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This study focuses on the stochastic modelling and analysis of a serial production network consisting of two manufacturing stations operating under a make-to-stock inventory policy. The outcome is a single type of product and every manufacturing station includes a machine and an output buffer. Both machines are gradually deteriorating during their operation. Deterioration results in a reduced production rate. Continuous-time Markov chain was used to model all the possible states the network transits over time due to the occurrence of certain events, such as client arrival, deterioration failure, production or repair completion. The structure of the Markov chain was thoroughly studied providing useful information, supporting the effort of numerical solving to determine the steady-state probabilities enabling the calculation of useful performance metrics like equipment availability, down time, idle time, utilisation and average inventory. Through a series of numerical experiments, the behaviour of the serial production network was examined while alternating its parameters. Interesting conclusions emerged regarding the factors affecting the operation of such production systems subjected to gradual deterioration. [ABSTRACT FROM AUTHOR]

This paper introduces a novel stochastic inverse method that utilizes perturbation theory and advanced intelligence techniques to solve the multi‐parameter identification problem of concrete dams using displacement field monitoring data. The proposed method considers the uncertainties associated with the dam displacement monitoring data, which are comprised of two distinct sources: the first is related to stochastic mechanical properties of the dam, and the second is due to observation errors. The displacements at different measuring points generated by dam mechanical properties exhibit spatial correlation, while the observation errors at different points can be considered statistically random. In this context, the inversion formulas are derived for unknown stochastic parameters of the dam by combining perturbation equations and Taylor expansion methods. An improved meta‐heuristic optimization method is employed to identify the mean of stochastic parameters, while mathematical and statistical methods are used to determine the variance of stochastic parameters. The feasibility of the proposed method is verified through numerical examples of a typical dam section under different conditions. Additionally, the paper discusses and demonstrates the applicability of this method in a practical dam project. Results indicate that this method can effectively capture the uncertainty of dam's mechanical properties and separates them from observation errors. [ABSTRACT FROM AUTHOR]

This paper proposes an integrated approach to group decision-making (GDM) by using stochastic preference analysis (SPA) and best-worst method (BWM). BWM preparation algorithm is proposed to obtain the best and worst of experts and the relative importance degree. Meanwhile, expert weights model and expert's priority vector model are proposed. Furthermore, the stochastic composite rank acceptability index, stochastic composite expected priority vector, stochastic composite expected rank and stochastic composite confidence factor are developed based on SPA to describe the ranks of alternatives based on SPA. Finally, a group stochastic preference analysis-best worst method (GSPA-BWM) algorithm is developed by analyzing the judgments space through Monte Carlo simulation. The experts can use this method to choose some of the outcomes which they find most useful to make reliable decisions. Examples and comparison analyses show that the proposed method is effective. [ABSTRACT FROM AUTHOR]

In the current study, we present a stochastic SAIS (unaware susceptible-aware susceptible-infectious-unaware susceptible) epidemic dynamic model on complex networks with multi-weights. The disease dynamic is influenced by random perturbations to the force of the infection rates, as well as awareness rates. To analyze the problem of extinction, we discuss both the stochastic asymptotic stability in the large and almost surely exponential stability of the trivial solution. Then, we get some sufficient conditions, which guarantee the stochastic persistence of infectious disease. Based on the Erdös-Réyni random graph, the numerical simulations are given. These not only validate our conclusions but also obtain else significative results. Both theoretical results and numerical simulations further reflect that improvement of risk awareness and reduction of decay in awareness are highly effective in preventing disease spread. And then, environmental noises play a significant role in disease transmission. [ABSTRACT FROM AUTHOR]

This paper investigates the examination of global asymptotic stability pertaining to uncertain complex-valued stochastic neural networks (UCVSNNs) with multiple time delays. This paper employs the real-imaginary separated activation function to establish an equivalence between complex-valued neural networks (CVNNs) and two real-valued activation functions, representing the real and imaginary parts respectively. This equivalence is utilised to analyse the original UCVSNNs model in a comprehensive manner. The global asymptotic stability of the studied UCVSNNs model is ensured by constructing an appropriate Lyapunov-Krasovskii generalised function and applying the $ It\hat {o} $ It o ˆ formula, linear matrix inequality (LMI) and other analytical techniques to derive the system stability and other sufficient conditions. In the meanwhile, we provide two numerical examples to demonstrate the reliability and benefit of the discovered results. [ABSTRACT FROM AUTHOR]

The document is an author index for Volume 17 of the International Journal of Biomathematics, published in 2024. It lists various authors and their respective articles on topics such as mathematical modeling of infectious diseases, predator-prey dynamics, and bifurcation analysis. The index covers a wide range of research areas within biomathematics, including vaccination effects, epidemic modeling, and chaos control. [Extracted from the article]

In this paper, we propose an epidemic model with the impact of information intervention and general incidence rate in deterministic and stochastic environment, respectively. The information intervention prompts susceptible individuals to change their behavior to protect themselves from infection. First, the asymptotic dynamics of the disease-free equilibrium and the unique endemic equilibrium are analyzed and the results indicate that the basic reproduction number is a pointy disease threshold about the stability under some conditions. Then, we formulate the corresponding stochastic model by perturbing the disease transmission rate and information response rate parameters by white noise terms and provide verifiable sufficient conditions for extinction and persistence in mean. Two sufficient conditions for extinction show that if the noise intensity of the disease transmission rate is large enough or small enough, the infected population of the stochastic system will tend to go extinct. For the persistence, we get the sufficient conditions which guarantee the infected population to be persistent in the mean. Finally, we perform some numerical simulations to compare the dynamic behaviors of the deterministic and the stochastic system. [ABSTRACT FROM AUTHOR]

The gradient discretisation method (GDM) – a generic framework encompassing many numerical methods – is studied for a general stochastic Stefan problem with multiplicative noise. The convergence of the numerical solutions is proved by compactness method using discrete functional analysis tools, Skorokhod theorem and the martingale representation theorem. The generic convergence results established in the GDM framework are applicable to a range of different numerical methods, including for example mass-lumped finite elements, but also some finite volume methods, mimetic methods, lowest-order virtual element methods, etc. Theoretical results are complemented by numerical tests based on two methods that fit in GDM framework. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic analysis method is proposed for extraction and evaluation of Power Distribution Map (PDM) in system Printed Circuit Board (PCB). This is conducted based on some high level data including placement and routing geometry, Power Distribution Network (PDN), component package parasitic, and Voltage Regulator Module (VRM). A simple model for supply current of two constituent blocks of electronic systems is analytically extracted. The worst-case simultaneous operation of all consumers are considered for PDM extraction. The approach is applied to a specific designed and fabricated mixed signal board. PDM is beneficial in the placement process of decoupling capacitance or noisy components in an optimum and right location. Also, the proposed approach can be considered as a verification step of PCB design flow and be applicable before routing only based on the placement data of components of the system. This enables the designer to predict the upcoming problems in layout and hastens the process of design verification. [ABSTRACT FROM AUTHOR]

This paper studies the stability of stochastic nonlinear time‐delay systems with arbitrary switching and its application. A novel Krasovskii‐type stability theorem is introduced for stochastic nonlinear systems featuring arbitrary switching and time‐delay. Unlike previous results, this stability result removes the restriction that the infinitesimal generator of Lyapunov–Krasovskii functional (i.e., LV$$ \mathcal{L}V $$) must be negative definite and allows LV$$ \mathcal{L}V $$ to be indefinite. As an application, the tracking control is studied for a class of stochastic switched systems with inverse dynamics and time‐delay. The assumption condition imposed on the inverse dynamic subsystem is weaker compared with most of existing findings. Finally, we illustrate the feasibility and effectiveness of proposed control strategy by two simulation examples. [ABSTRACT FROM AUTHOR]

Dyadic social interactions evoke complex dynamics between two agents that, while exchanging unequal levels of body autonomy and motor control, may find a fine balance to synergize, take turns, and gradually build social rapport. To study the evolution of such complex interactions, we currently rely exclusively on subjective pencil and paper means. Here, we complement this approach with objective biometrics of socio-motor behaviors conducive to socio-motor agency. Using a common clinical test as the backdrop of our study to probe social interactions between a child and a clinician, we demonstrate new ways to streamline the detection of social readiness potential in both typically developing and autistic children by uncovering a handful of tasks that enable quantification of levels of motor autonomy and levels of motor control. Using these biometrics of autonomy and control, we further highlight differences between males and females and uncover a new data type amenable to generalizing our results to any social setting. The new methods convert continuous dyadic bodily biorhythmic activity into spike trains and demonstrate that in the context of dyadic behavioral analyses, they are well characterized by a continuous Gamma process that can classify individual levels of our thus defined socio-motor agency during a dyadic exchange. Finally, we apply signal detection processing tools in a machine learning approach to show the validity of the streamlined version of the digitized ADOS test. We offer a new framework that combines stochastic analyses, nonlinear dynamics, and information theory to streamline and facilitate scaling the screening and tracking of social interactions with applications to autism. [ABSTRACT FROM AUTHOR]

ABSTRACT This article discusses the finite‐time boundedness (FTB) issue and L2$$ {L}_2 $$‐gain analysis for switched stochastic systems, particularly under the dual influence of DoS attacks and false data injection attacks, by employing a novel event‐triggered mechanism. Different from the moment calculation method, a probability‐based FTB is studied which offers more pertinence. To obtain a less conservative condition of FTB, a switched Lyapunov function is constructed. Additionally, a memory‐based dynamic event‐triggered mechanism is designed to reduce the amounts of triggering and mitigate the state response fluctuations. Based on the incomplete information above, state feedback controllers are devised to satisfy stochastic FTB, ensuring the successful attainment of finite‐time L2$$ {L}_2 $$‐gain. Sufficient conditions are cast into a convex optimization problem by LMIs which can be solved easily. Finally, a compared numerical example and an RLC series circuit are adopted to demonstrate the availability of the theoretical results. [ABSTRACT FROM AUTHOR]

AbstractAflatoxin B1 is a carcinogenic mycotoxin responsible for hepatocellular carcinoma in humans and animals. A two-dimensional combined stochastic sensor based on the physical modification of a gold dot with N-[5-methylpyridin-2yl] octadec-9-enamide was designed and validated for aflatoxin B1 determination in bovine and vegan milk. The working concentration range was between 0.1 fmol L−1 and 0.1 µmol L−1 with a sensitivity of 2.70 × 109 s−1mol−1L. The recovery values for aflatoxin B1 in the milk samples exceeded 95.00%, with relative standard deviations lower than 0.10%. [ABSTRACT FROM AUTHOR]

ABSTRACT This paper investigates the event‐triggered generalized extended state observer‐based estimation issue for a class of nonlinear networked control systems with unmodeled dynamics, external disturbances and multi‐channel attacks. In order to resist different forms of attack threats on multiple communication channels from sensors to the observer, Markov chain is introduced to describe the stochastic switching or jumping behavior between different attack modes. Considering the limited network resources, the measured outputs are transmitted to the observer only when the triggering conditions are met. Moreover, the parameters modeled by the Bernoulli process are adopted to help analyze potential random gain variations of the generalized extended state observer. By employing Lyapunov stability theory and stochastic systems analysis, sufficient conditions are derived to ensure that the augmented system is exponentially bounded in mean square, and the expected observer gains are further determined through linear matrix inequalities. Finally, a numerical example and a simulation related to the RLC series circuit system are conducted, illustrating the proposed method's effectiveness. [ABSTRACT FROM AUTHOR]

In this study, an intelligent computing framework is presented to explore the influence of unpredictable environmental factors on the spread of infections. A stochastic non-linear SIS epidemic model (SISEM) is examined that incorporates a non-linear incidence rate, and impact of random fluctuations on the disease transmission. The knacks of artificial neural networks Levenberg–Marquardt (ANNLMA) technique are exploited to illustrate the behavioral complexities of stochastic non-linear SISEM, which explores the dynamics of disease transmission in a stochastic environment and provides insights into the interactions between susceptible and infectious populations. The Milstein approach of order 1 generates a dataset for the proposed ANNLMA technique by varying integrated parameters, such as the rates of recovery, death, disease transmission, noise standard deviation and the entire population, for various SISEM scenarios. The referenced dataset is randomly divided into test, validation and train sets for the weight learning of the proposed ANNLMA. The viability of the ANNLMA is measured using intensive simulation-based investigations through analysis of mean squared errors, histograms, regression and autocorrelation studies. The investigations highlighted that the ANNLMA results closely match the reference results, illustrating convergence within the 10−2 to 10−7 range, indicating the validity of the proposed methodology. [ABSTRACT FROM AUTHOR]

In the study of partial differential equations (PDEs) with random initial data and singular stochastic PDEs with random forcing, we typically decompose a classically ill-defined solution map into two steps, where, in the first step, we use stochastic analysis to construct various stochastic objects. The simplest kind of such stochastic objects is the Wick powers of a basic stochastic term (namely a random linear solution, a stochastic convolution, or their sum). In the case of randomized initial data of a general function of negative regularity for studying nonlinear wave equations (NLW), we show necessity of imposing additional Fourier–Lebesgue regularity for constructing Wick powers by exhibiting examples of functions slightly outside L^2(\mathbb {T}^d) such that the associated Wick powers do not exist. This shows that probabilistic well-posedness theory for NLW with general randomized initial data fails in negative Sobolev spaces (even with renormalization). Similar examples also apply to stochastic NLW and stochastic nonlinear heat equations with general white-in-time stochastic forcing, showing necessity of appropriate Fourier–Lebesgue \gamma-radonifying regularity in the construction of the Wick powers of the associated stochastic convolution. [ABSTRACT FROM AUTHOR]

This research paper describes the development of a low-cost device for measuring wastewater flow rates in open channels, a significant advancement enabled by the evolution of microcomputers and processing techniques. A laboratory setup was constructed to validate the device's accuracy against a standard flow measurement method, optimizing key parameters to achieve a linear relationship between detected and set flow rates, while considering hardware limitations and energy efficiency. The central focus of the research was developing a method to measure the velocity of contaminated fluid using ultrasonic signals, employing the cross-correlation method for signal delay analysis in a stochastic environment. This was complemented by a procedure to measure fluid levels, also based on ultrasonic signals. The device's reliability was assessed through repeatability and uncertainty measurements, confirming its accuracy with an extended uncertainty not exceeding an average of 3.47% for flows above 40 L/min. The device has potential to provide valuable data on the operational dynamics of sanitary networks, crucial for developing and calibrating simulation models. [ABSTRACT FROM AUTHOR]

This paper investigates a stochastic SEIAIR epidemic model with nonlinear incidence and contacting distance to describe the transmission dynamics of COVID‐19. Firstly, we show the global existence of positive solution of the system. Then, using the Lyapunov function method and theory of stochastic analysis, we set out the sufficient conditions of the existence and uniqueness of an ergodic stationary distribution to the stochastic model. Furthermore, we obtain the sufficient condition for extinction of the disease. Finally, we go through some numerical simulations to demonstrate the theoretical results. Our study extends and improves the results of previous studies. [ABSTRACT FROM AUTHOR]

The aim of the present paper is first to propose a state-of-art of this domain. Second, some convergence results are established in the case of the Dirichlet distribution. This distribution has the advantage to include both the uniform case and the deterministic one. In a first part, the Dirichlet distribution is defined and some properties are supplied. In a second part, new results are established in connexion with former theorems. [ABSTRACT FROM AUTHOR]

Predicting slope stability is important for preventing and mitigating landslide disasters. This paper examines the existing approaches for analyzing slope stability. There are several established conventional approaches for slope stability analysis that can be applied in this context. However, in recent decades, soft computing methods has been extensively developed and employed in stochastic slope stability analysis, notably as surrogate models to improve computing efficiency in contrast to traditional approaches. Soft computing methods can deal with uncertainty and imprecision, which may be quantified using performance indices like coefficient of determination, in regression and accuracy in classification. This review study focuses on conventional methods such as the Bishop's method and Janbu's method, as well as soft computing models such as support vector machine, artificial neural network, Gaussian process regression, decision tree, etc. The advantages and limitations of soft computing techniques in relation to conventional methods have also been thoroughly covered in this paper. The achievements of soft computing methods are summarized from two aspects -predicting factor of safety and classification of slope stability. Key potential research challenges and future prospects are also given. [ABSTRACT FROM AUTHOR]

To meet the greenhouse gas reduction targets and address the uncertainty introduced by the surging penetration of stochastic renewable energy sources, energy storage systems are being deployed in microgrids. Relying solely on short-term uncertainty forecasts can result in substantial costs when making dispatch decisions for a storage system over an entire day. To mitigate this challenge, an adaptive robust optimization approach tailored for a hybrid hydrogen battery energy storage system (HBESS) operating within a microgrid is proposed, with a focus on efficient state-of-charge (SoC) planning to minimize microgrid expenses. The SoC ranges of the battery energy storage (BES) are determined in the dayahead stage. Concurrently, the power generated by fuel cells and consumed by electrolysis device are optimized. This is followed by the intraday stage, where BES dispatch decisions are made within a predetermined SoC range to accommodate the uncertainties realized. To address this uncertainty and solve the adaptive optimization problem with integer recourse variables in the intraday stage, we proposed an outer-inner column-and-constraint generation algorithm (outer-inner-CCG). Numerical analyses underscored the high effectiveness and efficiency of the proposed adaptive robust operation model in making decisions for HBESS dispatch. [ABSTRACT FROM AUTHOR]

A main challenge within inertial navigation systems involves attitude determination, which refers to the process of estimating the angles that define orientations. A new algorithm is presented to estimate a reliable and proper model for a low‐cost attitude and heading reference system (AHRS), while also, including long‐term global navigation satellite system (GNSS) outages with various dynamical manoeuvres. In the proposed approach, the initial AHRS model is continuously refined at each time step through the incorporation of complementary terms using a new prediction method. These complementary terms are determined using attitude information from the accelerometers output and the GNSS as reference systems. The proposed estimation technique undergoes mathematical analysis to ascertain stochastic stability and is further assessed through real‐world aerial experimental tests conducted with hardware‐in‐the‐loop mechanisation. The obtained results demonstrate a significant enhancement in the reliability and accuracy of the AHRS through the proposed estimation algorithm, even under GNSS blockages. The comparative results highlight the higher performance of the suggested data fusion scheme in providing a reliable and accurate model for the AHRS in normal conditions and assisting a powerful neural network‐based algorithm to provide reliable heading information even during long‐term GNSS outages under dynamical manoeuvres. [ABSTRACT FROM AUTHOR]

This study investigates the impact of uncertainties in soil properties, particularly the stochastic variations in shear modulus (G) and Poisson's ratio (ν), on the period lengthening ratio (T/T) and base-shear reduction ( Δν/ν) of structures, considering soil-structure interaction (SSI) according to ASCE/SEI 7-10 guidelines. The motivation behind this research is to enhance the understanding and prediction of how uncertainties in soil properties affect the seismic response of structures, aiming at improving building design and safety. This research was conducted using a Monte Carlo simulation approach, generating 500,000 random values for G and ν to evaluate the variations (mean ± standard deviation) in the period lengthening ratio of the soil-foundation- structure system and base-shear reduction. The obtained results indicate that incorporating stochastic variations in the soil properties more accurately reflects the complexity and inherent uncertainty of the soil properties. Specifically, uncertainties in the shear modulus (G) significantly affect the fundamental period, base-shear reduction, and foundation damping. Conversely, the Poisson's ratio (ν) appears to be an inert factor. These findings have implications for seismic-design practices, suggesting that a deterministic approach might not capture critical aspects of material variability, thus contributing to uncertainties in structural response. This study provides critical insights into the role of soil properties in the dynamic response of structures, contributing to the development of more resilient designs and improving seismic risk management strategies. [ABSTRACT FROM AUTHOR]

The stochastic finite element method is an important tool for structural reliability analysis. In order to improve the calculation efficiency, a stochastic finite element method based on the Krylov subspace is proposed for the static reliability analysis of structures. The first step of the proposed method is to preprocess the static response equation considering randomness to reduce the condition number of the coefficient matrix. The second step of the proposed method is to construct a Krylov subspace based on the preprocessed static response equation. Then, the static displacement of random sampling is expressed as a linear combination of subspace basis vectors to achieve the purpose of a fast solution. Finally, statistics and failure probability are calculated according to the static response obtained from thousands of random samples. Three numerical examples are given to compare the proposed method with the stochastic finite element method based on the Neumann series. The results show that the stochastic finite element method based on the Krylov subspace is more accurate and efficient than the stochastic finite element method based on the Neumann series. [ABSTRACT FROM AUTHOR]

This article addresses the static output feedback load frequency control (LFC) problem for semi‐Markov type interconnected multi‐area power systems (IMAPSs) through non‐fragile proportional‐integral (PI) strategy. Primarily, by roundly exploiting the dynamical properties and considering random mutations of the IMAPSs, the semi‐Markov jump process (MJP) is elaborately scheduled for establishing the dynamical model with precision. Subsequently, on account of the characteristic of geographical isolation, a memory‐like sampled‐data LFC mechanism considering time‐varying transmission delay for the semi‐Markov jump IMPASs is formulated accordingly. Additionally, the non‐fragile issue is explored for the PI controller gain fluctuations to meet the actual operation scenario. After that, a mode‐dependent two‐side polynomial‐type looped Lyapunov functional is constructed for enhancing flexibility. Then, in virtue of the stochastic analysis technique, some relaxed conditions guaranteeing stochastic stability with prescribed H∞$$ {H}_{\infty } $$ performance are thereby derived in the shape of linear matrix inequalities (LMIs). Ultimately, a numerical example is carried out to validate the efficacy of the developed control methodology. [ABSTRACT FROM AUTHOR]

This article is the first attempt in the open literature to investigate the impact of uncertainty in material properties on the critical buckling speed of rim-driven rotating laminated plates. The formulations are constructed using the isogeometric approach (IGA) and higher-order shear deformation theory (HSDT). Coriolis and centrifugal forces resulting from rotation are taken into consideration. The results of the current formulation are compared to the previous results and validated. The accuracy and flexibility of the RBFN-based surrogate model, designed for uncertainty analysis, is verified by comparing the result with Monte Carlo simulation (MCS). Through a variety of parametric experiments, the critical buckling speed of rotating laminates driven by a rim is stochastically analyzed. Variance-based sensitivity analysis is employed to identify the influence of individual material properties on the critical buckling speed. Further, the impact of sensitive properties on the probability of structural failure is estimated. This research can be used to forecast the probability of failure of a structure at various levels of material uncertainty associated with it. [ABSTRACT FROM AUTHOR]

This study introduces extended isogeometric analysis method (XIGA) as a tool to investigate fracture behavior in isotropic and orthotropic materials under uniaxial and biaxial mechanical loads. Utilizing isogeometric analysis knot spans to discretize the problem domain and second order perturbation technique within XIGA framework derives mean and coefficient of variance values for mixed-mode stress intensity factors (MMSIFs) by considering variations in input parameters, including crack length, crack angle and material elastic properties. Mixed-mode SIF is evaluated using the proper interaction integral method subjected to different loading conditions showcases versatility of the proposed approach. The alignment between the existing literature and Monte Carlo simulations demonstrates a robust correspondence, validating the accuracy and reliability of the stochastic XIGA technique. This research establishes the efficacy of the approach in comprehensively addressing fracture analysis across different mechanical loading scenarios. [ABSTRACT FROM AUTHOR]

We develop a measure-theoretic framework for dynamic Shapley values in Banach spaces, extending classical cooperative game theory to continuous-time, infinite-dimensional settings. We prove the existence and uniqueness of strong solutions to stochastic differential equations modeling competence evolution in Banach spaces, establishing sample path continuity and moment estimates. The dynamic Shapley value is rigorously defined as a càdlàg stochastic process with an axiomatic characterization. We derive a martingale representation for this process and establish its asymptotic properties, including a strong law of large numbers and a functional central limit theorem under α-mixing conditions. This framework provides a rigorous basis for analyzing dynamic value attribution in abstract spaces, with potential applications to economic and game-theoretic models. [ABSTRACT FROM AUTHOR]

A remarkably high growth has been observed in the uses of wireless sensor networks (WSNs), due to their momentous potential in various applications, namely the health sector, smart agriculture, safety systems, environmental monitoring, military operations, and many more. It is quite important that a WSN must have high reliability along with the least MTTF. This paper introduces a continuous-time Markov process, which is a special case of stochastic process, based on modeling of a wireless sensor network for analyzing the various reliability indices of the same. The modeling has been conducted by considering the different components, including the sensing unit, transceiver, microcontroller, power supply, standby power supply unit, and their failures/repairs, which may occur during their functioning. The study uncovered different important assessment parameters like reliability, components-wise reliability, MTTF, and sensitivity analysis. The critical components of a WSN are identified by incorporating the concept of sensitivity analysis. The outcomes emphasize that the proposed model will be ideal for understanding different reliability indices of WSNs and guiding researchers and potential users in developing a more robust wireless sensor network system. [ABSTRACT FROM AUTHOR]

Aiming at the problem of random environment interference in the process of strategy interaction and the behavioral evolution of an aerial attack–defense game, this paper considers the influence of the difference in the performance and value between both game players in terms of strategy evolution; explores the randomness of the complex battlefield environment, the uncertainty of the behavioral state of game players, and the limitations of the emergent situation; constructs a mathematical model of the stochastic evolution of an aerial-coordinated attack–defense game in uncertain environments; and studies the stability of the strategy interaction and behavioral decision-making process of both players of the aerial attack–defense game. Simulation results show that many factors of the performance and value between both game players have a greater impact on the strategy evolution trend in both game players, which not only causes changes in the results of the strategy selection but also affects the rate of strategy evolution for the game players. In addition, random environmental factors cause a certain degree of interference to the strategy evolution process of the game players, which usually accelerates the game players' strategy evolution rate and greatly affects the evolution process of the game players' strategy. This study can provide a theoretical basis and feasible reference for improving mission decision-making, response mechanisms, and system modeling of an aerial attack–defense game, which has important theoretical value and practical significance. [ABSTRACT FROM AUTHOR]

We examine stochastic phase models for the community effect of cardiac muscle cells. Our model extends the stochastic integrate-and-fire model by incorporating irreversibility after beating, induced beating, and refractoriness. We focus on investigating the expectation and variance in the synchronized beating interval. Specifically, for a single isolated cell, we obtain the closed-form expectation and variance in the beating interval, discovering that the coefficient of variation has an upper limit of 2 / 3 . For two coupled cells, we derive the partial differential equations for the expected synchronized beating intervals and the distribution density of phases. Furthermore, we consider the conventional Kuramoto model for both two- and N-cell models. We establish a new analysis using stochastic calculus to obtain the coefficient of variation in the synchronized beating interval, thereby improving upon existing literature. [ABSTRACT FROM AUTHOR]

Summary: This article considers the problem of edge‐based event‐triggered output feedback control for linear multi‐agent systems (MASs) with state‐independent process and measurement noise under undirected communication topologies. The main breakthroughs are the design of distributed event‐triggered output feedback control strategy and the stochastic stability analysis. Toward this, first, according to Kalman filtering theory, An observer is contrasted to optimally estimate the state of each agent. Next, a novel edge‐based event‐triggered mechanism (EBETM) is designed to reduce the communication frequency among agents effectively, and a positive interval between events is enforced in EBETM, which can eliminate the Zeno behavior. Then, stability of the estimation error and the consensus error systems is analyzed, the execution error is estimated and the almost sure consensus is achieved. Finally, a numerical example is given to show that MASs achieves almost sure consensus and there is a positive interval between the events of all edges. [ABSTRACT FROM AUTHOR]

This study proposes a stochastic method to analyse the propagation of hydraulic fractures affected by layered heterogeneity in rocks in a toughness-dominated regime. The study utilises the phase-field method in the context of two-dimensional finite element analysis to model the hydraulic fracture (HF) propagation in rock materials in laboratory scale. Field data on hydrogeologic properties of some rocks reveal that material heterogeneity may appear in the form of leptokurtic marginal distributions. Generalised sub-Gaussian (GSG) model is capable of capturing physical characteristics of such rocks, and it is employed to stochastically model rocks with layered lithologic heterogeneity by generating a large number of auto- and cross-correlated random fields for hydro-geomechanical properties. To investigate the sensitivity of the cracking response to the inherent characteristics of material heterogeneity, various GSG distribution forms are considered in Monte Carlo (MC) analyses. The HF's deviation from the theoretically predicted direction, which is perpendicular to the direction of the minimum in situ stress, is correlated with the distribution of hydro-geomechanical properties, showing a Gaussian-type distribution. This study concludes that the differential stress and the bedding orientation are the main factors affecting the HF deviation and the required breakdown pressure for initiating the HF propagation from a borehole. In the application of directional hydraulic fracturing (DHF), the effect of bedding layers becomes dominant when the bedding orientation is aligned with the direction of perforations in the boreholes. Highlights: The phase-field theory in the context of finite element method is employed for stochastic analysis of toughness-dominated hydraulic fracture propagation in layered heterogeneous rocks. Generalised sub-Gaussian random fields are generated to model the natural hydromechanical features in heterogeneous rocks. By order of importance, differential stress, i.e. the difference between maximum and minimum in situ stresses, and the bedding orientation are found to be the main factors in specifying the hydraulic fracture propagation path in layered heterogeneous rocks. Hydraulic fracture trajectories from perforated boreholes are mainly influenced by the orientation of the heterogeneous bedding layers with respect to the direction of the maximum in situ stress. [ABSTRACT FROM AUTHOR]

As an encouraged award rule in public procurement tenders, the "Most Economically Advantageous Tender" rule aims to determine the winning bidder considering quantitative and qualitative factors simultaneously by a group of experts. In such a rule, how to maintain a transparent procedure in accordance with governmental procurement regulations as well as guaranteeing fair evaluations of all bidders considering the risk behaviors of experts is a challenge. To fill this challenge, this study proposes a stochastic cross-efficiency data envelopment analysis (DEA) approach based on the prospect theory to determine the winner in public procurement tenders. Firstly, two cross-efficiency DEA models to maximize gains and minimize losses based on the prospect theory are developed to derive the cross-efficiencies of bidders. Next, a stochastic Benefit-of-the-Doubt (BoD) model, carried out by Monte Carlo simulation, is used to aggregate the diverse cross-efficiencies derived from the evaluations of different experts. The model can deduce a robust ranking of bidders without a priori setting of attribute weights and expert weights. For the challenging issue that experts cannot make evaluations precisely for qualitative factors with uncertain information, the hesitant fuzzy linguistic term set is applied to express the vagueness of expert judgments. An illustrative example is given to demonstrate the applicability and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

We study the sharp interface limit of the stochastic Cahn-Hilliard equation with cubic double-well potential and additive space-time white noise ε σ W, where ε>0 is an interfacial width parameter. We prove that, for a sufficiently large scaling constant σ>0, the stochastic Cahn-Hilliard equation converges to the deterministic Mullins-Sekerka/Hele-Shaw problem for ε→0. The convergence is shown in suitable fractional Sobolev norms as well as in the L p -norm for p∈(2,4] in spatial dimension d=2,3. This generalizes the existing result for the space-time white noise to dimension d=3 and improves the existing results for smooth noise, which were so far limited to p∈(2, d+2 2d+8) in spatial dimension d=2,3. As a byproduct of the analysis of the stochastic problem with space-time white noise, we identify minimal regularity requirements on the noise which allow convergence to the sharp interface limit in the H¹-norm and also provide improved convergence estimates for the sharp interface limit of the deterministic problem. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic SIQS epidemic model perturbed by both white and telephone noises is investigated. By constructing several suitable Lyapunov functions, we obtain sufficient conditions for the existence of ergodic stationary distribution of the positive solution. Moreover, by solving the Fokker–Planck equation, we obtain the exact expression of probability density function around the quasi-equilibrium of the stochastic model. In addition, sufficient conditions for the extinction are established. Finally, the results of this paper are further verified by numerical simulation. [ABSTRACT FROM AUTHOR]

A geotextile-reinforced retaining wall is a geotechnical structure with many design parameters. Hence, the uncertainty of the input parameters considerably affects the design of these structures. On the other hand, when the number of uncertain parameters increases, the time of this analysis increases drastically. Accordingly, the current study used an analytical method, namely, jointly distributed random variables (JDRV) method, that requires less running time than the simulation methods for stochastic analysis. For this purpose, stochastic analysis of the geotextile-reinforced retaining wall was carried out based on the limit equilibrium method (LEM), with soil parameters considered as uncertain variables. To verify the results, the probability density functions (PDFs) of the wall safety factors were compared with the Monte Carlo simulation (MCS). Next, to assess the effect of the external and internal stability modes on system reliability, the system reliability index was determined using the sequential compounding method (SCM). The results of the system reliability analysis revealed that, among the reliability indices of the components, the minimum values are attributed to the bearing capacity. The correlation between the rupture and pullout safety factors exhibited the maximum correlation, indicating that they are more dependent components than others. Based on the stochastic sensitivity analysis, the internal friction angle emerged as the most influential in the external and internal safety factors. [ABSTRACT FROM AUTHOR]

The focus of this article lies in the existence of global mild solutions for Hilfer fractional stochastic evolution equations (HFSEEs) on the positive semi-axis (0 , + ∞) with a derivative order greater than 3 2 and less than 2. A significant challenge, which also presents novelty here, is to extend the generalized Ascoli–Arzela (A–A) theorem established in Zhou and He (2022) to the stochastic case under the associated sine family { S (t) } t ≥ 0 not necessary compact. Then, by relying on our newly established generalized A–A theorem, standard stochastic analysis theory and Schauder's fixed point principle, we derive the existence of global mild solutions for the addressed system. Finally, we demonstrate the feasibility of our obtained results through an illustrative example. [ABSTRACT FROM AUTHOR]

Stochastic analysis of the absorbed power density (APD) on skin surface exposed to radiation of halfwave dipole at 10, 30 and 90 GHz and for different antenna‐body distances is presented. Skin tissue is modeled as a half‐space consisting of one layer (skin) or three layers (skin, fat and muscle) whose permittivities and conductivities are uncertain. Deterministic part is based on numerical solution of Pocklington equation via Galerkin Bubnov Indirect Boundary Element method (GB‐IBEM) and numerical integration of the corresponding field integrals. Uncertainty from tissue electric parameters is propagated to APD via non‐intrusive Stochastic Collocation method (SCM) in order to compute stochastic moments of APD. For 1‐layered model APD stochastic moments are computed with 3 deterministic simulations. On the other hand APD mean and variance for 3 layered model are successfully computed with 13 deterministic simulations while skewness and kurtosis require 85 deterministic simulations. The ratio of APD standard deviation and mean decreases with frequency thus indicating that the uncertainty in the tissue electric properties has smaller effect on APD uncertainty at higher frequencies. Finally, sensitivity analysis carried out for both 1‐layered and 3‐layered models indicates the same conclusions. At 10 GHz skin permittivity and conductivity are the two most important parameters. However, as frequency increases the impact of skin conductivity prevails. This indicates that in frequency range 10–90 GHz the APD uncertainty quantification and sensitivity analysis can be carried out by using only 2‐dimensional stochastic model. Key Points: The reported values for tissue permittivity and conductivity are scattered, thus introducing the uncertainty in the output absorbed power density (APD)Stochastic Collocation can assure the computation of APD stochastic moments with good accuracy at relatively low number of simulationsSensitivity analysis shows that the impact of the inner layers' permittivity and conductivity is negligible [ABSTRACT FROM AUTHOR]

The generalized tempered stable (GTS) distribution is an optimal choice for modeling disease propagation, as it effectively captures the heavy-tailed nature of such events. This attribute is crucial for evaluating the impact of large-scale outbreaks and formulating effective public health interventions. In our study, we introduce a comprehensive stochastic epidemic model that incorporates various intervention strategies and utilizes Lévy jumps characterized by the GTS distribution. Notably, our proposed stochastic system does not exhibit endemic or disease-free states, challenging the conventional approach of assessing disease persistence or extinction based on asymptotic behavior. To address this, we employed a novel stochastic analysis approach to demonstrate the potential for disease eradication or continuation. We provide numerical examples to highlight the importance of incorporating the GTS distribution in epidemiological modeling. These examples validate the accuracy of our results and compare our model's outcomes with those of a standard system using basic Lévy jumps. The purposeful use of the GTS distribution accounts for the heavy-tailed nature of disease incidence or vector abundance, enhancing the precision of models and predictions in epidemiology. [ABSTRACT FROM AUTHOR]

This article aimed to investigate the existence and stability of Besicovitch almost periodic ( B a p ) positive solutions for a stochastic generalized Mackey-Glass hematopoietic model. To begin with, we used stochastic analysis theory, inequality techniques, and fixed point theorems to prove the existence and uniqueness of L p -bounded and L p -uniformly continuous positive solutions for the model under consideration. Then, we used definitions to prove that this unique positive solution is also a B a p solution in finite-dimensional distributions. In addition, we established the global exponential stability of the B a p positive solution using reduction to absurdity. Finally, we provided a numerical example to verify the effectiveness of our conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we have discussed a class of second-order neutral stochastic differential evolution systems, based on the Wiener process, with random impulses and state-dependent delay. The system is an extension of impulsive stochastic differential equations, since its random effect is not only from stochastic disturbances but also from the random sequence of the impulse occurrence time. By using the cosine operator semigroup theory, stochastic analysis theorem, and the measure of noncompactness, the existence of solutions was obtained. Then, giving appropriate assumptions, the approximate controllability of the considered system was inferred. Finally, two examples were given to illustrate the effectiveness of our work. [ABSTRACT FROM AUTHOR]

This paper is concerned with almost sure exponential synchronization of multilayer complex networks with Markovian switching via aperiodically intermittent discrete observation noise. First, Markovian switching and multilayer interaction factors are taken into account simultaneously, which make our system more general compared with the existing literature. Meanwhile, the network architecture may be undirected or directed, and consequently, the adjacency matrix is symmetrical and asymmetrical. Second, the control strategy is based on aperiodically intermittent discrete observation noise, where the average control rate is integrated to depict the distributions of work/rest intervals of the control strategy from an overall perspective. Third, different from the work about p th moment exponential synchronization of network systems, by utilizing M-matrix theory and various stochastic analysis techniques including the Itô formula, the Gronwall inequality, and the Borel-Cantelli lemma, some criteria on almost sure exponential synchronization of multilayer complex networks with Markovian switching have been constructed and the upper bound of the duration time has been also estimated. Finally, several numerical simulations are exhibited to validate the effectiveness and feasibility of our analytical findings. [ABSTRACT FROM AUTHOR]

Based on the World Health Organization (WHO), Meningitis is a severe infection of the meninges, the membranes covering the brain and spinal cord. It is a devastating disease and remains a significant public health challenge. This study investigates a bacterial meningitis model through deterministic and stochastic versions. Four-compartment population dynamics explain the concept, particularly the susceptible population, carrier, infected, and recovered. The model predicts the nonnegative equilibrium points and reproduction number, i.e. the Meningitis-Free Equilibrium (MFE), and Meningitis-Existing Equilibrium (MEE). For the stochastic version of the existing deterministic model, the two methodologies studied are transition probabilities and non-parametric perturbations. Also, positivity, boundedness, extinction, and disease persistence are studied rigorously with the help of well-known theorems. Standard and nonstandard techniques such as Euler Maruyama, stochastic Euler, stochastic Runge Kutta, and stochastic nonstandard finite difference in the sense of delay have been presented for computational analysis of the stochastic model. Unfortunately, standard methods fail to restore the biological properties of the model, so the stochastic nonstandard finite difference approximation is offered as an efficient, low-cost, and independent of time step size. In addition, the convergence, local, and global stability around the equilibria of the nonstandard computational method is studied by assuming the perturbation effect is zero. The simulations and comparison of the methods are presented to support the theoretical results and for the best visualization of results. [ABSTRACT FROM AUTHOR]

Previous research on adolescent peer networks has mainly focused on friendship networks and their association with violence, but very limited research is available on peer rejection networks. This lack of knowledge hinders the effectiveness of preventing peer rejection and its negative effects. Based on the theory of the cycle of violence, the present study examines the extent to which parental physical abuse experiences, aggressive behavior toward peers and acceptance of violence are related to peer rejection networks at school. Social network analysis with a stochastic actor-oriented model of longitudinal data collected from high school students (Wave 1, n = 620; Wave 2, n = 590) confirms that adolescents who frequently use aggression toward their peers are more likely to be rejected, especially if those adolescents have experienced abuse. Similarly, peers are more likely to reject adolescents with high levels of accepting violence. The results also show that aggression toward peers generally tends to decrease over time but not for adolescents who reject a larger number of students. For students who reject many peers, aggression frequency increases. From the perspective of resilience theory, peer rejection, when combined with aggression toward peers and acceptance of violence, particularly in female adolescents, creates a significant risk factor for socio-emotional development. Therefore, tackling violence attitudes, experiences and behavior in the school environment and at home is crucial in overcoming the cycle of violence. [ABSTRACT FROM AUTHOR]

The Chaffee–Infante (CI) equation is a nonlinear equation that may be used to predict the complex dynamics of soliton propagation in a nonlinear optical medium. In this study, we elucidate soliton solutions of the CI equation by stochastic differential equations (SDEs) with the Wiener process. In excess of the modified auxiliary equation (MAE) method, we obtain new exact soliton solutions. By combining stochastic differential equations with the Wiener process, we explain the stochastic processes directing the magnitude of solitons within the basis of the CI equation, providing dynamic views on their behavior. The acquired solitary waves are depicted via 3D and 2D graphs to show their dynamics with and without Brownian motion. [ABSTRACT FROM AUTHOR]

Abstract.This article proposes a stochastic delayed SIRS epidemic model with nonlinear incidence to describe disease transmission in a stochastic environment. First, it proves that the model has a unique global positive solution and derives sufficient conditions for the extinction and persistence of the epidemic in the population under appropriate conditions. Then, by constructing suitable Lyapunov functions, the asymptotic behavior of the model around the disease-free equilibrium and endemic equilibrium points of the deterministic model is analyzed, and it is concluded that under certain conditions, the solution of the stochastic system randomly oscillates around these two equilibrium points. Finally, several numerical examples are provided to validate the theoretical results, illustrating the significant impact of stochastic perturbations and time delays on disease control. [ABSTRACT FROM AUTHOR]

Seismic isolation technologies for large‐span structures have rapidly developed alongside the popularization of the seismic resilience concept. To produce a high‐efficiency isolation technology with lower energy dissipation demands, this paper proposes a novel inerter‐enabled isolator (IeI) and a tailored input energy reduction‐oriented design method. The inerter‐based damper within the IeI is developed by combining the dashpot, tuning spring, and two inerters to facilitate the optimization of inerter distribution. Assuming the large‐span structure remains linear, the overall seismic input energy of the large‐span structure with IeIs and its allocation in the superstructure and additional damping are quantified using stochastic energy analysis. The advantages of the IeI over the conventional linear viscous damper (LVD) isolator are elucidated through dimensionless parametric analysis. Based on the results of parametric analysis, an input energy reduction‐oriented design method is proposed for the IeI, along with an easy‐to‐follow diagram that helps with preliminary design in practical applications. The effectiveness of the IeI and the proposed design method is validated through a design case study of a benchmark large‐span structure. The results demonstrate that the IeI reduces the seismic response of large‐span structures by simultaneously employing the input energy reduction effect of grounded inerters with the damping‐enhancing effect of inerter‐based dampers. The proposed design method effectively balances the performance of controlling the large‐span structure and the isolator displacement. Under consistent control performance and isolator displacement constraints, the IeI requires much less damping coefficient and energy dissipation capacity than the conventional LVD isolator. Moreover, leveraging the damping enhancement and input energy reduction effects, the IeI achieves comparable control performance to the conventional LVD isolator, even under stricter isolator displacement constraints. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic SVEIR epidemic model with saturated incidence and partial immunity is proposed. First, we define the basic reproduction number R0 and study the global asymptotic stability of disease-free equilibrium and endemic equilibrium of the deterministic epidemic model. Then we establish the existence and uniqueness of global positive solution, along with delineating sufficient conditions for disease extinction. By constructing appropriate Lyapunov functions, we analyze the asymptotic behavior of solutions to the stochastic epidemic model around the disease-free equilibrium and endemic equilibrium points of the deterministic epidemic model. Under certain conditions, the solution of the stochastic model fluctuates around the disease-free equilibrium point and the endemic equilibrium point, with the intensity of fluctuation proportional to the intensity of white noise. The existence of ergodic stationary distribution is proved by the Khasminskii method. Finally, numerical simulations are presented to illustrate our analysis results. [ABSTRACT FROM AUTHOR]