Mathematics

Neural temporal point processes (NTPPs) are powerful tools for modeling sequences of timestamped events with statistical temporal structure. Density-based NTPPs, in particular, are an interesting opportunity to merge the universal function approximation capability of neural networks with a defined statistical model in a way that has many potential applications. We demonstrate one such application to heartbeat dynamics, a physiologic point process. We specifically apply a lognormal mixture NTPP to compute instantaneous estimates of the mean and standard deviation of beat-to-beat intervals. We compare our results to the state of art (Barbieri et al.) point process model for heartbeat dynamics, which uses a more physiologically rigorous inverse Gaussian model. We find that the NTPP model maintains reasonable accuracy while improving upon robustness to noise.

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.

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.

Employing DLA methods, this paper explores the self-assembly of collagen fibers and resulting fibrosis at three scales up to the scale of regular lobule models. This allows a mechanistic exploration of the effects of collagen on drug transport (flow and diffusion) and metabolism. In addition, this method permits an analysis of fiber growth characteristics. First, variations of the DLA method of Parkinson et al (1994) will be used to generate multiple explicit collagen microfibril self-assembly using DLA particles in one dimension using cubic grid blocks of (4 mm)3 in a 240 x 20 x 20 grid model. The second stage will be to assess the consequences of various densities of these fibers in three dimensions on flow reductions at a higher scale. Here we utilize DLA methods in cubic grid blocks of (80 nm)3 to mimic 3D collagen self-assembly of fibrils. We then apply a pressure gradient or specified flow rates across a spatially gridded version of these models to quantify flow effects. This region represents a local zone of liver tissue affected by fibrosis. Analytic models of fibrotic effects on flow are employed for comparison. A third stage explores the implications of fibrosis in a liver lobule model using multiple grid blocks of size 3200 mm to represent the lobule tissue. Here, a continuum model of fiber density is employed, based on the previous two scales. The model also includes the effects of additional grid blocks representing sinusoidal flow paths found in the lobule. We contrast and quantify drug propagation and metabolism of molecular dissolved versus nanoparticle delivery vehicles in fibrotic media, achieved by upscaling explicit collagen distributions to appropriate average values.

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.

Synthetic data are becoming increasingly important for computational studies of cophylogeny, including machine learning inference, benchmarking, and method testing. Several generators have been proposed to produce such data, but each relies on different assumptions about host-symbiont coevolution. These assumptions are often implicit and rarely examined, even though results can depend strongly on the synthetic model being used. In this article, we present a systematic structural analysis of representative cophylogeny generators under controlled scenarios. The goal is to make their assumptions explicit and to understand how these choices shape the synthetic data they produce as well as the conclusions that may be drawn from them.

The initial response of populations to the SARS-CoV-2 virus reduced the incidence of COVID-19 cases. However, this success was shorted lived once most populations relaxed most restrictions, resulting in an increase in infections. This feedback contributed to additional pandemic waves. The temporal unfolding of behavioural changes in populations present a challenge to mathematical models for disease dynamics. Coupled behaviour-disease models with varying levels of complexity accounting for several factors have been used to capture behavioural dynamics and SARS-CoV-2 transmission, with varying results. To study the impact of model complexity on the predictive power of models, here we formulate five coupled behaviour-disease models with varying structure and number of parameters. We fit the models to SARS-CoV-2 infection incidence and stringency of control interventions from five European countries in the first wave, and study how well these fitted models predict the second wave. We show that models with more parameters do not necessarily have a greater ability to explain and predict key features of a pandemic wave. Hence, our results show that a relatively simple coupled behaviour-disease model with important parameters can do an adequate job of providing information about the pandemic wave. Additionally, our findings show that complex models can be country-specific, working better for some countries and poorly for others. We conclude that modellers should not always opt for the most complicated possible models, if the data do not support their use.

Scaling laws help determine the optimal data size for training large models but are established in domains where the target is deterministic. Physiological signals are different: heartbeat sequences are stochastic, so part of the error is irreducible even with large amounts of data. Metrics such as MAE do not account for non-deterministic behavior, and therefore assessing scaling requires evaluating distributional calibration (measuring how well predicted probability densities capture true conditional characteristics). We formulate a scaling law metric(n) = E + A n- and evaluate it with five metrics: accuracy (MAE, RMSE), distributional calibration (KS distance, goodness-of-fit), and training objective (negative log loss) using a neural temporal point process trained on a cohort of four-ECG datasets. The law fits all five metrics. While point accuracy is near saturation at n = 183, KS distance and goodness-of-fit improve by 6% and 12% respectively when extrapolated to 10,000 subjects, showing that scaling decisions in stochastic domains must be guided by distributional calibration rather than point accuracy.

AO_SCPLOWBSTRACTC_SCPLOWIn this work, we publish the 3D unsteady Navier-Stokes numerical simulations and meshes of coronary arteries reconstructed from invasive X-ray coronary angiograms acquired during in the Fractional Flow Reserve versus Angiography for Multivessel Evaluation 2 (FAME 2) trial. Out of the 914 clinical images, 779 vessels are successfully reconstructed and meshed. The remaining 135 vessels have been discarded since they exhibited self-intersecting geometry during the reconstruction process. The meshes are hexahedral and all of them have the same number of vertices and identical connectivity; their high quality is demonstrated using standard mesh quality indices. The simulations are performed using the Finite Element Method (FEM) with state-of-the-art coronary boundary conditions applied at the outlet. The motivation behind this effort relies from the scarcity of publicly available numerical haemodynamics data, despite the growing interest in data-driven modeling and machine learning techniques. The database is available at the link: https://doi.org/10.7910/DVN/GPCUNS

Animals use long-range signals, such as hormones and neural signals, to coordinate the actions of distant organs. There is no precise, quantitative framework that explains the problems these control systems must solve and thus predicts their behavior under varied conditions. We consider this problem in the context of blood glucose regulation by the hormone insulin, the failure of which produces diabetes. We show that existing mathematical models of glucose regulation admit equivalent control strategies with no hormones at all, and thus cannot explain the need for hormonal regulation. We therefore introduce a minimal model of inter-organ variations in local glucose, and show that control strategies based on local glucose measurements face severe trade-offs between different control objectives. In contrast, we show that hormonal control signals from the pancreas can overcome these limitations. By exposing the benefits of hormonal control, our work paves the way to a detailed understanding of physiological design principles, with possible implications for the engineering of an artificial pancreas.

High pathogenicity avian influenza (HPAI) H5N1 clade 2.3.4.4b has caused a global panzootic with unprecedented impacts on wildlife and livestock, making evidence-based disease mitigation and outbreak response critical. In this paper, we describe a spatiotemporal mechanistic model of infectious disease dynamics developed for the HPAI Modelling Challenge and its implications for forecasting and policy in Australia. To emulate emergency response conditions, we adapted an existing model for rapid deployment rather than developing a bespoke model. We refined the model iteratively across the challenge to better analyse the provided outbreak data. Throughout the challenge, we accurately forecast temporal trends and local outbreak spread, but could not predict rarer, long-distance dispersal events. The challenge ended before HPAI H5N1 was first detected in Australia (June 2026), providing a critical opportunity to test our response modelling readiness for an incursion in wildlife and potential spillover into commercial poultry. Our experience identifies three key considerations for Australia's HPAI H5N1 preparedness: targeted enhancements to our model to improve forecast precision and enable scenario-based policy evaluation; the critical value of pre-existing modelling infrastructure for rapid emergency response; and sustained collaboration between research and policy institutions to align modelling capabilities with outbreak response requirements.

We introduce a minimal individual based model for population intelligence that retains three structures absent from standard single agent descriptions: a manifold valued intelligence state, endogenous population turnover, and heritable lineage dependent reproductive fitness. The validated S^1 intelligence diffusion was extended with neutral logistic birth death dynamics. Each individual occupies an angle on the circle S^1; noisy mean field attraction produces collective synchronization; logistic birth death dynamics regulate population size; and reproductive rates can depend on lineage and position relative to designated safe or unsafe directions. This nested construction is intentionally small enough to admit an analytic equilibrium benchmark while remaining capable of selection, invasion, and safety transitions. Population size returned toward carrying capacity from (N(0)=200,800,1600), with tail means (775.7,800.3,805.1) for K=800. Across K=100 to 1600, the intelligence equilibrium error scaled as K^{-0.513} , consistent with the canonical K^{-1/2} fluctuation rate, while the extinction rate was zero in 120 runs over the simulated horizon. The mean order parameter remained close to the original theoretical (r*=0.7242), as neutral demography predicts. Directional reproductive selection shifts a safety score to +0.7447 or -0.7448 while synchronization remains approximately 0.75, demonstrating that coordination is not equivalent to safety. These are controlled numerical results, not asymptotic proofs.

The measurement of light received at the cornea of the eye is a paramount consideration for the understanding of the relation between environmental illumination and the non-image-forming effects of light. The field of view (FOV) at the cornea is less than a full hemisphere, because it is partially occluded by human facial morphology. The International Commission on Illumination (CIE) has defined a standard model of human FOV. A suitably designed physical occluder attached to the sensor (of a light meter) has been proposed as a means of incorporating the effect of human FOV when taking measurements. Similarly, when using simulation to predict light received at the cornea, a geometrical description of the occluder at the eye point(s) can be added to the 3D model of the scene. The first occluder model proposed to represent CIE human FOV was enumerated in terms of: the CIE definition; the radius of the occluder; and, the radius of the light sensor disc. We present a simpler model based only on the CIE definition and the occluder radius. Both models were tested using a virtual goniophotometer. Various sensor response functions describing the spatial sensitivity across the sensor disc, including several we characterized through laboratory measurements, were included in the test. For all functions considered, the performance of the simpler occluder model was equivalent to or better than the model first proposed.

Chronic wounds (principally pressure sores, venous leg ulcers and diabetic foot ulcers) are a drain on global health services and remain a major area of unmet clinical need. Chronic wounds are characterised by a bacterial biofilm (densely aggregated colonies of bacteria encased by a matrix of extracellular polymeric substances), which hinders innate immune response and can prevent wound healing. Bioactive glass (BG) fibres doped with antimicrobial metal ions, such as silver, can offer a promising treatment for chronic wound infections, where silver is well known for its antimicrobial activity against a range of pathogens and is commonly used in wound dressings. We first present a system of non-linear partial differential equations to model the treatment of a chronic wound biofilm infection with BG fibres. The BG fibres are assumed to have two mechanisms of action against the biofilm: physical disruption of the top layers of the biofilm by the BG fibres; and release of antimicrobial silver ions from the BG fibres, which then diffuse into the biofilm and can kill the bacteria. Treatment-associated parameters are estimated from in vitro experimental data using a combination of least-squares minimisation and Approximate Bayesian Computation (ABC). Sensitivity investigations are performed on other parameters that cannot currently be calculated experimentally to investigate their influence on treatment efficacy. We thus predict key parameter regimes that should lead to biofilm eradication, crucially informing the future design of metal-doped BG fibres to maximise treatment efficacy. Author summaryChronic wounds are a huge drain on global health services and will become even more problematic due to an ageing population. Current treatment methods are often unsuccessful, where treatment failure is exacerbated by the presence of a biofilm infection. Biofilms consist of communities of bacteria that adhere to the wound surface and produce extracellular polymeric substances, which can protect the bacteria by acting as both a physical and chemical barrier. More recently, there has been a focus on biofilm-based wound care, where the aim is to firstly eradicate the biofilm infection, which then enables wound healing to occur naturally. Our aim is to produce a novel treatment that can target and eradicate the biofilm infection, followed by directly assisting the wound healing. Bioactive glass (BG) fibres doped with silver offer a promising treatment as they have both anti-biofilm effects and can also stimulate the wound healing process. Here, we restrict attention to their anti-biofilm properties. By developing a mathematical model, we can predict treatment outcomes under several different scenarios, the results of which can then be utilised during design of the BG fibres. Using this combination of computational and experimental approaches, we reduce both the cost and time of optimising this promising treatment.

Cognitive workload (CWL) assessment is relevant to a range of applications, such as monitoring driver fatigue and pilot attention, surgeon workload during complex procedures, and astronaut cognitive fatigue during long-duration missions. Eye-tracking datasets are generally small, which hinders the generalizability of the AI models. Time-series foundation models (TSFMs) have shown promise in mitigating this limitation as they are pretrained on large corpora and can be effectively fine-tuned with limited task-specific data. Although cognitive workload measurement has been explored in controlled settings, the ability of TSFMs to generalize to unseen individuals for CWL classification from eye-tracking data has not been studied. In this paper, two TSFMs, MOMENT and Moirai, were evaluated for CWL classification and compared against CNN, FFN, and LSTM baselines on two publicly available eye-tracking datasets. We used subject-level five-fold cross-validation in which data from each test subject were held out during training. We report accuracy, AUC, and F1-score with 95% confidence intervals. On the class-balanced EM-COGLOAD dataset, the pretrained TSFMs generalized markedly better to unseen subjects, with Moirai reaching 0.918 AUC and MOMENT 0.882 AUC, while the task-specific baselines remained near 0.70 AUC. On the class-imbalanced COLET dataset, even though the performance of all the models decreased, MOMENT was the most robust (0.670 AUC). Both TSFMs were also the most stable across held-out subjects, indicating that pretrained representations generalize more consistently across individuals than task-specific models in data-scarce eye-tracking settings.

Human Papillomavirus (HPV) infection among men who have sex with men (MSM) has become a significant public health concern, particularly in countries where male vaccination is unavailable. Given the high susceptibility of MSM to HPV and anal cancer, and the unavailability of HPV vaccination for males in low- and middle-income countries (LMICs), there is a need to identify alternative interventions for reducing disease transmission and burden in this population. The novel mathematical model presented in this article couples smoking behavior dynamics with HPV transmission and anal cancer progression among MSM. Smoking reduction is introduced as an intervention to assess its effects on disease transmission and burden. The basic reproduction number (R0) is derived using the next-generation matrix method, and a global sensitivity analysis is performed using partial rank correlation coefficients (PRCC) to identify the influence of model parameters on RR0. Further, the theoretical analysis of the model reveals a backward bifurcation, implying that RR0 < 1 is necessary but not sufficient to eradicate the disease. The study finds that smoking reduction among MSM reduces HPV infection and anal cancer burden relative to baseline projections without intervention. The joint effect of smoking reduction and vaccination shows that the critical vaccination coverage needed to achieve RR0 <1 decreases as the level of smoking reduction increases. A similar outcome is observed for contact reduction. These findings highlight the importance of concurrent interventions, which can significantly curtail the spread of HPV and reduce disease burden in both the high-risk group and the general population.

Mitochondrial reactive oxygen species (ROS) are implicated in cardiac dysfunction, but complex dynamic interactions between ROS, intracellular calcium, and electrophysiology make it difficult to resolve mechanisms experimentally. We developed the Zukowski excitation-contraction-mitochondrial-ROS (ECM-ROS) model, a computational model that couples human ventricular electrophysiology with mitochondrial calcium handling, energetics, ROS production, and ROS dependent modulation of the ryanodine receptor, SERCA, L-type calcium current, and late sodium current. Model predictions were evaluated against independent experimental measurements of ROS induced changes in action potential duration and intracellular calcium. We then used the model to characterize ROS calcium feedback across physiological pacing rates and applied it to doxorubicin induced oxidative stress. Increasing cytosolic calcium produced nonlinear amplification of mitochondrial activity and cytosolic ROS, with greater amplification at faster pacing rates. Moderate ROS elevation initially enhanced calcium release, whereas greater oxidative stress depleted sarcoplasmic reticulum calcium stores. During simulated doxorubicin exposure, faster pacing lowered the level of oxidative stress required to produce calcium dysregulation and action potential prolongation. Mitochondrial ROS and calcium accumulation preceded detectable electrophysiological remodeling. In populations incorporating variability in ion channel expression, neither doxorubicin induced oxidative stress nor subtle pharmacological IKr block alone produced early afterdepolarizations. However, early afterdepolarizations were predicted to emerge with combined perturbations. These findings establish a computational framework for investigating bidirectional coupling among mitochondrial function, ROS, calcium handling, and human cardiac electrophysiology. The model generates testable predictions regarding the early detection of oxidative cardiac injury and the physiological conditions that increase susceptibility to arrhythmia.

Background and ObjectiveAccurately parameterizing dynamic, time-varying interactions in physiological systems is a methodological challenge, as global causal discovery methods may obscure transient, local fluctuations. This study introduces tempord, an open-source Python library designed to estimate local temporal orders and evaluate the short-term stability, directionality, and strength of causal links in non-stationary biological signals. MethodsThe algorithm estimates temporal relationships by keeping one signal stationary while iteratively shifting another one within a sliding window. To parameterize optimal inter-signal shifts (causal vector, CV), the framework utilizes linear modeling or time series distance metrics. The methodology was validated through a simulation study on synthetic bivariate signals with mathematically imposed dynamic phase delays, under both deterministic and noisy conditions. Furthermore, in-vivo capabilities were demonstrated by evaluating cardiorespiratory coupling dynamics across spontaneous and music-induced relaxation breathing states. ResultsThe simulation study demonstrated that the extracted CV trajectories precisely aligned with ground-truth temporal delays, assessed using mean absolute error and root mean square error for both noise-free and noisy synthetic data. In-vivo application demonstrated dynamic temporal stability and the detection of minor step changes during autonomic nervous system state transitions. ConclusionsThe tempord Python package bridges the gap between global causal discovery and local beat-by-beat statistical parameterization. It provides a robust "bottom-up" analytical instrument for investigating the transient mechanisms governing complex biological networks.

Background: Tuberculosis remains a persistent infectious disease whose control is complicated by latent infection, delayed treatment, incomplete recovery, reinfection, and continuing transmission from infectious individuals. Although treatment is central to tuberculosis management, it is frequently represented only as a transition parameter in mathematical models rather than as a separate epidemiological state. In this study, treatment was therefore incorporated explicitly as an independent compartment so that its influence on transmission, recovery, disease-induced mortality, and long-term disease persistence could be evaluated. Methods: A deterministic nonlinear compartmental model was formulated by dividing the total population into susceptible, exposed, actively infected, treated, and recovered classes. Reinfection of recovered individuals, progression from latent infection to active disease, movement of infectious individuals into treatment, treatment-associated recovery, natural mortality, and disease-induced mortality were included. Positivity and boundedness of the solutions were examined to establish biological validity. The basic reproduction number, R0, was derived through the next-generation matrix approach. Disease-free and endemic equilibria were determined, and their local and conditional global stability properties were investigated using Jacobian analysis, the Routh-Hurwitz criterion, center manifold theory, Lyapunov functions, and LaSalles invariance principle. Normalized sensitivity indices, Latin hypercube sampling, partial rank correlation coefficients, and numerical simulations were also applied. Results: The disease-free equilibrium was shown to be locally asymptotically stable when ,R0<1 whereas sustained transmission and a unique endemic equilibrium were associated with R0>1. Under the stated reduced-model assumptions, stability of the endemic equilibrium was established. Transmission-related parameters were identified as the strongest positive contributors to disease persistence. In contrast, treatment and recovery parameters were found to reduce the reproduction number and infectious burden. Numerical simulations indicated that stronger treatment implementation and reduced transmission opportunities produced substantial reductions in active tuberculosis cases. Conclusion: Treatment was shown to function as both a clinical pathway and an epidemiological control mechanism. The proposed framework may support the design of treatment-centered strategies for reducing tuberculosis prevalence and preventing long-term endemic persistence.

Crickets are gaining attention as sustainable protein sources because of their high nutritional value and low environmental impact. Growth models are essential tools for optimising production by predicting growth characteristics. However, previous studies have not compared multiple non-linear growth models for crickets or explicitly considered environmental factors. We analysed the growth patterns of the two-spotted cricket (Gryllus bimaculatus) and the Asian cricket (Teleogryllus occipitalis) at multiple temperatures (25.0, 27.5, 30.0, 32.5 and 35.0 {degrees}C) using three non-linear models (Gompertz model, logistic model, and von Bertalanffy model) and combined the predicted body mass with observed survival rates to predict the optimal harvest time and temperature. All three models fitted the data well (R2 [&ge;] 0.97 in both species). The asymptotic body mass was highest at 30.0 {degrees}C, and the growth rate constant increased with temperature, reaching its maximum at 35.0 {degrees}C except for the logistic model in G. bimaculatus (32.5 {degrees}C). In addition, the predicted value of harvest, calculated by combining predicted body mass and observed survival probability, was highest at 30.0 {degrees}C in both species, reaching 13.82 kg/m3 at 38 days in G. bimaculatus and 7.12 kg/m3 at 62 days in T. occipitalis. These results suggest that 30.0 {degrees}C is the most suitable constant-temperature condition for maximising predicted productivity, although the optimal harvest timing differs between species.