Search Results (240)

To improve the sampling efficiency of Markov Chain Monte Carlo in complex parameter spaces, this paper proposes an adaptive sampling method that integrates a swarm intelligence mechanism called the BeeSwarm-MH algorithm. The method combines global exploration by scout bees with local exploitation by worker bees. It employs multi-stage perturbation intensities and adaptive step-size tuning to enable efficient posterior sampling. Focusing on Bayesian inference for parameter estimation in the soliton solutions of the two-dimensional complex Ginzburg–Landau equation, we design a dedicated inference framework to systematically compare the performance of BeeSwarm-MH with the classical Metropolis–Hastings algorithm. Experimental results demonstrate that BeeSwarm-MH achieves comparable estimation accuracy while significantly reducing the required number of iterations and total computation time for convergence. Moreover, it exhibits superior global search capabilities and adaptive features, offering a practical approach for efficient Bayesian inference in complex physical models. Full article

In this article, we investigate the influence of viscosity on the evolution of the cosmos within the framework of the newly proposed $f(Q,L_m)$ gravity. We have considered a linear functional form $f(Q,L_m)=\alpha Q+\beta L_m$ with a bulk viscous coefficient $\zeta ={\zeta }_0+{\zeta }_{1}H$ for our analysis and obtained exact solutions to the field equations associated with a flat FLRW metric. In addition, we utilized Cosmic Chronometers (CC), CC + BAO, CC + BAO + GRB, and GRB data samples to determine the constrained values of independent parameters in the derived exact solution. The likelihood function and the Markov Chain Monte Carlo (MCMC) sampling technique are combined to yield the posterior probability using Bayesian statistical methods. Furthermore, by comparing our results with the standard cosmological model, we found that our considered model supports the acceleration of the universe in late time. Full article

This paper addresses the problem of optimal stabilization for stochastic dynamical systems characterized by Markov switches and concentration points of jumps, which is a scenario not adequately covered by classical stability conditions. Unlike traditional approaches requiring a strictly positive minimal interval between jumps, we allow jump moments to accumulate at a finite point. Utilizing Lyapunov function methods, we derive sufficient conditions for exponential stability in the mean square and asymptotic stability in probability. We provide explicit constructions of Lyapunov functions adapted to scenarios with jump concentration points and develop conditions under which these functions ensure system stability. For linear stochastic differential equations, the stabilization problem is further simplified to solving a system of Riccati-type matrix equations. This work provides essential theoretical foundations and practical methodologies for stabilizing complex stochastic systems that feature concentration points, expanding the applicability of optimal control theory. Full article

We present a formal framework for modeling neural network dynamics using Category Theory, specifically through Markov categories. In this setting, neural states are represented as objects and state transitions as Markov kernels, i.e., morphisms in the category. This categorical perspective offers an algebraic alternative to traditional approaches based on stochastic differential equations, enabling a rigorous and structured approach to studying neural dynamics as a stochastic process with topological insights. By abstracting neural states as submeasurable spaces and transitions as kernels, our framework bridges biological complexity with formal mathematical structure, providing a foundation for analyzing emergent behavior. As part of this approach, we incorporate concepts from Interacting Particle Systems and employ mean-field approximations to construct Markov kernels, which are then used to simulate neural dynamics via the Ising model. Our simulations reveal a shift from unimodal to multimodal transition distributions near critical temperatures, reinforcing the connection between emergent behavior and abrupt changes in system dynamics. Full article

We develop a symmetry-based variational theory that shows the coarse-grained balance of work inflow to heat outflow in a driven, dissipative system relaxed to the golden ratio. Two order-2 Möbius transformations—a self-dual flip and a self-similar shift—generate a discrete non-abelian subgroup of $\mathrm{PGL}(2,\mathbb{Q}\left(\sqrt{5}\right))$. Requiring any smooth, strictly convex Lyapunov functional to be invariant under both maps enforces a single non-equilibrium fixed point: the golden mean. We confirm this result by (i) a gradient-flow partial-differential equation, (ii) a birth–death Markov chain whose continuum limit is Fokker–Planck, (iii) a Martin–Siggia–Rose field theory, and (iv) exact Ward identities that protect the fixed point against noise. Microscopic kinetics merely set the approach rate; three parameter-free invariants emerge: a $62\%:38\%$ split between entropy production and useful power, an RG-invariant diffusion coefficient linking relaxation time and correlation length ${\mathcal{D}}_{\alpha }={\xi }^z/\tau$, and a $\vartheta ={45}^{\circ }$ eigen-angle that maps to the golden logarithmic spiral. The same dual symmetry underlies scaling laws in rotating turbulence, plant phyllotaxis, cortical avalanches, quantum critical metals, and even de-Sitter cosmology, providing a falsifiable, unifying principle for pattern formation far from equilibrium. Full article

This study investigates a stochastic production planning problem with regime-switching parameters, inspired by economic cycles impacting production and inventory costs. The model considers types of goods and employs a Markov chain to capture probabilistic regime transitions, coupled with a multidimensional Brownian motion representing stochastic demand dynamics. The production and inventory cost optimization problem is formulated as a quadratic cost functional, with the solution characterized by a regime-dependent system of elliptic partial differential equations (PDEs). Numerical solutions to the PDE system are computed using a monotone iteration algorithm, enabling quantitative analysis. Sensitivity analysis and model risk evaluation illustrate the effects of regime-dependent volatility, holding costs, and discount factors, revealing the conservative bias of regime-switching models when compared to static alternatives. Practical implications include optimizing production strategies under fluctuating economic conditions and exploring future extensions such as correlated Brownian dynamics, non-quadratic cost functions, and geometric inventory frameworks. In contrast to earlier studies that imposed static or overly simplified regime-switching assumptions, our work presents a fully integrated framework—combining optimal control theory, a regime-dependent system of elliptic PDEs, and comprehensive numerical and sensitivity analyses—to more accurately capture the complex stochastic dynamics of production planning and thereby deliver enhanced, actionable insights for modern manufacturing environments. Full article

Herein, expanded Hidden Markov Models (HMMs) are considered as potential deepfake generation and detection tools. The most specific model is the HMM, while the most general is the pairwise Markov chain (PMC). In between, the Markov observation model (MOM) is proposed, where the observations form a Markov chain conditionally on the hidden state. An expectation-maximization (EM) analog to the Baum–Welch algorithm is developed to estimate the transition probabilities as well as the initial hidden-state-observation joint distribution for all the models considered. This new EM algorithm also includes a recursive log-likelihood equation so that model selection can be performed (after parameter convergence). Once models have been learnt through the EM algorithm, deepfakes are generated through simulation, while they are detected using the log-likelihood. Our three models were compared empirically in terms of their generative and detective ability. PMC and MOM consistently produced the best deepfake generator and detector, respectively. Full article

This article discusses and compares approaches to the visualization of the danger zone formed as a result of spreading toxic substances during a fire at an industrial enterprise, to create predictive models and scenarios for evacuation and environmental protection measures. The purpose of this study is to analyze the features and conditions for the application of algorithms for predicting the spread of a danger zone, based on the Gauss equation and the probabilistic algorithm of a cellular automaton. The research is also aimed at the analysis of the consequences of a fire at an industrial enterprise, taking into account natural and climatic conditions, the development of the area, and the scale of the fire. The subject of this study is the development of software and algorithmic support for the visualization of the danger zone and analysis of the consequences of a fire, which can be confirmed by comparing a computational experiment and actual measurements of toxic substance concentrations. The main research methods include a Gaussian model and probabilistic, frontal, and empirical cellular automation. The results of the study represent the development of algorithms for a cellular automation model for the visual forecasting of a dangerous zone. They are characterized by taking into consideration the rules for filling the dispersion ellipse, as well as determining the effects of interaction with obstacles, which allows for a more accurate mathematical description of the spread of a cloud of toxic combustion products in densely built-up areas. Since the main problems of the cellular automation approach to modeling the dispersion of pollutants are the problems of speed and numerical diffusion, in this article the frontal cellular automation algorithm with a 16-point neighborhood pattern is used, which takes into account the features of the calculation scheme for finding the shortest path. Software and algorithmic support for an integrated system for the visualization and analysis of fire consequences at an industrial enterprise has been developed; the efficiency of the system has been confirmed by computational analysis and actual measurement. It has been shown that the future development of the visualization of dangerous zones during fires is associated with the integration of the Bayesian approach and stochastic forecasting algorithms based on Markov chains into the simulation model of a dangerous zone for the efficient assessment of uncertainties associated with complex atmospheric processes. Full article

The detection efficiency evaluation of sonars is crucial for optimizing task planning and resource scheduling. The existing static evaluation methods based on single indicators face significant challenges. First, static modeling has difficulty coping with complex scenes where the relative situation changes in real time in the task process. Second, a single evaluation dimension cannot characterize the data distribution characteristics of efficiency indicators. In this paper, we propose a multidimensional detection efficiency evaluation method for sonar search paths based on dynamic spatiotemporal interactions. We develop a dynamic multidimensional evaluation framework. It consists of three parts, namely, spatiotemporal discrete modeling, situational dynamic deduction, and probability-based statistical analysis. This framework can achieve dynamic quantitative expression of the sonar detection efficiency. Specifically, by accurately characterizing the spatiotemporal interaction process between the sonars and targets, we overcome the bottleneck in entire-path detection efficiency evaluation. We introduce a Markov chain model to guide the Monte Carlo sampling; it helps to specify the uncertain situations by constructing a high-fidelity target motion trajectory database. To simulate the actual sensor working state, we add observation error to the sensor, which significantly improves the authenticity of the target’s trajectories. For each discrete time point, the minimum mean square error is used to estimate the sonar detection probability and cumulative detection probability. Based on the above models, we construct the multidimensional sonar detection efficiency evaluation indicator system by implementing a confidence analysis, effective detection rate calculation, and a data volatility quantification analysis. We conducted relevant simulation studies by setting the source level parameter of the target base on the sonar equation. In the simulation, we took two actual sonar search paths as examples and conducted an efficiency evaluation based on multidimensional evaluation indicators, and compared the evaluation results corresponding to the two paths. The simulation results show that in the passive and active working modes of sonar, for the detection probability, the box length of path 2 is reduced by 0∼0.2 and 0∼0.5, respectively, compared to path 1 during the time period from T = 11 to T = 15. For the cumulative detection probability, during the time period from T = 15 to T = 20, the box length of path 2 decreased by 0∼0.1 and 0∼0.2, respectively, compared to path 1, and the variance decreased by 0∼0.02 and 0∼0.03, respectively, compared to path 1. The numerical simulation results show that the data distribution corresponding to path 2 is more concentrated and stable, and its search ability is better than path 1, which reflects the advantages of the proposed multidimensional evaluation method. Full article

Markov chain perturbation theory is a rapidly developing subfield of the theory of stochastic processes. This review outlines emerging applications of this theory in the analysis of stochastic models of chemical reactions, with a particular focus on biochemistry and molecular biology. We begin by discussing the general problem of approximate modeling in stochastic chemical kinetics. We then briefly review some essential mathematical results pertaining to perturbation bounds for continuous-time Markov chains, emphasizing the relationship between robustness under perturbations and the rate of exponential convergence to the stationary distribution. We illustrate the use of these results to analyze stochastic models of biochemical reactions by providing concrete examples. Particular attention is given to fundamental problems related to approximation accuracy in model reduction. These include the partial thermodynamic limit, the irreversible-reaction limit, parametric uncertainty analysis, and model reduction for linear reaction networks. We conclude by discussing generalizations and future developments of these methodologies, such as the need for time-inhomogeneous Markov models. Full article

We present a review of recent developments in cosmological models based on Finsler geometry, as well as geometric extensions of general relativity formulated within this framework. Finsler geometry generalizes Riemannian geometry by allowing the metric tensor to depend not only on position but also on an additional internal degree of freedom, typically represented by a vector field at each point of the spacetime manifold. We examine in detail the possibility that Finsler-type geometries can describe the physical properties of the gravitational interaction, as well as the cosmological dynamics. In particular, we present and review the implications of a particular implementation of Finsler geometry, based on the Barthel connection, and of the $(\alpha ,\beta )$ geometries, where $\alpha$ is a Riemannian metric, and $\beta$ is a one-form. For a specific construction of the deviation part $\beta$, in these classes of geometries, the Barthel connection coincides with the Levi–Civita connection of the associated Riemann metric. We review the properties of the gravitational field, and of the cosmological evolution in three types of geometries: the Barthel–Randers geometry, in which the Finsler metric function F is given by $F=\alpha +\beta$, in the Barthel–Kropina geometry, with $F={\alpha }^2/\beta$, and in the conformally transformed Barthel–Kropina geometry, respectively. After a brief presentation of the mathematical foundations of the Finslerian-type modified gravity theories, the generalized Friedmann equations in these geometries are written down by considering that the background Riemannian metric in the Randers and Kropina line elements is of Friedmann–Lemaitre–Robertson–Walker type. The matter energy balance equations are also presented, and they are interpreted from the point of view of the thermodynamics of irreversible processes in the presence of particle creation. We investigate the cosmological properties of the Barthel–Randers and Barthel–Kropina cosmological models in detail. In these scenarios, the additional geometric terms arising from the Finslerian structure can be interpreted as an effective geometric dark energy component, capable of generating an effective cosmological constant. Several cosmological solutions—both analytical and numerical—are obtained and compared against observational datasets, including Cosmic Chronometers, Type Ia Supernovae, and Baryon Acoustic Oscillations, using a Markov Chain Monte Carlo (MCMC) analysis. A direct comparison with the standard $\Lambda$CDM model is also carried out. The results indicate that Finslerian cosmological models provide a satisfactory fit to the observational data, suggesting they represent a viable alternative to the standard cosmological model based on general relativity. Full article

Salt concentration monitoring is crucial for industrial process control and wastewater management, yet existing methods often lack real-time capability or require invasive sampling. This paper presents a novel RFID wireless sensing system for noninvasive solution concentration monitoring, combining physical modeling with advanced estimation algorithms. By combining the Cole–Cole model and the slit cylindrical capacitor (SCC) model, the system establishes physics-based state-space models to characterize concentration-dependent RFID signal variations. The concentration dynamics are modeled as a hidden Markov process and tracked using an adaptive extended Kalman filter (AEKF). The AEKF algorithm avoids computationally expensive inversion of complex observation equations while automatically adjusting noise covariance matrices via innovation sequence. Experimental results demonstrate a mean relative error (MRE) of 2.8% for CaCl₂ solution across 2–10 g/L concentrations. Within the experimentally validated optimal range (2–8 g/L CaCl₂), the system maintains MRE below 3% under artificially introduced measurement noise, confirming its strong robustness. Compared with baseline approaches, the proposed AEKF algorithm shows improved performance in both accuracy and computational efficiency. Full article

As is well-known, the Kinetic Theory for Active Particles is a scheme of mathematical models based on a generalization of the Boltzmann equation. It must be nowadays acknowledged as one of the most versatile and effective tools to describe in mathematical terms the behavior of any system consisting of a large number of mutually interacting objects, no matter whether they also interact with the external world. In both cases, the description is stochastic, i.e., it aims to provide at each instant the probability distribution (or density) function on the set of possible states of the particles of the system. In other words, it describes the evolution of the system as a stochastic process. In a previous paper, we pointed out that such a process can be described in turn in terms of a special kind of vector time-continuous Markov Chain. These stochastic processes share important properties with many natural processes. The present paper aims to develop the discussion presented in that paper, in particular by considering and analyzing the case in which the transition matrices of the chain are neither constant (stationary Markov Chains) nor assigned functions of time (nonstationary Markov Chains). It is shown that this case expresses interactions of the system with the external world, with particular reference to random external events. Full article

The warehouse picking process is one of the most critical components of logistics operations. Human–robot collaboration (HRC) is seen as an important trend in warehouse picking, as it combines the strengths of both humans and robots in the picking process. However, in current human–robot collaboration frameworks, there is a lack of effective communication between humans and robots, which results in inefficient task execution during the picking process. To address this, this paper considers trust as a communication bridge between humans and robots and proposes the Stackelberg trust-based human–robot collaboration framework for warehouse picking, aiming to achieve efficient and effective human–robot collaborative picking. In this framework, HRC with trust for warehouse picking is defined as the Partially Observable Stochastic Game (POSG) model. We model human fatigue with the logistic function and incorporate its impact on the efficiency reward function of the POSG. Based on the POSG model, belief space is used to assess human trust, and human strategies are formed. An iterative Stackelberg trust strategy generation (ISTSG) algorithm is designed to achieve the optimal long-term collaboration benefits between humans and robots, which is solved by the Bellman equation. The generated human–robot decision profile is formalized as a Partially Observable Markov Decision Process (POMDP), and the properties of human–robot collaboration are specified as PCTL (probabilistic computation tree logic) with rewards, such as efficiency, accuracy, trust, and human fatigue. The probabilistic model checker PRISM is exploited to verify and analyze the corresponding properties of the POMDP. We take the popular human–robot collaboration robot TORU as a case study. The experimental results show that our framework improves the efficiency of human–robot collaboration for warehouse picking and reduces worker fatigue while ensuring the required accuracy of human–robot collaboration. Full article

This paper is devoted to the study of stochastic optimal control of averaged stochastic differential delay equations (SDDEs) with semi-Markov switchings and their applications in economics. By using the Dynkin formula and solution of the Dirichlet–Poisson problem, the Hamilton–Jacobi–Bellman (HJB) equation and the inverse HJB equation are derived. Applications are given to a new Ramsey stochastic models in economics, namely the averaged Ramsey diffusion model with semi-Markov switchings. A numerical example is presented as well. Full article