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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 article investigates the solvability and controllability of stochastic non-instantaneous impulsive Hilfer fractional switched differential equations with deviated arguments and fractional Brownian motion (fBm) in the finite-dimensional space. The first part focuses on analyzing the existence and uniqueness of solutions using the Banach fixed-point theorem. In the second part, controllability results are established for the considered system. This study introduces a new class of control functions designed to govern the system at the termination of time intervals and on each impulsive event, incorporating stochastic noise. This approach leads to comprehensive controllability outcomes, often termed as total controllability results. The theoretical results are primarily established using fixed-point theorem, fractional calculus, Laplace transform, stochastic analysis, and Mittag-Leffler function. A numerical example is provided to validate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

The primary focus of this article is to explore the existence and controllability of a new class of Sobolev-type Hilfer fractional stochastic Volterra-Fredholm integrodifferential systems in Hilbert spaces. Our main findings are grounded in ideas from fractional calculus, stochastic analysis, cosine families, and multivalued maps. To begin, we use Bohnenblust-Karlin's fixed point theorem to examine the existence of mild solutions for the given problem. Furthermore, we introduce a novel set of sufficient conditions for the considered nonlinear Hilfer fractional stochastic differential systems, and assuming that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the proposed theory. [ABSTRACT FROM AUTHOR]

This paper addresses the problems on the generalized exponential stability in pth $ (p\geq 2) $ (p ≥ 2) -moment, the dissipativity and the almost surely exponential stability of neutral stochastic systems with unbounded time-varying delay and Markovian switching. By using the generalized delay integral inequality, the Lyapunov–Krasovskii function methodology and the theory of stochastic analysis, some sufficient conditions for such systems are obtained to guarantee the generalized exponential stability in pth-moment, the dissipativity in pth-moment, and the almost sure generalized exponential stability, respectively. The time-varying delay is a measurable unbounded function. Finally, a numerical example is given to verify the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

This study aims to compare the results of stochastic and deterministic models and their corresponding optimal M&R actions considering different budget and deterioration rate uncertainty scenarios. Moreover, the impacts of uncertainty on network's scale are investigated. Therefore, this study applies Multi-Stage stochastic programming to model the uncertainty of these parameters in pavement M&R optimization. A new approach is proposed to investigate the effects of different uncertainty cases on the mentioned problem. Moreover, two pavement networks, including a large-scale and a small-scale, are utilized to evaluate the role of network size in the optimal solution to the pavement M&R optimization in the uncertainty conditions. Due to the high complexity of the large-scale M&R problem, Progressive Hedging Algorithm as an effective decomposition technique is applied. Three different uncertainty cases, including low, medium, and high are considered for the deterioration rate. Furthermore, two scenarios are taken into account for the budget: low reduction and high reduction. The results show that the probability of selecting preventive maintenance in the optimal M&R plan is increased by increasing the severity of uncertainty cases. Therefore, preventive maintenance is the most effective pavement treatment to reduce the adverse effects of budget and pavement deterioration uncertainty. [ABSTRACT FROM AUTHOR]

In this study, the structural parameters of porous Functionally Graded (FG) plates are regarded as random fields with spatial variability, and their impact on static bending and free vibration, are investigated along with sensitivity analysis. Higher-order shear deformation theories (HSDT) are employed to establish the displacement field of the plate. Various parameters, including thickness, Young's modulus, density, volume fraction index, and porosity parameter are treated as random fields, which are discretized by Karhunen-Loève (KL) method. The analysis of uncertainties concerning structural bending deflections and natural frequencies is conducted using modified perturbation stochastic method (MPSM) in conjunction with radial point interpolation method (RPIM). The investigation extends to exploring the sensitivities of the structural responses to these random fields. The results indicate that porous FG plates exhibit heightened sensitivity to variations in thickness, ceramic Young's modulus, and volume fraction index; alterations in external conditions do not exert an influence on these sensitivities; the porosity distribution type significantly impacts the sensitivities. [ABSTRACT FROM AUTHOR]

We consider the problem of estimating the trace of a matrix function f(A). In certain situations, in particular if f(A) cannot be well approximated by a low-rank matrix, combining probing methods based on graph colorings with stochastic trace estimation techniques can yield accurate approximations at moderate cost. So far, such methods have not been thoroughly analyzed, though, but were rather used as efficient heuristics by practitioners. In this manuscript, we perform a detailed analysis of stochastic probing methods and, in particular, expose conditions under which the expected approximation error in the stochastic probing method scales more favorably with the dimension of the matrix than the error in non-stochastic probing. Extending results from Aune, Simpson, and Eidsvik [Stat. Comput. 24 (2014), pp. 247–263], we also characterize situations in which using just one stochastic vector is always—not only in expectation—better than the deterministic probing method. Several numerical experiments illustrate our theory and compare with existing methods. [ABSTRACT FROM AUTHOR]

Numerical analysis for the stochastic Stokes equations is still challenging even though it has been well done for the corresponding deterministic equations. In particular, the pre-existing error estimates of finite element methods for the stochastic Stokes equations in the L^\infty (0, T; L^2(\Omega ; L^2)) norm all suffer from the order reduction with respect to the spatial discretizations. The best convergence result obtained for these fully discrete schemes is only half-order in time and first-order in space, which is not optimal in space in the traditional sense. The objective of this article is to establish strong convergence of O(\tau ^{1/2}+ h^2) in the L^\infty (0, T; L^2(\Omega ; L^2)) norm for approximating the velocity, and strong convergence of O(\tau ^{1/2}+ h) in the L^{\infty }(0, T;L^2(\Omega ;L^2)) norm for approximating the time integral of pressure, where \tau and h denote the temporal step size and spatial mesh size, respectively. The error estimates are of optimal order for the spatial discretization considered in this article (with MINI element), and consistent with the numerical experiments. The analysis is based on the fully discrete Stokes semigroup technique and the corresponding new estimates. [ABSTRACT FROM AUTHOR]

This study proposes a stochastic approach to assess the future tsunami potential globally, focusing on the inter-arrival time of tsunami events in the 14 most active tsunamigenic zones. Two methods, conditional probability (CP) and the total probability theorem (TPT), were employed to estimate tsunami potential. For CP, the occurrence of a tsunami over time was determined by selecting the best-fit stochastic model (Gamma, Lognormal, Weibull, or log-logistic distributions) based on the time of the last earthquake in each zone. In contrast, TPT calculated the probability as the product of the tsunami-to-earthquake ratio ‘r’ and the CP of the time zone [P (E)]. However, direct comparison between the probabilities obtained by the two methods proved challenging due to the maximum value ‘r’ can attain for a region in TPT. In contrast, CP values may extend to 1 over a longer period. The study evaluates the probability of future tsunami occurrences under two conditions: mixed tsunamis (any wave height) and tsunamis with wave heights exceeding 3 m. Zones with higher likelihoods of tsunami occurrences for both scenarios are identified and highlighted. The obtained probabilities were validated against respective zone threshold probabilities. Additionally, TPT-derived probabilities for tsunamis under mixed conditions reveal higher likelihoods in Zone 1 (Colombia, Ecuador, Brazil), succeeded by Zone 7 (Japan, China, North Korea), and Zone 11 (Solomon Islands, Vanuatu, New Caledonia). Conversely, the probability of tsunamis with wave heights exceeding 3 m is higher in Zone 3 (Cuba, Jamaica, Haiti), followed by Zone 9 (Malaysia, Brunei, Australia), and Zone 1 (Colombia, Ecuador, Brazil). These variations stem primarily from spatial changes in the global tsunami-to-earthquake ratio across distributed zones. This study contributes to a more comprehensive understanding of future tsunami potential, aiding decision-makers and planners in taking informed actions to mitigate potential risks. [ABSTRACT FROM AUTHOR]

AbstractBig data and high-dimensional optimization problems in operations research (OR) and artificial intelligence (AI) have brought stochastic gradients to the forefront. This article provides a view of research and applications in stochastic gradient estimation from multiple perspectives, as seminal advances have come from diverse and disparate research fields, including operations research/management science (OR/MS), industrial/systems engineering (ISE), optimal/stochastic control, statistics, and more recently from the computer science (CS) AI machine learning (ML) community. [ABSTRACT FROM AUTHOR]

This paper studied the prescribed-time platooning control problem for connected autonomous vehicles subject to unknown dynamics and stochastic actuator faults. Precisely, to compensate for the effect of unknown dynamic behaviour, the radial basis function-based adaptive observer design was developed that incorporates into the closed-loop control system, which enhances the robustness of the proposed control algorithm. In addition, physical actuator fault factors are also taken into account, which are denoted in terms of a Bernoulli-distributed stochastic variable. Lyapunov stability theory and the stochastic analysis method is used to derive the stability of the addressed control system. Finally, a numerical example with detailed simulation results is provided to illustrate the effectiveness of the proposed control design. [ABSTRACT FROM AUTHOR]

• Forecasting Model: Based on 14 (Mw > 4.1) earthquakes and peak of TEC anomalies. • Model Adequacy: Minimal differences observed in actual and forecasted earthquake. • Stochastic analysis: Anomalies over 16 days with 80 % likelihood of occurrence. • Regression: R2 ∼ 0.017 observed indicated limited influence of environmental factors. • Residual (TEC-Predicted) : >2σ anomalies during periods of maximum variability. In Northeast India, 17 earthquakes with Mw > 4.1 were recorded, with 14 of them preceded by significant anomalies in ionospheric Total Electron Content (TEC). Probability analysis showed that if TEC anomalies exceed 2σ for over 16 days, there is an 80 % likelihood of an earthquake. Multiple linear regression analysis revealed a low R2 (∼0.017) between hourly TEC and factors like Dst, Ap-Index, IMF-Bz, and F10.7. However, the models for hourly data were significant (p ∼2.08x10-14). Hence, we used multiple regressions on daily data to identify hours when independent variables best explained TEC variability. The study aims to develop a model to determine the epicentral distance, precursory time, and magnitude of potential near-field earthquakes in the Tezpur (Eastern Himalaya) region, based on TEC anomaly peaks. However, Mw > 4.1 earthquakes may not always show TEC perturbations due to factors like geography, solar activity, and radon. The findings are thoroughly discussed in the manuscript. [ABSTRACT FROM AUTHOR]

This paper presents an efficient numerical method for solving nonlinear stochastic delay integro-differential equations based on block pulse functions. Firstly, the equation is transformed into an algebraic system by the integral delay operator matrixes of block pulse functions. Then, error analysis is conducted on the method. Finally, some numerical examples are provided to validate the method. This work provides numerical solutions for the stochastic delay integro-differential equations by global approximation method. This method has the advantages of simple calculation and higher error accuracy. [ABSTRACT FROM AUTHOR]

In this study, we develop a stochastic model that captures the dynamics of HIV infection, encompassing susceptible individuals, asymptomatic HIV-positive individuals, and those exhibiting symptoms. Initially, we examine the existence and stability of both disease-free and endemic equilibria within the deterministic version of the model. Our analytical findings indicate that the basic reproduction number, R 0 , is a pivotal factor in determining the uniqueness and global stability of these equilibria. Furthermore, we explore the impact of environmental noise on the HIV disease model, identifying two critical thresholds, R 1 s and R 2 s (with R 2 s < R 1 s ). If R 1 s is less than unity, the disease is likely to be eradicated; conversely, if R 2 s exceeds unity, the disease will persist, and a unique stationary distribution will emerge. Additionally, our numerical simulations reveal that when R 2 s < 1 < R 1 s , the disease may still face extinction. From an epidemiological viewpoint, our observations suggest that a decrease in environmental noise intensity results in a reduction of the oscillation amplitude in the disease dynamics. Conversely, an increase in noise intensity is associated with a lower mean of infectious individuals and a left-skewed distribution. [ABSTRACT FROM AUTHOR]

This paper considers a stochastic model of microorganism flocculation incorporating two complementary nutrients. By introducing nonlinear perturbation, we analyze the influence of flocculations, microorganisms, and two nutrients on the model dynamic. The paper proves the existence and uniqueness of the stationary distribution in the stochastic model. Moreover, sufficient conditions for the extinction of microorganisms are established. Numerical simulations indicate that nonlinear perturbation makes the growth process of microorganisms more unpredictable, better reflecting the complicated variations in real-world environments. Noise interference is not always detrimental, but appropriate noise levels may promote the growth of microorganisms. [ABSTRACT FROM AUTHOR]

Mobile cloud computing (MCC) is a technological paradigm for providing services to mobile device (MD) users. A compromised MD may cause harm to both its user and to other MCC customers. This study explores the use of machine learning (ML) models and stochastic methods for the protection of Android MDs connected to the mobile cloud. To test the validity and feasibility of the proposed models and methods, the study adopted a proof-of-concept approach and developed a prototype system named MINDPRESS. The static component of MINDPRES assesses the risk of the apps installed on the MD. It uses a device-based ML model for static feature analysis and a cloud-based stochastic risk evaluator. The device-based hybrid component of MINDPRES monitors app behavior in real time. It deploys two ML models and functions as an intrusion detection and prevention system (IDPS). The performance evaluation results of the prototype showed that the accuracy achieved by the methods for static and hybrid risk evaluation compared well with results reported in recent work. Power consumption data indicated that MINDPRES did not create an overload. This study contributes a feasible and scalable framework for building distributed systems for the protection of the data and devices of MCC customers. [ABSTRACT FROM AUTHOR]

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]

Stochastic time-cost trade-off (TCT) problems are of significant concern to project managers because various uncertain factors have to be considered when making appropriate balance between project completion time and cost. In the paper we consider the stochastic TCT problem, where the project completion time (PCT) unreliability is involved and constrained to be less than a prescribed threshold. To tackle the concerned problem, previous studies have implemented the double loop procedure, where a genetic algorithm (GA) is used in the outer loop for optimization, and Monte Carlo simulation (MCS) is used in the inner loop for examining the unreliability constraint. The original double loop procedure is computationally inefficient, taking hours or days even for a small to medium project. The present study proposes an efficient simulation method, referred to as adaptive domain decomposition method (DDM), to replace MCS for credibly examining the unreliability constraint. By modifying the double loop procedure with adaptive DDM, the computational resources can be effectively allocated, and the computational efficiency can be greatly improved. As shown in the illustrative example, the modified procedure significantly outperforms the original procedure, and it is hundreds of times faster to obtain similar optimization results. With the great efficiency improvement, this study contributes to the widespread acceptance of stochastic TCT analysis in practical applications. [ABSTRACT FROM AUTHOR]

Handover is crucial for ensuring seamless connectivity in heterogeneous networks (HetNet) by enabling user equipment (UE) to switch its connection link between cells based on signal conditions. However, conventional analytical approaches ignored the distinctions between macro-cell to small-cell (M2S) and small-cell to macro-cell (S2M) scenarios during a handover decision-making process, which resulted in handover failures (HoF) or ping-pong handovers. Therefore, this paper proposes a novel framework, Do-SPN-PPP, that combines stochastic Petri net (SPN) and the Poisson point process (PPP) to quantitatively analyze M2S and S2M handover performance differences. The proposed framework also reveals and predicts how handover parameters affect UE residence time in a cell within the HetNet, and it exhibits a higher predictive accuracy compared with the traditional conventional analytical approach. In addition, the Monte Carlo simulation verified the Do-SPN-PPP framework, and the proposed framework exhibits a 96% reduction in computation time while maintaining a 95% confidence interval and 0.5% error tolerance compared with the simulation. [ABSTRACT FROM AUTHOR]

The stochasticity of power flow of distributed generations (DGs) and load in the microgrid has great influence on power flow distribution and voltage quality of the distribution network. For improving the voltage quality of the distribution network, the questions need to be further studied, which include the description of the stochasticity of the power flow in the microgrid and the impact of the microgrid into the distribution network on the power flow. Therefore, a novel stochastic power flow calculation and optimal control method for the microgrid based on multivariate stochastic factors fusion-sensitivity (MSFF-sensitivity) is proposed in this paper. Firstly, the multivariate stochastic factors fusion (MSFF) function is developed by using the probability density function to extract the stochasticity and correlation of power flow among different stochastic factors in the microgrid, which are effectively unified. Furthermore, the fusion-sensitivity (F-sensitivity) of the power flow in the microgrid integrated into the distribution network is constructed to accurately characterize the influence degree of various stochastic factors in the microgrid on the power flow of the distribution network. Based on this, the output power of the stochastic factor is adjusted to optimally control the power flow of the distribution network. Finally, the algorithm verification suggests that, compared with the conventional power flow methods, the method proposed in this paper is more suitable for the microgrid. The influence of stochastic power flow on the distribution network can be effectively reduced and the voltage quality of the distribution network can be improved by optimizing control of the power flow in the microgrid integrated into the distribution network. [ABSTRACT FROM AUTHOR]

Pairwise likelihood is a limited‐information method widely used to estimate latent variable models, including factor analysis of categorical data. It can often avoid evaluating high‐dimensional integrals and, thus, is computationally more efficient than relying on the full likelihood. Despite its computational advantage, the pairwise likelihood approach can still be demanding for large‐scale problems that involve many observed variables. We tackle this challenge by employing an approximation of the pairwise likelihood estimator, which is derived from an optimization procedure relying on stochastic gradients. The stochastic gradients are constructed by subsampling the pairwise log‐likelihood contributions, for which the subsampling scheme controls the per‐iteration computational complexity. The stochastic estimator is shown to be asymptotically equivalent to the pairwise likelihood one. However, finite‐sample performance can be improved by compounding the sampling variability of the data with the uncertainty introduced by the subsampling scheme. We demonstrate the performance of the proposed method using simulation studies and two real data applications. [ABSTRACT FROM AUTHOR]

Slope failures present substantial threats to public safety and economic losses. However, it remains challenging to achieve satisfactory performance due to insufficient datasets with machine learning (ML)-based slope stability assessment. In this study, an expanded physics-informed dataset was constructed by integrating historical case studies with data derived from nonintrusive stochastic analysis. The Bayesian ensemble learning model was employed to enhance prediction accuracy, with the Shapley additive explanations method employed to elucidate the contribution of each input variable. The proposed method displayed satisfactory performance, achieving an area under the curve of 0.9973, accuracy of 0.9727, and F1-score of 0.9729, surpassing the compared ML methods. Its robustness and generalization capabilities were confirmed through evaluations on diverse datasets and random seeds. Furthermore, a user-friendly graphical user interface was created for fast estimation of slope stability (FESS) using the trained prediction model. The performance of FESS was validated on a series of examples including the Australian Association for Computer-Aided Design referenced slope example EX1 and 77 in situ cases. This tool offers practitioners a high-performance solution, significantly reducing the effort required for slope stability assessments. [ABSTRACT FROM AUTHOR]

A significant aspect of offshore pipeline engineering involves evaluating the uplift resistance and failure probability of buried pipelines in clay, which are affected by factors such as pipeline geometry, soil characteristics, material properties, and loading conditions. Subsea marine clay is generally not homogeneous, leading to variations in undrained shear strength vertically and horizontally. As a result, the stochastic analysis method is suitable for accurately modeling such soil conditions. This study addresses these challenges using the Random Adaptive Finite Element Limit Analysis (RAFELA) to analyze the mean uplift resistance factor and the probability of failure for buried rectangular box pipelines in random clay. Seven key parameters are considered in the parametric study: the embedment depth ratio (H/B = 0.5, 1, 2, 4, and 6), width-to-height ratio (L/B = 0.5, 1, 2, 3, and 4), overburden factor (γH/μc = 0, 0.5, and 1), adhesion factor (α = 0, 0.5, and 1), load inclination (β = 0°, 45°, and 90°), coefficient of variation (CoVμc = 25% and 60%), and spatial correlation length (Θc = 0.125, 0.5, 1, 2, 4, and 8). The results are presented as dimensionless uplift resistance factors (μNran), probability of failure (Pf), as well as the corresponding safety factor (FS) for designing pipelines in random clay, ensuring practical designs that are both efficient and reliable. Additionally, this study compares its findings with pullout capacity factors derived from deterministic analyses reported in the literature. This study incorporates machine learning, specifically the Random Forest (RF) algorithm, to predict Pf based on parametric data. The RF model, trained on 500 samples (70% training, 30% testing), achieves high predictive accuracy, with R2 values of 99.12% and 97.29%, respectively. The Shapley Additive Explanations (SHAP) analysis identifies FS as the most influential factor, directly contributing to the reliability of the pipeline design, while α has the least impact. The analysis emphasizes the practical significance of FS in reducing failure probabilities while contextualizing its influence alongside other factors. The integration of the RAFELA with the RF offers a robust framework to address uncertainties in soil properties, enhancing reliability and efficiency in offshore pipeline engineering. [ABSTRACT FROM AUTHOR]

This paper presents one of the most interesting generalizations of Gaver's basic two-unit parallel system sustained by a cold standby unit and attended by a repairman with multiple vacations. The system was studied using the supplementary variables technique, like many other similar semi-Markov systems. D.P. Gaver, Jr. was the first to apply this method for constructing and studying reliability models, and since then it has been then widely used by other researchers to study various reliability problems. As a result, non-classical boundary value problem of mathematical physics with nonlocal boundary conditions has been obtained. Until now, a solution to this problem was obtained in terms of Laplace transforms. Naturally, the most significant part of the problem is a system of partial differential equations (Kolmogorov forward equations). In this study, we demonstrate that Kolmogorov equations are redundant and we can solve the problem by avoiding the necessity of using them. We present here a novel, purely probabilistic approach. The results are formulated as rigorous mathematical statements, offering a significant simplification in the reliability analysis of stochastic systems. Our findings show that this novel approach can be applied to study both semi-Markov and some non semi-Markov models where the supplementary variables technique is used. [ABSTRACT FROM AUTHOR]

We propose a learning dynamics to model how strategic agents repeatedly play a continuous game while relying on an information platform to learn an unknown payoff-relevant parameter. In each time step, the platform updates a belief estimate of the parameter based on players' strategies and realized payoffs using Bayes' rule. Then, players adopt a generic learning rule to adjust their strategies based on the updated belief. We present results on the convergence of beliefs and strategies and the properties of convergent fixed points of the dynamics. We obtain sufficient and necessary conditions for the existence of globally stable fixed points. We also provide sufficient conditions for the local stability of fixed points. These results provide an approach to analyzing the long-term outcomes that arise from the interplay between Bayesian belief learning and strategy learning in games and enable us to characterize conditions under which learning leads to a complete information equilibrium. Funding: Financial support from the Air Force Office of Scientific Research [Project Building Attack Resilience into Complex Networks], the Simons Institute [research fellowship], and a Michael Hammer Fellowship is gratefully acknowledged. [ABSTRACT FROM AUTHOR]

By taking medical reform policies into consideration, based on government subsidies and stochastic demands, this paper constructs a stochastic generalized Nash equilibrium model for non-profit and for-profit hospitals. To solve the equilibrium model, we use the Karush-Kuhn-Tucker conditions to reformulate the model into a stochastic mixed complementarity system. Furthermore, the stochastic mixed complementarity system is transformed equivalently into a system of stochastic nonlinear equations, which is solved by some Monte Carlo approximation techniques. The numerical results demonstrate that, in a mixed market, the medical procedures' prices of for-profit hospitals are almost 3 times that of non-profit hospitals, while the quality levels of for-profit hospitals are nearly 50% of non-profit hospitals' quality levels. Competition between non-profit and for-profit hospitals is beneficial for improving the cost control levels of non-profit hospitals. Sensitivity analysis confirms that increasing government subsidy rate does not affect non-profit hospitals' decisions, while cost control levels of for-profit hospitals significantly increase from 1, 000 to 18, 000. Increasing government subsidy rate or taxation rate promotes for-profit hospitals to increase cost control levels and causes no significant impact on non-profit hospitals. Increasing the reimbursement rate of medical insurance is helpful to reduce prices of medical procedures, increase cost control levels, improve medical welfare of patients, and promote orderly competition in a mixed medical market. These results offer valuable insights for effective management of a mixed market. [ABSTRACT FROM AUTHOR]

The current challenge faced by the global research community is how to effectively address, manage, and control the spread of infectious diseases. This research focuses on conducting a dynamic system analysis of a stochastic epidemic model capable of predicting the persistence or extinction of the dengue disease. Numerical methodology on deterministic procedures, i.e. Adams method and stochastic/probabilistic schemes, i.e. stochastic Runge–Kutta method, is employed to simulate and forecast the spread of disease. This study specifically employs two nonlinear mathematical systems, namely the deterministic vector-borne dengue epidemic (DVBDE) and the stochastic vector-borne dengue epidemic (SVBDE) models, for numerical treatment. The objective is to simulate the dynamics of these models and ascertain their dynamic behavior. The VBDE model segmented the population into the following five classes: susceptible population, infected population, recovered population, susceptible mosquitoes, and the infected mosquitoes. The approximate solution for the dynamic evolution for each population is calculated by generating a significant number of scenarios varying the infected population's recovery rate, human population birth rate, mosquitoes birth rate, contaminated people coming into contact with healthy people, the mortality rate of people, mosquitos population death rate and infected mosquito contact rate with population that is not infected. Comparative evaluations of the deterministic and stochastic models are presented, highlighting their unique characteristics and performance, through the execution of numerical simulations and analysis of the results. [ABSTRACT FROM AUTHOR]

In this study, we examine whether mild solutions to a fractional stochastic evolution system with a fractional Caputo derivative on an infinite interval exist and are attractive. We use semigroup theory, fractional calculus, stochastic analysis, compactness methods, and the measure of noncompactness (MNC) as the foundation for our methodologies. There are several suggested sufficient requirements for the existence of mild solutions to the stated problem. Examples that highlight the key findings are provided. [ABSTRACT FROM AUTHOR]

Organizations face fundamental challenges in managing knowledge flows across complex networks, yet existing frameworks often lack quantitative tools for optimization. We develop a novel stochastic multi-scale model introducing knowledge flow viscosity (KFV) to analyze organizational learning dynamics. This model quantifies resistance to knowledge transfer using a time-varying viscosity tensor, capturing both continuous learning processes and discrete knowledge acquisition events. Through renormalization group analysis, we establish the existence of critical thresholds in knowledge diffusion rates, characterizing phase transitions in organizational learning capacity. Numerical simulations demonstrate that targeted reductions in communication barriers near these thresholds can significantly enhance knowledge flow efficiency. The findings provide a mathematical foundation for understanding multi-level knowledge flow dynamics, suggesting precise conditions for effective interventions to optimize learning in complex organizational systems. [ABSTRACT FROM AUTHOR]

The one-dimensional quaternion fractional Fourier transform (1DQFRFT) introduces a fractional-order parameter that extends traditional Fourier transform techniques, providing new insights into the analysis of quaternion-valued signals. This paper presents a rigorous theoretical foundation for the 1DQFRFT, examining essential properties such as linearity, the Plancherel theorem, conjugate symmetry, convolution, and a generalized Parseval's theorem that collectively demonstrate the transform's analytical power. We further explore the 1DQFRFT's unique applications to probabilistic methods, particularly for modeling and analyzing stochastic processes within a quaternionic framework. By bridging quaternionic theory with probability, our study opens avenues for advanced applications in signal processing, communications, and applied mathematics, potentially driving significant advancements in these fields. [ABSTRACT FROM AUTHOR]

This paper investigates the existence and approximate controllability (ACA) of fractional neutral-type stochastic differential inclusions (NTSDIs) characterized by non-instantaneous impulses within a separable Hilbert space (HS) framework. Employing the Atangana–Baleanu–Caputo (ABC) derivative, we transform the system into an equivalent fixed-point (FP) problem through an integral operator. Subsequently, the Bohnenblust–Karlin FP theorem is leveraged to establish existence results. By assuming ACA of the corresponding linear system, we derive sufficient conditions for the ACA of the nonlinear stochastic impulsive control system. Our analysis relies on concepts from stochastic analysis, fractional calculus, FP theory, semigroup theory, and the theory of multivalued maps (MVMs). The theoretical findings are illustrated through a concrete example. [ABSTRACT FROM AUTHOR]

The successive generations of many species in nature are non-overlapping, and the data of biological samples is usually collected in discrete time, so using discrete-time models can better describe population changes. Pest control is an important part of agricultural production safety and ecological environment protection, but the process will be affected by environmental white noise. On the one hand, fluctuations in temperature can lead to variations in the density of pest and natural enemy populations. On the other hand, the effects of pesticides to pests are also influenced by white noise. Based on these, a stochastic discrete pest-natural enemy model with white noise and integrated pest management is established. Firstly, we discuss the stability of the equilibria of its corresponding deterministic discrete pest-natural enemy model. Secondly, based on the criterion of asymptotically mean-square stability of the zero solution of the general linear stochastic discrete model, sufficient conditions are obtained for the equilibria of the stochastic discrete pest-natural enemy model to be stable in probability. Then the numerical simulations are used to confirm the applications of the theoretical results and to discuss the effects of important parameters on the extinction of pest population. Finally, considering that white noise mainly affects the growth rate and mortality rate of pest and natural enemy populations, an improved stochastic discrete pest-natural enemy model is established, and we discuss the effects of the perturbation intensity of white noise on the persistence and extinction of population. [ABSTRACT FROM AUTHOR]

In the current work, we develop and analyse a prey–predator model as a semi-Kolmogorov population model in which the predator has an indirect effect on the prey. The functional response of the model is investigated as Holling type (II). We construct a stochastic environment because of the parameter's random essence to study the influence of environmental fluctuations on this model and introduce a stochastic version of the prey–predator model. Then we present a dynamical analysis of solutions, including existence, uniqueness, positivity, stochastic boundedness, and stochastic extinction of all prey. Finally, some numerical simulations are carried out to validate our theoretical findings and confirm the efficiency and adaptation of our stochastic model. [ABSTRACT FROM AUTHOR]

The article presents the development of a Rules-Based Energy Management System for a nanogrid that serves an electric vehicle charging station. This nanogrid is composed of photovoltaic generation, a wind turbine, a battery energy storage system, and a fast electric vehicle charger. The objective is to prioritize the use of renewable energy sources, reducing costs and promoting energy efficiency. The methodology includes forecasting models based on an Artificial Neural Network for photovoltaic generation, a parametric estimation for wind generation, and a Monte Carlo simulation to predict the energy consumption of electric vehicles. The developed algorithm makes decisions every 15 min, considering variables such as energy tariff, battery state of charge, renewable generation forecast, and energy consumption forecast. The results showed that the system adequately balances energy generation, consumption, and storage, even under forecasting uncertainties. The use of the Monte Carlo simulation was crucial for evaluating the financial impacts of forecast errors, enabling robust decision-making. This energy management system proved to be effective and sustainable for nanogrids dedicated to electric vehicle charging, with the potential to reduce operational costs and increase energy reliability and the use of renewable energy sources. [ABSTRACT FROM AUTHOR]

The paper focuses on the study of an epidemic model for the evolution of diseases, using stochastic models. We demonstrated the encoding of this intricate model into formalisms suitable for analysis with advanced stochastic model checkers. A co-infection model's dynamics were modeled as an Ito–Levy stochastic differential equations system, representing a compartmental system shaped by disease complexity. Initially, we established a deterministic system based on presumptions and disease-related traits. Through non-traditional analytical methods, two key asymptotic properties: eradication and continuation in the mean were demonstrated. Section 2 provides a detailed construction of the model. Section 3 results confirm that the outcome is biologically well-behaved. Utilizing simulations, we tested and confirmed the stability of all equilibrium points. The ergodic stationary distribution and extinction conditions of the system are thoroughly analyzed. Investigations were made into the stochastic system's probability density function, and digital simulations were employed to illustrate the probability density function and systems' extinction. Although infectious disease control and eradication are major public health goals, global eradication proves challenging. Local disease extinction is possible, but it may reoccur. Extinction is more feasible with a lower . Notably, our simulations showed that reducing the value significantly increases the likelihood of disease extinction and reduces the probability of future recurrence. Additionally, our study provides insights into the conditions under which a disease can persist or become extinct, contributing to more effective disease control strategies in public health. [ABSTRACT FROM AUTHOR]

In this article, we develop a computational approach for estimating the most likely trajectories describing rare events that correspond to the emergence of non-dominant genotypes. This work is based on the large deviations approach for discrete Markov chains describing the genetic evolution of large bacterial populations. We demonstrate that a gradient descent algorithm developed in this article results in the fast and accurate computation of most likely trajectories for a large number of bacterial genotypes. We supplement our analysis with extensive numerical simulations demonstrating the computational advantage of the designed gradient descent algorithm over other, more simplified, approaches. [ABSTRACT FROM AUTHOR]

We consider continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. We assume finite second-moment conditions and use the stochastic approximation technique for the analysis. In particular, we identify an appropriate ordinary differential equation (ODE) and show that either of the two events occurs with a certain probability: (a) the time-asymptotic proportion of the populations converges to the attractors or saddle points of the ODE, (b) it enters every neighbourhood and exits some neighbourhood of a saddle point infinitely often. We also prove a finite time approximation result for the stochastic trajectory. Further, we analyse a branching process with attack and acquisition, which captures the competition in online viral markets; for this case, the probability of approximation equals one. [ABSTRACT FROM AUTHOR]