Search Results (106)

Wood flooring manufacturers face complex challenges in dynamically allocating resources across multi-channel markets, characterized by channel conflicts, demand uncertainty, and long-term cumulative effects of decisions. Traditional static optimization or myopic approaches struggle to address these intertwined factors, particularly when critical market states like brand reputation and customer base cannot be precisely observed. This paper establishes a systematic and theoretically grounded online decision framework to tackle this problem. We first model the problem as a Partially Observable Stochastic Dynamic Game. The core innovation lies in introducing an unobservable market position vector as the central system state, whose evolution is jointly influenced by firm investments, inter-channel competition, and macroeconomic randomness. The model further captures production lead times, physical inventory dynamics, and saturation/cross-channel effects of marketing investments, constructing a high-fidelity dynamic system. To solve this complex model, we propose a hierarchical online learning and control algorithm named L-BAP (Lyapunov-based Bayesian Approximate Planning), which innovatively integrates three core modules. It employs particle filters for Bayesian inference to nonparametrically estimate latent market states online. Simultaneously, the algorithm constructs a Lyapunov optimization framework that transforms long-term discounted reward objectives into tractable single-period optimization problems through virtual debt queues, while ensuring stability of physical systems like inventory. Finally, the algorithm embeds a game-theoretic module to predict and respond to rational strategic reactions from each channel. We provide theoretical performance analysis, rigorously proving the mean-square boundedness of system queues and deriving the performance gap between long-term rewards and optimal policies under complete information. This bound clearly quantifies the trade-off between estimation accuracy (determined by particle count) and optimization parameters. Extensive simulations demonstrate that our L-BAP algorithm significantly outperforms several strong baselines—including myopic learning and decentralized reinforcement learning methods—across multiple dimensions: long-term profitability, inventory risk control, and customer service levels. Full article

A pinning boundary control strategy that can achieve the exponentially clustered synchronization of a specific class of complex networks is developed. Firstly, the studied model captures the essential features of networks, including spatial dependence, stochastic switching, noise perturbation, and time delays. Secondly, the proposed control algorithm can save the implementation cost and overcome environmental constraint by acting on the boundary of a few nodes. Thirdly, an average state related to the directed topology of the nodes in the same cluster is calculated as the target network. Finally, nonlinear simulations show that the proposed controller can solve the cluster synchronization of a directed coupled reaction–diffusion neural network with Markovian switching, stochastic noise and time delay. Full article

Exchange rate dynamics in OECD economies have been increasingly shaped by geopolitical tensions and systemic crises. Between 2010 and 2025, a sequence of major events including the European sovereign debt crisis, the COVID-19 pandemic, and the Russia–Ukraine conflict has amplified uncertainty and volatility in global financial markets. Using a Bayesian Time-Varying Parameter Vector Autoregression (TVP-VAR) model, this analysis investigates how geopolitical shocks are transmitted to exchange rate movements against the US dollar, capturing structural breaks, stochastic volatility, and heterogeneous time-varying relationships across countries. The empirical evidence reveals that exchange rates respond significantly but asymmetrically to geopolitical shocks, with more pronounced effects during periods of global turmoil and weaker reactions in stable phases. Furthermore, the sensitivity of exchange rates to geopolitical risk differs across economies, depending on institutional quality, trade exposure, and macroeconomic resilience. These findings highlight important asymmetries in the transmission of geopolitical uncertainty and underscore the heterogeneity of policy responses among advanced economies. From a practical perspective, the results provide valuable guidance for policymakers and international investors seeking to integrate geopolitical risk into monetary, fiscal, and risk management frameworks. Full article

To address the problem of the proton exchange membrane fuel cell (PEMFC) temperature management under stochastic disturbances, this paper integrates a PEMFC thermal model with a water pump model and establishes a nonlinear stochastic model for temperature regulation. The objective is to maintain the stack temperature at its optimal value. Due to the inherent complexity of the PEMFC electrochemical reactions, the thermal dynamics exhibit strong nonlinear characteristics. To tackle this issue, a control strategy based on the stochastic backstepping method is proposed. Furthermore, to cope with variations in membrane water content and ambient temperature during operation, we design stochastic estimator-based adaptive laws. Simulation results, considering both stochastic disturbances driven by tracking error and those driven by stack temperature and load current, indicate that the proposed control strategy effectively maintains the stack temperature at 343 K under various operating conditions, with a maximum deviation of 0.2 K, thereby confirming its effectiveness and robustness. Full article

This work presents a time-domain approach for characterizing the Ground Reaction Forces (GRFs) exerted by a pedestrian during running. It is focused on the vertical component, but the methodology is adaptable to other components or activities. The approach is developed from a statistical perspective. It relies on experimentally measured force-time series obtained from a healthy male pedestrian at eight step frequencies ranging from 130 to 200 steps/min. These data are subsequently used to build a stochastic data-driven model. The model is composed of multivariate normal distributions which represent the step patterns of each foot independently, capturing potential disparities between them. Additional univariate normal distributions represent the step scaling and the aerial phase, the latter with both feet off the ground. A dimensionality reduction procedure is also implemented to retain the essential geometric features of the steps using a sufficient set of random variables. This approach accounts for the intrinsic variability of running gait by assuming normality in the variables, validated through state-of-the-art statistical tests (Henze-Zirkler and Shapiro-Wilk) and the Box-Cox transformation. It enables the generation of virtual GRFs using pseudo-random numbers from the normal distributions. Results demonstrate strong agreement between virtual and experimental data. The virtual time signals reproduce the stochastic behavior, and their frequency content is also captured with deviations below 4.5%, most of them below 2%. This confirms that the method effectively models the inherent stochastic nature of running human gait. Full article

We present the spatial regime conversion method (SRCM), a novel hybrid modelling framework for simulating reaction–diffusion systems that adaptively combines stochastic discrete and deterministic continuum representations. Extending the regime conversion method (RCM) to spatial settings, the SRCM employs a discrete reaction–diffusion master equation (RDME) representation in regions of low concentration and continuum partial differential equations (PDEs) where concentrations are high, dynamically switching based on local thresholds. This is an advancement over the existing methods in the literature, requiring no fixed spatial interfaces, enabling efficient and accurate simulation of systems in which stochasticity plays a key role but is not required uniformly across the domain. We specify the full mathematical formulation of the SRCM, including conversion reactions, hybrid kinetic rules, and consistent numerical updates. The method is validated across several one-dimensional test systems, including simple diffusion from a region of high concentration, the formation of a morphogen gradient, and the propagation of FKPP travelling waves. The results show that the SRCM captures key stochastic features while offering substantial gains in computational efficiency over fully stochastic models. Full article

We present a hybrid partial differential equation-agent-based model (PDE-ABM). In our framework, tumor cells secrete tumor angiogenic factor (TAF), while endothelial cells chemotactically migrate and branch in response. Reaction–diffusion PDEs for TAF, oxygen, and cytotoxic drug are coupled to discrete stochastic dynamics of tumor cells and endothelial tip cells, ensuring multiscale integration. Motivated by observed perfusion heterogeneity in tumors and its pharmacokinetic consequences, we conduct a linear stability analysis for a reduced endothelial–TAF reaction–diffusion subsystem and derive an explicit finite-domain threshold for Turing instability. We demonstrate that bidirectional coupling, where endothelial cells both chemotactically migrate along TAF gradients and secrete TAF, is necessary and sufficient to generate spatially periodic vascular clusters and inter-cluster hypoxic regions. These emergent patterns produce heterogeneous drug penetration and resistant niches. Our results identify TAF clearance, chemotactic sensitivity, and endothelial motility as effective levers to homogenize perfusion. The model is two-dimensional and employs simplified kinetics, and we outline necessary extensions to three dimensions and saturable kinetics required for quantitative calibration. The study links reaction–diffusion mechanisms with clinical principles and suggests actionable strategies to mitigate resistance by targeting endothelial–TAF feedback. Full article

This study, grounded in traveling wave theory, develops a cross-scale reaction-diffusion model to describe nutrient-dependent bacterial growth on agar surfaces and applies it to in silico investigations of microbial population dynamics. The approach is based on the coupling of a modified Allen–Cahn equation with the formulation of quorum sensing signal dynamics, incorporating a nutrient-dependent regulatory threshold and stochastic diffusion. A closed-loop model of bacterial growth regulated by quorum sensing is developed through theoretical analysis, numerical simulations, and computational experiments.The model is implemented using Yanenko’s computational scheme, which incorporates corrective refinement via Heun’s method to account for nonlinear components. Numerical simulations are carried out in MATLAB, allowing for accurate computation of spatio-temporal patterns and facilitating the identification of key mechanisms governing the collective behavior of bacterial communities. Full article

Mathematical modeling is indispensable in oncology for unraveling the interplay between tumor growth, vascular remodeling, and therapeutic resistance. We present a hybrid modeling framework (continuum-discrete) and present its hybrid mathematical formulation as a coupled partial differential equation–agent-based (PDE-ABM) system. It couples reaction–diffusion fields for oxygen, drug, and tumor angiogenic factor (TAF) with discrete vessel agents and stochastic phenotype transitions in tumor cells. Stochastic phenotype switching is handled with an exact Gillespie algorithm (a Monte Carlo method that simulates random phenotype flips and their timing), while moment-closure methods (techniques that approximate higher-order statistical moments to obtain a closed, tractable PDE description) are used to derive mean-field PDE limits that connect microscale randomness to macroscopic dynamics. We provide existence/uniqueness results for the coupled PDE-ABM system, perform numerical analysis of discretization schemes, and derive analytically tractable continuum limits. By linking stochastic microdynamics and deterministic macrodynamics, this hybrid mathematical formulation—i.e., the coupled PDE-ABM system—captures bidirectional feedback between hypoxia-driven angiogenesis and resistance evolution and provides a rigorous foundation for predictive, multiscale oncology models. Full article

Keratinocytes are the primary cells of the epidermis layer in our skin. They play a crucial role in maintaining skin health, responding to injuries, and counteracting disease progression. Understanding their behaviour is essential for advancing wound healing therapies, improving outcomes in regenerative medicine, and developing numerical models that accurately mimic skin deformation. To create physically representative models, it is essential to evaluate the nuanced ways in which keratinocytes deform, interact, and respond to mechanical and biochemical signals. This has prompted researchers to investigate various computational methods that capture these dynamics effectively. This review summarises the main mathematical and biomechanical modelling techniques (with particular focus on the literature published since 2010). It includes reaction–diffusion frameworks, finite element analysis, viscoelastic models, stochastic simulations, and agent-based approaches. We also highlight how machine learning is being integrated to accelerate model calibration, improve image-based analyses, and enhance predictive simulations. While these models have significantly improved our understanding of keratinocyte function, many approaches rely on idealised assumptions. These may be two-dimensional unicellular analysis, simplistic material properties, or uncoupled analyses between mechanical and biochemical factors. We discuss the need for multiscale, integrative modelling frameworks that bridge these computational and experimental approaches. A more holistic representation of keratinocyte behaviour could enhance the development of personalised therapies, improve disease modelling, and refine bioengineered skin substitutes for clinical applications. Full article

This paper investigates the dispersion of atmospheric pollutants in urban environments using a fractional-order convection–diffusion-reaction model with dynamic line sources associated with vehicle traffic. The model includes Caputo fractional time derivatives and Riesz fractional space derivatives to account for memory effects and non-local transport phenomena characteristic of complex urban air flows. Vehicle trajectories are generated stochastically on the road network graph using Dijkstra’s algorithm, and each moving vehicle acts as a mobile line source of pollutant emissions. To reflect the daily variability of emissions, a time-dependent modulation function determined by unknown parameters is included in the source composition. These parameters are inferred by solving an inverse problem using synthetic concentration measurements from several fixed observation points throughout the area. The study presents two main contributions. Firstly, a detailed numerical analysis of how fractional derivatives affect pollutant dispersion under realistic time-varying mobile source conditions, and secondly, an evaluation of the performance of the proposed parameter estimation method for reconstructing time-varying emission rates. The results show that fractional-order models provide increased flexibility for representing anomalous transport and retention effects, and the proposed method allows for reliable recovery of emission dynamics from sparse measurements. Full article

The paradigm-shift idea of murburn concept is no hypothesis but developed directly from fundamental facts of cellular/ecological existence. Murburn involves spontaneous and stochastic interactions (mediated by murzymes) amongst the molecules and unbound ions of cells. It leads to effective charge separation (ECS) and formation/recruitment of diffusible reactive species (DRS, like radicals whose reactions enable ATP-synthesis and thermogenesis) and emission of radiations (UV/Vis to ELF). These processes also lead to a chemo-electromagnetic matrix (CEM), ascertaining that living cell/organism react/function as a coherent unit. Murburn concept propounds the true utility of oxygen: generating DRS (with catalytic and electrical properties) on the way to becoming water, the life solvent, and ultimately also leading to phase-based macroscopic homeostatic outcomes. Such a layout enables cells to become simple chemical engines (SCEs) with powering, coherence, homeostasis, electro-mechanical and sensing–response (PCHEMS; life’s short-term “intelligence”) abilities. In the current review, we discuss the coacervate nature of cells and dwell upon the ways and contexts in which various radiations (either incident or endogenously generated) could interact in the new scheme of cellular function. Presenting comparative evidence/arguments and listing of systems with murburn models, we argue that the new perceptions explain life processes better and urge the community to urgently adopt murburn bioenergetics and adapt to its views. Further, we touch upon some distinct scientific and sociological contexts with respect to the outreach of murburn concept. It is envisaged that greater awareness of murburn could enhance the longevity and quality of life and afford better approaches to therapies. 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

By introducing the concept of nanoreaction-based fluctuating mixing entropy, the challenge posed by the smallness of a closed molecular system is addressed through equilibrium statistical–mechanical averaging over fluctuating reaction extent. Based on the canonical partition function, the interplay between the mixing entropy and fluctuations in the reaction extent in nanoscale environments is unraveled while maintaining consistency with macroscopic behavior. The nanosystem size dependence of the mixing entropy, the reaction extent, and a concept termed the “reaction extent entropy” are modeled for the combination reactions $A+B\leftrightarrow 2C$ and the specific case of $H_2+I_2\leftrightarrow 2HI$. A distinct inverse correlation is found between the first two properties, revealing consistency with the nanoconfinement entropic effect on chemical equilibrium (NCECE). To obtain the time dependence of the instantaneous mixing entropy following equilibration, the Stochastic Simulation (Gillespie) Algorithm is employed. In particular, the smallest nanosystems exhibit a step-like behavior that deviates significantly from the smooth mean values and is associated with the discrete probability distribution of the reaction extent. As illustrated further for molecular adsorption and spin polarization, the current approach can be extended beyond nanoreactions to other confined systems with a limited number of species. Full article

Reaction–diffusion equations can model complex systems where randomness plays a role, capturing the interaction between diffusion processes and random fluctuations. The Kolmogorov equations associated with these systems play an important role in understanding the long-term behavior, stability, and control of such complex systems. In this paper, we investigate the existence of a classical solution for the Kolmogorov equation associated with a stochastic reaction–diffusion equation driven by nonlinear multiplicative trace-class noise. We also establish the existence of an invariant measure $\nu$ for the corresponding transition semigroup $P_t$, where the infinitesimal generator in $L^2(H,\nu )$ is identified as the closure of the Kolmogorov operator $K_0$. Full article