Against the backdrop of the ongoing green and low-carbon transition and rising supply chain security risks, firms’ green transformation is not necessarily accompanied by a simultaneous improvement in resilience. To examine the diffusion mechanisms of the green and high-resilience (G-R) strategy among firms and the associated policy boundaries under green constraints, this study develops a two-level Stackelberg-evolutionary game model in which the government makes the initial policy decision and the firm population subsequently evolves. Closed-loop capability is modeled as a variable jointly influenced by regulation and population adoption. Stability analysis and comparative statics characterize diffusion thresholds, while a prior distribution over the initial adoption state is used to evaluate long-run expected welfare. The results identify three evolutionary regimes: low-adoption lock-in, bistability, and diffusion toward high adoption. Closed-loop capability increases the relative payoff of the green and high-resilience strategy by reducing the net equivalent transition burden and improving resilience benefits, thereby lowering the internal diffusion threshold within bistable regions. However, when the G-R strategy retains a baseline payoff disadvantage at zero adoption, finite increases in pure population feedback cannot eliminate the local stability of the low-adoption state. Provided that all four distinct boundaries between evolutionary regimes exist and lie within the feasible policy domain, a positive target probability of reaching high adoption corresponds to a regulatory interval with both lower and upper bounds under a uniform prior. Diffusion reachability and welfare improvement do not necessarily coincide: among fixed-regulation scenarios that all achieve full reachability of high adoption, higher regulatory intensity may still yield lower long-run expected welfare. Standardized scenario analysis using electric vehicle battery recycling as a real-world reference further shows that, as capability and cost conditions vary, welfare-maximizing regulation can lie at the left boundary of the full-reachability interval, within that interval, or at zero regulation. Changes in the prior distribution can also shift the welfare optimum into a bistable region without altering the stability boundaries. These findings indicate that regulatory intensity should be aligned with existing capabilities and the distributional characteristics of the initial adoption state. Policy design should account for the development of the closed-loop capability base and the effciency with which regulation translates into capability improvements, while evaluating strategy diffusion and welfare improvement separately with due consideration of real resource costs.

Aggregate lifetime data record the number of complete failure lifetimes and their sum, and can be used for reliability inference when individual lifetimes are not separately recorded. Building on existing moment estimators, this paper investigates their inferential properties when aggregation sizes may vary randomly across systems. Strong consistency of the lifetime mean and variance estimators is established. Joint asymptotic normality is then derived under two sampling frameworks: a conditional framework given the aggregation-size sequence and an unconditional framework with random aggregation sizes. Finite-sample covariance matrices are also obtained under both frameworks, and their relationships with the corresponding asymptotic covariance matrices are clarified. An aggregation-size imbalance index is further introduced, and its effect on the precision of lifetime variance estimation is shown to depend on the excess kurtosis of the lifetime distribution. Monte Carlo simulation results are generally consistent with the theoretical asymptotic covariance formulas and demonstrate that the four confidence-interval construction methods considered in this study exhibit varying degrees of undercoverage in very small samples. Finally, a case study illustrates the implementation of the proposed inference procedure.

To address the high computational complexity and storage costs of support vector machine (SVM) training in large-scale data scenarios, this paper proposes an accelerated SVM algorithm based on space-filling design and hierarchical Thompson sampling, termed TSSVM. The proposed method first partitions the input space into a set of cells by space-filling design and regards each cell as a super-arm in a multi-armed bandit framework. Then, within each selected cell, training samples are treated as basic arms, and Thompson sampling is employed to adaptively select samples that are more likely to become support vectors. The reward is defined according to whether a selected sample becomes a support vector of the current subsample-based SVM. Forgetting factors are incorporated to adapt to the non-stationarity of support vector sets during iterations, and a stopping criterion based on the change of posterior means is developed. Theoretical properties are discussed from the perspective of probabilistic exploration. Numerical studies on simulated and real datasets demonstrate that TSSVM substantially reduces training time while maintaining classification accuracy close to that of the full-sample SVM. Compared with several existing subsampling and screening methods, TSSVM achieves a favorable balance between accuracy and computational effciency.

To examine how transmission during the ideation stage and renewed susceptibility after remission affect the population dynamics of adolescent non-suicidal self-injury (NSSI), this study develops an extended SEIR model with an exposed-state transmission weight and a re-susceptibility loop. Transmission from exposed individuals is treated as a hypothesis to be tested, while the feedback loop distinguishes renewed susceptibility, ideation formation, and behavioral onset. The next-generation matrix yields the basic reproduction number and its stage-specific decomposition. The analysis establishes equilibrium existence and local stability, global stability of the disease-free equilibrium, and uniform persistence of the active states. Analytical sensitivity and parameter scenarios distinguish effects on the invasion threshold from effects on endemic equilibrium levels. Under the baseline scenario, reducing the ideation-to-behavior transition rate mainly lowers the behavioral peak, whereas reducing the re-susceptibility rate mainly lowers the endemic equilibrium level. The model provides testable propositions on stage-specific transmission and feedback for subsequent parameter estimation and mechanism assessment using longitudinal data.

In this paper, we consider a second order primal-dual dynamical system with time scaling and Tikhonov regularization terms for solving convex-concave bilinear saddle-point problems. Under appropriate parameter settings, we not only establish the strong convergence of the solution trajectory of the dynamical system to the minimum-norm solution of the problem, but also derive the convergence of the velocity vector and the convergence rate of the primal-dual gap along the solution trajectory. Furthermore, through numerical experiments, we show the effectiveness and superiority of the obtained theoretical results.

Pricing data product transactions is an important component of promoting the market-oriented allocation of data factors. This paper incorporates the organizational boundary of data processing into the analytical framework of enterprise data product transaction pricing and examines the effects of different processing organization approaches on data quantity-quality level allocation, transaction pricing, and mode selection. By constructing two modes, namely, “internal processing- direct sales” and “outsourced processing-returned sales,” adopting an integrated utility function, applying the Stackelberg game and KKT conditions to solve for optimal decisions, and conducting numerical simulations and sensitivity analyses, the results show that: 1) Different processing organization approaches affect the optimal allocation of data quantity and quality levels by changing the data processing cost structure. The “internal processing-direct sales” mode is characterized by a larger data quantity and a relatively lower quality level, whereas the “outsourced processing-returned sales” mode is characterized by a smaller data quantity and a higher quality level. The two modes result in similar optimal sales prices through compensatory allocation between data quantity and quality levels. 2) An increase in the number of consumers and a higher level of consumer sensitivity increase the optimal data quantity, sales price, and enterprise profit, while increases in processing costs and the development profit margin reduce enterprise profit. 3) An enterprise’s choice of data processing organization approach depends on the relative profits of the two modes, and fixed costs, internal and external processing costs, and the development profit margin all give rise to corresponding mode-selection boundaries. This paper provides a theoretical basis for enterprises to select appropriate processing organization approaches and formulate transaction pricing strategies according to their data resource endowments and digital processing capabilities.

This paper aims to investigate the stability of semi-infinite vector optimization problems under general ordered sets, which are not required to be convex sets or cones. Firstly, utilizing relevant properties of recession cones and D^∞-lower semicontinuity of the constraint function g₀ with respect to first variable, the closedness of the constraint set mapping was obtained. Secondly, by virtue of the strict natural quasi D^∞-convexity of g₀ with respect to first variable and the Slater condition, the Berge lower semicontinuity of the constraint set mapping was established. Next, under functional perturbations of the constraint set, the Painlevé-Kuratowski convergence of the constraint sets was discussed. Finally, by employing the closedness and the Berge lower semicontinuity of the constraint set mapping as well as the Painlevé-Kuratowski convergence of constraint sets, the Berge upper semicontinuity of the weak efficient solution mapping for semi-infinite vector optimization problems under general ordering sets was obtained, and an illustrative example was provided to verify the feasibility of the obtained result.

With the rapid expansion of distributed photovoltaic (DPV) installations, the dispersed sources of end-of-life modules and intensified competition from informal recycling channels have made recycling market regulation an important issue in implementing extended producer responsibility (EPR). Under the EPR framework, this study develops a Stackelberg game model that incorporates competition between formal and informal recycling channels. Three recycling modes—manufacturer recycling, system integrator recycling, and formal third-party recycling—are considered to examine the effects of a deposit-refund policy and a reward-penalty policy on equilibrium decisions and supply chain macro-level performance. The results show that: (1) the joint implementation of the two policies increases the total recycling quantity and formal recycling rate, generating a joint governance effect; (2) a higher deposit improves environmental benefits but suppresses economic benefits, whereas a higher reward-penalty coeffcient generally enhances environmental benefits and social welfare; (3) the three recycling modes exhibit differentiated advantages, with the system integrator recycling mode generally performing better in terms of economic benefits and social welfare; and (4) market conditions and user behavioral characteristics significantly affect the equilibrium outcomes, with retail price sensitivity, the deposit interest coeffcient, and dual-channel competition characteristics altering the performance of different recycling modes.

This paper deals with a Tikhonov regularized second-order inertial dynamical system with implicit Hessian damping for solving unconstrained convex optimization problems. Depending on the different settings of the Tikhonov regularization parameter, we not only achieve fast convergence rates for the velocity approaching zero and the objective residual along the generated trajectory, but also establish both weak and strong convergence properties of the solution trajectory. Furthermore, numerical experiments are conducted to corroborate the theoretical results.

Effcient operation of water-to-water transshipment systems at seaports relies on accurate transshipment forecasts. However, existing research mainly focuses on monthly port-level data and overlooks daily dynamics from inland tributaries, limiting fine-grained management and real-time scheduling. This study targets daily export volumes of containers transported via inland tributaries for two top-ten ports in China and proposes a hybrid forecasting framework combining double decomposition and CNN-GRU-Attention. We first extract multi-frequency intrinsic mode functions (IMFs) via ICEEMDAN and then apply a CPO-optimized VMD for secondary decomposition to mitigate mode mixing and high-frequency noise. Subsequently, a deep model integrating CNN, GRU, and attention mechanisms predicts sub-series at different frequencies, capturing short-term fluctuations, cyclical variations, and long-term trends. Empirical results demonstrate that the proposed framework significantly outperforms benchmark methods in prediction accuracy and robustness, especially under complex temporal patterns. The framework provides practical tools for optimizing resource allocation, strengthening intermodal coordination, and supporting smarter port infrastructure.

The ε-constraint method is a classical scalarization approach for solving nonconvex multiobjective optimization problems, but it does not generally guarantee the proper efficiency of the resulting optimal solutions. The flexible ε-constraint method introduces a nonnegative surplus variable for each objective other than the primary one. Eliminating these variables yields an equivalent formulation with nonsmooth positive-part penalty terms, which makes it difficult to apply smooth optimization algorithms directly. To address this issue, we use the Chen-Harker-Kanzow-Smale (CHKS) function to smooth the positive-part penalty terms and develop a CHKS-smoothed flexible ε-constraint scalarization method involving only the original decision variables. Sufficient conditions for the existence of optimal solutions to the smoothed scalarized problem are provided, and an outer-limit result for its optimal solution sets is established as the smoothing parameter tends to zero. Without imposing any convexity assumptions, we prove that an optimal solution to the smoothed scalarized problem is a weakly efficient solution of the original multiobjective optimization problem when the penalty weights are nonnegative, an efficient solution when the penalty weights are strictly positive, and a properly efficient solution when, in addition, the objective image is bounded. An explicit bound on the trade-off constant is also derived. Furthermore, for any properly efficient solution of the original multiobjective optimization problem, an approximate solution to the smoothed scalarized problem can be obtained by choosing appropriate penalty weights. Numerical results show that the proposed method provides good approximations of nonconvex or disconnected Pareto fronts and achieves better approximation quality and coverage than the classical and flexible ε-constraint methods on some test problems.

In physical modeling and engineering control, nonlinear partial differential equations (PDEs) describing complex dynamical behaviors are often approximated by linear models under assumptions such as small amplitude, weak field, or small temperature difference. For instance, the leading-order component of the Einstein field equations reduces to the Poisson equation under the Newtonian approximation of weak fields, low velocities, and quasi-static conditions; the one-dimensional quasi-linear vibrating string equation simplifies to the linear wave equation under the assumption of small transverse vibrations. However, such linear approximations based on physical intuition often lack rigorous mathematical justification. This paper reviews the research background on the linear approximations of nonlinear PDEs and their associated control problems, focusing on recent advances in controllability and optimal control problems of quasi-linear parabolic equations. Unlike conventional control theory, this theory requires not only steering the systems toward a prescribed target or achieving performance optimization, but also quantitatively estimating the discrepancy between the solutions to the nonlinear system and its linear approximation, provided that this error is of higher order with respect to the given data. This indicates that, within an acceptable error margin, the nonlinear control problem can be effectively approximated by the corresponding linear control problem, thereby enhancing computational efficiency, reducing computational cost, and facilitating control design via mature linear system theory to achieve more refined analytical results.

Recommender systems capture users’ behavior patterns and preferences by mining interaction data between users and items. Although existing methods have achieved promising recommendation performance, the rapid development of various Internet applications has led to increasingly diverse user behavior scenarios, making it difficult for traditional recommender systems to effectively model users’ cross-type behavior patterns. To address this challenge, this paper proposes a multi-behavior recommendation model based on behavior-type features and multi-view contrastive learning (BTMVC). First, a multi-behavior interaction graph is constructed, and a behavior type-aware graph propagation mechanism is used to extract user behavior preferences, generating base representations of users and items. Then, multi-view contrastive learning is established. An InfoNCE-based cross-type behavior feature contrastive learning module is constructed between target and auxiliary behaviors, learn common and distinctive features of users and items among cross-type behaviors. Meanwhile, target behavior feature contrastive learning is built based on behavior similarity, which overcomes the negative transfer in cross-behavior contrastive learning by contrasting representations of similar users and thereby optimizes target behavior representations. Finally, an objective function based on a non-sampling loss is constructed to optimize model parameters, and the final recommendations are generated using the optimized user and item representations. Experiments on two real-world datasets validate the effectiveness and robustness of the proposed method.

The dual-credit policy significantly influences the development of the new energy vehicle (NEV) industry, and collaborative R&D between internet companies and traditional automakers is a key pathway to facilitate industrial intelligent transformation. This paper examines collaborations between internet companies and traditional automakers, constructing a differential game model that incorporates technological R&D capabilities and corporate reputation. It compares equilibrium outcomes across three scenarios: Nash non-cooperation, Stackelberg master-slave competition, and cooperative collaboration. The results indicate: 1) Technology R&D levels exhibit a monotonically increasing trend and converge under all three scenarios, while corporate reputation trajectories show a pattern of initial rising and then falling. 2) Mutual benefits reach their peak under cooperative game scenarios, followed by Stackelberg master-slave game scenarios. 3) Increasing the new energy credit ratio directly elevates the CAFC penalty points incurred by traditional automakers for producing gasoline vehicles. The new energy credit coefficient exerts a significant incentive effect on R&D investment. 4) The incentive effect of cost sharing on traditional automakers’ R&D investment is nonlinear. Once the sharing ratio exceeds a certain threshold, the incentive effect becomes negligible and fails to stimulate higher R&D investment from traditional automakers. Finally, this paper provides managerial implications for the dynamic optimization of the dual-credit policy and the design of cost-sharing mechanisms in collaborations between internet companies and traditional automakers.

Generative artificial intelligence (GAI) has introduced a new paradigm for information generation and dissemination, while also posing challenges for disinformation governance. Therefore, it is of great significance to explore effective GAI disinformation governance strategies for fostering a healthy information ecosystem. This paper considers the multi-layer characteristics of the GAI industrial chain, and investigates the disinformation governance mechanism in four types of scenarios for the data service provider, model service provider and digital content platform based on differential game theory. By solving the equilibrium strategies of each subject under different models, the study analyzes the improvement effects on user perception levels and disinformation governance effectiveness, identifying key parameters in the GAI disinformation governance process. The results show that, in terms of model comparison, the collaborative cooperation model achieves the best disinformation governance outcomes, realizing Pareto optimality for the overall benefits of the information ecosystem, while both government regulation and bidirectional cost-sharing models can effectively improve governance effectiveness. In terms of parameter sensitivity, the impact of the data service provider’s vertical coordination coeffcient on its effort level is constrained by cost thresholds; the contributions of each subject to user perception levels differ significantly; improvements in information generation quality and disinformation elimination exhibit a synergistic amplification effect on user perception levels; the governance process faces technical bottlenecks and decay issues; and the collaborative cooperation model significantly enhances the risk resilience of all subjects.

This paper proposes an estimation framework for the population-average conditional quantile treatment effect (CQTE) by combining jackknife model averaging (JMA) and covariate balancing. To address specification uncertainty in conditional quantile functions, jackknife model averaging for quantile regression is implemented separately in the treated and control samples. To reduce extrapolation induced by imbalance in covariate distributions, entropy balancing weights are introduced and two estimators are considered: a G-formula estimator and an entropy-balancing reweighted estimator. When all candidate models are misspecified, we show that the JMA weights are asymptotically optimal in terms of within-group excess final prediction error (EFPE). When at least one correctly specified conditional quantile model is included and misspecified models are separated from the truth in risk, the total weight assigned to the correct model set converges in probability to one. We also derive an explicit bound for the CQTE target error and establish sufficient conditions for consistency. Simulations with $n=800$ show that the JMA weight on the correct model approaches one as the signal strengthens. When all models are misspecified, JMA and cross-validation model averaging yield lower EFPE and CQTE-estimation root mean squared error (RMSE) than information-criterion methods, although low within-group prediction risk does not necessarily eliminate structural bias in the CQTE target. An application to birthweight data illustrates the proposed framework.

In Vehicle-to-Everything (V2X) environments, traffic signal control reshapes traffic demand and turning distributions through vehicle guidance and drivers’ compliance, thereby creating a feedback relationship between control decisions and traffic uncertainty that is difficult to capture with conventional fixed-distribution models. To address this issue, this paper studies network traffic signal control under decision-dependent uncertainty. An explicit mapping among control decisions, behavioral responses, and conditional distributions is established, and a rolling-horizon two-stage stochastic programming model is developed based on a linear network-loading representation. To alleviate the computational burden caused by the joint expansion of probability regimes and scenarios, a regime-aware distribution-specific L-shaped decomposition method is employed. Finally, out-of-sample experiments and network instances of different sizes are used to evaluate the proposed approach. The results show that the method can effectively characterize control-induced distributional changes and performs well in reducing operational risk and mitigating congestion propagation, while the decomposition strategy helps reduce the computational burden associated with the joint expansion of regimes and scenarios.

The introduction of an internal carbon trading mechanism changes the cost and revenue structure of the supply chain, and thus affects operational decisions, emission reduction decisions and digital technology adoption. This study treats the supplier’s level of digital technology adoption as an endogenous variable and develops a supplier-led Stackelberg model, with the manufacturer as the follower, under two carbon trading scenarios: external carbon trading only and the coexistence of internal and external carbon trading. The model is used to compare the effects of internal carbon trading, emission reduction and digital technology investment costs, and internal and external carbon prices on supply chain decisions. The results show that an internal carbon trading mechanism can improve the supply chain’s emission reduction level and digital technology adoption only when internal trading brings clear cost savings and the internal carbon price is set properly. Under these conditions, product sales and supply chain profitability also increase. Higher emission reduction and digital technology investment costs reduce the manufacturer’s emission reduction effort and the supplier’s digital technology investment, leading to lower product sales and lower profits for supply chain members. A higher internal carbon price increases product sales, emission reduction, digital technology adoption and the manufacturer’s profit, but its effect on the supplier’s profit depends on the manufacturer’s surplus carbon allowances. In addition, a higher external carbon price promotes the supply chain’s low-carbon and digital transformation only when the internal carbon price exceeds a critical threshold. These findings provide theoretical support for the design of hybrid carbon trading mechanisms and for firms’ investment decisions in low-carbon and digital technologies.

To investigate long-term epidemic dynamics under demographic turnover, we formulate a model structured by chronological age and infection age that incorporates births and natural deaths. By reformulating the system linearized at the disease-free equilibrium as a renewal equation for new infections, we derive a Volterra integral equation governing the production of newly infected individuals. This formulation yields a next-generation operator $\mathcal{K}$ with an explicit integral kernel. Under suitable regularity and boundedness assumptions, we prove that $\mathcal{K}$ is a positive compact operator and define the basic reproduction number as $\mathcal{R}_0=r(\mathcal{K})$. We further establish a relation between $\mathcal{R}_0$ and the spectral properties of the linearized system. If ($\mathcal{R}_0<1$, the disease-free equilibrium is globally asymptotically stable in the feasible state space, and the infection eventually dies out. If $\mathcal{R}_0>1$, the infection is uniformly persistent, provided that the solution semiflow is asymptotically smooth and the invariant sets on the boundary satisfy the required repelling condition. Numerical simulations agree with these threshold results, which provide a spectral criterion for disease extinction and persistence under demographic turnover.

Against the backdrop of the global energy transition and intensifying competition in photovoltaic technologies, cross-border innovation collaboration has become an important means of integrating heterogeneous knowledge resources and advancing core technologies in the photovoltaic industry. This study uses invention patents on photovoltaic cell structures, material systems, and key manufacturing processes from the IncoPat database to represent core technological innovation in the photovoltaic industry, and constructs applicant- and country-level innovation collaboration networks from co-application ties. A temporal exponential random graph model (TERGM) integrates endogenous network structures—including tie persistence, degree distribution, open two-paths, and local closure—with country attributes and bilateral cooperation conditions to examine the dynamic formation of cross-border innovation collaboration in the photovoltaic industry. The results show that core technological innovation in the global photovoltaic industry evolved from early dispersed exploration through global expansion and deepening Asia-Pacific participation to a recent phase of structural adjustment. TERGM estimates indicate significant positive associations for tie persistence and open two-paths, revealing the coexistence of path dependence and structural embeddedness. Lagged national patenting in core photovoltaic technologies, geographic contiguity, and a common offcial language are stably positively associated with current collaboration, whereas technological similarity, the depth of regional trade agreements, and political distance show no stable independent associations. Robustness tests and goodness-of-fit diagnostics based on 1,000 simulated networks indicate that the annual baseline model is broadly stable in both parameter estimates and structural fit. By placing structural dependence, country attributes, and bilateral conditions within a unified dynamic network framework, this study provides evidence on the dynamic evolution of the global photovoltaic industry innovation collaboration network.

This paper systematically reviews recent research results on parameter identification of generalized linear time-invariant dynamical systems with a Linear Fractional Transformation (LFT) structure, from three perspectives: parameter identifiability, parameter sloppiness, and parameter identification methods. For parameter identifiability, both global and local aspects are studied. For global identifiability, with frequency-domain experimental data, necessary and sufficient conditions based on numerical matrix rank tests are established under full-rank assumptions on transfer function matrices, together with a recursive frequency point search algorithm; with time-domain experimental data, conditions based on finite-dimensional bilinear equations are derived, which under an orthogonality assumption further reduce to a full rank test on polynomial matrix coefficient matrices. For local identifiability, necessary and sufficient conditions for generic local identifiability are derived with computationally feasible verification algorithms. For parameter sloppiness, absolute and relative sloppiness indices are introduced for both frequency-domain and time-domain data, reducing the computation to generalized eigenvalue problems with explicit formulas. For the parameter identification method, by introducing a class of excitation signal generating systems for continuous-time LTI systems, the intrinsic connection between the steady-state response and tangential interpolation of the transfer function matrix is revealed. A two-step identification method combining nonparametric and parametric estimation is proposed, and asymptotic unbiasedness and consistency are rigorously proved under persistent excitation conditions. The method supports nonuniform slow sampling and enables direct identification of continuoustime systems, offering strong engineering applicability. Finally, a numerical example is presented to validate the identification procedure for estimating the parameters characterizing the system response from nonuniformly and slowly sampled outputs. These studies provide a systematic theoretical framework and computational tools for parameter identification of continuous- and discrete-time dynamical systems with LFT structures.

For complex dynamical systems, safety is an important prerequisite in many practical scenarios. The application fields of safety-critical control include aircraft control, robotic control, and autonomous driving. For switched and hybrid systems, extensive theoretical investigation with practical applications has been a hot topic in recent years. In this work, we address the safety-critical stabilization problem for the general class of discrete-time switched linear autonomous systems. By assuming that the safe region is full-dimensional, compact, convex, and originsymmetric, we could induce the Minkowski function as a state norm. With this norm, we are to estimate the largest norm overshoot for each state on the upper unit sphere. In this way, we could approximate the safe initial domain that any state trajectory initiated from the domain is safe. From a computational viewpoint, the calculation of the largest overshoot plays a crucial role. Fortunately, by means of the pathwise state feedback switching strategy, we could approximate the safe initial domain with any pre-assigned accuracy at the cost of high computational load. A numerical example is presented to validate the design scheme.

Platform data sharing is a key instrument for unlocking the value of data elements, yet it faces the dual challenges of security risks and sharing inefficiency. Existing governance strategies often adopt a one-size-fits-all approach, which overlooks the heterogeneity of data granularity characteristics, namely update frequency, value density, and risk attributes. Based on these problems, this study constructs a Multi-Agent simulation model of data sharing platform governance from the perspective of information economics. A Particle Swarm Optimization algorithm is first employed to search for the optimal initial proportion distribution of shared data, thereby classifying platforms into coarse-, medium-, and fine-granularity-dominated types. For each type, dynamic learning strategies for deposit amounts and penalty intensity, together with differentiated access and exit rules, are designed as the core governance instruments. Simulation experiments are conducted in MATLAB. The following results and policy suggestions can be obtained. (1) Coarse-granularity platforms exhibit a dual-decline pattern of deposit and penalty intensity, and a trust governance model with low access and low exit thresholds is optimal. (2) Mediumgranularity platforms display an asymmetric pattern of declining deposit and stable penalty, and a flexibility governance model with flexible access-exit combinations is appropriate. (3) Finegranularity platforms demonstrate a scissors-gap pattern in which deposits slightly decline while penalty intensity continuously rises, and a strict screening model with low access and high exit thresholds is required. (4) Optimal governance strategies and mechanisms are systematically conditioned by platform granularity characteristics. It is suggested that government regulators and platform operators adopt differentiated governance modes according to granularity characteristics, so as to promote the efficiency and security of data sharing.

Emergency supplies reserves play an important role in disaster response and rescue operations. While existing literature mainly focuses on optimizing reserve quantities and choosing storage locations, the problem of quality degradation or obsolescence of emergency supplies due to prolonged storage has been overlooked. A practical solution to this problem is the periodic maintenance and updating of emergency supplies. However, non-compliance by storage facilities is common, and making regular inspections by regulatory authorities is necessary. In this study, we develop a game-theoretic framework to analyze the strategic interactions between the government and reserve repositories under disaster uncertainty, proposing inspection and maintenance strategies based on their different goals. The results show that governments should adjust funding to better align incentives with reserve repositories under various emergency scenarios. Higher penalty costs require more funding to encourage proactive maintenance, while lower penalty costs allow for reduced funding. Furthermore, decisions are also influenced by disaster risks and inspection costs. This research presents a game-theoretic coordination model that provides a clear basis for optimal resource allocation and adaptive regulatory policies.

Crude oil prices are influenced by numerous factors and exhibit high volatility and pronounced nonlinearity. To improve the forecasting accuracy of Shanghai crude oil futures prices, this study proposes a dual spatiotemporal attention autoencoder-Transformer model. The framework separately feeds market microstructure data, commodity and financial market data, and uncertainty data into three independent dual spatiotemporal attention autoencoders. In each autoencoder, the first spatiotemporal attention mechanism is placed before the encoder to assign different weights to the input data and identify their predictive value. The encoder-decoder structure then extracts more stable and informative features. A second spatiotemporal attention mechanism is introduced after the decoder and combined with a feature selection module to retain high-value features and remove low-value ones. Finally, the effective features extracted by the three autoencoders are concatenated and aligned before being fed into a Transformer for integrated forecasting. The empirical results show that the proposed model significantly outperforms all benchmark models in forecasting Shanghai crude oil futures prices. Its robustness is further confirmed through the Diebold-Mariano (DM) test, alternative training and test set splits, generalization tests, rolling-window tests, and ablation experiments. This study provides a new methodological framework for crude oil price forecasting and offers practical support for investors' risk management.

This paper constructs a stochastic SIHR epidemic model with regime-switching and mean-reverting Ornstein-Uhlenbeck (OU) process. The model can capture the evolution of isolated populations, the switching of prevention and control policies, as well as the mean-reverting stochastic disturbances, thereby better aligning with the complex stochastic characteristics of real-world epidemic transmission. In this paper, we prove the existence and uniqueness of a global positive solution and further obtain sufficient conditions for the extinction and persistence of the disease.Analysis indicates that increasing the confirmed isolation rate can effectively curb epidemic spread, and illustrates how the parameters of OU process and Q-matrix of regime-switching regulate disease transmission. Numerical simulations verify our theoretical findings and visualize the complementarity between two extinction criteria. This work enriches the theoretical framework of mean-reverting stochastic epidemic models with regime-switching and provides a theoretical basis for epidemic prevention decision-making.

This paper investigates the time-consistent reinsurance and investment problem with delay effect and inside information for an insurer. The insurer is allowed to purchase proportional reinsurance and invest its wealth in a financial market consisting of one risk-free asset and one risky asset. Both the insurer's surplus process and the price process of the risky asset are characterized by jump-diffusion models, where the two jump counting processes are correlated through common shocks. The insurer is assumed to possess inside information regarding future insurance claims from the beginning of the transaction. Moreover, taking into account the influence of historical performance, we describe the wealth process by the stochastic delay differential equation. Under dynamic mean–variance criterion, the corresponding extended Hamilton–Jacobi–Bellman (HJB) system of equations is established and solved by applying stochastic control theory. Consequently, the explicit expressions for the optimal time-consistent reinsurance and investment strategies and the optimal value function are derived. Finally, the numerical example is provided to analyze the effects of key model parameters on the optimal strategies and the optimal value function.

This paper studies the long-time asymptotic behavior of solutions to a star-shaped wave network system with locally degenerate Kelvin-Voigt damping. By means of frequency domain analysis, estimates of the decay rate for the system solutions are established for two distinct cases. First, for a network conducted by one undamped wave and several damped waves joined at a common node, it is shown that the decay rate is fully determined by the minimum degeneracy order of the damping coefficients. Furthermore, the investigation is extended to the general configuration where multiple undamped waves and multiple damped waves are coupled at a common vertex. Based on the properties of Diophantine approximation in number theory, under suitable conditions, an explicit decay rate of solutions to the network system is derived for this general model.

Under the dual background of centralized volume-based drug procurement and the continuous improvement of the medical insurance payment system in China, pharmaceutical retailers’ procurement mode has gradually shifted from single-source centralized procurement to dual-source procurement. Accounting for supply-side cost heterogeneity and demand-side perceived quality heterogeneity between originator drugs and centralized-procurement generics, along with the effect of insurance subsidies on patient purchasing behavior, this paper develops a three-echelon pharmaceutical supply chain Stackelberg game model consisting of the government, pharmaceutical suppliers, and competing pharmaceutical retailers. The study investigates retailers’ optimal procurement strategies under different medical insurance subsidy policies and their impacts on supply chain members’ profits, patient surplus, and social welfare. The results show that: 1) without medical insurance subsidies, retailers’ equilibrium procurement strategies depend on the trade-off between the production cost of originator drugs and the perceived quality difference of drugs. When the production cost of originator drugs is relatively low, retailers tend to adopt dual-source procurement, and a larger perceived quality difference further expands the applicable range of this strategy;2) medical insurance subsidy policies significantly affect retailers’ equilibrium strategies. When subsidies are provided only for centrally procured drugs, retailers tend to abandon the original drug market. When both types of drugs are subsidized, retailers choose different procurement modes based on the trade-off among subsidy intensity, production costs, and inter-retailer competition effects; 3) government subsidies do not necessarily improve social welfare, and excessive subsidies may intensify retailer competition and lead to a prisoner’s dilemma; 4) wholesale quantity discounts for centrally procured drugs strengthen retailers’ incentives to participate in centralized procurement, but such discounts should be coordinated with subsidy policies to avoid social welfare losses.

To address structural consensus insuffciency in social-network large-scale group decision-making, where opinions tend to stabilize within communities while remaining substantially divergent across communities, a weighted Louvain communitydetection and key-expert-driven hierarchical consensus method is proposed. First, a normal quantile-based semantic scale is employed to represent the non-equidistant semantics of probabilistic linguistic terms. Preference-content and evaluation-behavior information are extracted from expert assessments and integrated with social relationships to construct comprehensive edge weights, based on which expert communities with both network cohesion and negotiation compatibility are identified. Second, key experts are selected according to preference representativeness, intra-community connectivity, and inter-community connectivity, while different consensus states are diagnosed by jointly measuring intra-community stability and overall group coordination. Local repair is performed when some communities are internally unstable. When structural consensus is insuffcient, key experts undertake inter-community coordination, and ordinary members follow them within their respective communities, thereby forming a state-driven hierarchical feedback mechanism. The consensus-improvement and convergence properties of the feedback process are further analyzed theoretically. A case study, comparative experiments, and sensitivity analyses verify the rationality and effectiveness of the proposed method in community identification, consensus coordination, and result stability. The method therefore provides a structurally interpretable approach to reaching consensus under structural consensus insuffciency in social-network large-scale group decision-making.

Permutation polynomials have been widely used in cryptography, coding theory, combinatorial design, and other areas of mathematics and engineering. By applying the AGW criterion and determining the number of solutions to certain equations over finite fields, we propose five classes of permutation polynomials with special types. Compared to the known works, this paper not only characterizes more relaxed permutation conditions but also obtains new permutation polynomials. Specifically, we construct two classes of permutation polynomials with the form $\sum\limits_i(x^{2^m}+x+\delta)^{s_i}+x$ over $F_{2^{3m}}$ and three classes of permutation polynomials of the form $\sum\limits_i(x^{p^m}-x+\delta)^{s_i}+L(x)$ over $F_{p^{2m}}$, respectively. Finally, we formally prove that the permutation polynomials proposed in this paper are not quasi-multiplicatively equivalent to any currently known permutation polynomials.

The hull of a linear code plays an important role in determining the permutation equivalence of two linear codes and in characterizing the automorphism group of a linear code. Moreover, as an important class of self-orthogonal codes, the hull of a linear code can also be used to construct entanglement-assisted quantum error-correcting codes. Determining the parameters of the hull of a linear code is an important problem in coding theory. The paper investigates the hulls of negacyclic codes over $\mathbb{Z}_{2^a}$ of even length. The generator polynomials and the $2$-dimensions of the hulls of negacyclic codes over $\mathbb{Z}_{2^a}$ are given. The number of negacyclic codes over $\mathbb{Z}_{2^a}$ with a prescribed hull $2$-dimension is determined. An explicit formula for the average hull $2$-dimension of negacyclic codes of length $N$ over $\mathbb{Z}_{2^a}$ is derived. The upper and lower bounds for the average hull $2$-dimension are explored.

For linear discrete systems subject to deception attacks involving system perturbations, measurement noise, and unknown faults, a joint state and fault estimation method based on zonotopes is proposed. First, by analyzing the intrinsic characteristics of deception attacks, the zonotope boundary for deception attack signals is estimated, and this method can relax the non-negativity condition required in classical interval observer design. Second, based on the augmented system for state and fault estimation, a set of state variables for a Luenberger-type observer is formed, and through algebraic operations, an estimating set that envelops both the system state and faults is generated. Simultaneously, the optimal gain matrix for the ensemble estimation optimization criterion is obtained based on the minimum volume criterion of the zonotope. Finally, simulation results demonstrate that the proposed set-membership estimation algorithm accurately encapsulates the true state and system faults under attack conditions.

This paper proposes a novel adaptive control scheme for a one-dimensional unstable heat conduction equation with unknown control coefficients. Firstly, a new state observer is designed to estimate the system state, and a corresponding update law is constructed to estimate the reciprocal of the control coefficients. Unlike traditional state observers, the newly designed state observer in this paper relies on a specific control decomposition form, which eliminates the presence of both the unknown control coefficients and their estimates in the state observer. Consequently, the control design problem for the controlled object can be transformed into a control design problem for the state observer, effectively overcoming the challenges posed by the unknown control coefficients. The resulting closed-loop system is nonlinear, and its well-posedness and stability are proven mathematically. Additionally, some theoretical results are visually validated through numerical simulations. This paper is dedicated to commemorating the 90th birthday of Academician Chen Hanfu. We have selected this topic to celebrate Academician Chen's outstanding achievements in adaptive identification theory for stochastic systems.

Incorporating designated retail pharmacies into the outpatient pooling scheme is a critical part of the reform of the employee medical insurance system. This policy allows patients to obtain reimbursement for prescription drugs purchased at designated retail pharmacies, with the reimbursement rate aligned with that of primary healthcare institutions. Based on a pharmaceutical supply chain comprising a retail pharmacy, a hospital, and a drug supplier, this paper develops generalized Nash bargaining models, compares profits, consumer surplus, and social welfare under three scenarios: non-participation in the outpatient pooling scheme, participation in the outpatient pooling scheme without centralized procurement, and participation in both the outpatient pooling scheme and centralized procurement. Based on these comparisons, we derive the pharmacy’s optimal strategy from the perspectives of pharmacy profit, consumer surplus, and social welfare. The findings reveal that from the perspective of pharmacy profit, the pharmacy prefers to participate in the outpatient pooling scheme without centralized procurement only when its market share, additional unit operational cost, and price coefficient are all relatively large. From the perspective of consumer surplus, the pharmacy prefers to participate in both the outpatient pooling scheme and centralized procurement only when it has a relatively large market share and a relatively low operational cost. From the perspective of social welfare, the pharmacy prefers to participate in both the outpatient pooling scheme and centralized procurement only when the reimbursement rate or the price coefficient is relatively large. Regardless of whether pharmacy profit, consumer surplus, or social welfare is considered, non-participation in the outpatient pooling scheme is never the optimal strategy for the pharmacy. Furthermore, the equilibrium outcomes and their relative rankings across the three scenarios are jointly determined by the reimbursement rate, bargaining power, price coefficient, operational cost, and market share. The findings provide decision references for pharmacies’ operational model choice and offer theoretical references for improving their operational performance.

Since Robbins and Monro proposed stochastic approximation algorithms in the 1950s, such algorithms have found wide applications in systems and control, statistics, machine learning, and other fields. This paper focuses on stochastic approximation algorithms with extended truncation developed over the past three decades. It first reviews the historical developments of centralized stochastic approximation algorithms, including the probabilistic methods and ordinary differential equation (ODE) approaches for convergence analysis of stochastic approximation, as well as the trajectory-subsequence method for stochastic approximation with extended truncation. An illustrative application of stochastic approximation with extended truncation to recursive principal component analysis is then provided. Finally, recent advances of such algorithms in networked and distributed settings, namely distributed stochastic approximation algorithms with extended truncation, are presented.

This paper investigates distributed online aggregative games with time-varying constraint sets. First, the one-way Hausdorff distance is introduced to characterize the variations of constraint sets between consecutive time instants. Second, a distributed online mirror descent algorithm is developed based on the Bregman divergence, where the effect of gradient noise is also considered. Under standard assumptions including joint connectivity of communication topologies and strong convexity of the mirror function, we further derive a sublinear upper bound on the expected dynamic regret for the proposed algorithm. Finally, numerical simulations are conducted to verify the effectiveness of the proposed algorithm.

Driven by the demands of driving safety, traffic efficiency, and energy conservation, tracking control for unmanned vehicle platoons has garnered extensive attention. In practice, complex road and airflow conditions expose vehicles to strong nonlinearities, rendering accurate modeling challenging. Existing approaches typically rely on linearized models or assume bounded lumped disturbances and their derivatives—assumptions difficult to verify in real-world scenarios. To address these issues, this paper proposes a longitudinal active disturbance tracking control scheme based on an extended state observer (ESO) and saturation constraints. The ESO is employed to online estimate and compensate for unmeasurable system states and lumped disturbances in the feedback control loop. A saturation mechanism is introduced to prevent system divergence induced by high-order nonlinearities under large ESO gains. Via proof by contradiction, the global uniform boundedness of the closed-loop system is established, and both observation and tracking errors can be made arbitrarily small by increasing the ESO gain.Finally, numerical simulations and comparative analyses with the adaptive control and sliding‑mode control methods are carried out to verify the effectiveness and superiority of the proposed method.

Against the backdrop of the national policy objective of ``effectively preventing and mitigating risks faced by high-quality leading real estate enterprises,'' this study focuses on two key issues: the rapid transmission of risks among real estate enterprises and the multi-channel diffusion mechanisms underlying such risk propagation. We constructed a high-dimensional dynamic risk spillover network covering 123 real estate companies listed on the Shanghai and Shenzhen A-share markets from 2007 to 2023. This network identifies its multi-risk-center structure and reveals the dynamic spatiotemporal patterns of risk-originating nodes. Our findings reveal: (1) Real estate network risk spillover exhibits both a one-month cycle of direct financial market shocks and an ultra-short chain transmitting through financial channels to the macroeconomy within three months; (2) The network displays a decentralized structure——rising spillover intensity coincides with a significant decline in network concentration, indicating systemic risk originates from dispersed contributions by non-hub nodes, fundamentally conflicting with traditional finance's ``center-periphery'' risk models; (3) Further integration of block models and the Fruchterman-Reingold algorithm identifies a key risk-originating mechanism: bidirectional risk spillover clusters (averaging 26% of total nodes) serve as risk-emitting nodes, exhibiting dual spatiotemporal dynamics——a 61.5% interannual turnover rate in node sequence and 22% of nodes distributed at network peripheries with cross-regional linkage; (4) Within-industry risk spillovers in both the real estate sector and financial subsectors are stronger than cross-industry spillovers, but bidirectional risk spillovers between the real estate sector and financial subsectors remain at relatively high levels during most periods, with the real estate sector acting as a net risk transmitter to the financial sector as a whole. Regression analysis confirms that the bidirectional risk-spillover cluster is the primary contributor to risk spillovers, generating multicenter concurrent diffusion of network risk through subsystem spatial decoupling, homogeneous node responses, and the external coupling field. In light of the ``dispersed outbreaks and convergent transmission'' mechanism of risk among real estate firms, this paper proposes four regulatory approaches for supervisory authorities: weekly risk monitoring based on the Elastic-Net-VAR framework, targeted supervision of bidirectional risk-spillover clusters, enhanced cross-regional coordinated risk prevention and response, and a differentiated risk-monitoring framework for the real estate sector and financial subsectors. The findings also provide empirical evidence for promoting a shift in real estate risk governance from scale-based control toward a prevention and control paradigm centered on network functions.

Jet engine turbine blades are responsible for converting high-temperature, high-pressure gas into mechanical energy, and their materials must be able to withstand extremely high temperatures. To analyze the cooling performance of turbine blades, existing methods typically construct finite element models of varying fidelity for numerical simulation. However, high-fidelity models are computationally time-consuming and expensive, and high-fidelity experiments can only select a small number of experimental points for constructing a surrogate model, so nested experimental designs are commonly adopted. In view of the fact that generalized Latin hypercube designs often provide better predictive performance in many cases, this paper proposes a generalized nested space-filling design for constructing finite element surrogate models. The proposed design places more design points near the boundary of the experimental region and further provides a corresponding construction algorithm framework. Results from both numerical simulation analysis and actual finite element simulations indicate that the proposed new design performs better in model prediction.