Chaos: An Interdisciplinary Journal of Nonlinear Science

A key component of intraneuronal communication is the modulation of postsynaptic firing frequencies by stochastic transmitter release from presynaptic neurons. The time interval between successive postsynaptic firings is called the inter-spike interval (ISI), and understanding its statistics is integral to neural information processing. We start with a model of an excitatory chemical synapse with postsynaptic neuron firing governed as per a classical integrate-and-fire model. Using a first-passage time framework, we derive exact analytical results for the ISI statistical moments, revealing parameter regimes driving precision in postsynaptic action potential timing. Next, we extended this analysis to include both an excitatory and an inhibitory presynaptic connection onto the same postsynaptic neuron. We consider both a fixed postsynaptic-firing threshold and a threshold that adapts based on the postsynaptic membrane potential history. Our analysis shows that the latter adaptive threshold can result in scenarios where increasing the inhibitory input frequency increases the postsynaptic firing frequency. Moreover, we characterize parameter regimes where ISI noise is hypo-exponential or hyperexponential based on its coefficient of variation being less than or higher than one, respectively.

We describe an approach for analyzing biological networks using rows of the Krylov subspace of the adjacency matrix. Specifically, we explore the scenario where the Krylov subspace matrix is computed via power iteration using a non-random and potentially non-uniform initial vector that captures a specific biological state or perturbation. In this case, the rows the Krylov subspace matrix (i.e., Krylov trajectories) carry important functional information about the network nodes in the biological context represented by the initial vector. We demonstrate the utility of this approach for community detection and perturbation analysis using the C. Elegans neural network.

Voltage perturbations to a repetitively firing Hodgkin-Huxley (HH) model of neuronal spiking in the bistable regime with coexisting limit cycle and stable steady node can either lead to the spikes phase resetting or collapse to the stable steady state. The latter describes a non-firing hyperpolarized quiescent state of the neuron despite the presence of constant external current. Using asymptotic phase response curve (PRC), the impact of voltage perturbations on a repetitively firing HH model is studied here while it is diffusively coupled to another HH model under identical external stimulation. It is observed that the pre-perturbation state of synchronization and the coupling strength critically determine the PRC response of the perturbed HH dynamics. Higher coupling strengths of perfectly in-phase (anti-phase) synchronized HH models shrink (expand) the combinatorial space of perturbation strengths and the oscillation phases causing collapse to the quiescent state. This indicates reduced (enlarged) basin of attraction, viz. the null space, associated with the steady state in the HH phase space. The findings bear important implications to the spiking dynamics of diverse interneurons, as well as special cases of pyramidal neurons, coupled through electrical synapses via. gap junctions, and suggest the role of gap junction plasticity in tuning vulnerability to quiescent state in the presence of biological noise and spikelets.

In this work, the impact of outliers on the performance of machine learning and deep learning models is investigated, specifically for the case of histopathological images of colorectal cancer stained with Haematoxylin and Eosin. The evaluation of the impact is done through the systematic comparison of one machine learning model (Random Forests) and one deep learning model (ResNet-18). Both models were trained with the popular NCT-CRC-HE-VAL-100K dataset and tested on the CRC-HE-VAL-7K companion set. Then, a curation process was performed by analysing the divergence of patches based on chromatic, textural and topological features of the training set and removing outliers to repeat the training with a cleaned dataset. The results showed that machine learning models, can benefit more from improvements in the quality of data, than deep learning models. Further, the results suggest that deep learning models are more robust to outliers as, through the training process, the architectures can learn features other than those previously mentioned.

Foraging is a central decision-making behavior performed by all animals, essential to garnishing enough energy for an organism to survive. Similarly, mating is crucial for evolutionary continuity and offspring production. Mate choice is one of the central tenets of sexual selection, driving major evolutionary processes, and can be regarded as a decision-making process between potential mating partners. Often researchers have used coarse-grained models to describe macroscopic phenomenology pertaining to mate choice without detailed quantitative mechanisms of how animals use individual and environmental signals to guide their mating decisions. In this letter, we show that mate choice can be cast as a foraging problem, and we present an analytically tractable optimal foraging-inspired mechanistic theory of decision-making underlying mate choice. We begin from the premise that deciding upon which partner with which to mate is at its core a stochastic decision-making process. Agents adopt a variety of decision strategies, tuned by decision thresholds for leaving or committing to a mate. We find that sensitive leaving thresholds are favored independently of signal availability in the population. By contrast, optimal thresholds for committing to a mate depend upon signal availability in the population, with signal-rich populations generally favoring less eager strategies compared to signal-poor populations.

Resource sharing is a fundamental form of social exchange underlying the formation and maintenance of social bonds in humans and other species. While reciprocity has long been proposed as a key mechanism in group interactions, the dynamic processes underlying resource allocation remain poorly understood. In this study, we employed computational modeling to investigate the temporal dynamics of resource sharing in a novel group decision-making task across three experiments. We found that, beyond the well-documented reciprocity, participants exhibited consistent alternating behavior, characterized by the switching between potential recipients. This alternation was not driven by fairness concerns but reflected a strategic balance between maintaining stable partnerships and exploring alternatives. Crucially, a reinforcement learning model incorporating Theory of Mind (ToM) consistently outperformed all alternative models. These findings highlight the critical role of ToM in social decision-making and suggest that mentalizing others intentions may be essential for effective resource sharing and social bond formation.

A mean field model (MFM) is a mesoscopic description of neuronal population dynamics that can reduce the complexity of neural microcircuits into equations preserving key functional properties. The generation of a MFM is a complex mathematical process that starts with the incorporation of single neuron input/output relationships and local connectivity. Once neuron electroresponsiveness and synaptic properties are defined, in principle, the process can be automatized. Here we develop a tool for automatic MFM derivation from biophysically grounded spiking networks (Auto-MFM) by performing micro-to-mesoscale parameter remapping, estimating input/output relationships specific for different neuronal populations (i.e., transfer functions), and optimizing transfer function parameters. Auto-MFM was tested using a spiking cerebellar circuit as a generative model. The cerebellar MFM derived with Auto-MFM accurately reproduced cerebellar population dynamics of the corresponding spiking network, matching mean and time-varying firing rates across a wide range of stimulation patterns. Auto-MFM allowed us to model and explore physiological and pathological circuit variants; indeed, it was used to map ataxia-related structural connectivity alterations of the cerebellar network, in which Purkinje cells with simplified dendritic structure altered the cerebellar connectivity. Furthermore, Auto-MFM was used to create a library of cerebellar MFMs by sweeping the level of the excitatory conductance at mossy fiber - granule cell synapse, which is altered in several neuropathologies. Auto-MFM is thus proving a flexible and powerful tool to generate region-specific MFMs of healthy and pathological brain networks to be embedded in brain digital models.

Network-based epidemic models have been instrumental in understanding how contact structure shapes infectious disease dynamics, yet widely used frameworks such as Erd[o]s-Renyi, configuration-model, and stochastic block networks do not explicitly capture the combination of fully accessible (saturated) within-group interactions and constrained between-group connectivity characteristic of many real-world settings. Here, we introduce the Multi-Clique (MC) network model, a generative framework in which individuals are organised into fully connected cliques representing stable contact groups (e.g., households, classrooms, or workplaces), with a limited number of external connections governing inter-group transmission. Using stochastic susceptible-infectious-recovered (SIR) simulations on degree-matched networks, we compare epidemic dynamics on MC networks with those on classical random graph models. Despite having an identical mean degree, MC networks exhibit systematically distinct behaviour, including slower epidemic growth, reduced peak prevalence, increased fade-out probability, and delayed time to peak. These effects arise from rapid within but constrained between clique transmission, creating structural bottlenecks that standard models do not capture. The MC framework provides an interpretable, data-driven representation of recurrent contact structure, with parameters that map directly to observable quantities such as household and classroom sizes. By isolating the role of intergroup connectivity, the model offers a basis for evaluating targeted intervention strategies that reduce between-group mixing while preserving within-group interactions. Our results highlight the importance of explicitly representing the real-life clique-based network structure in epidemic models and suggest that classical degree-matched networks may systematically overestimate epidemic speed and intensity in structured populations.

The impact of cellular activities on large-scale brain dynamics is thought to determine brain functioning and disease, yet the causal relationships of neural mechanisms across scales remain unclear. Recently, the cerebellum has been reported to affect whole-brain dynamics during sensorimotor integration. To disclose the underlying mechanisms, we have developed a multiscale digital brain co-simulator, in which a spiking neural network of the olivo-cerebellar microcircuit is embedded in a mouse virtual brain and wired with other nodes using an atlas-based long-range connectome. Parameters and bi-directional interfaces between the spiking olivo-cerebellar network and other rate-coded modules were tuned to match experimental data of primary sensory and motor cortex (M1 and S1) power spectral densities and neuronal spiking rates. Then, the role of the cerebellar circuitry on sensorimotor integration was analyzed by lesioning critical circuit connections in silico. Simulations showed that spike processing within the cerebellar circuit is key to explaining the gamma-band coherence between M1 and S1 during sensorimotor integration. These results provide a mechanistic explanation of how the cerebellum promotes the formation of sensorimotor contingencies in relevant cortical modules as the basis of its critical role in sensorimotor prediction. On a broader perspective, this modelling approach opens new perspectives for the multiscale investigation of brain physiological and pathological states in relation to specific cellular and microcircuit properties.

Linking structural connectivity (SC) to functional connectivity (FC) through mechanistic models remains challenging in network neuroscience. In this study, empirical data of diffusion magnetic resonance imaging (dMRI) and resting-state functional MRI (rs-fMRI) were used to reconstruct SC and FC of a swine connectome. We evaluated a structurally constrained Kuramoto phase-oscillator framework to reproduce resting-state FC and then assessed the models sensitivity to traumatic brain injury (TBI) and its longitudinal progression post-TBI. A joint tuning procedure was implemented to calibrate data-informed natural frequencies and global coupling strength. The tuned Kuramoto model was then used to evolve oscillator phases constrained by the SC, followed by a Balloon-Windkessel hemodynamic model. The optimized model produced significant edge-wise correspondence between averaged simulated FC and the empirical FC (r = 0.61, p < 0.001). Graph-theoretical analysis across network densities (30-50%) showed strong agreement for global efficiency, characteristic path length, and clustering coefficient, while modularity and small-worldness exhibited deviations. Longitudinal analysis of the swine TBI dataset revealed modest reductions in structure-function coupling over time but no significant differences across injury severities. These results demonstrate that optimized Kuramoto models can reproduce key functional network features while preserving inter-subject variability.

As social beings, humans make decisions partly based on social interaction. Observing the behavior of others can lead to learning from and about them, potentially increasing trust and prompting trust-based behavioral changes. Observation-based decision making involves different neural structures. The orbitofrontal cortex (OFC) and lateral prefrontal cortex (LPFC) are known as neural structures mainly involved in processing emotional and cognitive decision values, respectively, while the anterior cingulate cortex (ACC) plays a pivotal role as a social hub, integrating the afferent expectancy signals from OFC and LPFC. This paper presents a neurocomputational model of the interplay between observational learning and trust, as well as their role in individual decision-making. Our model elucidates and predicts the emotional and rational behavioral changes of an individual influenced by observing the action-outcome association of an alleged expert. We have modeled the neurodynamics of three cortical structures (OFC, LPFC, and ACC) and their interactions, where the neural oscillatory properties, modeled with Dynamic Bayesian Probability, represent the observers attitude towards the expert and the decision options. As an example of an everyday behavioral situation related to climate change, we use the choice of transportation between home and work. The EEG-like simulation outputs from our model represent the presumed brain activity of an individual making such a choice, assuming the decision-maker is exposed to social information.

A fundamental goal in neuroscience is to understand how the brains physical architecture supports complex functional dynamics. While the relationship between structural connectivity and pairwise functional connectivity has been extensively studied, the anatomical basis of higher-order interactions remains poorly understood. In this study, we use multivariate information theory -specifically the O-information- to investigate how the human connectome constrains subsets of brain regions characterized by predominantly redundant or synergistic information sharing. By analyzing the topology and community embedding of these subsets, we reveal two different structural profiles. Redundant subsets are characterized by high internal connection density and strong weights. Their nodes have high clustering and occupy globally less central positions. In contrast, synergistic subsets consist of globally central nodes with high betweenness centrality. We further demonstrate that leveraging these structural features, in particular node centrality, significantly improves the identification of synergistic subsets compared to random sampling. Together, these results demonstrate that the human connectome imposes specific constraints on higher-order information sharing, extending structure-function relationships beyond pairwise interactions and providing new insight into the structural origins of multivariate functional organization.

Infectious disease surveillance systems in tropical countries show that respiratory disease incidence generally manifests as year-round activity with weak fluctuations and irregular seasonality. Previously, using a ten-year time series of influenza-like illness (ILI) collected from outpatient clinics in Ho Chi Minh City (HCMC), Vietnam, we found a combination of nonannual and annual signals driving these dynamics, but with unknown mechanisms. In this study, we use seven stochastic dynamical models incorporating humidity, temperature, and school term to investigate plausible mechanisms behind these annual and nonannual incidence trends. We use iterated filtering to fit the models and evaluate the models by comparing how well they replicate the combination of annual and nonannual signals. We find that a model including specific humidity, temperature, and school term best fits our observed data from HCMC and partially reproduces the irregular seasonality. The estimated effects from specific humidity and temperature on transmission are nonlinearly negative but weak. School dismissal is associated with decreased transmission, but also with low magnitude. Under these weak external drivers, we hypothesize that stochasticity makes a strong sub-annual cycle more likely to be observed in ILI disease dynamics. Our study shows a possible mechanism for respiratory disease dynamics in the tropics. When the external drivers are weak, the seasonality of respiratory disease dynamics is prone to the influence of stochasticity.

How genetically identical cells spontaneously break symmetry to assume divergent fates is a fundamental problem in developmental biology. While modern genomics has mapped the vast molecular repertoire involved in gene regulation, understanding the mechanism of cell state transitions that drive differentiation remains a formidable challenge. To address this, we use a reaction-kinetic framework to analyze recurring motifs of two and three competing master regulators. While typically such circuits are studied numerically, we show that assuming symmetry in nodes and interactions provides exact analytical description of the bifurcations governing cell fate transitions. We find that the possible cell fates across all considered topologies are dictated by a single dimensionless quantity, {beta}--the ratio of protein degradation to production rates. In the binary Toggle Switch (TS), decreasing {beta} destabilizes the symmetric (stem cell) state, giving rise to two asymmetric (differentiated) fates via a supercritical pitchfork bifurcation. In the three-component Toggle Triad (TT), low values of {beta} yield three asymmetric fates through subcritical pitchfork bifurcation, creating an intermediate range of {beta} where both symmetric and asymmetric fates are simultaneously stable. For the Self-Activating Toggle Switch (SATS), we identify a new parameter for the self-activation threshold ({theta}) and show that decreasing{theta} progressively stabilizes the uncommitted state, leading to a regime of tristability. Building on these temporal bifurcations, we next address the feasibility of spatial structure formation: can these multistable fates stably coexist within a spatial domain? Through a minimal model of cell-cell communication via free diffusion, we extend these motifs into reaction-diffusion systems, which reveals a direct role of network topology on spatial organization. We prove that any heterogeneous pattern in two-node circuits is inherently transient and unstable. In contrast, the three-node repressive network supports the stable spatial coexistence of differentiated phenotypes through pure diffusion, a phenomenon we analyze by studying heteroclinic interface solutions as building blocks. By reducing complex regulatory dynamics to tractable models with physically meaningful parameters, we establish a minimal framework which relates topology to cell fate. Finally, the effects of temporal multistability on pattern formation provide an excellent studying ground for morphogenesis, synthetic biology, and the overarching problem of spatiotemporal self-organization.

We introduce a spectral existence criterion for the evolution of cooperation in the form of the inequality{lambda} maxb > c, where{lambda} max is the leading eigenvalue of an interaction operator encoding population structure, and b and c represent benefit and cost tradeoffs, respectively. Nowaks five rules for the evolution of cooperation correspond to cases in which the cooperation condition reduces to a scalar assortment coefficient. These results follow from the Price equation, which sheds light on a long-standing debate on the role of inclusive fitness and evolutionary dynamics in explaining the evolution of cooperation.

Generalization is a fundamental criterion for evaluating learning effectiveness, a domain where biological intelligence excels yet artificial intelligence continues to face challenges. In biological learning and memory, the well-documented spacing effect shows that appropriately spaced intervals between learning trials can significantly improve behavioral performance. While multiple theories have been proposed to explain its underlying mechanisms, one compelling hypothesis is that spaced training promotes integration of input and innate variations, thereby enhancing generalization to novel but related scenarios. Here we examine this hypothesis by introducing a bio-inspired spacing effect into artificial neural networks, integrating input and innate variations across spaced intervals at the neuronal, synaptic, and network levels. These spaced ensemble strategies yield significant performance gains across various benchmark datasets and network architectures. Biological experiments on Drosophila further validate the complementary effect of appropriate variations and spaced intervals in improving generalization, which together reveal a convergent computational principle shared by biological learning and machine learning.

AI-based molecular dynamics simulation brings ab initio calculations to biomolecules in an efficient way, in which the machine learning force field (MLFF) locates at the central position by accurately predicting the molecular energies and forces. Most existing MLFFs assume localized interatomic interactions, limiting their ability to accurately model non-local interactions, which are crucial in biomolecular dynamics. In this study, we introduce ViSNet-PIMA, which efficiently learns non-local interactions by physics-informed multipole aggregator (PIMA) and accurately encodes molecular geometric information. ViSNet-PIMA outperforms all state-of-the-art MLFFs for energy and force predictions of different kinds of biomolecules and various conformations on MD22 and AIMD-Chig datasets, while adapting the PIMA blocks into other MLFFs further achieves 55.1% performance gains, demonstrating the superiority of ViSNet-PIMA and the universality of the model design. Furthermore, we propose AI2BMD-PIMA to incorporate ViSNet-PIMA into AI2BMD simulation program by introducing "Transfer Learning-Pretraining-Finetuning" scheme and replacing molecular mechanics-based non-local calculations among protein fragments with ViSNet-PIMA, which reduces AI2BMDs energy and force calculation errors by more than 50% for different protein conformations and protein folding and unfolding processes. ViSNet-PIMA advances ab initio calculation for the entire biomolecules, amplifying the application values of AI-based molecular dynamics simulations and property calculations in biochemical research.

Movement is costly, and animals are under strong selective pressure to move efficiently, yet, in patchy, dynamic landscapes, decision-making is inherently uncertain. We quantify the energetic savings achieved by using up-to-date information presented within social cues for reducing movement costs. We use an agent-based model, founded on realistic aeronautical rules and parametrised on the Andean condor (Vultur gryphus), to study movement in patchy landscapes. By explicitly considering altitude, flight results in a sequence of soaring and gliding in the 3D space. We investigate how the cost of movement to an overall goal varies when birds use social information from others that are either fixed in space or moving collectively to the common goal, and under different risk-taking speed strategies, from slow and cautious to fast and risky. The value of social information is operationalised as energetic savings in units of basal metabolic rate. Under low predictability, agents with intermediate risk and high social-information use exhibit lowest movement costs, with up to 41% energy savings over asocial movement. By extending classical aeronautical theory to social and variable environments we demonstrate the adaptive value of social information for efficient movement in patchy, unpredictable landscapes.

Neuronal activity alters extracellular ion concentrations and electric potentials. Ephaptic effects refer to the feedback influence that these extracellular changes can have on neuronal activity. While electric ephaptic effects occur on a fast timescale due to extracellular potential perturbations, ionic ephaptic effects are driven by slower, accumulative changes in ion concentrations. Among the previous computational studies of ephaptic effects, the vast majority have focused exclusively on electric effects, while ionic ephaptic effects have largely been neglected. In this work, we present an electrodiffusive computational framework consisting of two-compartment neurons that interact via a shared extracellular space. By accounting for both electric potentials and ion-concentration dynamics in a self-consistent manner, our framework enables us to explore the relative roles of electric and ionic ephaptic effects. Through numerical experiments, we demonstrate that ionic and electric ephaptic interactions play very different roles. While ionic ephaptic interactions increase population firing rates, electric ephaptic interactions primarily drive subtle shifts in spike timing. Furthermore, we show that these spike shifts cause the phase difference (the distance in spike times between a small collection of neurons) to converge to a stable, unique phase difference, which we coin the ephaptic intrinsic phase preference. Author summaryNeurons predominantly communicate through synapses: specialized contact points where a brief electrical signal, known as a spike or action potential, in one neuron influences another. Neurons generate these spikes by exchanging ions with the surrounding extracellular space. This way, spiking neurons alter extracellular ion concentrations and electric potentials. Since neurons are sensitive to such changes in their environment, they can also influence one another indirectly through the shared extracellular medium. This form of non-synaptic interaction is known as ephaptic coupling. Most computational models of neuronal activity neglect ephaptic interactions, and those that include them typically consider only electric effects while ignoring ionic contributions. As a result, the relative roles of electric and ionic ephaptic effects remain poorly understood. Here, we introduce a computational framework that accounts for both mechanisms in a self-consistent way. Our results show a functional distinction: ionic ephaptic effects act slowly, regulating population firing rates, whereas electric ephaptic effects act on millisecond timescales and subtly shift spike timing. These shifts cause spike-time differences between neurons to converge to a stable value, a phenomenon we call ephaptic intrinsic phase preference.

The connectivity of brain networks is extremely sparse due to metabolic, physical and spatial constraints. Although wiring sparsity can confer computational advantages for biological and artificial neural networks, sparse networks require fine parameter tuning and exhibit strong sensitivity to perturbations. How brains achieve their efficiency and robustness is unclear. Here we addressed this by analysing the dynamical properties of Echo State Networks with wiring based on the Drosophila melanogaster fruit fly connectome, compared with sparsity-matched random-wiring networks. We evaluated these networks on a set of eight cognitive tasks, and found that connectome-based neural networks (CoNNs) typically showed narrowly distributed task engagement across their neurons. The importance of a neuron for task performance correlated with its node degree, local clustering, and selfrecurrency, and these correlations were stronger in CoNNs than in random networks. CoNNs were more robust to neuronal loss, retaining their task performance and beneficial dynamical properties such as criticality and spectral radius better than random networks. Similarly, CoNNs were more robust to hyperparameter variations in both input and recurrent weight scaling. Using theoretical arguments and numerical simulations, we show that excess CoNN node self-recurrency is sufficient to explain this enhanced robustness. Overall, these results identify non-random features of connectome wiring that allow brains to reconcile extreme sparsity with reliable computation. SignificanceBrain networks support robust computation even though they operate under extreme wiring sparsity due to metabolic and spatial constraints. While sparse networks typically require fine-tuning and are sensitive to perturbations, we show that biological connectomes support specialised, efficient task engagement and remain robust to neuron loss and parameter variation. We identify excess neuronal selfrecurrency as a key structural feature underlying this stability. These results reveal how non-random connectivity stabilises computation in extremely sparse networks, providing principles for understanding brain function and designing robust, efficient artificial neural systems.