Disaster relief supplies are the core foundation for ensuring the basic survival needs of affected populations and supporting post-disaster reconstruction. The efficiency of their procurement and transportation directly impacts disaster response effectiveness. To address the limitations of dynamic responses, a tripartite game model involving the government, enterprises, and disaster victims is constructed to analyze the influence of time delay and trust on strategic decisions. Three operational modes are designed: decentralized decision-making without subsidies, decentralized decision-making with subsidies, and centralized decision-making. Optimal effort levels and equilibrium states are derived under these scenarios. Results indicate that: 1) Delays in the material procurement phase necessitate greater efforts from both government and enterprises, leading to postponed accumulation of supplies, which may result in material wastage; 2) Both subsidies and centralized decision-making contribute to the enhancement of rescue effectiveness. Subsidies can incentivize enterprises to increase input, but the government must dynamically adjust subsidy ratios to balance costs and benefits. Centralized decision-making, characterized by “high effort-high efficiency” while separating input and distribution but imposes higher demands on the speed of material procurement by both government and enterprises; 3) Under any mode, supply-demand mismatches and distrust among disaster victims reduce the level of effort from all three parties, and the phenomenon that is more pronounced under centralized decision-making. These findings provide a basis for designing dynamic subsidy policies, optimizing enterprise logistics capabilities, and implementing psychological interventions, contributing to the establishment of a resilient disaster relief supply chain system.

With the rapid development of the new energy vehicle industry, consumer adoption behavior has become a critical factor influencing the market diffusion of battery electric vehicles (BEVs). This study systematically analyzes key variables such as sales volume, vehicle stock, life cycle cost, and overall vehicle performance from the perspectives of micro-level consumer preferences and the macro-level policy environment. Based on the collection and statistical analysis of industry data, a forecasting model is constructed to provide a scientific projection of future market development. A comparative analysis with conventional fuel vehicles is further conducted to identify the major proportional factors constraining adoption intention. Moreover, a fuzzy logic control model is introduced, with corresponding control rules and membership functions established to dynamically simulate consumer adoption intentions for BEVs. The simulation results indicate that, alongside the continuous growth of BEV sales and stock, life cycle costs exhibit a significant downward trend while overall vehicle performance steadily improves, leading to a progressive increase in consumer adoption intention—from 0.11 in 2011 to 0.85 in 2031. By validating the simulation results against existing research findings and industry development trends, this study proposes policy recommendations aimed at promoting the healthy development of the BEV market and enhancing comprehensive vehicle performance, thereby providing both theoretical support and practical reference.

This paper proposes a class of spatial varying-coefficient autoregressive models with autocorrelated errors. The proposed framework simultaneously incorporates spatial correlation in the response variable and spatial autocorrelation in the error term within the spatial varying-coefficient setting, thereby jointly capturing both heterogeneity and dependency structures in spatial data to better reflect their complex characteristics. To overcome the endogeneity issue of the model, an effective three-stage estimation method is proposed that integrates local linear estimation, generalized method of moments (GMM), and profile least squares estimation methods, and the asymptotic properties of the estimators are derived. The Monte Carlo simulation results indicate that the estimation method for the studied model demonstrates good efficacy under finite samples. Empirical analysis based on the Boston housing price data further shows that this model significantly enhances the explanatory power of spatial economic phenomena.

In real applications, high-dimensional data are often accompanied by resampling noise, outliers and class imbalance problems, which pose severe challenges to machine learning algorithms such as support vector classification models. Although fuzzy support vector machine (FSVM) has demonstrated certain potential in outlier suppression and class imbalance handling, it still has significant room for improvement: 1) FSVM fails to effectively reduce biases caused by resampling noise; 2) FSVM exhibits high sensitivity to redundant features. To address these issues, this paper proposes an affinity and transformed class probability-based fuzzy sparse geometric twin support vector machine (ATFSGTSVM). The model measures the within-class affinity of each sample via the least squares one-class support vector machine, and adjusts the weight distribution of imbalanced data to reduce the interference of outliers, noise, and class imbalance on classification performance, and incorporates the $l_0$ norm penalty to achieve feature selection and redundant feature elimination. Due to the non-convexity, non-smoothness and discontinuity of the $l_0$ norm penalty, the corresponding optimization problem is difficult to solve directly. Inspired by the recently proposed variable sorted active set algorithm, this paper designs the ATF-VSAS algorithm for efficient solution of this problem. Experimental results show that, compared with advanced models in recent years, ATFSGTSVM achieves optimal performance in high-dimensional imbalanced data scenarios with noise and outliers.

Feature selection is a critical stage in the data mining modeling process. However, when the data exhibits class imbalance, existing feature selection methods often prioritize retaining features beneficial for classifying majority class instances, consequently leading to suboptimal classification performance for minority class instances. Given that minority class instances frequently hold greater significance in fields such as healthcare and finance, we propose a multi-stage feature selection method combining the Grey Wolf Optimization algorithm-dubbed MFS-GWO (Multi-stage Feature Selection combining Grey Wolf Optimization). MFS-GWO contributes in two ways: First, it integrates Filter and Wrapper techniques, effectively reducing the solution space size during feature combination optimization. Second, MFS-GWO strengthens the penalty for misclassifying minority class instances within its fitness function, thereby addressing the problem of minority class feature loss caused by class imbalance. Experimental results on a series of imbalanced datasets demonstrate that the MFS-GWO method can effectively reduce redundant features in the data, and the selected features enhance the model’s ability to identify minority class instances.

This paper investigates the cluster consensus problem for first- and second-order multi-agent systems under directed graphs. In conventional multiconsensus studies, the system is partitioned into multiple clusters, where agents within the same cluster converge to an identical steady-state value. However, under non?spanning-tree topologies, the resulting cluster partition may depend on the coupling strengths (edge weights) among agents, leading to non-unique clustering results. To overcome the limitation imposed by coupling weights, this paper introduces the concept of topological clusters, which are independent of coupling strengths. The proposed cluster partition is solely determined by the system.s interaction topology and ensures intra-cluster state consensus without relying on specific coupling weights. Firstly, for first-order signed networks, initial cluster division is carried out by analyzing the structural balance of the nodes. Then, a normalization transformation is applied to equivalently convert the original system into a first-order system model with all positive edge weights. Based on this, the system characterizes the topological structural features of the clusters and analyzes the temporal evolution of dynamic patterns under signed network topologies, and the resulting conclusions are mapped back to the signed network, thereby obtaining necessary and sufficient conditions for a set of nodes to form a topological cluster. Secondly, the analytical framework for topological clusters is extended to second-order systems, and the corresponding formation conditions are derived. Finally, numerical simulations are provided to verify that the multi-consensus behavior of the above first-order signed network and the second-order system is determined solely by the interaction topology of the system.

As the population ages, the issue of caring for elderly individuals with disabilities has become increasingly prominent. Long-term care insurance, serving as the core economic mechanism to address this challenge, urgently requires breakthroughs in its precise pricing mechanisms. Addressing the limitations of traditional research—which relies on linear models like logistic regression for estimating state transition probabilities—this study innovatively constructs a composite modeling framework integrating interpretable ensemble learning with non-homogeneous Markov chains. First, a four-state health transition model incorporating comprehensive multidimensional capabilities was developed based on 2021 National Healthcare Security Administration documents and CLHLS data. Subsequently, by comparing the performance of five single-layer ensemble learners and introducing a two-layer Stacking strategy, the accuracy of state prediction was significantly enhanced. SHAP explainability analysis was employed to quantify the impact of key features. Finally, the predicted transition probability matrix was embedded into a non-homogeneous Markov chain actuarial model for premium rate determination. The study demonstrates that this approach more accurately captures disability risks and dynamic care needs, providing an explainable decision basis for long-term care insurance product design.

This paper deals with a class of primal-dual dynamical systems with Hessian damping for solving strongly convex optimization. The existence and uniqueness theorem for the global strong solution of this system is first established. Subsequently, using Lyapunov analysis, some exponential convergence rates of the primal-dual gap, objective function residual and feasibility violation, as well as the strong convergence of the solution trajectory generated by the system are obtained. Furthermore, some numerical experiments are given to demonstrate that the system exhibits fast convergence and effectively reduces oscillation phenomena.

This paper focuses on the equilibrium analysis of a queueing system for two types of customers, incorporating catastrophe arrivals and partial removability. In this system, two types of customers arrive according to an exponential distribution. Upon the occurrence of a disaster, only the first portion of customers in the queue remain to be served, while the rest at the back leave immediately. The service rates for the remaining customers are subject to adjustment. Once the system completes serving these customers, it transitions into a maintenance state, during which the repair time follows an exponential distribution with a specified parameter. Based on the revenue-cost theory, we introduce a benefit function and perform equilibrium analysis for the customers. Additionally, when analyzing social welfare, both investment and construction costs are taken into account, leading to the formulation of an optimization problem aimed at identifying the comprehensive optimal strategy. We find that social welfare does not always increase with the number of customers retained after a disaster. Managers could weigh the construction costs against potential benefits and prudently stock emergency resources based on their capacity. Finally, numerical illustrations provide visual insights into how changes in various system parameters affect customer behavior strategies and social comprehensive benefits.

To provide scientific basis and strategic support for public opinion governance, this study investigates the dynamics and influencing factors of competitive information dissemination online. Integrating the theory of overlapping niches with online recommendation mechanisms, the SH2I3R competitive information propagation model is constructed. Micro-level Markov chain methods are employed for theoretical analysis to examine the propagation dynamics of competitive information within networks. Subsequently, the model's validity was validated through real-data fitting. Numerical simulations were conducted on WS small-world networks and BA scale-free networks to uncover intrinsic patterns of information propagation and analyze how key factors influence dissemination. Experimental results indicate that information propagation rate and credibility form the core of establishing dissemination advantages, while network topology, timeliness of release, and source node selection exert significant regulatory effects on propagation outcomes. Finally, based on experimental conclusions, this study proposes public opinion control strategies and effectiveness optimization strategies. These findings provide both theoretically profound and practically valuable references for government and relevant management departments to optimize public opinion control schemes and for information disseminators to enhance propagation effectiveness.

The implementation of corporate social responsibility (CSR) by e-commerce platforms has become an indispensable part of the practice of sustainable operation strategy, and has injected strong impetus into the whole e-commerce ecosystem and even the broader economic and social sustainable development. Meanwhile, the ecommerce platform not only acts as a crucial bridge linking merchants and consumers but also plays a vital role in addressing the financing challenges faced by manufacturing enterprises. Against this backdrop, this paper constructs a supply chain comprising a capital-constrained manufacturer and an e-commerce platform, considering two financing modes (bank financing vs. platform financing) under benchmark (nonCSR) and CSR implementation scenarios. Through Stackelberg game analysis, we reveal three key findings: 1) Under the non-CSR scenario, platform financing can achieve a “win-win-win-win” outcome for the manufacturer, e-commerce platform, consumers, and society when bank loan rate and platform lending rate satisfy specific proportional relationships. 2) When the e-commerce platform undertakes CSR, if the platform’s CSR commitment is low, retail price under platform financing is lower, while consumer surplus and social welfare are higher. Conversely, under bank financing, retail price is lower, and consumer surplus and social welfare are higher. 3) If the two loan interest rates satisfy specific conditions, both the e-commerce platform and the manufacturer can achieve a “win-win-win-win” outcome under financing mode. Comparing equilibrium outcomes under the two CSR scenarios, it is shown that under both financing modes (platform or bank financing), the e-commerce platform’s CSR commitment benefits supply chain members, consumers, and society.

Major marine oil spill accidents occur frequently, causing severe damage to the ecological environment and socioeconomic systems. Existing emergency resource scheduling methods are mostly based on static assumptions, making them inadequate for handling dynamically evolving demand, resource constraints, and multiobjective conflicts in real-world scenarios. To address these challenges, this study develops a dynamic demand modeling framework that incorporates oil diffusion, drift, evaporation, and emulsification processes to accurately capture the spatiotemporal evolution of emergency demand. Furthermore, a multi-objective intelligent optimization method is proposed with ecological damage, emergency response cost, and response efficiency as the primary objectives. Building upon a reinforcement learning framework, an improved Soft Actor-Critic (ISAC) algorithm is designed, introducing a dynamic weight adjustment mechanism to achieve real-time balancing among multiple objectives, thereby enhancing the adaptability and robustness of the scheduling strategy. Simulations based on a representative oil spill case in the Bohai Sea demonstrate that the proposed method outperforms traditional approaches in terms of environmental protection, cost efficiency, and response speed. The results also show strong generalization ability and strategic stability under complex dynamic conditions. This research provides both theoretical insights and practical tools for improving emergency management decision-making and mitigating pollution losses in large-scale marine oil spill incidents.

Financial rumors, fueled by professional terminology barriers, information asymmetry, the information explosion in the era of self-media, and the lowered threshold for generating false information through generative AI, are becoming increasingly harmful and diffcult to regulate. They not only threaten social stability but also pose risks to financial market stability and public wealth security. Examining the dissemination patterns of financial rumor debunking and identifying the factors influencing its effectiveness can offer a decision-making basis for improving rumor governance. This study analyzes 453 financial rumor debunking events on the Weibo platform from 2019 to 2024 using text analysis and network analysis. The results show that events related to corporate operations and labor relations attract higher dissemination heat and exhibit a pronounced proportion of negative sentiment due to their economic implications. Moreover, enterprises consistently represent a prominent theme in financial rumors and debunking information, and rumor debunking information dissemination evolves from predominantly single-issue bursts to increasingly evident cross-theme convergence. Based on these characteristics, an indicator system for analyzing rumor-refutation effectiveness is constructed. Using fuzzy-set Qualitative Comparative Analysis (fsQCA), we identify the influencing factors of refutation outcomes. The findings indicate that timely response from involved entities, rapid reaction speed, and high media engagement are core conditions for effective rumor refutation, with key factors varying across different event types. Finally, targeted recommendations are proposed to enhance debunking practices, providing theoretical support for regulatory authorities to implement scenario-specific interventions and contribute to a sound financial information environment.

Recently, Campana and Borzì have proposed a Pontryagin maximum principle-based sequential quadratic Hamiltonian method for solving differential games, and they prove the convergence of the optimization algorithm in the continuous time case. However, the convergence of the discrete version of the optimization procedure has not been yet tackled with. By combining Euler discretization scheme and sequential quadratic Hamiltonian method, this paper proposes an optimization algorithm for numerically solving differential games and proves its convergence. Numerical experiments demonstrate the effectiveness and convergence of the proposed algorithm.

This paper considers the missing effects induced by the omitted variables in panel data analysis. Omitted variables appear in many application fields, usually because of data unavailability or unobserved. In this article, we develop a panel data model with group structured intercepts for a panel data with unbalanced observations, which enables us to consider the omitted variable effects, especially for the individual-specific omitted variables, where the commonly used panel data model with un-observable interactive effects fails. As shown in empirical studies, the proposed model performs more effective than the existing models for omitted variables because the new model can account for the missing effects of any type of omitted variables. Finally, we apply the method to a pneumonia cost data. The proposed model has a significant improvement of R-square from 0.528 to 0.790, with only 1 more parameter included compared with the usual regression model. We also provide the predicted values of the total cost of pneumonia in different scenarios, which can provide some valuable reference for people on the total cost of pneumonia.

We use the modeling analysis method to examine the transnational patent licensing contracts selection and its impact. The bargaining game models for fixed-fee, royalty, and two-part tariff licensing contracts are established, where the foreign firm and the domestic firm first cooperate through bargaining, and then compete in production quantities. The results of this paper show that, foreign firm and domestic firm should not choose the fixed fee licensing contract, but choose royalty fee licensing contract or two-part tariff licensing contract according to the bargaining power and the degree of product differentiation competition. However, regardless of the form of licensing contract, high tariff will encourage the foreign firm to increase its production and lower the price of its products, which can serve the purpose of protecting the domestic firm. If the tariff rate is low enough, or if the tariff rate is high but the product differentiation is high, then it is profitable for the foreign firm to license the patent to the domestic firm. In addition, transnational patent licensing can bring about social welfare effects, in which the royalty licensing contract may achieve the purpose of maximizing both profit and social welfare.

Driven by the dual-carbon goals and the policy of replacing old home appliances with energy-efficient ones, uncovering consumers’ emotional preferences toward energy-saving appliances is crucial for enhancing product market penetration. Diverging from traditional survey-based research, this study constructs a domainspecific sentiment lexicon for energy-efficient appliances using online review data of first-tier energy-efficient air conditioners, refrigerators, and televisions from the JD.com platform, and proposes a natural language processing framework integrating improved sentiment analysis and topic modeling. By developing a domain sentiment lexicon and optimizing word segmentation strategies, the sentiment prediction accuracy of the SnowNLP model for energy-saving appliance reviews was elevated to 94.27%. The LDA topic model was employed to extract user-focused topics, enabling a cross-analysis of sentiment and themes. Results indicate that product performance (cooling/freshness/picture quality), aesthetic design, and cost-effectiveness are the primary drivers of positive feedback, whereas ”last-mile” installation services and delayed after-sales responses are the main sources of negative sentiment, with perceived brand reliability also prone to causing psychological gaps. Cross-category comparisons reveal heterogeneity in user preferences: air conditioner users prioritize brand and noise levels, refrigerator users emphasize space and quiet operation, and television users focus on picture quality and smooth performance. The integrated sentimenttopic analysis framework developed in this study provides data support and decisionmaking basis for enterprises to optimize products and service management based on user feedback. Accordingly, recommendations are proposed for enhancing costeffectiveness, refining installation and after-sales processes, and strengthening brand promise fulfillment and service transparency.

Under the dual environmental regulations, considering the differences in green preferences among entities is an effective approach to addressing the issues of insuffcient motivation and directional deviation in corporate green innovation, which holds significant importance for promoting green industrial transformation and achieving high-quality economic development. This paper constructs an evolutionary game model involving financial institutions, enterprises, and the government based on the limited rationality of the entities. Utilizing numerical simulation techniques, it analyzes the impact pathways of the synergistic effects of formal and informal environmental regulations on corporate green innovation under different green preferences. The study reveals that in the absence of environmental regulations, only enterprises with a strong green preference opt for green innovation, and whether financial institutions implement green finance policies does not influence these choices. Under weak dual environmental regulations, financial institutions with a high green preference encourage enterprises with lower green preferences to ultimately choose green innovation. In the context of strong dual environmental regulations, even enterprises with minimal green preferences will eventually opt for green innovation. Furthermore, as the intensity of informal or formal environmental regulations increases, the threshold green preference required for enterprises to implement green innovation significantly decreases. This research provides an in-depth explanation of the micro-mechanism by which dual environmental regulations and green preferences drive corporate green innovation, offering a crucial theoretical foundation for constructing a green innovation policy system with Chinese characteristics and accelerating the construction of ecological civilization.

In the process of responding to public opinion on accident and disaster emergencies, governments often face trade-offs between multiple objectives to minimize risks. However, most existing studies focus only on single risk factors or objectives, lacking in-depth exploration of multi-risk correlations and comprehensive objective balancing, which limits their applicability in complex real-world scenarios. To address this gap, this study integrates multi-objective optimization into the research on public opinion response in accident and disaster emergencies for the first time. First, the 5W1H analytical method is employed to propose a framework for identifying public opinion risk factors in accident and disaster emergencies, providing a systematic reference for government agencies to detect potential risks. Based on this framework, a novel multi-objective optimization decision-making model is constructed, considering risk correlations to help government agencies balance three key objectives in public opinion response: timeliness, clarity, and urgency, while seeking a reasonable trade-off among them. Subsequently, the NSGA-III algorithm is utilized to solve the proposed multi-objective optimization model. Finally, a real case study of the “Meida Highway Collapse” incident is conducted, integrating the 5W1H risk identification framework and the multi-objective model to validate its practical application effectiveness. This research not only provides government decision-making bodies with a scientific theoretical foundation and practical tools for managing public opinion in accident and disaster emergencies but also serves as an important reference for improving emergency management systems in such events.

It is known that the Heilbronn number of eight points in triangle is between 0.067789 and 0.067816, the eight points lie in certain small rectangular regions, respectively, and there are at most 11 minimal triangles in the optimal configuration. In this paper we proved that there are at least 8 minimal triangles through infinitesimal perturbation analysis and transformed the Heilbronn problem of eight points in triangle to 18 non-lnear programming problems, where the constraints are bilinear polynomial inequalities. We got the solution to one of the 18 non-linear programming problems using symbolic computation in a minimal polynomial of degree 7, proved that the solutions of other 17 problems are not exceed this value, and finally determined the Heilbronn optimal arrangement of eight points in triangles.

TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) is a convenient and effective group decision-making approach. However, in practical applications, the uncertainty of the criteria information and the limitation of Euclidean distance failure are overlooked, which affects the reliability of decisionmaking results. To address these issues, this paper introduces the normal cloud and then extends the classical TOPSIS method using cloud similarity. First, based on the drop distributional features, dispersion degree, and the overlap of envelope curves, the shape similarity, distance similarity, and overall similarity are defined. Second, experts are grouped, and corresponding weights are determined by accounting for their consensus. Next, the weight optimization model is constructed and solved using the Lagrange multiplier method. Finally, the comprehensive clouds of alternatives and ideal solutions are calculated, with their similarity serving as the decision basis to rank alternatives. Case studies and comparative results demonstrate that the proposed method can substantially enhance the ability to differentiate among similar alternatives while maintaining stability and effectiveness, thereby exhibiting strong application potential.

In causal inference, the balance of covariate distribution between treatment group and control group is a critical factor influencing the accuracy of effect estimation. The imbalance of covariate distribution can lead to bias in treatment effects estimation. Traditional propensity score matching methods, when addressing imbalance, not only discard unmatched samples but also heavily rely on model specification. This dependency often results in inaccurate matching, leading to bias and instability in effect estimation. These issues become particularly pronounced in scenarios with significant differences in covariate distributions. Thus, we proposes a Feature Transfer-Based Treatment Effect Estimation Model (FT-TEE), which tackles the problem of covariate distribution imbalance in causal inference from the perspective of feature representation, thereby enabling more accurate treatment effect estimation. Theoretical analysis establishes a generalization error bound for FT-TEE, demonstrating that controlling the distributional discrepancy between the treatment and control groups can effectively enhance the model’s generalization performance. This ensures the accuracy and robustness of treatment effect estimation. Numerical experiment results indicate that FT-TEE significantly improves the accuracy of effect estimation in cases of substantial covariate distribution discrepancies. Even in scenarios with minor covariate differences, FT-TEE maintains its advantages without negatively impacting estimation results. Finally, FT-TEE is applied to empirical data analysis, further confirming the feasibility of the model.

New drivers of economic development are key supports for promoting high-quality economic growth. The establishment of a unified national market, as a systematic task in building a new development paradigm, has become a crucial institutional factor affecting the cultivation of these new drivers. Based on a multidimensional construction of indicators for new drivers of economic development, this paper analyzes the macro-level impact of market integration from both linear and nonlinear perspectives. The results indicate that: regional disparities in market integration remain significant; the cultivation of new economic development drivers is insufficient in central and western regions; increased market integration has a positive effect on enhancing new drivers of economic development; and when the level of new drivers is low, market integration has a negative effect, whereas at higher levels, it plays a positive and facilitating role.

In response to the practical problem of inequitable profit allocation in current grain supply chains, this study investigates a three-tier supply chain system consisting of a grain supplier, a processor, and a retailer. By constructing a Stackelberg game model, we systematically compare the advantages and disadvantages of profit distribution under three scenarios: independent operation, pairwise cooperation, and full cooperation. Considering the limitations of the traditional Shapley value method, we improve it by introducing the cloud centroid approach from four dimensions—resource input, risk bearing, effort level, and contribution degree—so as to determine the correction values of the allocation factors in a more scientific manner. Numerical experiments show that the cloud-centroid-based improved model can effectively enhance the fairness and rationality of profit allocation in the grain supply chain. Such a more scientific distribution mechanism not only helps ensure the long-term stability and sustainable development of supply chain alliances, but also significantly improves overall coordination efficiency by stimulating the initiative of all participating entities.

Consolidating and expanding the achievements of poverty alleviation is the cornerstone of comprehensively advancing rural vitalization, while promoting the sustainable development of industrial assistance is the key to consolidating this cornerstone. At present, the widely adopted ”fixed-income” interest linkage mechanism in practice has a clear deviation from the ”equity-participation dividend” mechanism advocated by national policies. To this end, this paper takes asset-income-based industrial assistance as the research object, constructs a tripartite evolutionary game model involving local governments, business entities and poverty-alleviated households, and uses numerical simulation to analyze the impact of different parameters on the strategic evolution and system equilibrium of the three parties, so as to reveal the logic behind the choice of interest linkage mechanism in reality.The research shows that: (1) Against the background of poverty-alleviated households’ risk aversion, poor investment environment and declining interest rate level, local governments weigh between performance assessment and investment risks, and business entities focus on the goal of driving poverty-alleviated households to achieve comprehensive benefits. After a comprehensive assessment of their own net benefits, the three parties’ strategies evolve to a stable state where local governments implement strict regulatory measures, business entities actively drive poverty-alleviated households to increase income, and poverty-alleviated households choose the ”fixed-income” mode. (2) Suffcient policy and reputation benefits are the necessary conditions for local governments to implement strict regulation. (3) Increasing fiscal incentives and reducing the costs and risks of rural industrial projects can significantly enhance business entities’ willingness to actively drive poverty-alleviated households. (4) The higher the additional benefits of business entities and the lower the profit distribution ratio, the stronger the willingness of poverty-alleviated households to choose the equity-participation dividend mechanism.From the perspective of dynamic evolution, this paper reveals the formation mechanism of the deviation between policy advocacy and realistic preference, provides a theoretical explanation for understanding the universality of the ”fixed-income” interest linkage mechanism, and offers references for optimizing the asset-income-based industrial assistance model.

The rapid expansion of retailers' store brands and organizational restructuring toward independent business units have made the selection of store brand contract manufacturers a critical strategic decision. Based on a supply chain system comprising one manufacturer and one retailer, this paper develops a two-stage game-theoretic model to systematically compare equilibrium outcomes before and after division independence, as well as between sourcing from a brand manufacturer and a specialized contract manufacturer. It investigates how organizational restructuring influences the selection of store brand production partners. The findings reveal that regardless of whether a store-brand division is established, the retailer's optimal strategy is to select the brand manufacturer to produce the store brand when the products exhibit low substitutability. Under both organizational structures, there exists a possibility that dedicated contract manufacturer can achieve higher social welfare. The establishment of a store-brand division significantly reduces the probability of retailer choosing the dedicated contract manufacturer model, and strengthening the constraints imposed by contract manufacturing costs on this model. Under certain conditions, the establishment of business unit enhances consumer surplus and social welfare under both contract manufacturing models.

Controlling environmental pollution is a systematic project that requires joint efforts from multiple actors. Taking a collaborative governance perspective, we establish a four-player evolutionary game model to examine the dynamic strategy selection and system stability among the central government, local governments, firms and the public. Numerical analysis shows that the four groups are closely interdependent: a lax move by any one actor triggers a chain reaction that pushes the system away from the socially optimal state. Sustainable abatement emerges only when firms cut emissions strictly, local governments deliver effective regulation, the central government offers credible rewards and penalties, and citizens participate actively. We therefore propose an integrated package: a vertically coordinated oversight mechanism for governments, a balanced incentive–constraint regime for enterprises, and an information-rich participation platform for the public. The findings clarify the micro-mechanisms of multi-actor pollution control and provide an operational roadmap for building an efficient collaborative governance structure in China and other transitioning economies.

To address the insufficient analysis of the coupling mechanism and evolution law of multimodal elements in short video public opinion dissemination, this study proposes a three-layer hypernetwork model integrating cover vision, audio features, and text semantics. We adopt BERT, CNN-VGG16, and MFCC to extract multimodal features, design a cross-modal topic discovery algorithm based on hyperedge similarity, and construct a three-dimensional situation awareness framework of “topic discovery-topic evolution-emotional migration” combined with the life cycle theory. An empirical analysis is conducted using the “Dongfang Zhenxuan's short composition” incident as a case study. The results show that multimodal collaboration generates information gain, forming the core dissemination path of public opinion; the hypernetwork model outperforms traditional methods in structural interpretability and public opinion characterization by virtue of its explicit multimodal coupling mechanism; public opinion evolution presents a four-stage dynamic balance, with a strong coupling relationship between topics and emotions—topics related to the incident's origin are the most positive, while those about consequences carry the main negative emotions. This research provides a new paradigm for short video public opinion analysis and offers theoretical support and methodological references for public opinion governance and guidance.

To address the issue of delivery delays, a decision-making model for on-time delivery services with delay compensation is constructed to explore the management issues of e-commerce platforms regarding time commitment and service optimization. The study finds that: 1)Consumer willingness to pay exhibits a non-linear threshold effect: when the waiting time is moderate and the probability of delay is high, the service fee is perceived by some consumers as a "dual guarantee" of risk aversion and economic compensation. In this case, the e-commerce platform can increase its profit by implementing a consumer-oriented strategy. 2)When both waiting time and delay probability exceed a specific threshold, the e-commerce platform can achieve a Pareto optimal equilibrium by adopting a collaborative management strategy with merchants, thus restructuring the supply chain coordination model. 3)Even in low time-cost scenarios, some consumers still demonstrate willingness to pay for the delay compensation service.

This paper investigates the mean square error of the sample mean and the properties of its estimator under median ranked set sampling from asymmetric distributions. Previous studies have shown that for certain asymmetric distributions, the efficiency of the estimator for the population mean based on median ranked set sampling (MRSS) may decrease compared to the estimator based on simple random sampling as the set size increases. This demonstrates that set size plays a key role in sampling efficiency. The set size is generally selected from 2 to 7 in practice. In this study, we also investigates a general procedure for selecting the optimal set size in MRSS sample mean from asymmetric distributions for a given sample size, when the set size ranges from 2 to 7. Subsequently, the optimal set size for the MRSS sample mean under certain asymmetric distributions is identified. The results demonstrate that the optimal set size indeed leads to enhanced sampling efficiency. The real data analysis is provided to illustrate the numerical findings.

With the accelerating intelligent transformation of e-commerce platforms, enterprises face multiple challenges in the deployment of intelligent customer service systems and the implementation of human-machine cooperation, including declining service quality and the adaptation to different sales models. This paper uses the e-commerce supply chain as the research object under the resale and reseller modes, respectively. It builds four different e-commerce supply chain decision-making models of intelligent online customer service/human-machine cooperation strategy, investigates how well the human-machine cooperation strategy works to solve the intelligent customer service quality problem, examines how consumer sensitivity to service quality level and artificial customer service application cost affects the choice of e-commerce supply chain sales mode, and outlines the boundaries of artificial online customer service's application in the e-commerce supply chain. The findings of this paper are as follows: (1) The human-machine cooperation strategy encourages manufacturers to be more likely to choose the resale model. Manufacturers are only likely to switch to the reseller model when the probability of consumers transferring to human customer service is low. E-commerce platforms tend to prefer the resale (reseller) model under high (low) commission rates when the artificial customer service application cost is not significantly low; (2) When consumers’ cost of concern regarding the reliability of human capabilities is low, the human-machine cooperation strategy can improve intelligent customer service quality in both the resale and reseller models, as long as the artificial customer service application cost remains low. However, once this attention cost rises significantly, the improvement effect becomes markedly constrained; (3) Under the resale model, manufacturers exhibit greater momentum in promoting the application of human customer service, whereas under the reseller model, both firms can only achieve mutual benefits from the application of human customer service when specific conditions are met.

In the era of new media, online public opinion events often “emerge” indirectly or continuously in cyberspace, giving rise to resonance phenomena due to shared subjects, similar issues, and emotional resonance. From the perspective of complexity, a systematic study of the internal mechanisms, action pathways, and influencing factors of online public opinion resonance provides a theoretical basis for the government to effectively guide and govern the online public opinion ecosystem. Firstly, this study analyzes the theoretical framework of online public opinion resonance from a complexity perspective. Secondly, it systematically explores the influencing factors of various systems related to online public opinion resonance and constructs causal loop diagrams. Finally, based on the influencing factors and action pathways of public opinion resonance, a dynamic model is constructed and simulated. Through simulation, it is concluded that optimizing the cyberspace structure, focusing on the intrinsic attributes of public opinion, enhancing the competence of mainstream media, empowering authoritative government reporting, and strengthening collaborative governance involving multiple factors can contribute to constructing a favorable chain of netizen interactions, clarifying the information chain of public opinion events, improving the channels for information dissemination, coordinating and integrating the entire chain, and optimizing the management chain of public opinion resonance. Consequently, these measures can effectively guide and prevent the social impacts triggered by emotional resonance in online public opinion.

As a primary mode of transportation for urban commuters, the metro is characterized by smooth operation, punctuality, efficiency, and high capacity. During the morning rush hour, passengers often engage in various activities such as relaxation, document writing, and email processing while on board. However, in-carriage crowding directly affects the utility of these activities, leading to varying commuting experiences. This study incorporates the utility and heterogeneity of in-carriage activities to develop departure time choice models for both homogeneous and heterogeneous commuters during peak hours. It explores the dynamic relationship between commuters' departure time decisions, activity utility, and crowding levels, as well as the influence of in-carriage activity utility on travel behavior. Numerical simulations are conducted to validate the theoretical models and to examine how the proportion of heterogeneous commuters and the crowding interference coefficient affect departure rates. The results indicate that ignoring the utility of in-carriage activities can lead commuters to misjudge the characteristics of the morning peak, specifically by underestimating its duration and overestimating the degree of crowding.

Given the limitation of the classic Black-Scholes model that assumes volatility to be a constant, stochastic volatility models have emerged as a research hotspot in the field of financial derivatives pricing. As a typical representative of stochastic volatility models, the Heston model has been widely adopted in both academia and industry due to its analytical closed-form solution for European option pricing. However, this model involves five parameters to be estimated, which renders its parameter estimation problem remarkably challenging. Meanwhile, the high-frequency trading paradigm imposes more stringent requirements on the real-time performance of parameter estimation. How to obtain high-precision parameter estimation results within a limited time window has become an urgent key issue in this field. At present, existing parameter estimation algorithms for stochastic volatility models generally face the dilemma that pricing accuracy and estimation real-time performance are difficult to balance. To meet the parameter estimation requirements of the Heston model in high-frequency trading scenarios, this paper proposes a two-stage heuristic optimization algorithm. The core idea of the algorithm can be summarized as follows: in the offline training phase, the genetic algorithm is applied to estimate parameters for historical option trading data samples, so as to construct a training set and capture the complex nonlinear mapping between option trading data and model parameters by using a convolutional neural network. In the online estimation phase, for new option trading instances to be estimated, the well-trained convolutional neural network is leveraged to generate a high-quality initial population for the particle swarm optimization, and then the particle swarm optimization is used to achieve accurate parameter estimation. To verify the effectiveness of the proposed algorithm, comparative experiments are designed. A systematic comparative analysis is conducted between the proposed two-stage heuristic algorithm, the standalone genetic algorithm and the standalone particle swarm optimization algorithm, from the two core dimensions of algorithm convergence speed and option pricing accuracy. Numerical experimental results demonstrate that the two-stage heuristic algorithm proposed in this paper exhibits excellent effectiveness and feasibility in the parameter estimation task of the Heston model under high-frequency trading scenarios.

Sparsity is a crucial assumption in high-dimensional modeling, as only a small subset of variables typically exert significant influence on the response in high-dimensional regression analysis. Based on varying coefficient models, this paper proposes a Varying Sparse Coefficient Mixed-Effects Quantile Regression(VSCMEQ) model for longitudinal data, which incorporates variable selection. In this model, the coefficient functions are estimated using B-splines, and penalties are imposed on both random and fixed effects to investigate the influence of relevant important factors, including varying effects and constant effects. Finally, the proposed method is applied to the Primary Biliary Cirrhosis (PBC) dataset to analyze disease progression, identifying the influence of significant factors on disease progression (biomarkers) at different quantiles.

This study addresses hypothesis testing and interval estimation for fixed effects and variance component functions in the context of a skew-normal unbalanced two-way classification random effects model. Firstly, we develop an exact test for the fixed effect based on the skew-F distribution. Secondly, we propose test statistics and confidence intervals for the single variance component, the sum of variance components, and the ratio of variance components using both Bootstrap and generalized approaches. The above constructed statistical methods based on variance component functions are significant generalizations of existing results for normal, balanced, and one-way classification scenarios. Through Monte Carlo simulations, we demonstrate that the proposed methods exhibit robust statistical performance, effectively controlling the Type I error probability while achieving high power under various parameter configurations and sample sizes. Finally, we illustrate the practical utility of these methods by applying them to a case study analyzing classified producer price indices (PPI) for industrial products in 28 provinces, autonomous regions, and municipalities of China from 2016 to 2023.

Rapidly allocating relief resources across multi-stage and multi-regional settings under uncertain demand is a major challenge in humanitarian logistics. This study addresses complex post-disaster scenarios characterized by incomplete demand information and dynamically changing transportation networks, and proposes a two-stage robust optimization framework that integrates artificial intelligence (AI) technology with mobile facilities (MFs) to support resource pre-positioning and multi-period relief allocation. In the first stage, mobile facilities and volunteers are pre-deployed, and AI-assisted path planning is utilized to establish an initial response configuration; in the second stage, relief supplies are allocated and delivered across multiple periods as updated demand information becomes available. The model characterizes demand uncertainty via an uncertainty set and proves, under the $L_1$-norm, its equivalence to a deterministic formulation as well as the existence of an optimal allocation strategy. Numerical experiments demonstrate that, without AI support, the robust optimization model achieves better cost performance and greater stability across different scales than deterministic and stochastic models. With the incorporation of AI, rescue costs decrease significantly for all model types, with the robust model benefiting the most, reflecting the synergistic value of combining AI and robust optimization. Sensitivity analysis further indicates that both path network complexity and individual facility capacity have substantial impacts on system performance; enhancing facility capacity can further strengthen the combined advantages of intelligent scheduling and robust optimization. This study introduces a dual-mode collaborative path-planning mechanism and a two-stage robust optimization decision-making framework, offering reliable support for resource pre-positioning, transportation scheduling, and dynamic decision-making under uncertain relief demands. The proposed framework is applicable not only to natural disasters but also to public health emergencies and supply chain disruptions. Future work may incorporate distributed robust optimization and efficient solution algorithms to enhance performance in large-scale, highly complex disaster response scenarios.

For the optimal control problem of nonlinear systems subject to input constraints and external disturbances, an event-triggered control method is proposed. Existing event-triggered schemes can effectively alleviate the computational and communication burden of the system, but they lack flexible adjustment of the triggering threshold according to the real-time operating state. Within a zero-sum differential game framework, the optimal control-disturbance pair is first derived, and a dynamic event-triggering condition for the two players is designed to reduce the communication load. Furthermore, a nonlinear dynamic tuning parameter is introduced so that the triggering threshold can dynamically match the current operating state of the system, thereby prioritizing computational and communication resources in fast-response phases and actively suppressing the triggering frequency during steady-operation periods, achieving a reasonable trade-off between control performance and communication-resource consumption. In addition, a weight-update law incorporating experience replay is designed, which effectively overcomes the dependence on the persistence of excitation condition and the initial admissible control. Theoretical analysis shows that the closed-loop system state and all neural-network weight estimation errors are uniformly ultimately bounded (UUB), and Zeno behavior is excluded. Finally, simulations on a spring-mass-damper system and a single-link manipulator system are carried out to evaluate the algorithm performance in terms of the number of triggering instants, triggering rate, and average state norm, and the results verify the effectiveness and superiority of the proposed method.

This paper presents a numerical method for solving a class of nonlinear complementarity problems (NCPs) motivated by traffic assignment. Building on the spectral three-term Hestenes-Stiefel (HS) conjugate gradient method (Appl. Numer. Math. 192: 41-56, 2023) for unconstrained optimization, we extend and apply it to solve NCPs. First, we introduce a new spectral three-term HS-type search direction based on an adaptive mechanism. This direction is independent of any line search procedure and possesses sufficient descent and trust-region-like properties. By incorporating the inertial acceleration technique and an adaptive line search, we develop an inertial spectral three-term conjugate gradient projection method. Under standard assumptions, we establish the global convergence of the proposed method. Preliminary numerical experiments demonstrate that the method exhibits favorable performance compared to several existing methods for solving NCPs. Finally, the proposed method is applied to traffic assignment problems to further illustrate its practical potential.

It is essential to promote energy enterprise’s low-carbon technology innovation activity, which is helpful to advance the green and low-carbon transformation of energy. Based on the restart opportunity of the Chinese certified emission reduction scheme, this paper constructed a stochastic evolutionary game model to explore the impact of the simultaneous implementation of a mandatory carbon quota trading system (MCTS) and a voluntary certified emission reduction trading system (VCTS) on low-carbon technology innovation of emission control enterprises and clean energy enterprises in power industry. The results indicate that: 1) The simultaneous implementation of MCTS and VCTS demonstrates a significant institutional synergy effect, capable of incentivizing low-carbon technology innovation in both types of enterprises. However, the incentive for clean energy enterprises, which possess greater market power, is comparatively weaker, indicating that market power can diminish the incentive effect of the simultaneous implementation of MCTS and VCTS on low-carbon technology innovation. 2) In scenarios where initial carbon quotas are allocated freely, variations in the CCER offset ratio do not exert a significant overall influence on low-carbon technology innovation in both types of enterprises. This indicates that the current CCER offset ratio of 5% is appropriate, considering the maturity of the existing carbon trading market, characterized by free allocation of initial carbon quotas and a carbon quota price of 62.29 yuan per ton. 3) An increase in the carbon quota price and the proportion of paid allocation does not substantially affect the low-carbon technology innovation of clean energy enterprises. However, the former is beneficial for promoting low-carbon technology innovation of emission control enterprises, while the latter has a significant negative impact on emission control enterprises’ low-carbon technology innovation. 4) The optimal CCER offset ratio required to incentivize low-carbon technology innovation of emission control enterprises increases with higher carbon quota price or a greater proportion of paid allocation. The research in this paper was a re-examination of the “Porter hypothesis” from the perspective of institutional synergy, and provided policy inspiration for improving China’s carbon trading scheme.