lo-Hi and DataSAIL splitters the frontier inflates error more on average, though no split is uniformly hardest. An audit of 31,561 marine natural products further shows that OOD status and agreement with legacy ADMET predictions depend on the molecular view, endpoint and teacher coverage. Split construction and label provenance are important evaluation constraints in their own right, and the tested training penalties do not resolve the frontier failures we observe.

Soil harbors much of Earth's bacterial life. The activity of these bacteria governs plant growth, carbon and nitrogen cycling, and the response of land to a changing climate. Understanding this activity is difficult, however: soil is structurally and chemically heterogeneous and optically opaque, and its bacteria not only respond to their surroundings but continually reshape them, a two-way feedback that most idealized experiments and theories overlook. Here we review how this dynamic feedback governs the physics of bacterial motility, growth, and sensing in soil across three scales -- the single pore, the mesoscale of many pores, and the broader landscape.

This paper provides two results that are useful in the study of the existence and the stability properties of almost periodic solutions for a given dynamical system. The obtained results are generalizations of recent results for periodic systems and are applied to the global entrainment problem in nonlinear time-invariant control systems. It is shown that local exponential stability for the unforced system and input-to-state stability with respect to small inputs can guarantee global entrainment to small almost periodic inputs. In this way, global entrainment is shown in Lotka-Volterra systems with a Volterra-Lyapunov stable interaction matrix. All results can be extended to the uniformly recurrent case.

Machine learning interatomic potentials (MLPs) have revolutionized atomistic modeling, offering the potential to replace traditional methods like Density Functional Theory (DFT). However, inference time of MLPs is orders of magnitude slower than that of classical force fields, hindering real-world applications for biomolecular systems that require timescales of microseconds and beyond. Implicit solvent MLPs can address this issue, but are faced with data challenges associated with coarse-grained modeling. Consequently, previous approaches relied on empirical force field data, thereby inherently limiting the MLP's accuracy. Here, we introduce the Transferable Water Implicit Network (TWIN), an implicit water MLP parametrized entirely by an Equivariant Graph Neural Network and trained solely on ab initio and experimental labels. We demonstrate TWIN's transferability across drug-like molecules, peptides, and proteins, achieving excellent results on ab initio and experimental crystallographic and NMR benchmarks, consistently outperforming previous machine-learning-based implicit solvent or coarse-grained models. Furthermore, TWIN closely matches DFT-based explicit solvent MLPs while providing a two-order-of-magnitude faster timestep evaluation, paving the way for efficient ab initio-level modeling of biomolecular systems in aqueous environments.

A trained molecular property model can be refined at test time by correcting each prediction with the measured labels of the most similar training molecules, a retraining-free procedure we call neighbor fusion; evidential neural networks make it principled by using their aleatoric and epistemic uncertainty to parameterize a Bayesian update. Our main contribution, PG-EVIKAL, learns a property-distance metric to re-rank structurally similar neighbors by their property relevance before fusion, building on EVIKAL (scalar Kalman filter) and GP-EVIKAL (Gaussian process variant handling correlated neighbors). Evaluated on 16 molecular datasets, PG-EVIKAL reduces RMSE relative to the evidential model baseline on 14 of them, with a median reduction of 19.4%, and improves calibration; in sequential-assay scenarios it further incorporates newly measured molecules, refining predictions as they arrive without retraining. This work demonstrates that evidential uncertainty decomposition is not merely a calibration objective but an actionable inference resource that enables test-time refinement of molecular property predictions.

We are interested in the long-time behaviour of the ecological dynamics of two competing species in a spatially heterogeneous environment consisting of two habitat types. Our goal is to provide conditions for the persistence of the two populations. First, we consider a spatially continuous model, formalized as an infinite-dimensional system of integro-differential equations. We show that if each species would persist if it were alone, then mutual invasibility of each other's monospecific equilibrium is a sufficient condition for long time survival of both species. Second, we introduce a finite-dimensional system of ordinary differential equations which approximate the spatial dynamics by averaging over a finite number of habitat types. We derive an analogous sufficient condition for stable coexistence, and show that in this case, there exists a positive coexistence equilibrium. Finally, we complete our theoretical result using a simulation study. Our results indicate that mutual invasibility also is a necessary condition for stable coexistence in both models. In addition, we show that the finite-dimensional model underestimates species' persistance, which indicates that spatial heterogeneity promotes survival.

This paper addresses the optimal control of epidemic dynamics under conflicting socio-economic objectives. We propose an economic Model Predictive Control (MPC) framework, applied to an extended SEIR-V (Susceptible-Exposed-Infected-Recovered-Vaccinated) compartmental model to govern the spread of an infectious disease while minimizing economic disruption. The control problem is formulated as a constrained nonlinear optimization problem, in which the controller dynamically adjusts social interaction levels (transmission rate beta) and vaccination efforts to minimize a composite cost function that penalizes fatalities, healthcare capacity violations, and economic losses. We conduct a rigorous sensitivity analysis of the prediction horizon N, demonstrating that the closed loop is robust to the horizon choice and that N = 35 days minimizes the realized cost. Furthermore, both the closed-loop solution and an open-loop turnpike analysis across diverse initial conditions reveal that the celebrated "Hammer and Dance" mitigation strategy emerges naturally as the mathematical optimum: the optimal trajectories anchor to a unique suppression turnpike (maximum lockdown) to drive hospitalizations toward the disease-free equilibrium before progressively reopening the economy. Through a turnpike-based argument we establish practical asymptotic stability of the optimal operating point, providing a mathematically grounded decision-support tool for pandemic policy.

Phylogenetic networks are used to represent the evolutionary history of species. Due to biological interpretations and computational advantages, researchers have focused on restricted classes of phylogenetic networks, such as tree-child, orchard, and tree-based. These classes capture different notions of tree-likeness: tree-child networks require every internal vertex to have a taxon reachable by a tree path, orchard networks are trees with horizontal arcs (for modelling histories rife with horizontal gene transfers), and tree-based networks are trees with additional (not-necessarily horizontal) arcs. A natural question to ask is ``how far is a given network from belonging to a particular class?'' This motivates the study of proximity measures, which measure the minimum number of graph modifications required to transform a network into one belonging to a particular class. In this paper, we consider three proximity measures based on leaf addition, valid arc deletion, and arc deletion. We study pairwise comparability of the proximity measures, prove complexity results, and derive extremal bounds for the classes of tree, tree-child, orchard, and tree-based networks.

This article defines a partial order structure to study the relationship between levels and contents of conscious subjective experience in a single mathematical set-up. We understand phenomenal structure as extrapolated relationships among experiences, instead of fixed properties of specific experiences. Our mathematical account is based on multilayer network theory. Multilayer theory is a generalization of graph and network theory, widely used in several scientific domains. This structure is also the underlying conceptual and mathematical structure of most current models of conscious experience. From our simple set of assumptions, yet rigorous analysis, we conclude that assuming the comparison and quantification among phenomenal experiences yield only partial comparison, rather than commonly assumed absolute comparability. This has implications for evolutionary and animal consciousness: evolution may encompass diverse modes of experiencing, not necessarily implying larger ones on an absolute scale. Our characterization elucidates structural constraints on experiential comparisons imposed by assumptions and choices made by modellers as active participants in the scientific process. In summary, in light of our phenomenological intuitions, it might be right that some experiences carry qualitative aspects that make them incompatible or non-comparable with other experiences, quantitatively speaking. Some experiences are comparable (e.g. at some experiential levels), but others are not. These results have direct implications for consciousness science, evolution and animal consciousness.

We present a computational model of the mechanisms that may determine infant behavior in the "mobile paradigm". This paradigm has been used in developmental psychology to explore how infants learn the sensory effects of their actions. In this paradigm, a mobile (an articulated and movable object hanging above an infant's crib) is connected to one of the infant's limbs, prompting the infant to preferentially move that "connected" limb. This ability to detect a "sensorimotor contingency" is considered to be a foundational cognitive ability in development. To understand how infants learn sensorimotor contingencies, we built a model that attempts to replicate infant behavior. Our model incorporates a neural network, action-outcome prediction, exploration, motor noise, preferred activity level, and biologically inspired motor control. We find that simulations with our model replicate the classic findings in the literature showing preferential movement of the connected limb. An interesting observation is that the model sometimes exhibits a burst of movement after the mobile is disconnected, shedding light on a similar occasional finding in infants. In addition to these general findings, the simulations also replicate data from two recent more detailed studies using a connection with the mobile that was either gradual or all-or-none. A series of ablation studies further shows that the inclusion of mechanisms of action-outcome prediction, exploration, motor noise, and biologically inspired motor control was essential for the model to correctly replicate infant behavior. This suggests that these components are also involved in infant sensorimotor learning.

How does the information flow between different brain regions during various stimuli? This is the question we aim to address by studying complex cognitive paradigms in terms of Information Theory. To assess creativity and the emergence of patterns from a Shannon perspective, we applied a range of tools, including Entropy Density, Effective Measure Complexity, and the Lempel-Ziv distance. These entropic tools enable the detection of both linear and non-linear dynamics without relying on pre-established parameters, models, or prior assumptions about the data. To identify connections between different brain regions, we analyse task-based fMRI data from subjects during motor, working memory, emotion recognition, and language stimuli to gain insight into these complex cognitive processes. Since this method does not rely on prior knowledge, it is particularly well-suited for exploratory research, facilitating the discovery of previously unidentified connections or patterns in the brain. The capacity to identify non-linear dynamics is especially important for studying brain connectivity, as the brain exhibits significant non-linear interactions across multiple functional levels.

Although computational phenotyping is a central informatics activity with resulting cohorts supporting a wide variety of applications, it is time-intensive because of manual data review. We previously assessed the ability of LLMs to perform computational phenotyping tasks using computable phenotypes for ARF respiratory support therapies. They successfully performed concept classification and classification of single-therapy phenotypes but underperformed on multi-therapy phenotypes. To better understand issues with these complex tasks, we expanded PHEONA, a generalizable framework for evaluation of LLMs, to include methods specifically for evaluating faulty reasoning. We assessed the responses of two lightweight non-reasoning LLMs (Mistral Small 24 billion and Phi-4 14 billion) and one lightweight reasoning LLM (Qwen-distilled DeepSeek-r1 32 billion) both with and without prompt modifications to identify explanation correctness errors and unfaithfulness errors during phenotyping. For experiments without prompt modifications, both errors were present across all models. For experiments with prompt modifications, we observed that adding specific few-shot examples aligned with an incorrect phenotype almost always reduced accuracy when compared to the unbiased prompt. Since reasoning errors were ubiquitous across models, our enhancement of PHEONA to include a component for assessing faulty reasoning provides a practical framework for evaluating LLM reasoning and empirical evidence that reasoning errors occur during complex computational phenotyping. While insights from reasoning errors can help prompt refinement, a deeper understanding of why LLM reasoning errors occur will likely require further development and refinement of interpretability methods.

The encounter of artificial intelligence with consciousness research is often framed as a challenge: could this science determine whether such systems are conscious? We suggest it is equally an opportunity to expand and test the scope of existing theories of consciousness. Current approaches remain polarized. Computational functionalism emphasizes abstract organization, often realized through neural correlates of consciousness, while biological naturalism insists that consciousness is tied to living embodiment. Both positions risk anthropocentrism and limit the possibility of recognizing non-biological forms of subjectivity. To move beyond this impasse, we propose a dual-resolution framework that defines the ontological and epistemic conditions for consciousness. This approach combines the Information Theory of Individuality, which defines the ontological conditions of informational autonomy and self-maintenance, with the Moment-to-Moment theory, which specifies the epistemic conditions of temporal updating and phenomenological unfolding. This integration reframes consciousness as the epistemic expression of individuated systems in substrate-independent informational terms, offering a generalizable theory of consciousness and positioning AI as a promising testbed for its emergence.

Games have long been a microcosm for studying planning and reasoning in both natural and artificial intelligence (AI), often focusing on expert-level or even super-human play. But real life also pushes human intelligence along a different frontier, requiring people to flexibly navigate decision-making problems that they have never thought about before. Here, we use novice gameplay to study how people reason about new problem settings. Through a series of large-scale behavioral studies with over 1000 participants and 121 two-player strategic board games (almost all novel to our participants), we show that people are systematic and adaptively rational in how they play a game for the first time, or evaluate a game (e.g., how fair or how fun it is likely to be) before they have played it even once. We explain these capacities via a computational cognitive model that we call the 'Intuitive Gamer', a model based on mechanisms of fast and flat (depth-limited) goal-directed probabilistic simulation. Our work offers new insights into how people rapidly evaluate, act, and make suggestions when encountering novel problems, and could inform the design of more flexible and human-like AI systems that can determine not just how to solve new tasks, but whether a task is worth thinking about at all.

Viruses are microscopic infectious agents that require a host cell for replication. Viral replication occurs in several stages, and the completion time for each stage varies due to differences in the cellular environment. Thus, the time to complete each stage in viral replication is a random variable. However, no analytic expression exists for the viral population at the cellular level when the completion time for each process constituting viral replication is a random variable. This paper presents a simplified model of viral replication, treating each stage as a renewal process with independently and identically distributed completion times. Using the proposed model, we derive an analytical formula for viral populations at the cellular level, based on viewing viral replication as a birth-death process. The mean viral count is expressed via probability density functions representing the completion time for each step in the replication process. This work validates the results with stochastic simulations. This study provides a new quantitative framework for understanding viral infection dynamics.

Computer simulations of complex population genetic models are an essential tool for making sense of the large-scale datasets of multiple genome sequences from a single species that are becoming increasingly available. A widely used approach for reducing computing time is to simulate populations that are much smaller than the natural populations that they are intended to represent, by using parameters such as selection coefficients and mutation rates whose products with the population size correspond to those of the natural populations. This approach has come to be known as rescaling, and is justified by the theory of the genetics of finite populations. Recently, however, there have been criticisms of this practice, which have brought to light situations in which it can lead to erroneous conclusions. This paper reviews the theoretical basis for rescaling, and relates it to current practice in population genetics simulations. It shows that some population genetic statistics are scaleable while others are not. Additionally, it shows that there are likely to be problems with rescaling when simulating large chromosomal regions, due to the non-linear relation between the physical distance between a pair of separate nucleotide sites and the frequency of recombination between them. Other difficulties with rescaling can arise in connection with simulations of selection on complex traits, and with populations that reproduce partly by self-fertilization or asexual reproduction. A number of recommendations are made for good practice in relation to rescaling.

Motivation: Opioid use disorder (OUD) often arises after prescription opioid exposure and follows transitions among onset, remission, and relapse. Linked EHR-survey resources such as the All of Us Research Program enable stage-specific risk modeling and connection to intervention options. Results: We built a multi-stage framework to model time-to-onset, time-to-remission, and time-to-relapse after remission using All of Us EHR and survey data. For each participant we derived longitudinal predictors from clinical conditions and survey concepts, including recent (1/3/12-month) event counts, cumulative exposures, and time since last event. We fit regularized Cox models for each transition and aggregated selection frequencies and hazard ratios to identify a compact set of high-confidence predictors. Pain, mental health, and polysubstance use contributed across stages: chronic pain syndromes, tobacco/nicotine dependence, anxiety and depressive disorders, and cannabis dependence prominently predicted onset and relapse, whereas tobacco dependence during remission and other remission-coded conditions were strongly associated with transition to remission. To support therapeutic prioritization, we constructed a therapy knowledge graph integrating genetic targets, biological pathways, and published evidence to map identified risk factors to candidate treatments in recent OUD studies and clinical guidelines.

The brain achieves stability and plasticity in a topologically complex, shifting world through Metric-Topology Factorization (MTF), separating discrete topological indexing for context selection from continuous metric condensation for local inference. Semantically rich environments defy single globally contractive geometries, causing obstructions under shifts, so intelligence factorizes these: the hippocampus provides sparse signatures indexing manifold identity, while the neocortex untangles geometry hierarchically. In the ventral stream, a dynamic-programming-like process quotients symmetries (e.g., translation, scale), transforming non-convex sensory mazes into separable bowls. Offline replay and consolidation amortize transformations for rapid task switching. Dreaming in REM involves stochastic hippocampal traversal to expose and regularize latent structures. Consciousness arises from resolving topological uncertainty into stable embeddings, with awareness for unamortized states. Evolutionarily, transitions like sensorimotor control to language expand topological complexity, demanding advanced indexing-metric separation. Intelligence emerges via recalibrating context-specific geometries, converting global navigation into local dynamics, not deeper search.

Working memory -- the ability to store and recall precise temporal patterns of neural activity -- remains an open challenge for spiking neural networks (SNNs). We propose a recurrent SNN of $N$ neurons in which each synapse is equipped with $D = 41$ delays, modelled as a weight tensor $\mathbf{W} \in \mathbb{R}^{N \times N \times D}$ and trained end-to-end with surrogate-gradient backpropagation through time. The network stores $M$ arbitrary target spike patterns by representing each as a sequential chain of overlapping Spiking Motifs: contiguous windows of length $D$ that uniquely predict spikes at the next time step. On a synthetic benchmark of $M=16$ patterns ($N=512$ neurons, $T=1000$ steps), training achieves a mean F1 score of $1.0$, with recall emerging first near the clamped initialisation window and propagating forward in time. This result demonstrates that heterogeneous delays provide an efficient substrate for working memory in SNNs, enabling energy-efficient neuromorphic edge deployment.

Identity by descent (IBD) tracts and runs of homozygosity (ROH) represent the theoretical and observable sides of chromosomal autozygosity. However, the formal relationship between their length distributions has yet to be established. A coalescent framework is developed here that unifies both concepts within a single analytical formalism, with applications to inferring effective population size (Ne) and detecting selection signatures. Closed-form probability density functions are derived for IBD tract lengths and extended to the observable ROH length distribution by explicitly modelling the displacement of autozygosity boundaries from true recombination breakpoints to the nearest heterozygous flanking marker sites. Mutation, gene conversion, finite marker density, and marker heterozygosity are incorporated as parameters linking IBD tracts to ROH. Background selection introduces a systematic upward bias in apparent tract lengths that requires a generation-dependent Ne that cannot be captured by a single constant value. Selective sweeps produce an asymmetric distortion of the length distribution around a neutral focal site. The sign of this asymmetry indicates the side of the focal site on which the selected locus resides. This directional signal is transient, dissipating quickly after the sweep. In contrast, the signature given by the local Ne reduction persists considerably longer, making the two signatures complementary to determine the age of the sweep. Computational tools are provided to predict tract length distributions under background selection and complete or partial selective sweeps. The application of the theory is illustrated by detecting and localising the selective sweep associated with lactase persistence in European human populations.

The origin of life is often framed primarily as a chemical problem, yet life s defining feature is evolution. Advances in geochemistry, prebiotic chemistry and molecular biology have suggested diverse scenarios for the emergence of genomes, metabolism and cellular compartments on the early Earth, but most of these models ignore the relevance of a population genetics perspective. Here, we argue that origin of life research must expand from asking simply how life began to exploring how it evolved from pre biological systems. Synthesizing evidence from comparative genomics, phylogenetics, biochemistry, and geoscience, we emphasize that the last universal common ancestor (LUCA) was already a complex, ecologically adapted population of cells far removed from the starting point of life, implying a deep, pre LUCA evolutionary history. We highlight how population genetics, ecology, and synthetic biology can constrain origin of life scenarios by making explicit the roles of selection, drift, mutation, horizontal gene transfer, parasites and compartmentalization in shaping early communities. Finally, we outline an evolutionary research agenda spanning proto metabolic autocatalytic networks, protocells, and the emergence of translation and the transition to DNA genomes, such that qualitative models can be formalized through evolution driven hypotheses testable with theory and laboratory experiments, including those with synthetic cells.

Clinical interpretation often assumes that observable performance sufficiently reflects the organization of an adaptive system. The preceding Level 3 study showed that neither an aggregated scalar score nor a static exploratory UMAP embedding uniquely resolved the occlusal observational probes. This study introduces Level 4, centered on observed longitudinal viability. Using an exploratory single-case design in a participant with Parkinson's disease, gait was recorded with instrumented insoles under three probes: neutral natural occlusion (ONL), a nominal 2.5-degree increase in vertical dimension of occlusion (OC2.5), and a nominal 3-degree increase (OC3). Two sessions were conducted eleven weeks apart. A common PCA representation was used to compare M1-M2 centroid displacement. In the selected PC1-PC2 plane, OC3 showed the smallest Euclidean displacement, ONL an intermediate displacement, and OC2.5 the largest. This ordering was preserved in most bootstrap iterations but was not preserved after Mahalanobis covariance normalization, showing that within-condition dispersion contributes to the result. Level 4 therefore provides a retrospective, representation-dependent proxy for longitudinal reorganization when static representations remain non-identifying. The findings are exploratory and non-causal. They do not establish distinct physiological states, a causal occlusal effect, a validated viability threshold, a therapeutic optimum, or a covariance-independent ranking.

Science is constitutively third-personal: its findings are in principle reproducible by any observer, independent of perspective, and answerable to measurement. This is the source of its power and also its limit when it comes to phenomena that are first-personal. While it is obvious that a science of the Meaning of Life is unattainable, researchers have not drawn the same conclusion for consciousness -- in its phenomenal dimension, the qualia of seeing red, of feeling pain, of being anything at all. I argue they should. The hard problem of consciousness is not a scientific problem awaiting better tools or a more ambitious theory, but a category error. The same structural problem applies to machine consciousness: neither attribution nor denial is scientifically adjudicable. Beyond subjective consciousness, aspects of cognition, such as deliberative thinking and understanding, also have an irreducibly first-personal, experiential dimension that places them outside the reach of third-person scientific explanation. I situate science within a broader ecology of understanding and argue that, while a unified framework addressing both the objective and the subjective may be unattainable, practical questions about consciousness, including in machines and nonhuman animals, can nonetheless be navigated.

Large language models (LLMs) demonstrate remarkable reasoning capabilities, yet their stateless architecture fundamentally limits deployment in long-horizon research workflows requiring multi-session continuity and quantitative rigor. Here we present Ensemble QSP, a multi-agent framework featuring a three-layer hierarchical memory architecture that keeps injected context bounded and constant in project duration (mid-term project state: median 301 tokens, max 4,050, across 104 runs) by capping each state category and evicting completed work, enabling continuous autonomous operation without context degradation. The system orchestrates five specialist worker agents under domain-expert principal investigators, enforcing physical constraints through physics-based checklists and structured-domain knowledge. Comprehensive benchmarking demonstrates robust autonomous pharmacokinetic-pharmacodynamic model selection without human intervention, consistent result quality across both lower-cost and frontier LLMs, improved PK parameter recovery relative to single-agent baselines, and stable model selection across linguistically diverse prompts of the same task. Feature-level ablation across physiologically based pharmacokinetic (PBPK) models spanning a broad complexity range shows that PI-agent oversight improves debugging efficiency while preserving final accuracy across conditions. The architecture is structurally domain-agnostic, adding a new scientific domain requires only a new PI agent configuration.

Ramkrishna, Kompala, and Tsao proposed the cybernetic model of microbial growth, in which cells allocate enzyme synthesis resources according to a matching rule that mimics rational decision-making. The matching rule was later shown to be optimal under general assumptions about the underlying return-on-investment structure, yet the specific objective the cell maximizes, and the constraints bounding that choice, were never written down as an explicit economic decision. Here we supply that missing decision, recasting cybernetic enzyme-synthesis control as a consumer choice problem from microeconomic theory: the cell allocates a limited proteome budget among competing catabolic enzymes as a linear program (LP), maximizing a linear growth utility subject to a linear proteome budget constraint. Because the utility is linear, the LP's solution is geometric: whenever the iso-utility line's slope differs from the budget constraint's, the optimum is a corner, and the entire proteome budget is allocated to the enzyme for the single most profitable substrate. Corner solutions correspond to diauxic growth, and sequential substrate consumption follows from the choice of corner rather than a distinct regulatory mechanism. Only when the two slopes coincide does the optimum spread across the entire budget line instead of concentrating at a single corner; this degenerate case underlies simultaneous substrate use. Using only parameters estimated independently from single-substrate experiments, the LP-derived cybernetic variables reproduced the diauxic and triauxic batch growth of Klebsiella oxytoca on glucose-xylose and glucose-xylose-lactose mixtures, achieving a fit comparable to the classical matching law. Thus, sequential substrate use is the generic outcome of growth-maximizing specialization under perfect substitutability, and co-utilization is the degenerate case of equal profitability.

We introduce new kinetic equations modeling opinion dynamics inside a population of individuals, whose propensity to interact with each other is described by their level of social activity. We show that opinion polarization can arise among agents with a low activity level, while active ones develop a consensus, highlighting the importance of social interactions to prevent the formation of extreme opinions. Moreover, we present a realistic control strategy aimed at reducing the number of inactive agents and increasing the number of socially active ones. At last, we prove several (weak and strong) convergence to equilibrium results for such controlled model. In particular, by considering additional interactions between individuals and opinion leaders capable of steering the average opinion of the population, we use entropy method-like techniques to estimate the relaxation toward equilibrium of solutions to a Fokker-Planck equation with time-dependent coefficients.

Medical image segmentation using deep learning (DL) has enabled the development of automated analysis pipelines for large-scale population studies. However, state-of-the-art DL methods are prone to hallucinations, which can result in anatomically implausible segmentations. With manual correction impractical at scale, automated quality control (QC) techniques have to address the challenge. While promising, existing QC methods are organ-specific, limiting their generalizability and usability beyond their original intended task. To overcome this limitation, we propose no-new Quality Control (nnQC), a robust QC framework based on a diffusion-generative paradigm that self-adapts to any input organ dataset. Central to nnQC is a novel Team of Experts (ToE) architecture, where two specialized experts independently encode 3D spatial awareness, represented by the relative spatial position of an axial slice, and anatomical information derived from visual features from the original image. A weighted conditional module dynamically combines the pair of independent embeddings, or opinions to condition the sampling mechanism within a diffusion process, enabling the generation of a spatially aware pseudo-ground truth for predicting QC scores. Within its framework, nnQC integrates fingerprint adaptation to ensure adaptability across organs, datasets, and imaging modalities. We evaluated nnQC on seven organs using twelve publicly available datasets. Our results demonstrate that nnQC consistently outperforms state-of-the-art methods across all experiments, including cases where segmentation masks are highly degraded or completely missing, confirming its versatility and effectiveness across different organs.

Bacteriophage-bacteria interactions are central to microbial ecology, influencing evolution, biogeochemical cycles, and pathogen behavior. Most theoretical models assume static environments and passive bacterial hosts, neglecting the joint effects of bacterial traits and environmental fluctuations on coexistence dynamics. This limitation hinders the prediction of microbial persistence in dynamic ecosystems such as soils and oceans. Using a minimal ordinary differential equation framework, we demonstrate that environmental fluctuations can suppress destructive oscillations through resonance, promoting coexistence where static models otherwise predict collapse. Counterintuitively, we find that lower bacterial growth rates are helpful in enhancing survival under high infection pressure, elucidating the observed post-infection growth reduction. Our studies highlight bacterial hosts as active builders of ecological dynamics and environmental variation as a potential stabilizing force. Our findings thus bridge a theory-experiment gap and provide a framework for predicting microbial responses to environmental stress, which might have potential implications for phage therapy, microbiome management, and climate-impacted community resilience as well.

To develop a deep-learning method for achieving fast high-resolution MR elastography from highly undersampled data without the need of high-quality training dataset. We first framed the deep neural network representation as a nonlinear extension of the linear subspace model, then used it to represent and reconstruct MRE image repetitions from undersampled k-space data. The network weights were learned using a multi-level k-space consistent loss. To further enhance reconstruction quality, phase-contrast specific magnitude and phase priors were incorporated, including the similarity of anatomical structures and smoothness of wave-induced harmonic displacement. Experiments were conducted using both 3D gradient-echo spiral and multi-slice spin-echo spiral MRE datasets. Compared to the conventional linear subspace-based approaches, the nonlinear network representation method was able to produce superior image reconstruction with suppressed noise and artifacts from a single in-plane spiral arm per MRE repetition (e.g., 2mm isotropic resolution in 1 min with a total R=10), yielding comparable stiffness estimation to the fully sampled data. This work demonstrated the feasibility of using deep network representations to model and reconstruct MRE images from highly-undersampled data, a nonlinear extension of the subspace-based approaches.

We present a new solution concept called evolutionarily stable Stackelberg equilibrium (SESS). We study the Stackelberg evolutionary game setting in which there is a single leading player and a symmetric population of followers. The leader selects an optimal mixed strategy, anticipating that the follower population plays an evolutionarily stable strategy (ESS) in the induced subgame and may satisfy additional ecological conditions. We consider both leader-optimal and leader-pessimal selection among ESSs, which arise as special cases of our framework. Prior approaches to Stackelberg evolutionary games either define the follower response via evolutionary dynamics or assume rational best-response behavior, without explicitly enforcing stability against invasion by mutations. We present algorithms for computing SESS in discrete and continuous games, and validate the latter empirically. Our model applies naturally to biological settings; for example, in cancer treatment the leader represents the physician and the followers correspond to competing cancer cell phenotypes.

We introduce new kinetic equations to describe epidemics' spread while accounting for individuals' opinions on protective behaviors. Opinion exchanges occur on a social network represented by a graphon, whose choice strongly influences the dynamics and leads to the emergence of complex nonlinear phenomena, like the creation of opinion leaders or the spontaneous formation of epidemic waves. Starting from individual-based interactions, we derive a nonlinear nonlocal Fokker-Planck model involving reaction terms and degenerate drift-diffusion operators, which depend on the underlying graphon. We establish rigorous results of convergence to equilibrium in $L^1$ space, via relative entropy estimates, and in homogeneous Sobolev spaces $\dot{H}^{-s}$, $s \in \big(\frac{1}{2}, 1\big)$, using Fourier-based techniques. We then design a structure-preserving scheme for the coupled opinion-epidemiological system, highlighting graphon effects: opinion leaders supporting protective behaviors limit disease spread, whereas influenceable individuals may shift toward opposing views, worsening epidemics. At last, we introduce a time-dependent quantity analogous to the effective reproduction number, whose oscillations are linked with the formation of epidemic waves. Notably, these waves are not induced by an explicit external forcing but they naturally emerge from the interactions between agents, depending on the connectivity level prescribed by the graphon.

In biomechanical systems, observable performance is often used as a proxy for underlying organization, although similar outputs may arise from different adaptive configurations. This study considers the vertical dimension of occlusion (VDO) as a constraint applied to an adaptive neuromechanical system. A single-case design in a patient with Parkinson's disease enabled repeated intra-individual gait observations under six occlusal probes. Three complementary analytical levels were examined: (i) an aggregated scalar score of observable performance, (ii) a conceptual dynamical systems framework, and (iii) an exploratory UMAP representation of 55 standardized biomechanical variables from 270 M1 observations. The revised Level 1 analysis showed that the relative ranking of OC2.5 and OC3 depended on score construction, while their scalar distributions remained close. The Level 3 embedding showed substantial overlap among all six probes and did not identify independently separated condition-specific clusters. OC2.5 and OC3 displayed limited centroid displacement but broad observation-level overlap. The principal result is therefore representational non-identifiability: neither the aggregated score nor the selected low-dimensional embedding uniquely identifies an occlusal-condition-specific system state. VDO is interpreted as a constraint parameter rather than a causal determinant. The findings are exploratory, model dependent, and non causal. They do not establish distinct physiological states, an optimal VDO, clinical thresholds, or diagnostic, predictive, mechanistic, or prescriptive validity.

From subcellular structures to entire organisms, many natural systems generate complex organisation through self-organisation: local interactions that collectively give rise to global structure without any blueprint of the outcome. Yet a significant portion of the information driving such processes is not produced by self-organisation itself, instead, it is often offloaded to initial conditions of the system. Biological development is a prime example, where maternal pre-patterns encode positional and symmetry-breaking information that scaffolds the self-organising process. From maternal morphogen gradients in early embryogenesis to tissue-level morphogenetic pre-patterns guiding organ formation, this transfer of information to initial conditions, analogous to a memory-compute trade-off in computational systems, is a fundamental part of developmental processes. In this work, we study this offloading phenomenon by introducing a model that jointly learns both the self-organisation rules and the pre-patterns, allowing their interplay to be varied and measured under controlled conditions: a Neural Cellular Automaton (NCA) paired with a learned coordinate-based pattern generator (SIREN), both trained simultaneously to generate a set of patterns. We provide information-theoretic analyses of how information is distributed between pre-patterns and the self-organising process, and show that jointly learning both components yields improvements in robustness, encoding capacity, and symmetry breaking over purely self-organising alternatives. Our analysis further suggests that effective pre-patterns do not simply approximate their targets; rather, they bias the developmental dynamics in ways that facilitate convergence, pointing to a non-trivial relationship between the structure of initial conditions and the dynamics of self-organisation.

Understanding adaptive biomechanical systems requires distinguishing observable performance, static multivariate representation, longitudinal displacement, and internal approximation of observed change. This study introduces Level 5, which examines whether the M1-M2 transformation observed in a single-subject gait dataset can be approximated within a selected PCA representation. Gait was recorded with instrumented insoles in a participant with Parkinson's disease under six occlusal observational probes during two sessions eleven weeks apart. A simplified feed-forward neural network was trained to approximate M2 PC1-PC2 coordinates from M1 coordinates, occlusal-probe descriptors, and the longitudinal-transition indicator. In the core analysis aligned with Level 4, the model preserved the Euclidean centroid-displacement hierarchy dOC3 < dONL < dOC2.5. In the extended six-probe analysis, it preserved the broad structure of the exploratory ordering. Held-out M2 and leave-condition-out analyses provided internal tests beyond the full-dataset fit, while a within-session analysis described probe positions relative to ONL. The term predictive is used only in a restricted methodological sense. The model does not provide prospective clinical prediction, patient-level forecasting, or generalization to unseen individuals. Occlusal conditions are treated as observational probes applied during measurement, not as continuous causal drivers of longitudinal evolution. The findings are exploratory, retrospective, representation dependent, and non causal. They do not establish causal occlusal effects, validated viability thresholds, therapeutic superiority, distinct physiological states, or generalizable predictive validity.