Search Results (1,290)

Banks must balance deposit stability, loan expansion, and regulatory compliance while operating under liquidity constraints and financial risks. This study presents a mathematical model to examine the dynamics of bank deposits and loans under the influence of liquidity mechanisms and regulatory policies. The model proceeds in three stages: a deterministic nonlinear model, a dynamic optimal control model, and a stochastic model. Under the deterministic model, deposit withdrawals are liquidity-dependent, leading to a feedback mechanism in which liquidity improves deposit stability while financing loan growth. The theoretical results demonstrate the model’s positive and bounded solutions and show the existence and local stability of equilibria. Several parameters are based on regulatory policies or calibrated from Indonesian banking data, while the unknown parameters are estimated using the particle swarm optimization (PSO) algorithm. The results show that the proposed model is capable of fitting and predicting the data and has slightly lower mean absolute percentage errors for in-sample and out-of-sample compared with the benchmark model, and achieves comparable directional forecasting performance based on the index of directionality. Sensitivity analysis shows that the capital adequacy ratio supports lending, whereas an increased reserve requirement limits lending. An optimal control approach is developed by considering the reserve and capital requirements as time-varying policy variables. By applying Pontryagin’s maximum principle, we establish the necessary conditions for optimality. Numerical experiments demonstrate that the optimal control regulation enhances financial ratios, particularly the loan-to-deposit and liquidity ratios, at a reasonable cost. Finally, the stochastic model accounts for random variations in withdrawals and credit risks. Simulation-based observations reveal that although the system becomes more volatile, the mean dynamics are close to the deterministic case. Our framework offers a data-based and analytically tractable approach for studying the dynamics of banking variables and the effects of regulatory policies. The proposed model provides a mathematical tool for assessing the long-term effects of regulatory policies on banking performance and can assist bank managers and regulators in designing strategies that balance lending activity and liquidity resilience. Full article

This paper investigates the stabilization of unstable third-order Multiple-Input Multiple-Output (MIMO) systems whose interaction structure is described by a doubly stochastic combined matrix, also known as the Relative Gain Array (RGA). Starting from systems with negative Niederlinski index, we derive necessary and sufficient conditions under which stability can be recovered through diagonal perturbations while preserving the doubly stochastic structure of the combined matrix. By exploiting the canonical representation of matrices associated with a prescribed combined matrix and the invariance properties under diagonal equivalence, the problem is reduced to a structured parametric form that allows a complete algebraic characterization. Special attention is given to perturbations involving the (1, 1) entry and one additional diagonal entry, leading to explicit bounds on the perturbation parameters that guarantee stabilization. The results extend previous papers on diagonal perturbations of combined matrices and provide a constructive method for stabilizing MIMO systems without altering their interaction pattern. Numerical examples illustrate the applicability of the proposed approach. Full article

The accelerating integration of renewable energy sources into modern power grids has created unprecedented operational challenges, with significant system cost volatility under extreme uncertainty events. To address this challenge, this paper presents a risk-aware stochastic approximate dynamic programming (SADP) algorithm based on machine learning and parallel computing architectures. The algorithm learns optimal coordination strategies for source-grid-load-storage resources while explicitly quantifying and mitigating tail risk events that conventional approaches overlook. First, a risk-averse stochastic optimization model is constructed, which captures the complex interdependencies between renewable generation uncertainty, demand variability, and flexible resource coordination through second-order cone programming formulations. This model integrates the GlueVaR (Glued Value-at-Risk) metric, enabling simultaneous optimization across multiple risk horizons with adjustable conservatism parameters. Second, to solve the established model efficiently, an SADP algorithm based on risk-averse approximate value functions (RAVFs) is proposed, in which the training process of the RAVFs employs machine learning principles to directly encode risk preferences into operational decisions. By integrating GlueVaR into offline training across 5000 probabilistically weighted scenarios, the algorithm discovers emergent coordination patterns between distributed resources, which are rarely identified by human operators. Third, a large-scale parallel computing architecture is implemented for the SADP algorithm. This architecture decomposes the multi-period optimization problem into single-period coordinated sub-problems. During offline training, parallel computing of a series of single-period sub-problems can be performed across all probabilistic scenarios, significantly reducing training time. Extensive validation on both the modified IEEE 33-bus and 69-bus systems with integrated wind turbines, photovoltaic plants, energy storage systems, and demand response capabilities demonstrates remarkable performance improvements. Convergence analysis reveals that the AVFs stabilize within 30 training iterations, achieving sub-160 s solution times in online application even for complex networks with heterogeneous resources. By enabling real-time risk-aware decision-making under severe uncertainty, the proposed method provides grid operators with actionable strategies that balance economic efficiency and operational resilience. Full article

Object detection in unmanned aerial vehicle (UAV) imagery suffers from severe scale variation, dense object packing, and prohibitive computational cost when conventional detectors exhaustively evaluate high-resolution frames. Reinforcement learning (RL)-based sequential detectors offer a promising alternative by formulating localization as an active search process, yet existing methods are limited by discrete-time state transitions, sparse reward signals, and premature policy collapse. In this paper, we propose HRL-Det, a hierarchical reinforcement learning framework that addresses these challenges through two tightly coupled innovations. First, a Neural ODE-driven Continuous-Time Bellman State Evolution module models the agent’s state dynamics as a stochastic differential equation governed by the Hamilton–Jacobi–Bellman equation, enabling fine-grained temporal reasoning with memory-efficient adjoint-based backpropagation. Second, a Lyapunov-Guided Entropy-Regularized Reward Shaping mechanism constructs convergence-promoting dense rewards informed by Lyapunov stability analysis while maintaining exploration diversity through maximum entropy optimization. Extensive experiments on VisDrone2019, DroneVehicle, and MS COCO 2017 show that HRL-Det achieves mAP@0.5 of 0.412, 0.812, and 0.735, respectively, outperforming existing RL-based detectors and achieving competitive accuracy relative to representative non-RL detectors under the same COCO metric, while requiring only 17.3 M parameters and an average of 6.3 search steps per object. Full article

Typhoon-eye sensing places unmanned aerial vehicle (UAV) swarms in a setting where the wind field that carries the target signal also displaces aircraft, drains energy, weakens links, and increases failure risk. A rule that improves only routing or only motion can therefore move the swarm into another failure mode. This paper proposes a risk-driven cross-layer coordination scheme for such missions. A bounded risk index, computed from isolation, connectivity loss, and wind intensity, acts as a supervisory variable for multi-hop reachability maintenance, isolated-node recovery, and layered altitude adaptation. For evaluation, graph reachability is separated from useful data return through a degraded multi-hop aggregation model that includes distance loss, wind-dependent reliability, rain-induced packet loss, relay forwarding loss, and mothership collection capacity. The simulator combines a bounded Holland-type storm field, stochastic turbulence, nonlinear propulsion energy consumption, and wind-dependent structural failure. Against three literature-inspired baselines, two AI-inspired comparators, and six ablation variants, the method keeps a balanced profile across connectivity, isolation, wind exposure, data collection, and survival. In 30-run steady-state robustness tests under heavy-rain attenuation, the full strategy showed clear gains over routing-only and multi-agent reinforcement learning (MARL)-routing comparators in connectivity and isolation, but did not uniformly dominate topology reconstruction or the multi-agent deep deterministic policy gradient–artificial potential field (MADDPG-APF) recovery comparator. The results indicate that, in storm-dominated swarm sensing, resilience comes mainly from coordinating exposure reduction with topology stabilization, rather than from optimizing a single layer. Full article

Accurate object detection in agricultural environments remains challenging due to illumination variation, background clutter, partial occlusion, and overlapping fruits. Conventional object detection methods mainly rely on deterministic data augmentation strategies or feature-level refinement, which often exhibit limited robustness under complex field conditions. To address this issue, this paper proposes a Diffusion-Regularized Object Detection (DROD) framework for robust pineapple target detection in agricultural imagery. The proposed framework introduces a mathematically grounded forward diffusion and diffusion-guided representation mechanism directly in the image domain, where stochastic perturbations are generated through forward diffusion and semantically meaningful image representations are learned via diffusion-guided representation. A unified optimization framework and theoretical analyses of perturbation propagation, Lipschitz stability, and training convergence are further established to provide mathematical support for the proposed method. Extensive experiments were conducted on a self-constructed dataset containing 1600 real-world pineapple images collected under practical agricultural conditions. Comparative evaluations involving YOLOv8-s, YOLOv8-l, traditional data augmentation, and the recent JTA:GAN method demonstrate that the proposed DROD framework consistently achieves the best detection performance in terms of Precision, Recall, mAP@0.5, and mAP@0.5:0.95 while maintaining computational complexity and inference speed comparable to the original YOLOv8 architecture. Furthermore, ablation studies, diffusion parameter sensitivity analysis, visualization analysis, and experimental validation under different perturbation levels consistently verify the effectiveness and robustness of the proposed diffusion mechanism. These results demonstrate that diffusion-based regularization provides an effective and computationally efficient solution for robust agricultural object detection and offers a practical framework for intelligent precision agriculture applications. Full article

This paper presents a decentralized adaptive generalized-minimum-variance (GMV) control framework for large-scale stochastic nonlinear systems composed of interconnected multi-input multi-output (MIMO) Hammerstein subsystems with unknown time-varying parameters. Each subsystem consists of a coupled multivariable static nonlinearity represented on a known invertible basis, followed by a matrix-polynomial dynamic block affected by colored noise and delayed input–output interconnections. The proposed scheme estimates only identifiable composite Hammerstein parameters through a decentralized recursive extended least-squares algorithm with forgetting, thereby avoiding the non-unique separation of nonlinear and linear gains. A constructive matrix Diophantine identity is established to derive an optimal multi-step predictor, leading to a GMV control law expressed as a multivariable polynomial equation in the current input. Sufficient conditions for real solvability, mean-square boundedness, and near-optimal adaptive tracking are provided using Hadamard–Lévy global-diffeomorphism, minimum-phase, small-gain, persistent-excitation, strict-positive-realness, and convex-projection arguments, and the implemented controller—inexact Newton solver with fallback and persistent dither—is itself covered by the analysis. The analysis further shows that delayed interconnections become measurable and can be exactly compensated, while robustness to basis under-modeling is explicitly quantified. Simulation results on an interconnected two-subsystem MIMO Hammerstein process with coupled cubic nonlinearities, colored noise, delayed interactions, and time-varying parameters—run in the forgetting-factor regime required by the theory, with measured persistent excitation and complete solver diagnostics—demonstrate operational-noise-floor tracking and a $2.3$-fold mean-RMSE reduction relative to the strongest linear-MIMO surrogate, while a channel-wise SISO Hammerstein design fails structurally and a feedback-linearization controller with exactly known nonlinearity offers no advantage. The study further demonstrates scalability on a chain of four subsystems with size-independent per-subsystem computational cost, validates a physically motivated interconnected coupled-tank network with progressive-valve nonlinearities, and confirms agreement between the observed stability limits and the predicted small-gain boundary. Full article

To address the challenge of effectively stabilizing inherently unstable hybrid stochastic McKean–Vlasov equations (HMVSDEs) while simultaneously minimizing control costs, this paper proposes a novel control strategy termed aperiodically intermittent control (AIC). Under the global Lipschitz condition, we first establish the existence and uniqueness theorem for the solutions to HMVSDEs. Subsequently, we derive a generalized It$\widehat{o}$ formula for HMVSDEs, based on which we construct a Lyapunov functional that explicitly incorporates both the law (distribution) of the solution and the underlying Markovian switching process. By employing the Lyapunov functional method, we rigorously construct AIC for the unstable HMVSDEs and analyze the mean-square exponential stability of the controlled system. Furthermore, we demonstrate the applicability of the proposed AIC strategy through a mean-field stochastic Cohen–Grossberg–Hopfield neural network model. Finally, a numerical example is provided to illustrate the effectiveness and practical feasibility of the developed control approach. Full article

This study examines likelihood-based estimation of the joint survival function $S(t_1,t_2)=Pr\{T^{\left(1\right)}>t_1,T^{\left(2\right)}>t_2\}$ for systems with two competing failure modes observed under right censoring. Rather than introducing a new distributional family, the study compares established dependence mechanisms within a common observed-data framework. Exponential and Weibull margins are combined with three types of dependence: Archimedean copulas, represented by the Gumbel and Clayton families; shared gamma frailty, used to model latent measurement-level heterogeneity; and Marshall–Olkin extensions, used to represent common shocks and simultaneous failures. The same observation scheme, likelihood construction, censoring design, and performance criteria are used across models. Model performance is evaluated through Monte Carlo simulation using bias, integrated mean squared error, and empirical coverage, and the workflow is illustrated with the Device G reliability data. The results show that ignoring dependence can distort joint survival estimates, especially under moderate or high censoring. They also show that copula, frailty, and Marshall–Olkin specifications can lead to different reliability assessments because they encode different stochastic mechanisms. The estimation workflow includes multi-start optimization and diagnostics for boundary solutions, Hessian stability, and irregular likelihood behavior. Full article

This study proposes a stochastic time-delay pheromone feedback model to describe ant foraging dynamics, and investigates how response delays and environmental noise jointly induce stochastic oscillations and reorganize the system’s probabilistic structure. By employing near-Hopf center-mode projection and stochastic averaging, we derive the first-order stochastic amplitude equation and analyze the stochastic dynamical properties near the deterministic delay-induced Hopf bifurcation. Subsequently, normalized Shannon entropy and Jensen–Shannon divergence, computed relative to a pre-Hopf stochastic stationary reference distribution, are used to quantify uncertainty expansion and distributional reorganization in the stationary amplitude distribution and reconstructed state-variable distributions. The analytical results are supported by numerical simulations, which indicate that response delay primarily determines the transition from stable foraging to oscillatory behavior, while noise intensity mainly affects the dispersion and uncertainty of the amplitude distribution. Information-theoretic metrics further reveal noise-induced uncertainty growth and delay-induced probabilistic restructuring. This study elucidates the stability regulation mechanisms of ant foraging systems under stochastic conditions from a combined dynamical and information-theoretic perspective, and provides a theoretical reference for the design of delayed feedback in swarm intelligence systems. Full article

The inverse kinematics (IK) problem of the UR3 collaborative manipulator is addressed through a singularity-aware optimization framework and a statistically grounded benchmarking methodology. The IK task is formulated as a full-pose optimization problem minimizing a physically scaled residual combining Cartesian position and orientation errors. Emphasizing consistency between error formulation and optimization paradigms, a matrix-based pose-error representation is adopted as a numerically stable residual for stochastic search. Simultaneously, a smooth Jacobian-conditioning penalty is incorporated to mitigate instability near ill-conditioned configurations. Five metaheuristic solvers (PSO, GWO, GA, JADE, ALO) are implemented under a unified, reproducible experimental protocol with common maximum search settings. The Levenberg–Marquardt (LM) numerical method is included as a deterministic baseline to compare gradient-based precision against derivative-free global exploration. Performance is evaluated across nominal, industrial, and near-singular poses using 1000 Monte Carlo runs per configuration. Final-solution accuracy, variability, and computational time are analyzed directly from the Monte Carlo outcome distributions, descriptive statistics, and nonparametric rank-based tests. Results indicate that LM achieves superior numerical precision and computational speed. Among the metaheuristics, GA provides the lowest mean objective values and the smallest objective dispersion across the three tested poses, whereas JADE is the fastest solver. GWO provides an intermediate solution profile, with competitive objective values and substantially shorter execution times than GA and ALO. The optimized solutions are first verified in a RoboDK virtual environment. Subsequently, representative GWO-based configurations are experimentally validated on a physical UR3 robot through both isolated static poses and a continuous multi-pose trajectory tracking task, confirming practical kinematic feasibility and sequential stability. The proposed framework establishes a reproducible benchmark for statistically robust evaluation of metaheuristic-based IK optimization in collaborative robotics. Full article

Rural distribution networks increasingly face voltage quality challenges due to high penetration of distributed renewable energy, heterogeneous rural load behavior, and long radial feeder structures with limited voltage regulation capability. Photovoltaic generation variability and agricultural load fluctuations can lead to voltage rise, reverse power flow, and branch congestion, particularly in weak rural grids. Conventional deterministic voltage control approaches relying on tap changers and capacitor banks often struggle to maintain stable voltage profiles under stochastic operating conditions. This paper proposes a risk-aware coordinated operation framework for rural multi-energy microgrids that integrates stochastic scenario modeling, voltage state perception, and adaptive optimization-based control. Renewable generation uncertainty and rural load variability are represented through correlated scenario generation and Wasserstein-distance-based scenario reduction, where 100 raw joint photovoltaic-load trajectories are reduced to 20 representative scenarios after convergence and distributional-fidelity tests. A stochastic optimization model is developed to coordinate photovoltaic inverters, battery energy storage systems, demand-side flexibility, and reactive compensation devices while satisfying network power-flow, voltage-security, storage, and communication-delay-aware implementation constraints. To mitigate extreme voltage deviation events, the framework incorporates a Conditional Value-at-Risk formulation that penalizes tail-risk voltage violations and maintains voltages within a preferred operating band of $0.97$–$1.03$ p.u. Case studies on a modified IEEE 33-bus rural distribution system with $2.00$ MW of photovoltaic capacity and $2.50$ MWh of battery storage demonstrate consistent performance improvements across deterministic, risk-neutral stochastic, chance-constrained, and robust baselines. The proposed strategy reduces peak branch loading from $0.95$ in the deterministic benchmark to $0.72$, while the $95\mathrm{th}$ percentile voltage deviation risk decreases from $0.0071$ p.u.${}^2$ to $0.0020$ p.u.${}^2$. Sensitivity, scenario-convergence, scalability, and seasonal representative-day analyses further confirm that the CVaR layer suppresses rare but severe voltage excursions without imposing excessive curtailment or computational burden. Full article

Beneficial and pathogenic fungal inoculation can substantially influence plant growth by reshaping rhizosphere microbial communities. However, how different fungal inoculants differentially affect microbial community assembly processes, co-occurrence network stability, keystone taxa distribution, and their potential associations with plant growth remains poorly understood. Cucumber was used as the model plant, and Fusarium oxysporum (pathogenic, Foc) and Trichoderma guizhouense (beneficial, Tri) were selected as inoculants. 16S rRNA and ITS2 amplicon sequencing were used to investigate the diversity, composition, assembly processes, and co-occurrence network structure of rhizosphere bacterial and fungal communities, respectively. In addition, we used Zi–Pi topological role analysis, functional prediction, Mantel tests and random forest to characterize keystone taxa and link microbial assembly, network stability to plant nutrient and biomass traits. Foc decreased bacterial diversity while Tri increased it. Tri was associated with greater microbial network connectivity and complexity, as well as network characteristics consistent with higher inferred stability, with more connector keystone taxa enriched in glycan and terpenoid metabolic functions; by contrast, Foc simplified network structure and enriched saprotrophic fungal keystones. Bacterial assembly shifted toward deterministic processes under Foc, whereas stochastic processes remained predominant in Tri and control treatments. Random forest further confirmed divergent drivers: bacterial assembly depended mostly on community composition, while fungal assembly was regulated by plant nutrients and fungal diversity. All microbial properties were tightly linked to plant biomass and nutrient accumulation. Collectively, beneficial and pathogenic fungi exert opposing influences on rhizosphere microbial organization: Tri was associated with more connected microbial communities and a greater diversity of predicted functional traits, whereas Foc strengthened environmental filtering and simplified community structure, with plant–microbe–nutrient feedbacks likely contributing to rhizosphere assembly and ecosystem functionality. Full article

This work aims to study and improve the long-term stability of conductimetric biosensors for urea detection in clinical and environmental samples, which are fundamentally limited by complex thermal and temporal drifts due to temperature-sensitive enzyme kinetics, variations in ionic mobility, and the progressive degradation of the sensing layer. The biosensor targets the urea concentration range 0.01–30 mM, validated against experimental data and covering the clinically relevant range for blood urea detection (2.5–7.5 mM), urine (20–40 mM), and environmental monitoring applications. Conventional calibration techniques, such as the conventional calibration method (based on reference measurements), and purely deterministic correction methods, such as deterministic methods (based on known fixed equations), often prove insufficient because they struggle to capture the non-stationary and inherently stochastic nature of these drifts. In this work, we propose an original hybrid probabilistic framework that synergistically combines machine learning and Bayesian inference for robust adaptive drift compensation. A Random Forest model is first implemented to model the deterministic nonlinear relationships between environmental parameters (temperature, pH, CO₂ concentration) and the sensor response. The residual temporal drift is then explicitly modeled as a non-stationary latent stochastic process using Bayesian inference based on a Gaussian process. This approach allows continuous online model updating, real-time uncertainty quantification, and automatic detection of anomalies. The models were trained and validated on a large dataset obtained from multiphysics simulations carried out in COMSOL Multiphysics 5.6. These simulations incorporated enzymatic reactions, thermal effects, and chemical dynamics taking place inside the sensor. Experimental results show that the hybrid approach substantially enhances sensor performance, lowering the root mean square error (RMSE) to below 0.8 μS/cm (corresponding to less than 0.5% of the full-scale response) over a wide temperature range (15–45 °C) and across extended operating periods. This represents a clear improvement over conventional compensation method. By merging the predictive power of ensemble learning with a probabilistic Bayesian model of dynamic drift, this study introduces a fresh perspective on the design of intelligent, self-adaptive, and drift-resistant conductimetric biosensors. The proposed framework holds strong potential for reliable, long-term autonomous operation in urea reliable, long-term autonomous operation in urea monitoring across biomedical diagnostics (kidney/liver function assessment) and environmental surveillance (water eutrophication prevention). Full article

In this study, a comprehensive stochastic and fractional-order modeling framework is developed to investigate the dynamic behavior of a shunt DC motor under random disturbances and memory effects. The motor dynamics are formulated as a system of stochastic differential equations incorporating Gaussian noise to represent uncertainties in the electrical and mechanical subsystems. The existence, stochastic ultimate boundedness, stationary distribution, and ergodic properties of the proposed model are established. To further enhance modeling capabilities, a modified Atangana–Baleanu–Caputo (mABC) fractional operator is introduced, enabling the incorporation of nonlocal memory effects inherent in electromechanical systems. The series solution is derived using the Laplace transform and the Adomian decomposition method to handle nonlinearities. Qualitative analysis of the solution is performed through fixed-point theory, while stability assessments utilize the T-Picard method. The results of the numerical simulation indicate that the stochastic model exhibits limited variability around the operating regimes, whereas the fractional-order representation is more effective at smoothing transient responses and limiting oscillatory behavior. The study proposes a realistic and adaptable method to analyze the dynamics of shunt DC motors with uncertainty and also presents useful information for the design and control of electromechanical systems. Full article