Federated learning enables privacy-preserving distributed intelligence but faces challenges in balancing computation, communication, and privacy in heterogeneous networks. To address these issues, this paper proposes a privacy-preserving U-shaped split federated learning (USFL) framework for space–air–ground–sea integrated networks. The proposed architecture combines split learning and federated learning in a U-shaped structure, ensuring that both raw data and labels remain localized at client devices. In addition, a differential privacy mechanism is introduced to perturb intermediate features during transmission, enhancing resistance to inference attacks. A mathematical framework is established to model the learning process under resource constraints, and the convergence behavior and privacy loss are theoretically analyzed. Experimental results on the SeaShips dataset demonstrate that the proposed method achieves competitive accuracy compared with centralized and existing distributed approaches, while reducing communication overhead and improving privacy protection. These results validate the effectiveness of the proposed framework for secure and efficient distributed learning in complex network environments.

This paper investigates duopoly competition under both constant and decreasing returns to scale in a market characterized by an isoelastic demand function, where firms adjust their strategies using a gradient adjustment mechanism. To establish the stability conditions of the model, we adopt different analytical approaches depending on the type of returns to scale. Under constant returns to scale, we employ a traditional approach by deriving the closed-form solution of the Nash equilibrium and analyzing the Jacobian matrix to verify whether the moduli of all eigenvalues are less than one. In contrast, under decreasing returns to scale, we analyze the local stability of the Nash equilibrium using symbolic computation methods without deriving a closed-form solution. The results show that when firms have heterogeneous costs, the model can exhibit both period-doubling and Neimark–Sacker bifurcations under both types of returns to scale. However, when costs are homogeneous, only period-doubling bifurcations occur. Numerical simulations support these analytical results and further demonstrate the emergence of complex dynamics, including chaotic behavior.

Solving constrained multiobjective optimization problems (CMOPs) is highly challenging due to the presence of complicated feasible regions, intense conflicts among objectives, and unevenly distributed constraints. As a result, conventional methods relying on a single constraint-handling mechanism frequently fail to maintain a stable equilibrium among solution feasibility, diversity, and convergence. To overcome these bottlenecks, this article introduces AFFCMO, a novel adaptive feasibility-guided framework tailored for constrained multiobjective optimization. At its core, the proposed approach utilizes a coevolutionary dual-population architecture that divides the search process into two distinct tasks. Specifically, an auxiliary population is tasked with global exploration, while a primary population focuses on the intensive exploitation of discovered feasible areas. To achieve this, the primary population leverages a DE/current-to-pbest/1 differential evolution strategy to closely approximate the constrained Pareto front. Simultaneously, the auxiliary population expands the search space using a mutation operator that adapts to the current evolutionary stage. Furthermore, exploration is bolstered by a multicriterion environmental selection scheme designed for the auxiliary group. By combining Euclidean geometric distributions, constraint relaxation, and value modeling inspired by epidemic dynamics, this strategy successfully preserves valuable infeasible solutions that can guide the search. Additionally, a dynamic resource allocation strategy based on historical search feedback and Thompson sampling is incorporated. This mechanism continuously evaluates the recent search contributions of both populations and adaptively adjusts their offspring sizes, thereby reducing the bias introduced by static allocation schemes. This mechanism continuously assesses the actual search contributions of both populations, allowing for the adaptive resizing of offspring generations and thereby eliminating the inherent biases of static allocation methods. Comprehensive empirical evaluations are conducted on 47 benchmark problems from four distinct test suites. The results indicate that AFFCMO significantly outperforms seven contemporary multiobjective evolutionary algorithms in terms of exploring complex feasible regions, preserving solution diversity, and achieving high convergence accuracy.

This paper proposes a recursive method for constructing intra-resolvable balanced incomplete block designs (BIBDs). The approach exploits the algebraic and geometric structure of finite projective geometries over Galois fields to generate resolvable designs with improved efficiency in terms of the number of blocks and treatment replications. The recursive procedure produces symmetric and uniform designs that are particularly suitable for high-dimensional settings. By systematically nesting resolvable blocks, we derive a new class of balanced n-ary designs that are both economical and scalable. These designs hold significant value for the statistical community, offering broad applicability in resource-constrained experimental environments such as precision agriculture, high-throughput drug screening, and computer-based simulation studies. We provide theoretical foundations through explicit constructions and comparative evaluations, demonstrating the advantages of our method over classical approaches.

Amid tightening emission rules and growing cold-chain demand, ports face complex multi-objective scheduling under dual uncertainties in vessel arrivals and operations. This work develops a multi-objective chance-constrained stochastic MILP model for joint berth, QC, and OPS scheduling. Heavy-tailed operational delays are managed via chance constraints, converting Weibull distributions to time buffers, while convex formulations allow piecewise cargo damage penalties to be computed linearly. A reinforcement learning-based adaptive large neighborhood search (RL-ALNS) algorithm is proposed to solve this NP-hard continuous-time problem, integrating a spatiotemporal decoder and an MDP-based selector to ensure microgrid limits and efficiency. Simulations demonstrate RL-ALNS’s superior Pareto convergence versus conventional heuristics. The model cuts the 95th-percentile tail risk by 46.59% and actual costs by 24.44% under mild delays, compared to deterministic scheduling. Overall, it quantifies the non-linear cost–emission–reliability trade-off, providing a robust tool for port decision-making.

This study investigated the forecasting performance of the South African gold sales series using the seasonal autoregressive integrated moving average (SARIMA), generalised autoregressive conditionally heteroscedastic (GARCH), general regression neural network (GRNN) and artificial neural network (ANN)-based extreme learning machine (ELM). This study employed traditional methods and a recently developed ML method for single hidden-layer feed-forward neural networks (SLFNs). The findings revealed that <!-- MathType@Translator@5@5@MathML2 (no namespace).tdl@MathML 2.0 (no namespace)@ -->

This study investigates a range of parameter estimation methods for the Half-Logistic Inverse Rayleigh Distribution (HLIRD) under two distinct sampling frameworks: ranked set sampling (RSS) and simple random sampling (SRS). The estimation techniques considered include maximum likelihood estimation, ordinary and weighted least squares, and the maximum and minimum product of spacings methods. Model adequacy is evaluated using five goodness-of-fit criteria: the Anderson–Darling (AD) statistic, its right- and left-tail variants, the second-order left-tail AD statistic, and the Cramér–von Mises statistic. An extensive simulation study is conducted to thoroughly evaluate and compare the performance of the proposed estimators while maintaining a fixed total number of observations across both sampling schemes. The practical relevance of the proposed methods is further illustrated through an application to a real dataset consisting of 69 carbon fiber specimens, with tensile strength measurements (in GPa) recorded at a gauge length of 20 mm. The numerical results demonstrate that estimators based on RSS consistently outperform their SRS counterparts across all considered performance measures, including mean squared error, bias, and mean absolute relative error. Overall, the findings highlight the advantages of employing RSS for parameter estimation of the HLIRD, particularly due to its superior efficiency in small-sample scenarios.

Mathematical modeling plays a key role in understanding and optimizing transport system operations under uncertain and dynamic conditions. This study proposes a data-driven predictive framework for estimating passenger-accepted vehicle occupancy, addressing a critical gap in transport system planning under public health-related constraints. Using data from a structured survey conducted across seven Southeast European countries (N = 476), the study integrates statistical analysis and machine learning approaches to model acceptable occupancy levels across multiple transport modes, including passenger cars, taxis, tourist buses, and public buses. The problem is formulated as a predictive mapping between multidimensional input variables and occupancy acceptance levels, modeled using both probabilistic and nonlinear function approximation methods. The results highlight that age, gender, and area of residence are the most significant determinants of occupancy acceptance, while education level has limited predictive relevance. Furthermore, a multi-layer feedforward artificial neural network is developed to capture nonlinear relationships between variables, achieving strong predictive performance (minimum MSE = 0.0089). The main contribution of this research lies in linking behavioral data with predictive modeling to quantify acceptable occupancy thresholds and support realistic simulation of passenger responses in crisis conditions. The proposed modeling framework contributes to transport system planning, enabling data-driven capacity management, enhanced safety strategies, and improved resilience of passenger transport operations.

Amid the global transition to carbon neutrality, tidal current energy has become a strategic sustainable energy resource due to its high predictability, power density, and environmental compatibility. Horizontal-axis turbines show great potential for marine energy harvesting, yet the large-scale commercialization of tidal turbines is severely hindered by complex wake dynamics and the lack of reliable, efficient prediction tools for out-of-distribution (OOD) operating conditions. Traditional high-fidelity CFD methods are computationally prohibitive for engineering optimization, while conventional data-driven surrogate models suffer from poor extrapolation performance, extrapolation collapse near training parameter boundaries, and the absence of uncertainty quantification. To address these bottlenecks, this study focuses on the OOD extrapolation of wake flow prediction across tip speed ratio (TSR) distributions for a single horizontal-axis tidal turbine. A CFD-generated spatiotemporal benchmark dataset is constructed for comparative OOD evaluation across various TSR conditions with 9504 total samples. A novel physics-constrained Fourier neural operator framework named TSR-FNO is proposed to improve OOD generalization. The model integrates TSR–Lipschitz regularization to suppress extrapolation collapse and Monte Carlo Dropout to provide reliable uncertainty estimation. Extensive experiments demonstrate that the proposed method effectively reduces prediction error in unseen TSR regimes, mitigates performance degradation in far-field extrapolation, and produces well-calibrated uncertainty estimates consistent with actual prediction confidence. This work provides a data-driven surrogate modeling strategy for fast and reliable wake prediction on a common CFD-generated benchmark, supporting the efficient design, array layout optimization, and engineering deployment of tidal current energy systems.

Numerous applications from electrical engineering and mechanical structures are mathematically modeled using dynamical systems theory. Our paper concerns the behaviors of a 3D dynamic system in terms of damped or periodical oscillations and asymptotic representation, considering the dependence on three physical parameters. This system is explicitly integrated via a smooth-function solution of a third–order nonlinear differential equation, which means that the obtained exact parametric solutions describe a heteroclinical orbit. The modified Optimal Parametric Iteration Method (mOPIM) is used to study the influence of the physical parameters. The advantages of the applied method include the small number of iterations due to due to the appropriate choice of auxiliary convergence control functions. The mOPIM solutions are in good agreement with the corresponding numerical results and this aspect is highlighted qualitatively by figures and quantitatively by tables, respectively, in this work. The accuracy of the obtained solutions is assessed via a comparison with the OPIM method and the iterative solutions using 5–8 iterations, via an iterative method. A qualitative analysis of errors is performed.