Search Results (527)

Wind is an important abiotic factor that may influence predator–prey interactions. In this paper, we propose and analyze a stochastic predator–prey model in which the predator attack rate is described by a unimodal function of a fixed wind-intensity index. We establish the global existence, uniqueness, and positivity of solutions, together with stochastic ultimate boundedness, and derive a sufficient condition for the existence of a unique ergodic stationary distribution. A key analytical feature is that the Foster–Lyapunov recurrence argument is completed without quadratic predator self-limitation by exploiting the negative contribution generated by linear predator mortality. The resulting condition $\lambda >0$ incorporates effective predation, density dependence, wind modulation, predator mortality, and population-level environmental noise, and is a sufficient rather than necessary condition. Numerical parameter sweeps based on the complete expression for $\lambda$ and simulations using a logarithmic Euler–Maruyama scheme illustrate parameter-specific changes in the sufficient-condition quantity and in the post-burn-in empirical population distributions. Full article

This paper investigates a segmented reconfigurable intelligent surface (RIS)-enabled backscatter communication riding over ambient non-orthogonal multiple-access (NOMA) signals. For a practical hardware, a simultaneous adjustment of the reflection coefficients of the RIS elements in phase and continuously in amplitude is physically not feasible, contradicting the conventional symbiotic approach of continuously adjusting the amplitude of the reflection coefficient from 0 to one. To address this bottleneck, a novel on–off mechanism of the RIS’s reflecting elements for symbiotic backscatter NOMA systems is proposed. To begin with, the coexistence outage probability and the ergodic capacity of the proposed system are analyzed for diverse dispersed end users and the corresponding performance boundaries in the high signal-to-noise-ratio (SNR) regime are subsequently characterized. In addition, Monte Carlo simulations are provided to verify the correctness of the proposed analytical framework. Finally, the numerical results show that the transmission effectiveness of the proposed on–off mechanism approaches that of the ideal continuous one with an increase in the number of RIS elements. The findings also reveal that the proposed on–off mechanism offers the advantage of reduced reflection coefficient control vis-à-vis the deployment of the underlying RIS-enabled symbiotic backscatter system without the need to adjust the reflection coefficient in amplitude and in phase simultaneously. Full article

This paper develops a pointwise distributional theory for linear wavelet density and regression estimation from randomly right-censored observations exhibiting stationary ergodic dependence. In contrast to the prevailing literature, which typically relies on quantitative mixing conditions, our analysis is conducted under ergodicity alone, thereby encompassing substantially broader classes of dependent processes. We establish asymptotic normality for an oracle inverse-probability-weighted estimator based on the true censoring distribution and for its feasible counterpart obtained through Kaplan–Meier substitution. A central result shows that estimating the censoring distribution has no first-order effect on the limiting law, so that the feasible and oracle procedures are asymptotically equivalent. The proof strategy departs from conventional covariance inequalities and blocking arguments and instead combines a martingale-predictable decomposition with martingale central limit theory and ergodic convergence of conditional moments. The framework is further extended to a broad family of wavelet regression functionals involving transformed responses. To render the asymptotic theory directly usable for statistical inference, we introduce a randomly weighted procedure that consistently reproduces the limiting distribution of the feasible estimator. This yields asymptotically valid pointwise confidence intervals without requiring explicit estimation of the unknown asymptotic variance or the introduction of additional smoothing parameters. The scope of the theory includes several important non-mixing and long-range dependent models, while an extensive simulation study demonstrates the finite-sample accuracy and robustness of the proposed inferential methodology. Full article

The rapid proliferation of Internet of Things (IoT) technologies and smart grids has substantially intensified the cybersecurity challenges associated with smart energy meters (SEMs). The data collected by the plugs are transmitted via a wireless communication protocol to a smart electricity meter that acts as a local gateway. This meter centralizes the information from the various sensors, may perform data pre-processing, aggregation, or validation operations, and then forwards the information to a central server. The main contributions of this system can be categorized into two key aspects. First, the implementation of a centralized wireless local energy consumption network using the Wi-Fi protocol to coordinate smart plugs over distances of up to 20 m. Second, the real-time acquisition of power characteristics and the remote control (ON/OFF switching) of household appliances for direct appliance-level submetering purposes. Data collected by the smart meter are transmitted to a processing unit through a Semtech SX1276 LoRa transceiver communication link. The central server constitutes the processing and storage layer of the system: it receives the collected data, archives it in a dedicated database, and makes it available through analysis, visualization, and decision-support tools. This architecture enables real-time monitoring of energy consumption, anomaly detection, optimization of electrical resource use, and the development of effective energy management strategies for smart electrical grids. Although current smart meter architectures incorporate multi-layer protection mechanisms at the hardware, communication, and data levels, additional security measures are required to counter advanced cyber threats aimed at data interception and manipulation. This paper improves the security framework of smart energy meters by integrating a chaos-based encryption layer to ensure secure data transmission. Chaotic systems exhibit intrinsic properties such as sensitivity to initial conditions, pseudo-randomness, and ergodicity, which render them particularly suitable for cryptographic applications. The proposed framework employs a Lorenz-based chaotic encryption module to secure SEM-utility data exchanges. Full article

Many bargaining problems allocate control over heterogeneous issues rather than a single scalar surplus. This paper studies a two-player game-theoretic Nash bargaining problem over a continuum of issues with stochastic valuation fields. Taking the classical maximum Nash welfare cutoff allocation as a benchmark, we characterize the selected agreement as an endogenous excursion set of the log-relative valuation field. We then study its economic geometry: stationarity and ergodicity yield deterministic many-issue payoff limits, a finite-domain perturbation formula separates local shocks from global cutoff feedback, Kac–Rice methods describe boundary intensity, and a perimeter penalty for fragmented contracts turns the bargain into a finite perimeter variational problem. At regular boundary points, the complexity-penalized bargain satisfies a curvature-adjusted bargaining condition. The analysis connects cooperative game theory, Nash bargaining, fair division, random field geometry, and contract complexity. Full article

We consider the estimation of partial derivatives of multivariate regression-type functionals from incomplete observations generated by a discrete-time strictly stationary ergodic process. The response variable is subject to a missing-at-random (MAR) mechanism, whereas the covariates are fully observed. Building upon the complete-data wavelet methodology developed in Didi and Bouzebda (2025), we construct inverse-probability-weighted empirical wavelet estimators that compensate for the selection bias induced by missing responses. When the propensity score is unknown, a feasible estimator is obtained by replacing the oracle weights with a nonparametric Nadaraya–Watson estimator. The analysis is carried out under stationary ergodicity without imposing mixing assumptions. The estimation error is decomposed into three analytically distinct components: the deterministic multiresolution approximation error, the stochastic fluctuation of the oracle inverse-probability-weighted estimator, and the additional error arising from propensity score estimation. This decomposition makes it possible to isolate the respective effects of approximation, dependence, and missingness within a unified asymptotic framework. Under explicit assumptions on the multiresolution approximation, missingness mechanism, conditional density stabilization, moment conditions, and accuracy of the propensity estimator, we establish non-asymptotic integrated mean squared error bounds together with their asymptotic rates. We further prove almost-sure uniform consistency over compact subsets of the interior of the support and derive a pointwise central limit theorem for both the oracle and feasible estimators. The limiting variance explicitly reflects the information loss induced by inverse probability weighting, and for general orthogonal projection kernels is formulated under the corresponding dyadic-phase condition. The general methodology is specialized to the estimation of first- and second-order derivatives of ordinary regression functions. A finite-sample simulation study investigates the empirical behavior of the proposed estimators under stationary ergodic dependence and MAR missingness, examines the influence of both the wavelet resolution level and the propensity-score bandwidth, evaluates the finite-sample performance of the asymptotic confidence intervals, and compares the proposed procedure with oracle, complete-case, and competing nonparametric estimators. The numerical results are consistent with the theoretical analysis and illustrate the respective contributions of wavelet approximation, inverse probability weighting, and propensity score estimation to the overall estimation error. When the propensity score is identically equal to one, the proposed methodology reduces to the corresponding complete-data wavelet estimator. Full article

Zentropy theory has emerged as a multiscale thermodynamic framework that bridges quantum mechanics, statistical mechanics, and macroscopic materials behavior by embedding internal degrees of freedom within configurational ensembles. This review summarizes its theoretical foundations, representative applications, current limitations, and future directions. By incorporating intrinsic configurational entropy and free-energy-based statistical weighting, zentropy theory enables improved descriptions of phase stability, thermal expansion, and phase transitions in materials such as ferroelectrics, magnetic systems, high-entropy materials, and superconductors. Recent extensions also connect zentropy with artificial intelligence through data-driven thermodynamic modeling. Despite these advances, several challenges remain, including the ambiguity of configurational coarse-graining, strong cross-degree-of-freedom coupling, propagation of density functional theory errors, and limited applicability to delocalized or non-crystalline states. Future progress will require theoretical advances, including non-ergodic extensions, rigorous mathematical treatment of recursive multiscale entropy, and improved descriptions of low-temperature quantum effects. These efforts should be complemented by standardized software workflows, machine learning integration, and robust uncertainty quantification. Addressing these bottlenecks will help to further develop zentropy theory as a critically assessed framework for multiscale thermodynamic modeling and materials design. Full article

This paper analyzes the ergodic sum rate of zero-forcing beamforming with semi-orthogonal user selection (ZFBF-SUS) in multiuser multiple-input multiple-output (MU-MIMO) downlink channels with one-bit analog-to-digital converters (ADCs) at the receivers. Although ZFBF-SUS has been widely studied under the conventional assumption of infinite-resolution ADCs, its ergodic performance with one-bit ADC receivers has not been fully characterized. To address this issue, we derive analytical approximations for the ergodic sum rate by considering the achievable rate expression induced by one-bit quantization. For mathematical tractability, the achievable rate of each selected user is approximated as a function of its channel gain under the condition that the selected users are nearly orthogonal and the number of users is sufficiently large. Moreover, the channel gain of each scheduled user is characterized using maximum order statistics of Gamma random variables, while the size of the SUS candidate set is approximated by exploiting the semi-orthogonality condition. We further derive an asymptotic sum-rate expression with respect to the number of users by applying extreme value theory. Simulation results verify the validity of the proposed analytical approximations and show that the derived expressions accurately capture the ergodic sum-rate behavior of ZFBF-SUS with one-bit ADC receivers, especially when the number of users is large and the SUS threshold is properly chosen. Full article

This work analyzes the ergodic capacity behavior of reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output (MIMO) systems with a finite and arbitrary number of antennas and RIS elements under Nakagami-m fading conditions. By combining Hadamard’s determinant inequality with the Cauchy–Schwarz inequality, this work derives a dimensionally consistent closed-form upper bound on the ergodic capacity in terms of the Meijer G-function. Subsequently, it is demonstrated that at a high signal-to-noise ratio (SNR), a simplified expression for the capacity upper bound can be derived, enabling an analytical assessment of how the fading parameter influences the ergodic capacity. The study also explores the asymptotic behavior in the large-system regime, where the number of antennas or RIS elements tends to infinity. Monte Carlo (MC) simulations confirm the accuracy of the proposed bound and scaling laws. Full article

Path-dependent dynamic systems are often analysed through separate metric, stochastic, econometric or nonlinear methods, while their integration within a unified architecture remains limited. This study develops and validates a Hybrid Dynamic Modelling Framework (HDMF) for path-dependent stochastic systems, using EU-27 digital public service trajectories during 2017–2022 as an empirical application. The framework combines DTW-TimeSeriesKMeans clustering, Markov transition analysis, PVAR, SEM and MLP approximation. The findings answer the four research questions sequentially. First, EU digital public service development is represented by three distinct trajectory regimes rather than a single convergence path. Second, the Markov layer shows strong diagonal dominance, limited mobility and practical non-ergodicity over the finite observation horizon, indicating persistent state dependence. Third, the PVAR layer confirms dynamic stability and bounded feedback within the institutional–digital system. Fourth, the SEM and MLP layers identify governance as a coherent latent institutional structure and reveal nonlinear predictive heterogeneity, suggesting possible threshold-type behaviour. Overall, the findings support the HDMF as a coherent multilayer architecture for modelling complex path-dependent systems and demonstrate its empirical usefulness through the EU digital public service case. Full article

Sparse ergodic control provides a natural framework for long-run stochastic decision-making under resource constraints. Existing formulations, however, are typically restricted to control-affine systems with control-independent diffusion. When the diffusion coefficient depends explicitly on the control input, the associated ergodic Hamilton–Jacobi–Bellman (HJB) equation becomes non-separable through the term $\mathrm{t}\mathrm{r}\left[a\left(x, u\right){\nabla }^{2}V\right]$, so classical arguments based on control-affine separability no longer apply directly. In this work, we study sparse ergodic control of stochastic systems with control-dependent diffusion and nonlinear dynamics within a viscosity-solution and learning-based framework. To address the discontinuous ${\mathsf{\ell }}_0$-type sparsity penalty, we introduce smooth non-convex sparsity approximations that preserve differentiability while retaining sparse threshold behavior. Within a viscosity-solution framework, we analyze the existence and uniqueness properties of the associated ergodic pair and establish localized approximation error estimates for the smooth approximation. We further characterize a quasi-threshold sparse structure of the resulting optimal feedback policies in non-affine stochastic systems with control-dependent noise. On the computational side, we develop a Physics-Informed Neural Network (PINN)-based solver with adaptive residual-driven sampling for high-dimensional sparse ergodic HJB equations, together with a distributed monotone-inspired iterative scheme for weakly coupled multi-agent systems. Numerical experiments on multi-robot swarm navigation and renewable-integrated smart-grid control demonstrate that the proposed methods produce sparse control policies while preserving stable long-run performance under stochastic disturbances. Full article

This paper investigates the long-term behavior of diffusion models in population dynamics before absorption. By establishing the intrinsic ultracontractivity of the associated Markov semigroups, we obtain sharp quantitative estimates for three fundamental limiting objects: the quasi-stationary distribution, the quasi-ergodic distribution, and the mean quasi-ergodic distribution. Specifically, we determine their domains of attraction and prove that convergence to each occurs at an exponential rate. Moreover, we show that the conditioned Q-process is uniformly exponentially ergodic, and we characterize the mixing speed of the original process in terms of the spectral gap. These results provide a unified framework for understanding pre-absorption dynamics in population processes. Full article

To address the inherent limitations of the traditional Animated Oat Optimization Algorithm (AOO), including poor uniformity of initial random population distribution and insufficient dynamic balance between global exploration and local exploitation, this paper proposes an Enhanced Animated Oat Optimization Algorithm (EAOO) incorporating multi-strategy improvements. First, the Sinusoidal chaotic map is introduced to replace the original random initialization method. Leveraging the ergodicity and uniformity of chaotic sequences, the spatial distribution of the population is optimized, and the diversity of the initial population is significantly enhanced. Second, a nonlinear disturbance factor is embedded into the position update of leaders during both the exploration and exploitation phases, enabling dynamic and adaptive adjustment of the search range. This effectively balances the algorithm’s capabilities in global exploration and local exploitation. Finally, an adaptive t-distribution mutation operator, combined with a dynamic selection strategy, is integrated. The degrees of freedom are adaptively adjusted throughout the iterative process, allowing the algorithm to switch between global escape and local fine-search modes, thereby overcoming the premature convergence deficiency of the original algorithm. Simulation and comparative experiments are conducted based on the CEC2017 and CEC2020 benchmark function suites. Systematic evaluations are carried out from multiple perspectives, including optimization accuracy, convergence speed, and statistical significance. The experimental results demonstrate that the proposed EAOO achieves superior comprehensive performance across various complex function types—including unimodal, multimodal, hybrid, and composite functions—exhibiting higher optimization accuracy, faster convergence speed, and stronger robustness. Statistical tests further confirm the significant performance differences between EAOO and the compared algorithms. Furthermore, EAOO is applied to two typical constrained engineering optimization problems: welded beam design and pressure vessel design. The simulation results show that EAOO yields better structural design parameters and lower manufacturing costs, demonstrating outstanding practical value and broad application prospects in solving high-dimensional, nonlinear, constrained engineering optimization problems. Full article

In this paper, consideration is given to the class of birth-and-death processes with possibly state-dependent and time-varying transition intensities and a finite state space. Several techniques are available in the literature for the computation of the long-run (limiting) time-dependent performance characteristics of such processes. Whenever a solution technique is combined with a limiting regime detection method, its efficiency may be improved. It is intuitively reasonable to expect that, if additional information about the process is available, a limiting regime detection method may allow one to save more computation effort. In this paper, we demonstrate that the logarithmic norm method, which is one of the methods with which to provide ergodicity bounds for continuous-time Markov chains with discrete state space, can be utilized in such a way. When the exact values of the transition intensities of the (ergodic) birth-and-death process are known and are such that it is clear that one group of states is visited less often than the other, the method allows one to detect the limiting regime rapidly. We illustrate numerically the results obtained within the queueing theory context by considering the activity of the total number of customers in a multi-server finite-capacity queue with periodic arrival and service intensities. Full article