Chaos, Solitons & Fractals

In this study, we develop a mathematical model of the hypothalamic pituitary adrenal (HPA) axis and systematically investigate the model complexity required to reproduce observed hormone dynamics. The model is fitted to ACTH and cortisol measurements from five healthy volunteers reported in the literature. We show that simultaneous reproduction of both hormone profiles requires a delay differential equation model with at least five state variables among the model architectures considered. Following fitting the volunteer data, we investigate the response of the model to sustained stress using bifurcation analysis. The coupled system exhibits bifurcations over a range of stress intensities. This analysis reveals bifurcations whose critical stress thresholds depend strongly on the modulatory state of the system. These results provide a mathematical framework for investigating transitions between physiological and dysregulated HPA axis dynamics, which may be related to states of health and disease.

Interception of moving objects is a universal pattern of animal behavior with many industrial applications. Inspired by the behavior of the characid fish Brycon guatemalensis, which catches fruits falling onto the surface of a river, we study one-shot (i.e., open-loop) interceptions using both stochastic optimal control theory and reinforcement learning. In the first instance, an agent actuates a control (wait time before launch and heading angle) to meet its target, given a noisy estimate of the target initial state. In a minimal setting, where launch velocity and actuated control are constants, we show that the optimal wait time is attenuated by noise in both the target measurement and control actuation, as well as agent energy conservation. We then derive an upper bound for the heading angle variance which scales as the ratio of the non-vanishing optimal interception error to the initial planar separation. Complementing our control framework, our deep reinforcement learning approach shows that the neural network representing the fish first learns the value function for the interception, then learns how to aim, and finally learns the optimal wait time. Beyond the specific problem at hand, our results may also have applications to problems with little time for feedback or corrections such as perching, landing, and docking.

Non-exponential residence times give rise to history-dependent or memory effects in epidemic dynamics, yet their mathematical formulations remain fragmented. Here we develop a unified framework for a history-dependent SEIR model with general latent- and infectious-period distributions. We first establish the equivalence between the stage-age and renewal formulations and show that both admit a unified transition-flow representation. We then introduce the concept of a transition-flow multiplier, which provides a direct link between residence-time distributions and transition flows. When the multiplier is a weighted sum of shifted power functions, the model admits an exact representation in terms of Riemann-Liouville or tempered Riemann-Liouville fractional operators, providing a first-principles foundation for fractional epidemic models. Finally, using Euler-Lotka equations and stochastic-order arguments, we characterize how the latent- and infectious-period distributions shape epidemic growth and decay. A longer latent period slows both early growth and late decay, while, at fixed means, greater variability in the latent period accelerates early growth but slows late decay, whereas greater variability in the infectious period slows both.

Multiview data analysis has become increasingly important for integrating heterogeneous information from multiple data sources. Cooperative learning provides a flexible framework for multiview integration by bridging early and late fusion strategies. However, its use of squared loss makes it sensitive to outliers. In this study, we propose robust cooperative learning based on the soft-IPOD framework. The proposed method introduces an observation-specific outlier absorption vector into the cooperative learning objective, thereby reducing the influence of outlying observations while preserving information sharing across views. The resulting optimization problem can be formulated as a weighted Lasso-type problem using an augmented design matrix and can be naturally extended to more than two data views. Numerical simulations and a real-data application to labor onset prediction demonstrate the predictive performance of the proposed method in the presence of outliers.

Background: Attention-Deficit/Hyperactivity Disorder (ADHD) is a common neurodevelopmental disorder characterized by persistent symptoms of inattention, hyperactivity, and impulsivity that significantly affect cognitive, academic, and social functioning. Although electroencephalography (EEG) has emerged as a promising non-invasive tool for identifying objective neurophysiological biomarkers of ADHD because of its high temporal resolution and cost-effectiveness, many existing machine learning studies rely on single-domain EEG features, which may not adequately capture the complex functional organization of the brain. Methods: This study proposes a subject-level EEG classification framework that integrates three complementary feature domains: spectral characteristics, weighted Phase Lag Index (wPLI)-based functional connectivity, and topological descriptors derived from persistent homology. EEG recordings from 121 subjects were preprocessed and segmented into overlapping windows for feature extraction. Window-level features were aggregated to generate subject-level representations. Recursive Feature Elimination (RFE) was employed to select the 110 most informative features from an initial set of 1,043 descriptors. Five machine learning classifiers, including Support Vector Machine (SVM), Random Forest, XGBoost, CatBoost, and Multi-Layer Perceptron (MLP), were evaluated using stratified five-fold cross-validation. An ablation study was further conducted to assess the contribution of each feature domain. Model interpretability was investigated using SHapley Additive exPlanations (SHAP) and Local Interpretable Model-agnostic Explanations (LIME), two widely adopted Explainable Artificial Intelligence techniques for interpreting machine learning models. Results: Among the evaluated classifiers, the SVM achieved the highest classification performance, yielding an accuracy of 80.17%, an F1-score of 80.95%, a balanced accuracy of 80.14%, a receiver operating characteristic area under the curve (ROC-AUC) of 86.72%, and a precision recall area under the curve (PR-AUC) of 87.34%. The ablation study demonstrated that combining spectral, functional connectivity, and topological features consistently outperformed individual feature domains, highlighting the complementary nature of these representations. Explainable AI analyses further identified functional connectivity features as the primary contributors to classification performance while confirming the additional value of spectral and topological descriptors. Conclusions: The proposed framework demonstrates that integrating spectral analysis, functional connectivity, and topological data analysis provides an effective and interpretable approach for subject-level ADHD classification from EEG recordings. The combination of recursive feature selection, multi-domain feature fusion, ablation analysis, and Explainable Artificial Intelligence establishes a transparent and reproducible pipeline that may facilitate the development of reliable EEG-based clinical decision-support systems for ADHD.

Recurrent cortical circuits are hypothesized to perform Bayesian posterior sampling through their stochastic dynamics. Yet identifying which sampling algorithm a circuit intrinsically implements, as opposed to mapping manually designing algorithms onto circuits, requires rigorous theoretical analysis of the biological circuit dynamics, and remains a fundamental open challenge because of the analytical intractability of nonlinear recurrent dynamics. Here, we tackle this challenge through comprehensive theoretical analysis of analytically tractable nonlinear recurrent circuit dynamics used in neuroscience research-- the continuous attractor network (CAN). Surprisingly, we find that the circuit, without any non-Gaussian components in its connectivity or internal variability, intrinsically emerges heavy-tailed subspaces dynamics described as scale-mixture Langevin posterior sampling. The mechanism emerges from the circuits own nonlinear dynamics: divisive normalization renders the overall population activation Gamma-distributed which multiplicatively modulates the time constant of the Langevin sampling in the stimulus feature subspace. Eventually, this scale-mixture structure produces a heavy-tailed (Student-t) sampling step size distribution, significantly accelerating the sampling speed. Moreover, the scale-mixture Langevin sampling approaches a Levy-like regime in the weak input limit. Our results analytically identify an intrinsic circuit algorithm embedded in subspaces of nonlinear recurrent dynamics, and establish a minimal circuit mechanism for endogenous heavy-tail statistics without any explicit non-Gaussian components.

The sex ratio at birth (SRB), or secondary sex ratio, is stable, with more boys born alive, but shifts after major events. Acute stress may reduce SRB through disproportionate male fetal loss, while sexual intercourse patterns around conception are associated with offspring sex. We examined whether Brazil's April 2021 Gamma-wave mortality peak was followed by an SRB decline within the previously reported stress-sensitive 3-5 month window. We analysed >81 million live births (1997-2024) from Brazil's Live Birth Information System (SINASC) using pre-pandemic autoregressive forecasts with 95% prediction intervals (PIs). In July 2021, SRB was 50.951% versus 51.185% expected, below the 95% PI (50.968-51.402%), indicating fewer boys. All five macroregions were below expectation, largest in the North, including Amazonas, where Gamma was first identified. Monte Carlo simulation showed that, under usual SRB patterns, a decline with this timing and consistency across Brazil would occur about once in 200 simulations (probability 0.00467), making July 2021 unusual. In February 2023, SRB was 51.441% versus 51.220% expected, above the 95% PI (51.003-51.438%), indicating more boys, nine months after Brazil ended its COVID-19 emergency, suggesting increased sexual intercourse after pandemic relaxation. In April 2023, SRB was 50.956% versus 51.221% expected, below the 95% PI (51.004-51.439%), indicating fewer boys, four months after Pele's death. A comparable UK decline followed Princess Diana's death 4-5 months later. Gamma was prespecified; later observations are hypothesis-generating. These findings highlight SRB's population-level utility and warrant investigation of stress-related and behavioural pathways; ecological design precludes causality.

Automated surveillance systems can prove to be extremely useful in detecting outbreaks of respiratory diseases that need further epidemiological investigation. In order for the system to be effective, careful attention has to be paid to the baseline used, absence of the observations, and the use of proper statistical methods. As a solution, the paper describes EpiAlert, a weekly surveillance system based on CDC FluView ILINet. The system is able to transform the number of ILI visits and the total number of visits into a ILI prevalence for the region, create the first reference from the three previous years using a +/- 2-week interval, transform the rate value, and apply two different detectors - CUSUM and EWMA. CUSUM is set at k=0.5 and h=5, whereas EWMA uses {lambda}=0.2 and H=2.7 values. Among the 55 districts, the system gives 45,138 pieces of information about the disease by transforming 44,297 pieces of data into alerts. It is found that there are 2,820 alerts in total (out of which 2,711 alerts used CUSUM, 402 used EWMA, and 293 used both detectors). Additionally, the experiments show that the sensitivity of the device depends greatly on the detector. The latest statistics can be tracked in the report for week 37 of 2026 that recently concluded in West.

In many natural dynamical systems, tipping points emerge where slowly changing external factors induce shifts from one state to another, known as critical transitions or bifurcations. In epidemic systems, detecting these transitions is important for outbreak preparedness. Various statistical indicators like lag-1 autocorrelation and variance have been employed as early warning signals (EWS) of critical transitions by showing how the dynamics of the system exhibit critical slowing down (CSD) near the transition. More recently, deep learning-based algorithms have been developed that attempt to more accurately detect and classify bifurcations; however, they are limited by the systems simulated in the training dataset, the length of the time series, and have not been rigorously evaluated on real-world epidemic data spanning multiple geographic regions. In this paper, we evaluate existing deep learning-based bifurcation prediction models, on a CDC-curated dataset containing weekly influenza hospital admissions across all fifty U.S. states and the nation as a whole. We develop a pipeline for data preparation, reproduction number (Rt) estimation using the EpyEstim package (a Python implementation of the EpiEstim framework [4]), and bifurcation point identification. We systematically evaluate the models under several windowing strategies, including rolling, expanding, and fixed-length windows, and report accuracy, precision, recall, F1 score, and specificity. Our best-performing configuration (expanding window, length 100) achieves an accuracy of 90.09%, precision of 72.86%, recall of 96.23%, and F1 score of 82.93%. We additionally discuss Markov Regime Switching models as an alternative framework for detecting epidemic transitions. Our findings indicate that these models can generalize to real-world, state-level influenza data and are capable of online/real-time prediction.

We explored the role of proprioceptive feedback from Ia afferents in intra-muscle synergies stabilizing muscle force with the help of muscle vibration, which is known to increase presynaptic inhibition of those afferents to alpha-motoneurons. Healthy young adults performed an accurate three-finger force production task by pressing with the index, middle and ring fingers of the dominant (right) hand. This was done without vibration and with vibration applied to the extrinsic finger flexors, extensors, both muscles, the palm, or biceps brachii. High-density electromyography was used to identify motor units in both finger flexors and extensors. The raster plots of motor units were converted into firing frequency functions and then subjected to principal component analysis to extract stable motor unit groups (MU-modes). The uncontrolled manifold (UCM) analysis was used to quantify the variance components affecting and not affecting force, and the synergy index in the MU-mode space. Contrary to our expectations, the synergy index did not drop under any vibration condition and showed an increase during vibration applied simultaneously to both flexor and extensor muscles. This was primarily associated with a drop in the component of variance affecting the force magnitude. The results speak against an important role of monosynaptic Ia-afferent projections to alpha-motoneurons in the formation of intra-muscle synergies. They suggest that muscle vibration can play the role of a noisy signal decreasing performance-affecting variance via stochastic resonance effects.

Simulation models are widely used to support counterfactual inference in settings where direct experimental validation is difficult or infeasible. However, for phenomenological models calibrated to observational time series, goodness-of-fit does not necessarily establish that the structural assumptions underlying such inferences are uniquely supported by the data. Here, we examine this issue using a published COVID-19 transmission model for Japan that incorporates empirical inputs including human mobility, variant prevalence, and vaccination and has been used to estimate the effects of alternative vaccination scenarios. Using the publicly archived code together with a reconstructed substitute for a restricted-access input file required by the released implementation, we first reproduced the published model behaviour. We then performed two complementary computational stress tests. First, the vaccination-related input was suppressed and the remaining parameters were re-estimated against the original epidemic trajectory. Second, as a complementary test of trajectory-level flexibility, the model was refitted to synthetic target series with qualitatively different temporal structures while retaining the empirical mobility and variant inputs. The model retained substantial fitting capacity in both tests: suppression of the vaccination-related input caused only a limited deterioration in fit to the original trajectory, while qualitatively different synthetic trajectories could also be reproduced through parameter adjustment. Variation in fitted parameters across these conditions was also consistent with compensatory parameter behaviour. These results do not imply that vaccination had no effect or that the original model is invalid. Rather, they provide empirical evidence that, in this case, goodness-of-fit to the observed epidemic trajectory alone does not uniquely support the structural interpretation required for vaccination-related counterfactual inference. The study illustrates the value of reproducible computational stress testing as a complement to, rather than a substitute for, formal identifiability or model-comparison analyses.

Nitrogen dioxide (NO2) is a widespread air pollutant associated with the risk and prevalence of various respiratory infectious diseases. Epidemiological studies have reported associations between NO2 exposure and COVID-19 incidence, and biological evidence indicates that NO2 exposure increases vulnerability to infection. Motivated by these findings and by the scarcity of mechanistic epidemic models that incorporate air pollutant data, here we introduce an NO2- and mobility-informed metapopulation model and study the first COVID-19 wave in Oklahoma. County-level NO2 concentrations enter the infection rates through a first-order parameterization, alongside high-resolution mobility patterns capturing heterogeneous inter-county connectivity. Using numerical simulations, we demonstrate that higher environmental sensitivity produces earlier and more synchronized outbreaks across counties, while lower sensitivity yields delayed, asynchronous trajectories. When fitted to county-level COVID-19 incidence data, our model outperformed the classic SIR model (fitted independently in each county) in over 75% of counties in Oklahoma across all standard error metrics. The improvements were even more pronounced in forecasting tasks across epidemic stages, with county-level win rates against the SIR model of 59.74% (surge), 87.01% (peak), 80.52% (post-peak), and 88.31% (decline) by nRMSE. To isolate the contribution of NO2, we compared our model against a mobility-only model with NO2 removed and homogeneous infection rates across counties. The NO2 term improved county-level forecasts during the surge (94.81% of counties by nRMSE), post-peak (88.31%), and peak (62.34%) stages, though not during the early and decline stages, suggesting that NO2 information can generate better forecasts than mobility alone during periods of high incidence. Our results demonstrate that environmental exposure can enter the transmission structure of a mechanistic epidemic model directly and that doing so yields measurable forecasting gains.

Game theory in biology started as an attempt to model animal contests by making assumptions about the fitness costs individuals pay in aggressive interactions. Among the different approaches, a notable one is to construct mechanistic models, using assumptions about behaviours and cognitive processes. Reinforcement learning is an important cognitive process, and we use it here to model pairwise and coalitional contests. We study situations where territorial neighbours become so-called dear enemies. A defending individual can get help from a neighbour through a defender-neighbour coalition against a challenger attempting territory takeover. In our model, coalition members have an advantage in contests in terms of costs of aggression, with the challenger being exposed to aggression from both members and each member only receiving part of the aggression from the challenger. We find that notable costs of border conflicts between neighbours, together with substantial advantages for coalitions, favour intervention. Neighbours intervene when they can help weaker defenders, in this way avoiding costs of border renegotiation with a new and potentially stronger territory owner. We also introduce different forms of perceived costs into the model, which we show correspond to the range from pure mutual assessment to partial self-assessment.

We develop a general geometrical framework for growth processes in which the growth rate depends exponentially on the number of active growth-supporting components. The framework separates the fraction of active components from the size of the accessible component space, allowing qualitatively different growth laws to arise from the same underlying construction. Bacterial population growth provides an example of a fixed-size component space controlled primarily by activation and deactivation, whereas examples such as human population growth or speciation provide an expanding component space in which interactions between individuals promote further growth. This motivates a Replicative geometrical law, dX/dt= X exp({beta} X^{gamma}), whose exponent characterizes the scaling of the effective growth-supporting component space and is tested against historical human-population regimes and eukaryotic lineage-through-time data. For innovation indicators such as patents and arXiv manuscript submissions, where an existing item need not itself reproduce, the same construction motivates a Direct Geometrical production law without the prefactor X. The framework therefore provides a common description of fixed and expanding component spaces while distinguishing Replicative from Direct Geometrical growth.

We present a network model that enables a navigating agent to shape the spatial and temporal structure of its paths through its environment. The model is inspired by the insect fan-shaped body. In it, a recurrent neural network receives an input that encodes an agent's velocity vector. Meanwhile, network activity determines the setpoint of a control loop that influences this velocity vector through motor outputs. The network thus guides future movement using memory of past movement. We illustrate how the network's dynamics determine the trajectory features it extracts to produce the setpoint. We then relate the joint dynamics of network activity and the agent's velocity vector to the structure of the resulting paths. This network can produce paths suitable for different forms of exploration. It can also stabilize movements initiated by lower-level systems. Our analyses illustrate how recurrent neural dynamics and memory can shape behavior when embedded in closed loops.

Astrocytes actively regulate synaptic transmission and neuronal excitability, yet their role in orchestrating macroscopic cortical network regimes and slow-wave oscillations remains an active area of reasearch. This study investigates how bidirectional neuron astrocyte interactions shape emergent population dynamics using a computational network model of excitatory and inhibitory neurons coupled to an astrocyte. The results identify astrocytic feedback topology, rather than astrocytic coupling strength alone, as a key determinant of emergent cortical network dynamics. By systematically dissecting pathway-specific connectivity, it has been shown that the neuronal population driving astrocytic activation and the neuronal population receiving gliotransmission jointly determine whether the network occupies asynchronous irregular (AI), synchronous irregular (SI), synchronous regular(SR), asynchronous regular(AR) or quiescent regimes.Directing gliotransmission selectively onto excitatory neurons consistently promotes population synchrony regardless of the population influencing astrocytic dynamics, whereas selective modulation of inhibitory interneurons induces network quiescence via strong suppression. Under dual-target gliotransmission, network synchrony is dictated by the population driving astrocytic dynamics: excitatory-only drive promotes synchrony, while combined or inhibitory-specific drive preserves asynchronous states. Furthermore, the model reveals that astrocytic signaling kinetics provide an additional temporal control mechanism that regulates the frequency and persistence of self sustained up states.

Brain network organization emerges from ongoing network dynamics that continuously create, maintain, and reorganize connectivity patterns. At both the structural and functional levels, these dynamics shape network evolution throughout the lifespan. Here, we introduce a data-driven framework based on Stochastic Actor-Oriented Models (SAOMs), which model longitudinal network changes as a process of local edge formation and dissolution driven by local-connectivity factors. Applied to functional and structural brain networks from an aging cohort, the resulting models recovered a set of interacting mechanisms that collectively promote hub formation, short-range connectivity, and modular organization. These factors were derived through a novel data-driven factor-selection procedure rather than specified a priori, allowing network mechanisms underlying longitudinal change to be identified directly from observations. Functional networks exhibited substantially higher rates of change than structural networks, suggesting more frequent opportunities for network maintenance and reorganization. Structural networks additionally showed despecification in the hub-forming mechanisms with cognitive impairment. These results support a view of brain network organization as an actively maintained process emerging from ongoing local connectivity dynamics. More broadly, this framework provides a general approach for studying longitudinal network dynamics through the estimation of network-generating mechanisms over time.

Host immunity acquired through prior infections is a key factor shaping the spread of emerging variants. However, accounting for complete infection histories in mathematical models is challenging because the number of possible histories grows exponentially with the number of variants. Here, we present a flexible framework for modeling the co-circulation of multiple variants emerging at arbitrary times while incorporating cross-immunity and variant-specific characteristics. We introduce three tractable approximations: truncation, which retains only infection histories up to a given number of strains; one variant at a time, which is exact when variants circulation does not overlap; and two variants at a time, which is exact when at most two strains co-circulate. We systematically evaluate these approximations across a range of cross-immunity levels and inter-variant emergence delays. Truncation approximations perform best under short emergence delays and strong cross-immunity, whereas the other approaches outperform them at longer delays. When applied to SARS-CoV-2 variant dynamics, the second-order truncation and the two variants at a time approximation accurately capture incidence patterns, whereas the other approaches perform well only for specific subsets of variants. These results identify the parameter regimes in which simplifying assumptions remain valid, provide guidance for model selection, and highlight the key role of infection history in shaping epidemic trajectories.

The discrepancy between chronological age and predicted brain age, derived from neuroimaging data, serves as a biomarker for neurological health. However, the exact electroencephalography (EEG) mechanisms contributing to the variation of brain age are yet to be understood. This paper comprehensively investigated the relationship between brain age estimated from EEG-based functional connectivity and cognitive or mental manifestations of healthy adults. A mean absolute error (MAE) of 5.97 and R-squared (R2) of 0.85 were reported for training data, while an MAE of 10.73 and R2 of 0.56 were reported for the prediction data. Increased brain age was found to be negatively related to the scores of memory and attention tasks. Most young adults (19 of 26) suffering from mental symptoms such as addictions, depression, phobia, and anorexia nervosa demonstrated higher brain age than their chronological age. Alcohol consumption was also significantly correlated to the difference between brain and chronological ages. The functional connectivity of frontal and central motor regions was found to be most distinguishing between individuals with high and low brain ages. These brain regions were significantly correlated with brain age but not chronological age, suggesting a relatively stronger relationship with biological age. Ablation studies further confirmed the importance of the frontal brain and all bands EEG in the prediction of brain age. This work advances the understanding of EEG mechanisms contributing to brain age and could provide an interpretation for physiological or psychological conditions associated with brain age.

Coal-fired power plants remain a major source of fine particulate matter (PM2.5) exposure and mortality in the United States. Announced retirement dates mark when those burdens are expected to end, but rising electricity demand, partly from data centers supporting cloud computing and artificial intelligence, has led utilities and regulators to revisit them. Of 50 coal plants scheduled in January 2024 to retire before 2035, 20 had later or removed dates by January 2026. Projecting coal PM2.5 and mortality among Medicare beneficiaries from the 20 plants for 2026-2035, we estimate the revised schedule would result in 1,256 additional deaths (1,136 to 1,376), raising mortality to 3.1 times the original burden. Eighteen plants operate in balancing authorities with hyperscale data-center demand, and federal orders and utility filings supporting several plants' operation cited data-center growth. Retirement schedules are revised faster than health consequences are assessed, and those delays carry a measurable mortality cost.