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The significance of HER-1 and CA 125 lies in their ability to guide cancer diagnosis, treatment, and monitoring, improving personalized care and enhancing prognostic accuracy. The utilization of HER-1 and CA 125 as screening biomarkers for the anticipation of early-stage cancer and monitoring cancer progression is expanding due to the invasive and costly nature of present techniques. In this study, a novel stochastic sensor was developed for the simultaneous determination of HER-1 and CA 125 in whole blood, saliva, and gastric tumor tissue samples using a fast, easy, inexpensive, and portable method. The stochastic sensor was prepared by electropolymerization of cysteine on the surface of the Au-TiO 2 @rGO/SPCE sensor. The Au-TiO 2 @rGO nanocomposite was synthesized using a simple chemical reduction process. The proposed sensor showed wide linear concentration ranges and very low limits of quantification (LOQ). The concentration ranges were from 3.9 × 10 -14 to 3.9 × 10 -8  µg mL -1 , with a LOQ of 3.9 × 10 -14  µg mL -1 for HER-1. For CA 125, the concentration ranges were from 8.3 × 10 -14 to 8.3 × 10 -10 U mL -1 , with a LOQ of 8.3 × 10 -14 U mL -1 . Both biomarkers exhibit precise discrimination in different biological samples, with recoveries above 96.78% and RSD values below 0.04%. With a confidence level of 99%, the Student t-test revealed that there is no statistically significant difference between the outcomes obtained by using the poly-Cys/Au-TiO 2 @rGO/SPCE sensor for screening examinations of biological samples. This was determined because the results were not significantly different from one another., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature.)

Foraging for resources is an essential process for the daily life of an ant colony. What makes this process so fascinating is the self-organization of ants into trails using chemical pheromone in the absence of direct communication. Here we present a stochastic lattice model that captures essential features of foraging ant dynamics inspired by recent agent-based models while forgoing more detailed interactions that may not be essential to trail formation. Nevertheless, our model's results coincide with those presented in more sophisticated theoretical models and experiments. Furthermore, it captures the phenomenon of multiple trail formation in environments with multiple food sources. This latter phenomenon is not described well by other more detailed models. We complement the stochastic lattice model by describing a macroscopic PDE which captures the basic structure of lattice model. The PDE provides a continuum framework for the first-principle interactions described in the stochastic lattice model and is amenable to analysis. Linear stability analysis of this PDE facilitates a computational study of the impact various parameters impart on trail formation. We also highlight universal features of the modeling framework that may allow this simple formation to be used to study complex systems beyond ants., (© 2024. The Author(s).)

Stochastic delayed modeling has a significant non-pharmaceutical intervention to control transmission dynamics of infectious diseases and its results are close to the reality of nature. The covid-19 has been controlled globally but there is still a threat and appears in different variants like omicron and SARS-CoV-2 etc. globally. This article, considered pattern a mathematical model based on Susceptible, Infected, and recovered populations with highly nonlinear incidence rates. we studied the dynamics of the coronavirus model; a newly proposed version is a stochastic delayed model that is based on nonlinear stochastic delayed differential equations (SDDEs). Transition probabilities and parametric perturbation methods were used for the construction of the stochastic delayed model. The fundamental properties like positivity, boundedness, existence and uniqueness, and stability results of equilibria of the model with certain conditions of reproduction number are studied regularly. Also, the extinction and persistence of disease are studied with the help of well-known theorems. The numerical methods used to find a visualization of results due to the complexity of stochastic delayed differential equations. Furthermore, for computational analysis, we implemented existing methods in the literature and compared their results with the proposed method like nonstandard finite difference for stochastic delayed model. The proposed method restores all dynamical properties of the model with a free choice of time steps., (© 2024. The Author(s).)

To explore the influence of state changes on brucellosis, a stochastic brucellosis model with semi-Markovian switchings and diffusion is proposed in this paper. When there is no switching, we introduce a critical value R s and obtain the exponential stability in mean square when R s < 1 by using the stochastic Lyapunov function method. Sudden climate changes can drive changes in transmission rate of brucellosis, which can be modelled by a semi-Markov process. We study the influence of stationary distribution of semi-Markov process on extinction of brucellosis in switching environment including both stable states, during which brucellosis dies out, and unstable states, during which brucellosis persists. The results show that increasing the frequencies and average dwell times in stable states to certain extent can ensure the extinction of brucellosis. Finally, numerical simulations are given to illustrate the analytical results. We also suggest that herdsmen should reduce the densities of animal habitation to decrease the contact rate, increase slaughter rate of animals and apply disinfection measures to kill brucella., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

Objective: Random noise, such as white or pink noise, has been shown to have beneficial effects on the performance of individuals with (elevated traits of) ADHD. Both the state regulation deficit (SRD) account and the moderate brain arousal (MBA) model argue that this effect is due to enhanced cognitive arousal. The MBA model specifically attributes this to random noise affecting dopaminergic (DA) transmission via stochastic resonance (SR). However, he requirement of SR and the role of DA have not yet been properly examined. To test this, proper control conditions are needed., Method: To examine the requirement of SR, 60 neurotypical adults with varying levels of ADHD traits performed a slow two-choice reaction time (S1-S2) task in three auditory conditions: pink (random) noise, a pure 100 Hz tone (non-random noise), and silence. All participants also completed the Attention Network Test (ANT) in two conditions (pink noise and silence) to inspect the effect on executive network efficiency which may serve as a proxy measure of DA. ADHD traits were assessed via self-report., Results: Auditory stimulation improved performance on the S1-S2 task in participants with elevated ADHD traits, however this was the case for both pink noise and the pure tone. Pink noise did not affect executive network efficiency, irrespective of ADHD traits., Conclusions: Our results suggest that stochastic resonance is not required for pink noise to have a beneficial effect on ADHD-related performance. Pink noise did not affect our DA proxy measure, however this negative finding should be interpreted with caution. Our results cast doubt on the tenets of the MBA model, warranting further research., Competing Interests: Declaration of competing interest The authors have no competing interests to declare., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

In HIV drug therapy, the high variability of CD4 + T cells and viral loads brings uncertainty to the determination of treatment options and the ultimate treatment efficacy, which may be the result of poor drug adherence. We develop a dynamical HIV model coupled with pharmacokinetics, driven by drug adherence as a random variable, and systematically study the uncertainty quantification, aiming to construct the relationship between drug adherence and therapeutic effect. Using adaptive generalized polynomial chaos, stochastic solutions are approximated as polynomials of input random parameters. Numerical simulations show that results obtained by this method are in good agreement, compared with results obtained through Monte Carlo sampling, which helps to verify the accuracy of approximation. Based on these expansions, we calculate the time-dependent probability density functions of this system theoretically and numerically. To verify the applicability of this model, we fit clinical data of four HIV patients, and the goodness of fit results demonstrate that the proposed random model depicts the dynamics of HIV well. Sensitivity analyses based on the Sobol index indicate that the randomness of drug effect has the greatest impact on both CD4 + T cells and viral loads, compared to random initial values, which further highlights the significance of drug adherence. The proposed models and qualitative analysis results, along with monitoring CD4 + T cells counts and viral loads, evaluate the influence of drug adherence on HIV treatment, which helps to better interpret clinical data with fluctuations and makes several contributions to the design of individual-based optimal antiretroviral strategies., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

Theoretical computational models are widely used to describe latent cognitive processes. However, these models do not equally explain data across participants, with some individuals showing a bigger predictive gap than others. In the current study, we examined the use of theory-independent models, specifically recurrent neural networks (RNNs), to classify the source of a predictive gap in the observed data of a single individual. This approach aims to identify whether the low predictability of behavioral data is mainly due to noisy decision-making or misspecification of the theoretical model. First, we used computer simulation in the context of reinforcement learning to demonstrate that RNNs can be used to identify model misspecification in simulated agents with varying degrees of behavioral noise. Specifically, both prediction performance and the number of RNN training epochs (i.e., the point of early stopping) can be used to estimate the amount of stochasticity in the data. Second, we applied our approach to an empirical dataset where the actions of low IQ participants, compared with high IQ participants, showed lower predictability by a well-known theoretical model (i.e., Daw's hybrid model for the two-step task). Both the predictive gap and the point of early stopping of the RNN suggested that model misspecification is similar across individuals. This led us to a provisional conclusion that low IQ subjects are mostly noisier compared to their high IQ peers, rather than being more misspecified by the theoretical model. We discuss the implications and limitations of this approach, considering the growing literature in both theoretical and data-driven computational modeling in decision-making science., Competing Interests: YG, MS, NS No competing interests declared, (© 2024, Ger et al.)

In this study, a latest version of COVID-19 pandemic is hand overed. A Stochastic post COVID-19 delayed model is developed to explore the spread of COVID-19 as well as omicron variant with the correlation of heart attack. This article provides an eradication of the COVID-19 and omicron variant as well as the population who have heart attack after post COVID-19 of these epidemic diseases. Then the existence and uniqueness of global positive solution are studied. Ensuing, In this article, we classify COVID-19 virus and omicron variant which go to extinction and become persistent in mean. By using Lyapunov function, the existence of ergodic stationary distribution are established. Later from the persistent disease as well as extinction, heart disease are ready to develop in the human body. By Eventually, an optimal control strategies are introduced in the form of stochastic post COVID-19 delayed model to control two different types of virus. Finally, the numerical simulation are presented to determine the behavior of dynamical system by utilizing the real data of United Kingdom., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier B.V. All rights reserved.)

The actual ideal of the literature is to probe the effect of external undulation on prevalence of COVID-19. Owing to some environmental influences, we enhanced our model to the stochastic perturbations. In this article, we scrutinize a stochastic epidemic COVID-19 model with seven states of epidemiological classification. Incipiently, a sophisticated biological system with the effect of time lags put forward copious strategies. At the outset, aim of this work is to explore the existence and uniqueness of global positive solution. Moment exponential stability are upheld. By fabricating a suitable lyapunov function, the sufficient conditions for the persistence of the disease and the existence of an ergodic stationary distribution are established. To regulate the widespread of COVID-19 infection, the main intent is to curb the disease with the succor of three control measures. Finally, the theoretical results bring into being alive in the form of graphical visualization. By nurturing the comparison study, the parameters of the model system come up with real data of most afflicted countries that layout premier consequences., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier B.V. All rights reserved.)

Mechanisms underlying the effects of ecological disturbance on aquatic ecosystems remain uncertain in subtropical regions. Here, we used a proxy-based approach to explore the community dynamics of testate amoebae (Arcellinida and Euglyphida) in two subtropical deep reservoirs (Tingxi and Shidou) in Xiamen, southeastern China, over a three-year period. Specifically, we employed drought and typhoon events recorded by weather station as proxies for ecological disturbance and chlorophyll-a estimated through fluorometry as a proxy for testate amoeba food. We addressed three questions: (1) Does typhoon-induced ecological disturbance affect the distribution patterns of testate amoebae in subtropical reservoirs? (2) Do typhoon- and drought-induced ecological disturbances affect the testate amoeba community across different water layers of subtropical reservoirs similarly? (3) Do stochastic or deterministic processes shaping the testate amoeba community over time exhibit similar patterns in different water layers of subtropical reservoirs? The typhoon-induced ecological disturbance resulted in pronounced shifts in the distribution patterns of testate amoebae, characterized by lower shell influx in surface waters (11-12 ind. mL -1 d -1 ) and higher shell influx in middle and bottom waters (12-22 ind. mL -1 d -1 ). The impact of typhoon-and drought-induced ecological disturbance was more pronounced in surface waters, and its pure explanation accounted for 29.5-35.5 % community variation in a variation partitioning analysis. The effect of stochastic processes revealed by the neutral model increased with water depths, accounting for 63.3-76.5 % of the community variation in the surface, 77.4-82.6 % in the middle, and 82.8-88.1 % in the bottom water. The effect of deterministic processes shown by the null model decreased with water depth and remained relatively low across all water layers. These results suggest contrasting patterns of assembly mechanisms underlying the testate amoeba community responses to ecological disturbance, with the balance perhaps shaped by water depth and the average water residence time in a reservoir., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier B.V. All rights reserved.)

Without heritable variation natural selection cannot effect evolutionary change. In the case of group selection, there must be variation in the population of groups. Where does this variation come from? One source of variation is from the stochastic birth-death processes that occur within groups. This is where variation between groups comes from in most mathematical models of group selection. Here, we argue that another important source of variation between groups is fission, the (generally random) group-level reproduction where parent groups split into two or more offspring groups. We construct a simple model of the fissioning process with a parameter that controls how much variation is produced among the offspring groups. We then illustrate the effect of that parameter with some examples. In most models of group selection in the literature, no variation is produced during group reproduction events; that is, groups "clone" themselves when they reproduce. Fission is often a more biologically realistic method of group reproduction, and it can significantly increase the efficacy of group selection., (© The Author(s) 2024. Published by Oxford University Press on behalf of The Society for the Study of Evolution (SSE). Published by Oxford University Press on behalf of The Society for the Study of Evolution (SSE). All rights reserved. For commercial re-use, please contact reprints@oup.com for reprints and translation rights for reprints. All other permissions can be obtained through our RightsLink service via the Permissions link on the article page on our site—for further information please contact journals.permissions@oup.com.)

The United States Environmental Protection Agency (USEPA) Four-step-Method (FSM) is a straightforward and extensively utilized tool for evaluating regional health risks, However, the complex and heterogeneous groundwater environment system causes great uncertainty in the assessment process. Triangular stochastic simulation (TSS) possesses certain advantages in solving uncertainty problems, but its inadequacy with discrete data reveals limitations in this aspect. To solve the above problems, this study proposes to construct trapezoidal fuzzy number-Monte Carlo stochastic simulation (TFN-MCSS) to compensate for the shortcomings of the first two methods. This method adopted trapezoidal fuzzy number (TFN) analysis to comprehensively consider the characteristics of a large dispersion of water quality monitoring data and the uncertainty of the human health risk assessment (HHRA) process. Concurrently, to overcome the subjectivity and uncertainty of artificially determining the interval of TFN in traditional methods, the slope was used to select the most probable interval value (TMPIV) of TFN combined with the α-truncated set technique (α-TST) and MCSS. Based on these, a TFN-MCSS was constructed and applied to groundwater HHRA in western Jilin Province. First, the groundwater chemical characteristic determination and water quality evaluation in western Jilin were performed to identify the main pollution indicators, and the health risk effects of pollutants in groundwater of different aquifers at different time periods on adults and children were evaluated using the TFN-MCSS. The uncertainty and sensitivity were analyzed, and the primary risk control indicators were identified and compared to FSM and TSS. The results reveal that TFN-MCSS was more sensitive to data and could reduce the uncertainty of assessment process. It indicated that over a 10-year period, the health risks associated with unconfined groundwater (UW) and confined water (CW) decreased by greater than 52 %. However, the highest total non-carcinogenic risk index (THI) was 1.3-fold higher than the safety threshold, and this posed a health risk., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Authors. Published by Elsevier Inc. All rights reserved.)

Noise is a ubiquitous component of motor systems that leads to behavioral variability of all types of movements. Nonetheless, systems-based models investigating human movements are generally deterministic and explain only the central tendencies like mean trajectories. In this paper, a novel approach to modeling kinematic variability of movements is presented and tested on the oculomotor system. This approach reconciles the two prominent philosophies of saccade control: displacement-based control versus velocity-based control. This was achieved by quantifying the variability in saccadic eye movements and developing a stochastic model of its control. The proposed stochastic dual model generated significantly better fits of inter-trial variances of the saccade trajectories compared to existing models. These results suggest that the saccadic system can flexibly use the information of both desired displacement and velocity for its control. This study presents a potential framework for investigating computational principles of motor control in the presence of noise utilizing stochastic modeling of kinematic variability., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

The Wells-Riley model has been widely used to estimate airborne infection risk, typically from a deterministic point of view (i.e., focusing on the average number of infections) or in terms of a per capita probability of infection. Some of its main limitations relate to considering well-mixed air, steady-state concentration of pathogen in the air, a particular amount of time for the indoor interaction, and that all individuals are homogeneous and behave equally. Here, we revisit the Wells-Riley model, providing a mathematical formalism for its stochastic version, where the number of infected individuals follows a Binomial distribution. Then, we extend the Wells-Riley methodology to consider transient behaviours, randomness, and population heterogeneity. In particular, we provide analytical solutions for the number of infections and the per capita probability of infection when: (i) susceptible individuals remain in the room after the infector leaves, (ii) the duration of the indoor interaction is random/unknown, and (iii) infectors have heterogeneous quanta production rates (or the quanta production rate of the infector is random/unknown). We illustrate the applicability of our new formulations through two case studies: infection risk due to an infectious healthcare worker (HCW) visiting a patient, and exposure during lunch for uncertain meal times in different dining settings. Our results highlight that infection risk to a susceptible who remains in the space after the infector leaves can be nonnegligible, and highlight the importance of incorporating uncertainty in the duration of the indoor interaction and the infectivity of the infector when estimating risk., (© 2024 The Authors. Risk Analysis published by Wiley Periodicals LLC on behalf of Society for Risk Analysis.)

Synchronization is one of the most striking instances of collective behavior, occurring in many natural phenomena. For example, in some ant species, ants are inactive within the nest most of the time, but their bursts of activity are highly synchronized and involve the entire nest population. Here we revisit a simulation model that generates this synchronized rhythmic activity through autocatalytic behavior, i.e., active ants can activate inactive ants, followed by a period of rest. We derive a set of delay differential equations that provide an accurate description of the simulations for large ant colonies. Analysis of the fixed-point solutions, complemented by numerical integration of the equations, indicates the existence of stable limit-cycle solutions when the rest period is greater than a threshold and the event of spontaneous activation of inactive ants is very unlikely, so that most of the arousal of ants is done by active ants. Furthermore, we argue that the persistent oscillations observed in the simulations for colonies of finite size are due to resonant amplification of demographic noise., Competing Interests: Declaration of competing interest None, (Copyright © 2024 Elsevier Inc. All rights reserved.)

In this paper, we introduce a stochastic two-strain epidemic model driven by Lévy noise describing the interaction between four compartments; susceptible, infected individuals by the first strain, infected ones by the second strain and the recovered individuals. The forces of infection, for both strains, are represented by saturated incidence rates. Our study begins with the investigation of unique global solution of the suggested mathematical model. Then, it moves to the determination of sufficient conditions of extinction and persistence in mean of the two-strain disease. In order to illustrate the theoretical findings, we give some numerical simulations., Competing Interests: Declaration of competing interest The authors declare no conflict of interest regarding the publication of this paper., (Copyright © 2024 Elsevier Inc. All rights reserved.)

Background: Although the dynamics of the middle ear (ME) have been modeled since the mid-twentieth century, only recently stochastic approaches started to be applied. In this study, a stochastic model of the ME was utilized to predict the ME dynamics under both healthy and pathological conditions., Methods: The deterministic ME model is based on a lumped-parameter representation, while the stochastic model was developed using a probabilistic non-parametric approach that randomizes the deterministic model. Subsequently, the ME model was modified to represent the ME under pathological conditions. Furthermore, the simulated data was used to develop a classifier model of the ME condition based on a machine learning algorithm., Results: The ME model under healthy conditions exhibited good agreement with statistical experimental results. The ranges of probabilities from models under pathological conditions were qualitatively compared to individual experimental data, revealing similarities. Moreover, the classifier model presented promising results., Discussion: The results aimed to elucidate how the ME dynamics, under different conditions, can overlap across various frequency ranges. Despite the promising results, improvements in the stochastic and classifier models are necessary. Nevertheless, this study serves as a starting point that can yield valuable tools for researchers and clinicians., Competing Interests: Declaration of competing interest We have no conflicts of interest to disclose., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

Foot-and-mouth disease (FMD) is an important endemic disease in livestock in Southeast Asia. Transboundary movement of animals may result in the transnational disease spread. A major cattle market is located at the Thailand-Myanmar border, where most cattle imported from Myanmar are traded. In this study, we built a stochastic susceptible-exposed-infectious-recovered (SEIR) model to investigate the effectiveness of a private animal quarantine service center in preventing FMDV from entering the major cattle market. We computed with different parameters and found that, with 50 % vaccine effectiveness, the risk of releasing infected cattle to the market per batch was generally low during the quarantine period of 21 and 28 days, with the risk ranging from 0.071 to 0.078 and 0.032 to 0.036, respectively. Despite the best scenario, the zero-risk state is difficult to attain. The sensitivity analysis highlights that the percentage of immune animals before entering the quarantine centers and the vaccine effectiveness are important factors. In conclusion, the 21-day quarantine period mitigates the risk of FMDV introduction into the cattle market. This control measure should be rigorously maintained to sustainably prevent FMDV outbreaks through transboundary animal movements, especially among countries in FMD-endemic regions., Competing Interests: Declaration of Competing Interest None., (Copyright © 2024 The Authors. Published by Elsevier B.V. All rights reserved.)

Background: Malaria is the world's most fatal and challenging parasitic disease, caused by the Plasmodium parasite, which is transmitted to humans by the bites of infected female mosquitoes. Bangladesh is the most vulnerable region to spread malaria because of its geographic position. In this paper, we have considered the dynamics of vector-host models and observed the stochastic behavior. This study elaborates on the seasonal variability and calculates the probability of disease outbreaks., Methods: We present a model for malaria disease transmission and develop its corresponding continuous-time Markov chain (CTMC) representation. The proposed vector-host models illustrate the malaria transmission model along with sensitivity analysis. The deterministic model with CTMC curves is depicted to show the randomness in real scenarios. Sequentially, we expand these studies to a time-varying stochastic vector-host model that incorporates seasonal variability. Phase plane analysis is conducted to explore the characteristics of the disease, examine interactions among various compartments, and evaluate the impact of key parameters. The branching process approximation is developed for the corresponding vector-host model to calculate the probability outbreak. Numerous numerical results are accomplished to observe the analytical investigation., Results: Seasonality and contact patterns affect the dynamics of disease outbreaks. The numerical illustration provides that the probability of a disease outbreak depends on the infected host or vector. Additionally, periodic transmission rates have a great influence on the probability outbreak. The basic reproduction number (R 0 ) is derived, which is the main justification for studying the dynamical behavior of epidemic models., Conclusions: Seasonal variability significantly impacts malaria transmission, and the probability of disease outbreaks is influenced by time and the initial number of infected individuals. Moreover, the branching process approximation is applicable when the population size is large enough and the basic reproduction number is less than 1. In the future, such analysis can help decision-makers understand the impact of various parameters and their stochastic behavior in the vector-host model to prevent such types of disease outbreaks., Competing Interests: Declaration of competing interest The authors declare no conflict of interest., (Copyright © 2024 Elsevier B.V. All rights reserved.)

The ICU is a specialized hospital department that offers critical care to patients at high risk. The massive burden of ICU-requiring care requires accurate and timely ICU outcome predictions for alleviating the economic and healthcare burdens imposed by critical care needs. Existing research faces challenges such as feature extraction difficulties, low accuracy, and resource-intensive features. Some studies have explored deep learning models that utilize raw clinical inputs. However, these models are considered non-interpretable black boxes, which prevents their wide application. The objective of the study is to develop a new method using stochastic signal analysis and machine learning techniques to effectively extract features with strong predictive power from ICU patients' real-time time series of vital signs for accurate and timely ICU outcome prediction. The results show the proposed method extracted meaningful features and outperforms baseline methods, including APACHE IV (AUC = 0.750), deep learning-based models (AUC = 0.732, 0.712, 0.698, 0.722), and statistical feature classification methods (AUC = 0.765) by a large margin (AUC = 0.869). The proposed method has clinical, management, and administrative implications since it enables healthcare professionals to identify deviations from prognostications timely and accurately and, therefore, to conduct proper interventions.

Noise is generally considered to be detrimental. In the right conditions, however, noise can improve signal detection or information transmission. This counterintuitive phenomenon is called stochastic resonance (SR). SR has generated significant interdisciplinary interest, particularly in physics, engineering, and medical and environmental sciences. In this review, we discuss a growing empirical literature that suggests that noise at the right intensity may improve the detection and processing of auditory, sensorimotor, and visual stimuli. We focus particularly on applications of SR in sensory biology and investigate whether SR-based technologies present a pathway to improve outcomes for individuals living with sensory impairments. We conclude that there is considerable evidence supporting the application of SR in developing sensory prosthetics. However, the progression of SR-based technologies is variable across the sensory modalities. We suggest opportunities for further advancements in each modality, considering the best approaches to maximise benefits and capitalise on progress already made. Overall, SR can offer opportunities to improve existing technologies or to motivate innovations., (Copyright © 2024 International Federation of Clinical Neurophysiology. Published by Elsevier B.V. All rights reserved.)

In epidemiology, realistic disease dynamics often require Susceptible-Exposed-Infected-Recovered (SEIR)-like models because they account for incubation periods before individuals become infectious. However, for the sake of analytical tractability, simpler Susceptible-Infected-Recovered (SIR) models are commonly used, despite their lack of biological realism. Bridging these models is crucial for accurately estimating parameters and fitting models to observed data, particularly in population-level studies of infectious diseases. This paper investigates stochastic versions of the SEIR and SIR frameworks and demonstrates that the SEIR model can be effectively approximated by a SIR model with time-dependent infection and recovery rates. The validity of this approximation is supported by the derivation of a large-population Functional Law of Large Numbers (FLLN) limit and a finite-population concentration inequality. To apply this approximation in practice, the paper introduces a parameter inference methodology based on the Dynamic Survival Analysis (DSA) survival analysis framework. This method enables the fitting of the SIR model to data simulated from the more complex SEIR dynamics, as illustrated through simulated experiments., Competing Interests: Declaration of competing interest The authors declare no conflicts of interest., (Copyright © 2024 The Authors. Published by Elsevier Inc. All rights reserved.)

The pan-cancer initiative aims to study the origin patterns of cancer cell, the processes of carcinogenesis, and the signaling pathways from a perspective that spans across different types of cancer. The construction of the pan-cancer related gene regulatory network is helpful to excavate the commonalities in regulatory relationships among different types of cancers. It also aids in understanding the mechanisms behind cancer occurrence and development, which is of great scientific significance for cancer prevention and treatment. In light of the high dimension and large sample size of pan-cancer omics data, a causal pan-cancer gene regulation network inference algorithm based on stochastic complexity is proposed. With the network construction strategy of local first and then global, the stochastic complexity is used in the conditional independence test and causal direction inference for the candidate adjacent node set of the target nodes. This approach aims to decrease the time complexity and error rate of causal network learning. By applying this algorithm to the sample data of seven types of cancers in the TCGA database, including breast cancer, lung adenocarcinoma, and so on, the pan-cancer related causal regulatory networks are constructed, and their biological significance is verified. The experimental results show that this algorithm can eliminate the redundant regulatory relationships effectively and infer the pan-cancer regulatory network more accurately (https://github.com/LindeEugen/CNI-SC)., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Authors. Published by Elsevier B.V. All rights reserved.)

The dynamics of locally interacting particles that are distributed in space give rise to a multitude of complex behaviours. However the simulation of reaction-diffusion processes which model such systems is highly computationally expensive, the cost increasing rapidly with the size of space. Here, we devise a graph neural network based approach that uses cheap Monte Carlo simulations of reaction-diffusion processes in a small space to cast predictions of the dynamics of the same processes in a much larger and complex space, including spaces modelled by networks with heterogeneous topology. By applying the method to two biological examples, we show that it leads to accurate results in a small fraction of the computation time of standard stochastic simulation methods. The scalability and accuracy of the method suggest it is a promising approach for studying reaction-diffusion processes in complex spatial domains such as those modelling biochemical reactions, population evolution and epidemic spreading., Competing Interests: Declaration of competing interest The authors declare no conflict of interests., (Copyright © 2024 The Author(s). Published by Elsevier Inc. All rights reserved.)

Pinus kwangtungensis is an endangered evergreen conifer tree species, and its in situ conservation has been considered one of the most critical issues. However, relative protection is limited by the lack of understanding of its community structure and underlying assembly processes. To study how the species diversity and assembly processes of Pinus kwangtungensis coniferous forest (CF) differed with regional climax community, this study established a series forest dynamic plots both in CF and evergreen deciduous broadleaved mixed forest (EDBM). By performing comparison analysis and PER-SIMPER approaches, we quantified the differences in species diversity and community assembly rules. The results showed that the species α-diversity of CF differed greatly from the EDBM both in species richness and evenness. In addition, the stochastic process acted a more important role in determining species composition, indicating the uncertainty in presence of species. The soil phosphorus and changeable calcium content were the main factors driving the differences in biodiversity, which the importance of soil nutrient factors in driving species composition. Our study highlighted that we should consider the community structure and ecological process when conducting conservation of Pinus kwangtungensis ., Competing Interests: Yeheng Wang is employed by Zibo Real Estate Registration Center., (©2024 Fan et al.)

We study the stochastic hydrodynamics of colonies of flagellated swimming cells, typified by multicellular choanoflagellates, which can form both rosette and chainlike shapes. The objective is to link cell-scale dynamics to colony-scale dynamics for various colonial morphologies. Via autoregressive stochastic models for the cycle-averaged flagellar force dynamics and statistical models for demographic cell-to-cell variability in flagellar properties and placement, we derive effective transport properties of the colonies, including cell-to-cell variability. We provide the most quantitative detail on disclike geometries to model rosettes, but also present formulas for the dynamics of general planar colony morphologies, which includes planar chain-like configurations., (© 2024. The Author(s), under exclusive licence to the Society for Mathematical Biology.)

Exploring the temporal dynamics of biological communities can offer valuable insights into the underlying mechanisms driving changes in biodiversity in the context of short and long-term effects of climate fluctuations. However, an understanding of how temporal shifts in climatic fluctuations influence the spatial patterns of the temporary ecological processes remains unexplored. This study examined the relative importance of temporary deterministic and stochastic processes (i.e., the influence of environmental filtering compared to stochastic variation within the same community) on community dynamics across watersheds in 15 rivers of the European Iberian Peninsula using 21 years of data. This study was divided into two time periods (i.e., 1997-2006 and 2007-2017). The climatic differences between the periods included decreasing levels and heightened variability of precipitation. Additionally, there were declining minimum temperatures and rising maximum temperatures, accompanied by reduced fluctuations in both minimum and maximum temperatures. Water quality and its variations also occur along an elevation pattern and changed over the time period studied. Spatial patterns of the relative importance of the ecological processes shifted between the two decades. The significance of stochastic processes increased with elevation in the earlier period, although no clear elevation pattern emerged in the later period. At the same time, the importance of deterministic processes decreased with elevation in the earlier period, and there was no clear pattern of elevation in the later period. An understanding of the patterns in community dynamics existing at various elevations over time can lay the groundwork for predicting and mitigating the impacts of short-term climate changes on biodiversity and guide appropriate conservation actions., Competing Interests: Declaration of competing interest The authors declare no conflict of interest., (Copyright © 2024 Elsevier B.V. All rights reserved.)

Super-resolution single-molecule localization microscopy (SMLM) of presynaptic active zones (AZs) and postsynaptic densities contributed to the observation of protein nanoclusters that are involved in defining functional characteristics and in plasticity of synaptic connections. Among SMLM techniques, direct stochastic optical reconstruction microscopy ( d STORM) depends on organic fluorophores that exert high brightness and reliable photoswitching. While multicolor imaging is highly desirable, the requirements necessary for high-quality d STORM make it challenging to identify combinations of equally performing, spectrally separated dyes. Red-excited carbocyanine dyes, e.g., Alexa Fluor 647 (AF647) or Cy5, are currently regarded as "gold standard" fluorophores for d STORM imaging. However, a recent study introduced a set of chemically modified rhodamine dyes, including CF583R, that promise to display similar performance in d STORM. In this study, we defined CF583R's performance compared to AF647 and CF568 based on a nanoscopic analysis of Bruchpilot (Brp), a nanotopologically well-characterized scaffold protein at Drosophila melanogaster AZs. We demonstrate equal suitability of AF647, CF568 and CF583R for basal AZ morphometry, while in Brp subcluster analysis CF583R outperforms CF568 and is on par with AF647. Thus, the AF647/CF583R combination will be useful in future d STORM-based analyses of AZs and other subcellularly located marker molecules and their role in physiological and pathophysiological contexts.

Arthropods harbor complex microbiota that play a pivotal role in host fitness. While multiple factors, like host species and diet, shape microbiota in arthropods, their impact on community assembly in wild insects remains largely unknown. In this study, we surveyed bacterial and fungal community assembly in nine sympatric wild insect species that share a common citrus fruit diet. Source tracking analysis suggested that these insects acquire some bacteria and fungi from the citrus fruit with varying degrees. Although sharing a common diet led to microbiota convergence, the diversity, composition, and network of both bacterial and fungal communities varied significantly among surveyed insect groups. Null model analysis indicated that stochastic processes, particularly dispersal limitation and drift, are primary drivers of structuring insect bacterial and fungal communities. Importantly, the influence of each community assembly process varied strongly depending on the host species. Thus, we proposed a speculative view that the host specificity of the microbiome and mycobiome assembly is widespread in wild insects despite sharing the same regional species pool. Overall, this research solidifies the importance of host species in shaping microbiomes and mycobiomes, providing novel insights into their assembly mechanisms in wild insects., Importance: Since the microbiome has been shown to impact insect fitness, a mechanistic understanding of community assembly has potentially significant applications but remains largely unexplored. In this paper, we investigate bacterial and fungal community assembly in nine sympatric wild insect species that share a common diet. The main findings indicate that stochastic processes drive the divergence of microbiomes and mycobiomes in nine sympatric wild insect species. These findings offer novel insights into the assembly mechanisms of microbiomes and mycobiomes in wild insects., Competing Interests: The authors declare no conflict of interest.

Single-cell transcriptomics reveals significant variations in transcriptional activity across cells. Yet, it remains challenging to identify mechanisms of transcription dynamics from static snapshots. It is thus still unknown what drives global transcription dynamics in single cells. We present a stochastic model of gene expression with cell size- and cell cycle-dependent rates in growing and dividing cells that harnesses temporal dimensions of single-cell RNA sequencing through metabolic labeling protocols and cel lcycle reporters. We develop a parallel and highly scalable approximate Bayesian computation method that corrects for technical variation and accurately quantifies absolute burst frequency, burst size, and degradation rate along the cell cycle at a transcriptome-wide scale. Using Bayesian model selection, we reveal scaling between transcription rates and cell size and unveil waves of gene regulation across the cell cycle-dependent transcriptome. Our study shows that stochastic modeling of dynamical correlations identifies global mechanisms of transcription regulation. A record of this paper's transparent peer review process is included in the supplemental information., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2024 The Authors. Published by Elsevier Inc. All rights reserved.)

The ultraviolet (UV) radiation triggers a pigmentation response in human skin, wherein, melanocytes rapidly activate divergent maturation and proliferation programs. Using single-cell sequencing, we demonstrate that these 2 programs are segregated in distinct subpopulations in melanocytes of human and zebrafish skin. The coexistence of these 2 cell states in cultured melanocytes suggests possible cell autonomy. Luria-Delbrück fluctuation test reveals that the initial establishment of these states is stochastic. Tracking of pigmenting cells ascertains that the stochastically acquired state is faithfully propagated in the progeny. A systemic approach combining single-cell multi-omics (RNA+ATAC) coupled to enhancer mapping with H3K27 acetylation successfully identified state-specific transcriptional networks. This comprehensive analysis led to the construction of a gene regulatory network (GRN) that under the influence of noise, establishes a bistable system of pigmentation and proliferation at the population level. This GRN recapitulates melanocyte behaviour in response to external cues that reinforce either of the states. Our work highlights that inherent stochasticity within melanocytes establishes dedicated states, and the mature state is sustained by selective enhancers mark through histone acetylation. While the initial cue triggers a proliferation response, the continued signal activates and maintains the pigmenting subpopulation via epigenetic imprinting. Thereby our study provides the basis of coexistence of distinct populations which ensures effective pigmentation response while preserving the self-renewal capacity., Competing Interests: RSG is the co-founder of Vyome Biosciences Pvt Ltd., a biopharmaceutical company working in the area of dermatology. Other authors declare no competing interest., (Copyright: © 2024 Aggarwal et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Human liver-type phosphofructokinase 1 (PFKL) has been shown to regulate glucose flux as a scaffolder arranging glycolytic and gluconeogenic enzymes into a multienzyme metabolic condensate, the glucosome. However, it has remained elusive of how phase separation of PFKL is governed and initiates glucosome formation in living cells, thus hampering to understand a mechanism of glucosome formation and its functional contribution to human cells. In this work, we developed a stochastic model in silico using the principle of Langevin dynamics to investigate how biological properties of PFKL contribute to the condensate formation. The significance of an intermolecular interaction between PFKLs, an effective concentration of PFKL at a region of interest, and its own self-assembled filaments in formation of PFKL condensates and control of their sizes were demonstrated by molecular dynamics simulation using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). Such biological properties that define intracellular dynamics of PFKL appear to be essential for phase separation of PFKL, which may represent an initiation step for the formation of glucosome condensates. Collectively, our computational study provides mechanistic insights of glucosome formation, particularly an initial stage through the formation of PFKL condensates in living human cells., (© 2024. The Author(s).)

The Chinese government has implemented environmental regulations to address the deterioration of air quality associated with rapid industrialization. However, there is no consensus on whether environmental regulations are beneficial to environmental performance. The technical challenges related to endogeneity and spatial correlation may bias the estimation of the emission reduction effect of regulations. In this study, we comprehensively evaluate the environmental performance of sulfur dioxide regulations in Chinese cities using a novel stochastic frontier model that introduces the single control function to correct estimation errors caused by spatial spillovers and endogeneity. Our analysis emphasizes that insufficient resolution of endogeneity or spatial spillovers may lead to underestimation or neglect of the environmental performance improvements achieved by these regulations. On the contrary, our revised research results indicate that regulations aimed at reducing sulfur dioxide emissions not only successfully control sulfur dioxide emissions, but also have a positive impact on reducing carbon emissions. In addition, we conduct in-depth research on the mechanisms by which environmental regulations improve performance by stimulating green technology innovation and promoting industrial structure upgrading. Based on our research findings, we propose policy recommendations to establish a city cooperation mechanism of technology exchange to achieve synergistic emission reduction and strengthen regional factor circulation., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Inc. All rights reserved.)

Even in large systems, the effect of noise arising from when populations are initially small can persist to be measurable on the macroscale. A deterministic approximation to a stochastic model will fail to capture this effect, but it can be accurately approximated by including an additional random time-shift to the initial conditions. We present a efficient numerical method to compute this time-shift distribution for a large class of stochastic models. The method relies on differentiation of certain functional equations, which we show can be effectively automated by deriving rules for different types of model rates that arise commonly when mass-action mixing is assumed. Explicit computation of the time-shift distribution can be used to build a practical tool for the efficient generation of macroscopic trajectories of stochastic population models, without the need for costly stochastic simulations. Full code is provided to implement the calculations and we demonstrate the method on an epidemic model and a model of within-host viral dynamics., (© 2024. The Author(s).)

The strength of molecular interactions is characterized by their dissociation constants (K D ). Only high-affinity interactions (K D  ≤ 10 -8  M) are extensively investigated and support binary on/off switches. However, such analyses have discounted the presence of low-affinity binders (K D  > 10 -5  M) in the cellular environment. We assess the potential influence of low-affinity binders on high-affinity interactions. By employing Gillespie stochastic simulations and continuous methods, we demonstrate that the presence of low-affinity binders can alter the kinetics and the steady state of high-affinity interactions. We refer to this effect as 'herd regulation' and have evaluated its possible impact in two different contexts including sex determination in Drosophila melanogaster and in signalling systems that employ molecular thresholds. We have also suggested experiments to validate herd regulation in vitro. We speculate that low-affinity binders are prevalent in biological contexts where the outcomes depend on molecular thresholds impacting homoeostatic regulation., (© 2024. The Author(s).)

Human behaviors have non-negligible impacts on spread of contagious disease. For instance, large-scale gathering and high mobility of population could lead to accelerated disease transmission, while public behavioral changes in response to pandemics may effectively reduce contacts and suppress the peak of the outbreak. In order to understand how spatial characteristics like population mobility and clustering interplay with epidemic outbreaks, we formulate a stochastic-statistical environment-epidemic dynamic system (SEEDS) via an agent-based biased random walk model on a two-dimensional lattice. The "popularity" and "awareness" variables are taken into consideration to capture human natural and preventive behavioral factors, which are assumed to guide and bias agent movement in a combined way. It is found that the presence of the spatial heterogeneity, like social influence locality and spatial clustering induced by self-aggregation, potentially suppresses the contacts between agents and consequently flats the epidemic curve. Surprisedly, disease responses might not necessarily reduce the susceptibility of informed individuals and even aggravate disease outbreak if each individual responds independently upon their awareness. The disease control is achieved effectively only if there are coordinated public-health interventions and public compliance to these measures. Therefore, our model may be useful for quantitative evaluations of a variety of public-health policies., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Xiong et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

While in hospite Symbiodiniaceae dinoflagellates are essential for coral health, ambient free-living counterparts are crucial for coral recruitment and resilience. Comparing free-living and in hospite Symbiodiniaceae communities can potentially provide insights into endosymbiont acquisition and recurrent recruitment in bleaching recovery. In this study, we studied coral-endosymbiotic and ambient free-living Symbiodiniaceae communities in the South China Sea. We collected samples from 183 coral and ambient plankton samples and conducted metabarcoding to investigate the diversity distribution, driving factors, and assembly mechanisms of the two groups of Symbiodiniaceae. Results revealed Cladocopium C1 and Durusdinium D1 as dominant genotypes. We detected a higher genotypic diversity in free-living than in hospite symbiodiniacean communities, but with shared dominant genotypes. This indicates a genetically diverse pool of Symbiodiniaceae available for recruitment by corals. Strikingly, we found that the cooler area had more Symbiodiniaceae thermosensitive genotypes, whereas the warmer area had more Symbiodiniaceae thermotolerant genotypes. Furthermore, in hospite and free-living Symbiodiniaceae communities were similarly affected by environmental factors, but shaped by different assembly mechanisms. The in hospite communities were controlled mainly by deterministic processes, whereas the ambient communities by stochastic processes. This study sheds light on the genetic diversity of source environmental Symbiodiniaceae and differential assembly mechanisms influencing Symbiodiniaceae inside and outside corals.IMPORTANCESymbiodiniaceae dinoflagellates play a pivotal role as key primary producers within coral reef ecosystems. Coral-endosymbiotic Symbiodiniaceae communities have been extensively studied, but relatively little work has been reported on the free-living Symbiodiniaceae community. Conducting a comparative analysis between sympatric coral-endosymbiotic and free-living Symbiodiniaceae communities can potentially enhance the understanding of how endosymbiont communities change in response to changing environments and the mechanisms driving these changes. Our findings shed light on the genetic diversity of source environmental Symbiodiniaceae and differential assembly mechanisms shaping free-living and in hospite Symbiodiniaceae communities, with implications in evaluating the adaptive and resilient capacity of corals in response to future climate change., Competing Interests: The authors declare no conflict of interest.

This study presents a computational investigation of a stochastic Zika virus along with optimal control model using the Legendre spectral collocation method (LSCM). By accumulation of stochasticity into the model through the proposed stochastic differential equations, we appropriating the random fluctuations essential in the progression and disease transmission. The stability, convergence and accuracy properties of the LSCM are conscientiously analyzed and also demonstrating its strength for solving the complex epidemiological models. Moreover, the study evaluates the various control strategies, such as treatment, prevention and treatment pesticide control, and identifies optimal combinations that the intervention costs and also minimize the proposed infection rates. The basic properties of the given model, such as the reproduction number, were determined with and without the presence of the control strategies. For R 0 < 0 , the model satisfies the disease-free equilibrium, in this case the disease die out after some time, while for R 0 > 1 , then endemic equilibrium is satisfied, in this case the disease spread in the population at higher scale. The fundamental findings acknowledge the significant impact of stochastic phonemes on the robustness and effectiveness of control strategies that accelerating the need for cost-effective and multi-faceted approaches. In last the results provide the valuable insights for public health department to enabling more impressive mitigation of Zika virus outbreaks and management in real-world scenarios., (© 2024. The Author(s).)

During cell division, the mitotic spindle moves dynamically through the cell to position the chromosomes and determine the ultimate spatial position of the two daughter cells. These movements have been attributed to the action of cortical force generators which pull on the astral microtubules to position the spindle, as well as pushing events by these same microtubules against the cell cortex and plasma membrane. Attachment and detachment of cortical force generators working antagonistically against centring forces of microtubules have been modelled previously (Grill et al. in Phys Rev Lett 94:108104, 2005) via stochastic simulations and mean-field Fokker-Planck equations (describing random motion of force generators) to predict oscillations of a spindle pole in one spatial dimension. Using systematic asymptotic methods, we reduce the Fokker-Planck system to a set of ordinary differential equations (ODEs), consistent with a set proposed by Grill et al., which can provide accurate predictions of the conditions for the Fokker-Planck system to exhibit oscillations. In the limit of small restoring forces, we derive an algebraic prediction of the amplitude of spindle-pole oscillations and demonstrate the relaxation structure of nonlinear oscillations. We also show how noise-induced oscillations can arise in stochastic simulations for conditions in which the mean-field Fokker-Planck system predicts stability, but for which the period can be estimated directly by the ODE model and the amplitude by a related stochastic differential equation that incorporates random binding kinetics., (© 2024. The Author(s).)

Gene-gene interactions are crucial to the control of sub-cellular processes but our understanding of their stochastic dynamics is hindered by the lack of simulation methods that can accurately and efficiently predict how the distributions of gene product numbers vary across parameter space. To overcome these difficulties, here we present Holimap (high-order linear-mapping approximation), an approach that approximates the protein or mRNA number distributions of a complex gene regulatory network by the distributions of a much simpler reaction system. We demonstrate Holimap's computational advantages over conventional methods by applying it to predict the stochastic time-dependent dynamics of various gene networks, including transcriptional networks ranging from simple autoregulatory loops to complex randomly connected networks, post-transcriptional networks, and post-translational networks. Holimap is ideally suited to study how the intricate network of gene-gene interactions results in precise coordination and control of gene expression., (© 2024. The Author(s).)

The curse-of-dimensionality taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solving high-dimensional partial differential equations (PDEs), as Richard E. Bellman first pointed out over 60 years ago. While there has been some recent success in solving numerical PDEs in high dimensions, such computations are prohibitively expensive, and true scaling of general nonlinear PDEs to high dimensions has never been achieved. We develop a new method of scaling up physics-informed neural networks (PINNs) to solve arbitrary high-dimensional PDEs. The new method, called Stochastic Dimension Gradient Descent (SDGD), decomposes a gradient of PDEs' and PINNs' residual into pieces corresponding to different dimensions and randomly samples a subset of these dimensional pieces in each iteration of training PINNs. We prove theoretically the convergence and other desired properties of the proposed method. We demonstrate in various diverse tests that the proposed method can solve many notoriously hard high-dimensional PDEs, including the Hamilton-Jacobi-Bellman (HJB) and the Schrödinger equations in tens of thousands of dimensions very fast on a single GPU using the PINNs mesh-free approach. Notably, we solve nonlinear PDEs with nontrivial, anisotropic, and inseparable solutions in less than one hour for 1000 dimensions and in 12 h for 100,000 dimensions on a single GPU using SDGD with PINNs. Since SDGD is a general training methodology of PINNs, it can be applied to any current and future variants of PINNs to scale them up for arbitrary high-dimensional PDEs., Competing Interests: Declaration of competing interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Zheyuan Hu, Kenji Kawaguchi reports financial support was provided by Government of Singapore Ministry of Education. Khemraj Shukla, George Em Karniadakis reports financial support was provided by US Department of Energy. George Em Karniadakis reports financial support was provided by Office of Naval Research. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

The stochastic food chain model is an important model within the field of ecological research. Since existing models are difficult to describe the influence of cross-diffusion and random factors on the evolution of species populations, this work is concerned with a stochastic cross-diffusion three-species food chain model with prey-taxis, in which the direction of predators' movement is opposite to the gradient of prey, i.e., a higher density of prey. The existence and uniqueness of martingale solutions are established in a Hilbert space by using the stochastic Galerkin approximation method, the tightness criterion, Jakubowski's generalization of the Skorokhod theorem, and the Vitali convergence theorem. Furthermore, asymptotic behaviors around the steady states of the stochastic cross-diffusion three-species food chain model in the time mean sense are investigated. Finally, numerical simulations are carried out to illustrate the results of our analysis., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

In this paper, we investigate a finite population undergoing evolution through an island model with partial dispersal and without mutation, where generations are discrete and non-overlapping. The population is structured into D demes, each containing N individuals of two possible types, A and B, whose viability coefficients, s A and s B , respectively, vary randomly from one generation to the next. We assume that the means, variances and covariance of the viability coefficients are inversely proportional to the number of demes D, while higher-order moments are negligible in comparison to 1/D. We use a discrete-time Markov chain with two timescales to model the evolutionary process, and we demonstrate that as the number of demes D approaches infinity, the accelerated Markov chain converges to a diffusion process for any deme size N≥2. This diffusion process allows us to evaluate the fixation probability of type A following its introduction as a single mutant in a population that was fixed for type B. We explore the impact of increasing the variability in the viability coefficients on this fixation probability. At least when N is large enough, it is shown that increasing this variability for type B or decreasing it for type A leads to an increase in the fixation probability of a single A. The effect of the population-scaled variances, σ A 2 and σ B 2 , can even cancel the effects of the population-scaled means, μ A and μ B . We also show that the fixation probability of a single A increases as the deme-scaled migration rate increases. Moreover, this probability is higher for type A than for type B if the population-scaled geometric mean viability coefficient is higher for type A than for type B, which means that μ A -σ A 2 /2>μ B -σ B 2 /2., (Copyright © 2024 Elsevier Inc. All rights reserved.)

We study the metastability, internal frequencies, activation mechanism, energy transfer, and the collective base-flipping in a mesoscopic DNA via resonance with specific electric fields. Our new mesoscopic DNA model takes into account not only the issues of helicity and the coupling of an electric field with the base dipole moments, but also includes environmental effects, such as fluid viscosity and thermal noise. Also, all the parameter values are chosen to best represent the typical values for the opening and closing dynamics of a DNA. Our study shows that while the mesoscopic DNA is metastable and robust to environmental effects, it is vulnerable to certain frequencies that could be targeted by specific THz fields for triggering its collective base-flipping dynamics and causing large amplitude separation of base pairs. Based on applying the Freidlin-Wentzell method of stochastic averaging and the newly developed theory of resonant enhancement to our mesoscopic DNA model, our semi-analytic estimates show that the required fields should be THz fields with frequencies around 0.28 THz and with amplitudes in the order of 450 kV/cm. These estimates compare well with the experimental data of Titova et al., which have demonstrated that they could affect the function of DNA in human skin tissues by THz pulses with frequencies around 0.5 THz and with a peak electric field at 220 kV/cm. Moreover, our estimates also conform to a number of other experimental results, which appeared in the last couple years., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

In Athreya et al. (2021), models from population genetics were used to define stochastic dynamics in the space of graphons arising as continuum limits of dense graphs. In the present paper we exhibit an example of a simple neutral population genetics model for which this dynamics is a Markovian diffusion that can be characterized as the solution of a martingale problem. In particular, we consider a Markov chain in the space of finite graphs that resembles a Moran model with resampling and mutation. We encode the finite graphs as graphemes, which can be represented as a triple consisting of a vertex set (or more generally, a topological space), an adjacency matrix, and a sampling (Borel) measure. We equip the space of graphons with convergence of sample subgraph densities and show that the grapheme-valued Markov chain converges to a grapheme-valued diffusion as the number of vertices goes to infinity. We show that the grapheme-valued diffusion has a stationary distribution that is linked to the Griffiths-Engen-McCloskey (GEM) distribution. In a companion paper (Greven et al. 2023), we build up a general theory for obtaining grapheme-valued diffusions via genealogies of models in population genetics., (Copyright © 2024 The Author(s). Published by Elsevier Inc. All rights reserved.)

Exploring the stochastic intricacies of bone microstructure is a promising way to make progress on the practical issue of bone fracture. This study investigates the fracture of human complete ribs subjected to bending and using acoustic emission (AE) for microfailure detection. As the strain increases, the number of AE signals per unit of time rises until, beyond a certain threshold, an avalanche of signals occurs, indicating the aggregation of numerous microfailures into a macroscopic fracture. Since microfailures appear randomly throughout the bending test, and given the lack of a deterministic law and the random nature of microfailures during the bending test, we opted to develop a stochastic model to account for their occurrence within the irregular and random microstructure of the cortical bone. Notable discoveries encompass the significant correlation between adjusted parameters of the stochastic model and the total number of microfailures with anthropometric variables such as age and body mass index (BMI). The progression of microfailures with strain is significantly more pronounced with age and BMI, as measured by the rate of bone deterioration. In addition, the rate of microfailures is significantly impacted by BMI alone. It is also observed that the average energy of the identified AE events adheres to a precisely defined Pareto distribution for every specimen, with the principal exponent exhibiting a significant correlation with anthropometric variables. From a mathematical standpoint, the model can be described as a double Cox stochastic and explosive (coxplosive process) model. This further provides insight into the reason why the ribs of older individuals are considerably less resilient than those of younger individuals, breaking under a considerably lower maximum strain ( ε max )., (© 2024. The Author(s).)

In this paper, we design a new class of coupled neural networks with stochastically intermittent disturbances, in which the perturbation mechanism is different from other existed random neural networks. It is significant to construct the new models, which can simulate a class of the real neural networks in the disturbed environment, and the fast synchronization control strategies are studied by an adjustable parameter α. A controller with coupling signal is designed to study the exponential synchronization problem, meanwhile, another effective controller with not only adjustable synchronization rate but also with infinite gain avoided is used to investigate the preset-time synchronization. The fast synchronization conditions have been obtained by Lyapunov stability principle, Laplacian matrix and some inequality techniques. A numerical example shows the effectiveness of the control schemes, and the different control factors for synchronization rate are given to discuss the control effect. In particular, the image encryption-decryption based on drive-response networks has been successfully applied., Competing Interests: Declaration of competing interest The authors declare that they have no competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. No potential conflict of interest was reported by the authors., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

The timely detection of disease outbreaks through reliable early warning signals (EWSs) is indispensable for effective public health mitigation strategies. Nevertheless, the intricate dynamics of real-world disease spread, often influenced by diverse sources of noise and limited data in the early stages of outbreaks, pose a significant challenge in developing reliable EWSs, as the performance of existing indicators varies with extrinsic and intrinsic noises. Here, we address the challenge of modelling disease when the measurements are corrupted by additive white noise, multiplicative environmental noise and demographic noise into a standard epidemic mathematical model. To navigate the complexities introduced by these noise sources, we employ a deep learning algorithm that provides EWS in infectious disease outbreaks by training on noise-induced disease-spreading models. The indicator's effectiveness is demonstrated through its application to real-world COVID-19 cases in Edmonton and simulated time series derived from diverse disease spread models affected by noise. Notably, the indicator captures an impending transition in a time series of disease outbreaks and outperforms existing indicators. This study contributes to advancing early warning capabilities by addressing the intricate dynamics inherent in real-world disease spread, presenting a promising avenue for enhancing public health preparedness and response efforts.

The coalescent is a stochastic process representing ancestral lineages in a population undergoing neutral genetic drift. Originally defined for a well-mixed population, the coalescent has been adapted in various ways to accommodate spatial, age, and class structure, along with other features of real-world populations. To further extend the range of population structures to which coalescent theory applies, we formulate a coalescent process for a broad class of neutral drift models with arbitrary - but fixed - spatial, age, sex, and class structure, haploid or diploid genetics, and any fixed mating pattern. Here, the coalescent is represented as a random sequence of mappings [Formula: see text] from a finite set G to itself. The set G represents the "sites" (in individuals, in particular locations and/or classes) at which these alleles can live. The state of the coalescent, C t :G→G, maps each site g∈G to the site containing g's ancestor, t time-steps into the past. Using this representation, we define and analyze coalescence time, coalescence branch length, mutations prior to coalescence, and stationary probabilities of identity-by-descent and identity-by-state. For low mutation, we provide a recipe for computing identity-by-descent and identity-by-state probabilities via the coalescent. Applying our results to a diploid population with arbitrary sex ratio r, we find that measures of genetic dissimilarity, among any set of sites, are scaled by 4r(1-r) relative to the even sex ratio case., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Authors. Published by Elsevier Inc. All rights reserved.)

In recent years, distributed stochastic algorithms have become increasingly useful in the field of machine learning. However, similar to traditional stochastic algorithms, they face a challenge where achieving high fitness on the training set does not necessarily result in good performance on the test set. To address this issue, we propose to use of a distributed network topology to improve the generalization ability of the algorithms. We specifically focus on the Sharpness-Aware Minimization (SAM) algorithm, which relies on perturbation weights to find the maximum point with better generalization ability. In this paper, we present the decentralized stochastic sharpness-aware minimization (D-SSAM) algorithm, which incorporates the distributed network topology. We also provide sublinear convergence results for non-convex targets, which is comparable to consequence of Decentralized Stochastic Gradient Descent (DSGD). Finally, we empirically demonstrate the effectiveness of these results in deep networks and discuss their relationship to the generalization behavior of SAM., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Ltd. All rights reserved.)