Chaos, Solitons & Fractals

Mass-conserved reaction-diffusion systems are used as mathematical models for various phenomena such as cell polarity. Numerical simulations of this system present transient dynamics in which multiple stripe patterns converge to spatially monotonic patterns. Previous studies indicated that the transient dynamics are driven by a mass conservation law and by variations in the amount of substance contained in each pattern, which we refer to as "pattern flux". However, it is challenging to mathematically investigate these pattern dynamics. In this study, we introduce a reaction-diffusion compartment model to investigate the pattern dynamics in view of the conservation law and the pattern flux. This model is defined on multiple intervals (compartments), and diffusive couplings are imposed on each boundary of the compartments. Corresponding to the transient dynamics in the original system, we consider the dynamics around stripe patterns in the compartment model. We derive ordinary differential equations describing the pattern dynamics of the compartment model and analyze the existence and stability of equilibria for the reduced ODE with respect to the boundary parameters. For a specific parameter setting, we obtained results consistent with previous studies. Moreover, we present that the stripe patterns in the compartment model are potentially stabilized by changing the parameter, which is not observed in the original system. We expect that the methodology developed in this paper is extendable to various directions, such as membrane-induced pattern control.

In this study, resource-constrained learning methods were developed as a model for the learning behavior of the fly brain, specifically the mushroom body. Recent research on the mushroom bodies of flies shows that unfamiliar odors activate certain output neurons (MBONs); however, these effects are rapidly suppressed upon repeated exposure to the same odor. Such MBON behaviors appear to reflect odor learning. We investigated how flies continue learning about odors throughout their lives despite their small brains. Researchers have suggested that learning about new odors can help flies forget existing memories. Therefore, we hypothesized that the main reason for continual learning is that it serves as a strategy for forgetting. To test the validity of this hypothesis, we designed three models using a kernel perceptron. This approach is suitable for estimating ongoing learning capacity within a budget. According to the results of computer simulations and theoretical analysis, the model demonstrated the importance of forgetting mechanisms for two reasons: first, to prepare for subsequent learning sessions, and second, to reduce the negative effects of deleting memories.

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.

The brain is believed to process information efficiently in a different manner from deep learning-based artificial intelligence (AI). Brain-like next-generation AI is gaining attention owing to its potential to perform human-like, highly adaptive, robust, and power-efficient computation. To realize such AI, one crucial approach is the bottom-up implementation of the neuronal systems, capturing their electrophysiological characteristics in electronic circuits. However, this neuromorphic approach generally focuses on simplified neuronal models that do not refer to many biological findings. Developing closer-to-brain models is a natural direction that serve as a fundamental computing model for next-generation AI. One of the constraints of neuromorphic circuits is the bit resolution of synaptic efficacy memory, as the memory footprint scales with it precision. Although low-resolution synaptic efficacy is essential for minimizing memory circuit footprint and energy consumption, it generally leads to performance degradation in many tasks such as the spatio-temporal spike pattern detection. This study proposed a closer-to-brain learning rule that incorporates heterosynaptic plasticity (HP) induced by glutamate spillover. It is demonstrated that our model mitigates the performance degradation associated with low-bit resolution synaptic efficacy, achieving the pattern detection success rate with 3-bit resolution synaptic efficacy, which is comparable to 64-bit floating-point precision. Furthermore, the findings of the study indicate that HP based model accelerates the convergence of the synaptic effcacy and effectively potentiates the synapses relevant to the pattern detection while suppressing irrelevant ones, thereby promoting a bimodal distribution of synaptic efficacies. These findings may provide a basic framework for constructing an energy-efficient, brain-like next-generation AI that maintains high performance under hardware constraints.

Alzheimers disease (AD) is characterized by the accumulation of amyloid-{beta} (A{beta}), yet the specific link between plaque burden and cognitive decline remains a subject of intense investigation. This paper presents a mathematical model that simulates the coupled dynamics of A{beta} monomers, soluble oligomers, and fibrillar species in the brain tissue. By modifying existing moment equations to include a dedicated conservation equation for A{beta} monomers, the model explores how various microscopic processes, such as primary nucleation, surface-catalyzed secondary nucleation, fibril elongation, and fragmentation, contribute to macroscopic disease progression. Central to this study is the concept of "accumulated neurotoxicity" as a surrogate marker of biological age, defined as the time-integrated concentration of soluble A{beta} oligomers. Unlike plaque burden, accumulated neurotoxicity cannot be reversed, and the harm it causes depends critically on the sequence of events that produced it. Numerical results demonstrate that while plaque burden and neurotoxicity both increase over time, their relationship is non-linear and highly sensitive to the efficiency of protein degradation machinery. Specifically, impaired degradation leads to a rapid advancement of biological age relative to calendar age. The model further identifies oligomer dissociation and fibril fragmentation as potential protective mechanisms that can counterintuitively reduce neurotoxic burden by diverting monomers away from the soluble oligomer pool. These findings provide a quantitative framework for understanding why individuals with similar plaque burdens may experience vastly different cognitive outcomes, underscoring the importance of targeting soluble oligomers early in therapeutic interventions.

In previous studies by the author on binocular vision with the asymmetric eye (AE), which models a healthy human eye with misaligned optical components, the results were primarily presented in the Rodrigues vector (RV) framework and supported by simulations and 3D visualizations in GeoGebras dynamic geometry environment. In this paper, the novel geometric kinematics of the human eye, i.e., the eye with misaligned optics, and simplified assumptions about eye rotations (the eyes translational movements are disregarded) are developed within the framework of rigid-body rotations. Despite the eyes misaligned optical components (all eyes axes differ), the geometric formulation, which can only be approximated, yields excellent accuracy as demonstrated by simulations. The originality of the analysis lies in a precise geometric decomposition of the eyes posture changes into torsion-free (geodesic) and torsional (non-geodesic) rotations. This decomposition is extended to the corresponding decomposition of the angular velocity. A novel derivation of the eyes angular velocity from the RV formulation of the eye kinematics is proposed.

Sylvatic Yellow Fever (YF) is an infectious mosquito-borne disease with significant epidemiological relevance due to its widespread distribution and high lethality for human and non-human primates, particularly in tropical regions of the planet such as in Brazil. Identifying regions and periods of high environmental suitability for the occurrence of YF is essential for preventing or mitigating its burden, as it enables the efficient allocation of surveillance efforts, prevention, and implementation of control measures. Environmental modeling of YF occurrence has proven to be an effective approach toward this goal; however, its effectiveness strongly depends on the modeling framework's capabilities as well as the spatial and temporal precision of all associated data. We propose a fine-scale geospatial modeling of YF environmental suitability that is based on a generative machine-learning ensemble method built on a large set of high-resolution environmental covariates. First, we take the spatiotemporal statistical description of the environment of each of the 545 YF cases from 2019--2024 up to 30 m/monthly resolution at three buffer scales: 100 m, 500 m, and 1000 m ratios. Then, we perform a feature selection and train hundreds of One-Class Support Vector Machine submodels to form a robust ensemble model, whose predictions are projected to a 1x1 km resolution grid of Brazil under several metrics, exceeding seven million ensemble evaluations. The predictions ranked the Southern Brazil region with the highest mean suitability for YF, with a level of 0.64; Southeast comes next with 0.46, followed closely by Central-West region (0.44), North (0.39), and finally Northeast (0.28). The model exhibited high uncertainty for the North region, indicating that data collection efforts are much needed in this region. As for the environmental covariates, a feature analysis pointed out that Land use and cover accounts for the largest influence in the model output.

Sensorimotor learning and tool use involve synchronizing with external dynamics. Many everyday tools possess nonlinear hidden dynamics. Here we investigate how learning to synchronize with the complex dynamics of a tool depends on the degree of predictability and reciprocal coupling between user and tool. We introduce the concept of optimal coupling to measure adaptive user-tool coordination. Groups of participants practiced tracking an auditory stimulus in three conditions: 1) the tool was non-interactive and produced a periodic stimulus, 2) non-interactive and unstable stimulus, and 3) unstable but interactive stimulus which was coupled weakly to the participants movements and thus afforded control. Learning, retention, and transfer to visual modality were assessed using unpracticed test stimuli. Directional effective coupling was quantified using transfer entropy. Results showed that learning tended to be task-specific and there was no transfer to the visual modality. Interactive unstable practice exhibited some retention and generalization. We found a convergent reorganization of coupling during practice with the interactive unstable tool: stimulus-to-human coupling started high and decreased while human-to-stimulus coupling started low and increased. This suggests that embodiment of personalized rehabilitation technologies brings optimal reciprocal coupling in which sensorimotor-tool control is consistent with the minimal intervention principle postulated for within-body control.

Road traffic accidents represent a global public safety crisis, necessitating advanced computational tools for accurate injury severity prediction and effective decision support. This study evaluates high-performing ensemble machine learning models, including AdaBoost, XGBoost, LightGBM, HistGBRT, CatBoost, Gradient Boosting, NGBoost, and Random Forest, using a comprehensive National Highway Traffic Safety Administration (NHTSA) dataset from 2018 to 2022. While all models demonstrated exceptional predictive accuracy, with HistGBRT achieving the highest overall accuracy of 92.26%, a defining achievement of this work is the perfect classification (100% precision and recall) of fatal injuries across all ensemble architectures. To bridge the gap between predictive performance and actionable intelligence, this research integrates SHapley Additive exPlanations (SHAP) to provide both global insights into dataset-wide risk factors and local, instance-specific rationales for individual crash events. The global analysis identified ethnicity, airbag deployment, and harmful event type as primary drivers of injury severity, while local force and waterfall plots revealed the precise "push and pull" of variables for specific incidents. The results offer a robust, interpretable framework for stakeholders tasked with improving traffic safety and mitigating crash-related harm.

Pulmonary embolism (PE) is a sudden blockage of lung arteries, usually caused by a blood clot that travels from the deep veins of the legs. As the world becomes more sedentary and lifestyle diseases emerge, deaths from PE are expected to rise in the next 20 years. For instance, the United States records annual deaths of 60 per 100,000 people. The degree to which these deaths are affected by demographic, socioeconomic and environmental predisposing factors as well as how they vary across time and space remains an open science question. In this paper, we conduct a detailed statistical and spatial-temporal study PE mortality counts across US counties from 2005 to 2022. Our study shows that study shows that PE mortality is not randomly distributed in space and time but concentrated in most counties in Arkansas, Mississippi, Kansas, Missouri, Oklahoma, Louisiana, Nebraska, Tennessee, and Texas. We also established that age is a statistically significant predictor (mean coefficient of 0.52) of PE mortality especially in counties of Mississippi, Kansas, Missouri, Tennessee, Illinois, Kentucky, Texas and Virginia. Our results thus provide empirical support for prioritizing regionally targeted PE prevention policies. Furthermore, the adopted county-level analysis uncovered granular geographic patterns that are usually obscured in state or national level analysis. Our study thus provides actionable evidence to support geographically tailored strategies aimed at reducing mortality by pinpointing counties with consistently elevated PE mortality risk at different timescales.

Against the backdrop of global climate change and accelerating population mobility in 2025, chikungunya fever (CHIKF) exhibited a trend of worldwide spread, significantly increasing the difficulty of controlling tropical mosquito-borne diseases. To enhance the precision of intervention strategies, this study developed an age- and sex-structured human-mosquito interaction dynamic model based on data from the largest CHIKF outbreak ever recorded in China, and conducted a targeted analysis of prevention and control strategies. By decomposing the basic reproduction number and examining population heterogeneity, asymptomatic males aged 15-59 years were identified as the core transmission group. Optimal control analysis revealed that the synergistic implementation of three measures-- reducing the effective human-to-mosquito transmission rate, reducing the effective mosquito-to-human transmission rate, and suppressing mosquito population density--could reduce the overall infection rate by 95.7586%. Among these, mosquito population suppression should be prioritized as a universal core strategy; however, its protective effect on females aged 60 years and above was relatively weak, warranting particular attention. The study further demonstrated that asymmetric intensity combinations targeting these three intervention pathways--such as intensity profiles of "10%, 90%, 90%" or "60%, 80%, 90%"--could achieve effective outbreak control. This research elucidates population-specific transmission patterns and key pathways for intervention intensity, providing a theoretical and strategic foundation for the precise control of mosquito-borne diseases. It also provides actionable operational insights to support rapid response and strategy optimization for future emerging outbreaks. Author summaryCHIKF is a mosquito-borne viral disease that is gradually spreading from tropical regions to other areas. To achieve more precise control of this disease, we developed an age- and sex-structured analytical model based on the largest CHIKF outbreak in China, aiming to provide a scientific basis for responding to potential future outbreaks with inherent uncertainties. The study found that asymptomatic males aged 15-59 years were the primary drivers of transmission and should be prioritized as a key population for reducing viral spread in prevention efforts. When evaluating the effectiveness of different intervention strategies, females aged 60 years and above were the least affected by the implemented measures, indicating that this group should strengthen personal protection to lower their infection risk. Among all control measures, mosquito suppression was the most effective, suggesting that vector control strategies should be prioritized in future outbreak responses.

BackgroundTo control leishmaniasis, chemotherapy drugs are currently under development. However, these drugs often exhibit poor efficacy and are associated with toxicity, adverse effects, and drug resistance. At present, no specific drug is available for the treatment of leishmaniasis. Meanwhile, vaccine research is ongoing. Recent studies have analysed some experimental vaccines using mathematical models. AimIn previous work, drug targeting was focused on the entire human body rather than specifically addressing infected macrophages and parasites. In our current approach, we aim to eliminate infected macrophages and parasites through nano-drug design. Specifically, we utilise two types of nanoparticles: iron oxide and citric acid-coated iron oxide. Moving forward, we plan to advance this strategy using mathematical modelling of macrophage-parasite interactions. MethodsWe design PDE-based models of macrophages and parasites, incorporating cytokine dynamics, to support nano-drug development. Drug efficacy is estimated using posterior distributions to analyse phenotypic fluctuations of macrophages and parasites during the design phase. We investigate implicit and semi-implicit treatment schemes, focusing on energy decay properties. To model drug flow during treatment, we introduce a three-phase moving boundary problem. Comparative analyses are conducted to evaluate macrophage and parasite behaviour with and without treatment. Finally, the entire framework is implemented within a virtual lab environment. ResultsThe results show that the nano-drug exhibits better efficacy compared to combined drug doses. We analysed and compared two types of nano-drug particles: iron oxide and citric acid-coated iron oxide. We discuss how the drug effectively targets and eliminates infected macrophages and parasites. ConclusionOur models results and simulations will support researchers conducting further studies in nano-drug design for leishmaniasis. These simulations are performed within a virtual lab environment.

Infectious disease dynamics are strongly shaped by human mobility, social structure, and heterogeneous contact patterns, yet many epidemic models do not jointly capture these features. This study develops a spatial metapopulation epidemic model incorporating recurrent group-switch interactions to represent real-world transmission processes. Building on the Movement-Interaction-Return framework, the model integrates household structure, age-stratified contacts, and mobility between locations within a single SEIR framework. Using UK demographic, mobility, and social contact data, the model quantifies how within- and between-group interactions, mobility rates, and location connectivity influence epidemic spread. Both deterministic and stochastic simulations are implemented to analyse outbreak dynamics, variability, and fade-out probabilities for COVID-19-like and Ebola-like infections. Results shows that highly connected locations drive faster transmission, earlier epidemic peaks, and greater difficulty in containment, whereas larger but less connected locations tend to produce slower, more localised outbreaks despite their population size. Comparative analysis reveals that COVID-19-like infections spread rapidly and remain difficult to control even under interventions, while Ebola-like infections exhibit slower dynamics and are more effectively contained, particularly under targeted measures. Non-pharmaceutical interventions, particularly widespread closures, substantially reduce infections, hospitalisations, and deaths, although effectiveness depends on timing and pathogen characteristics. These findings highlight the importance of integrating mobility, clustering, and demographic heterogeneity to inform targeted and effective epidemic control strategies.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has continuously evolved since its emergence in the human population in 2019. As of 1st August 2025, more than 1,700 Omicron subvariants have been designated by the Pango nomenclature system. The Pango nomenclature system designates a new lineage based on genetic and epidemiological information of SARS-CoV-2 strains. However, there is a possibility that strains that have similar genetic backgrounds and the same phenotype are given different Pango lineage names. In this paper, we propose a new algorithm, called FindPart-w, which can identify groups of viral lineages that share the same relative effective reproduction numbers. We introduced a new lineage replacement model, called the constrained RelRe model, which constrains groups of lineages to have the same relative effective reproduction numbers. The FindPart-w algorithm searches the equality constraints that minimise the Akaike Information Criterion of constrained RelRe models. Using hypothetical observation count data created by simulation, we found that the FindPart-w algorithm can identify groups of lineages having the same relative effective reproduction number in a practical computational time. Applying FindPart-w to actual real-world data of time-stamped lineage counts from the United States, we found that the Pango lineage nomenclature system may have given different lineage names to SARS-CoV-2 strains even if they have the same relative effective reproduction number and similar genetic backgrounds. In conclusion, this study showed that viruses that had the same relative effective reproduction number were identifiable from temporal count data of viral sequences. These findings will contribute to the future development of lineage designation systems that consider both genetic backgrounds and transmissibilities of lineages.

Finite element (FE) head models are valuable tools for investigating brain injury mechanics, with their reliability critically dependent on accurate material modelling. White matter (WM) is often considered mechanically anisotropic due to its aligned axonal fiber architecture and is commonly represented using fiber-reinforced hyperelastic formulations such as the Gasser-Ogden-Holzapfel (GOH) model. A fundamental assumption of the GOH model is that fibers contribute only in tension and not in compression, requiring the use of tension-compression switches. However, inconsistencies were noted in the formulation of tension-compression switches with the influence on computational biomechanics unknown. To address this knowledge gap, three commonly used switching schemes - differing in both the switching parameter and the treatment of compressed fibers - were theoretically elaborated and numerical implementation within the GOH framework to simulate the mechanical anisotropy of WM in impact simulations. Results from the case-based and group-level analyses demonstrated that both the switching parameter and the treatment of compressed fibers affected WM deformation. Significant cross-scheme strain differences were noted in the first principal strain at the element level and fiber strain at the fiber level. These findings highlighted the mechanical role of tension-compression switch in the GOH-based brain modelling and advocated the adoption of fiber stretch itself as the switching parameter to discriminate the tensile and compressive fibers. The current study provides important guidance for the anisotropic constitutive models in brain tissue and calls for direct verification of the tension-compression switch hypothesis in axonal fibers.

Schizophrenia (SZ) is a chronic and complex mental disorder associated with neurobiological deficits. The complexity and heterogeneity of schizophrenia symptoms pose challenges for objective diagnosis, which is currently based on behavioral and clinical manifestations. Furthermore, other psychiatric disorders such as bipolar disorder or major depressive disorder are often misdiagnosed as schizophrenia. Consequently, manual screening through psychiatrist-patient interviews is not entirely reliable. This study aims to develop an automated SZ diagnosis scheme using electroencephalogram (EEG) signals as a complementary tool to assist psychiatrists. A novel method is proposed, utilizing features from time, frequency, and time-frequency domains to classify EEG signals from schizophrenia patients and healthy individuals. Time-domain features, frequency-domain features, as well as nonlinear and statistical features were extracted, and 10 feature combinations were selected based on importance using a hybrid mutual information and Sequential Forward Feature Selection approach. Classification was performed using K-nearest neighbors (KNN), weighted KNN, linear and nonlinear support vector machines (SVM) with radial basis function kernels, decision trees, linear discriminant analysis, and the naive Bayes method. Remarkably, three classifiers achieved 100% accuracy.

Understanding how animals produce a versatile locomotor repertoire requires unraveling the interplay between higher centers, decentralized locomotor circuits, and sensory feedback. However, the principles governing their integration remain elusive. We investigated amphibious centipedes through stepwise neural lesions and neuromechanical modeling. Behavioral experiments revealed that while decentralized circuits autonomously generate coordination, the brain and subesophageal ganglion provide situational flexibility, such as modulating trunk undulation and initiating leg folding. Integrating these findings, our model demonstrated how higher centers selectively inhibit or release lower circuit dynamics. Simulations verified that varying only a few descending control parameters reproduces transitions between slow walking, fast walking, and swimming. This work may capture the essence of the locomotor circuitry that harnesses decentralized self-organization to coordinate the bodys large degrees of freedom.

Routine ICU data offers valuable insights into daily physiological rhythms. While traditional methods assume these cycles maintain fixed periods and amplitudes, their inherent variability requires dynamic estimation of instantaneous trends. Wavelet transform effectively resolves circadian oscillations, especially for frequently measured vital parameters. We present novel extensions to the Continuous Wavelet Transform (CWT) power spectral analysis to better detect and segment subtle temporal patterns. Using this approach, we uncover hidden circadian patterns in cardiovascular vitals such as Heart Rate (HR) and Mean Blood Pressure (MBP) measured over five days in a retrospective cohort of 855 ICU patients. By quantifying non-stationary rhythms, we identified diurnal and semi-diurnal oscillations varying in period and power according to delirium and deep sedation. Notably, HR exhibits a clear diurnal and semi-diurnal rhythm when delirium is absent. Overall, our framework supports the CWT as a powerful tool for analyzing complex physiological signals, particularly vital signs. Crucially, our findings suggest that cardiovascular rhythm disruption can be associated with ICU-related delirium and deep sedation.

Variability in gene expression among single cells and growing cell populations can arise from the stochastic nature of protein synthesis, which often occurs in random bursts. This study investigates the variability in the expression of a growth-sustaining protein, whose concentration is regulated by a negative feedback loop due to cell growth-induced dilution. We model the distribution of protein concentration using a Chapman-Kolmogorov equation for single cells and a population balance equation for growing cell populations. For single cells, we derive an explicit solution for the protein concentration distribution in state space and represent it as a Bessel function in Laplace space. For growing populations, we find that the distribution satisfies a Heun differential equation with singular boundary conditions. By addressing the central connection problem for the Heun equation, we quantify the population-level protein distribution and determine the Mathusian parameter, which characterizes population growth. This work provides a comprehensive analytical framework for understanding how stochastic protein synthesis impacts gene expression variability and population dynamics.

Despite the remarkable progress of artificial intelligence represented by large language models, how AI technologies can contribute to the construction of evidence in evidence-based medicine (EBM) remains an overlooked issue. Now, we need an AI that can be compatible with EBM. In the present paper, we aim to propose an example analysis that may contribute to this approach using variable Vision Transformer.