Against the backdrop of the continuous accumulation of local government hidden debt risks and the intensifying regional credit linkages, systematically uncovering the risk transmission mechanism of China’s municipal bond market holds significant practical value for safeguarding against systemic financial risks. Based on provincial municipal bond credit spread data from 2015 to 2024, this study constructs a multiplex network of risk contagion to systematically identify the directions and paths of inter-provincial risk transmission. Furthermore, a TVP-VAR-SV model is employed to analyze the time-varying influence of macroeconomic variables on the intensity of risk contagion. The results indicate that: first, the multiplex network framework, compared with traditional single-layer network methods, more effectively identifies hidden transmission paths and risk hubs; second, risk diffusion exhibits pronounced regional heterogeneity and fiscal stratification; and third, macroeconomic fluctuations exert a strong time-varying effect on the intensity of risk contagion. This research transcends the limitations of single-layer network analysis, providing a novel identification tool for municipal bond risks and offering a scientific foundation for the construction of risk identification mechanisms and differentiated regional risk supervision.

With the rapid advancement of digital technologies, the deep integration of the digital economy and digital national defense has become a critical pathway for enhancing national strategic capabilities. Drawing on systems science and synergy theory, this study constructs a multi-level theoretical analysis framework encompassing foundational coupling mechanisms, institutional compatibility mechanisms, bidirectional transformation mechanisms, collaborative innovation mechanisms, and holistic linkage mechanisms. The Analytic Hierarchy Process (AHP) is employed to quantitatively evaluate the weights and interactions among these mechanisms. The results indicate that the holistic linkage mechanism has the highest weight at the criterion level in the synergistic development of digital economy and digital national defense, while the weights of collaborative innovation mechanism and bidirectional transformation mechanism are relatively close. Additionally, open scientific collaboration and innovation show the highest weight at the indicator level. Based on this, a double helix structure model for the synergistic development of digital economy and digital national defense is constructed, and the reliability of the double helix structure model is confirmed by taking the military civilian technology collaborative innovation system as an example, clarifying the interaction relationship between the double strands and bases of the double helix structure. Our findings provide a theoretical basis for optimizing resource allocation and enhancing national strategic capabilities in the context of digital transformation.

For the distributed optimization problem over weakly connected directed graphs, this paper investigates a distributed optimization method. Firstly, the original graph is decomposed into multiple strongly connected subgraphs using a block Laplacian matrix. The convergence of each subgraph is demonstrated using a distributed optimization algorithm based on Hessian matrix and Lyapunov stability theory. Secondly, an exponential decaying bias term is introduced to adjust the Lyapunov function of the inter-subgraph connections for a weakly connected graph with imbalanced weights, the convergence of the inter-subgraph is analyzed, and the convergence of the entire weakly connected graph is proved, ultimately achieving the global optimization objective. Finally, by introducing an event triggering mechanism based on periodic sampling, the communication frequency is reduced. In addition, theoretical bounds for convergence have been provided and the efficacy of the proposed method has been demonstrated through numerical simulations.

Index tracking is an important topic in financial economics, which aims to replicate a specific market index (e.g., the CSI 300 Index) by constructing a portfolio, so as to achieve returns that closely match those of the target index. However, due to the frequent presence of noise and outliers in financial data, traditional tracking models based on least squares loss often lack robustness, leading to high tracking errors. To address this, this paper introduces a novel sparse regression model that combines the proposed RoBoS loss function with the LASSO penalty. The RoBoS loss is both non-convex and smooth, enabling it to effectively mitigate the impact of noise and outliers and improve prediction accuracy. We derive the finite sample breakdown point and the influence function for the new model estimator, providing theoretical guarantees of robustness from a statistical perspective. Based on the concept of proximal gradient descent idea, we further develop an efficient numerical algorithm for model estimation. Extensive numerical simulations and empirical analyses are conducted to systematically evaluate the performance of the proposed model. The results demonstrate that, compared to existing models, the RoBoS loss-based sparse regression method exhibits stronger robustness, higher prediction accuracy, and achieves lower tracking errors in tracking CSI 300 Index.

Harnessing ecosystems to enhance carbon sink capacity is a key means of synergizing energy conservation and emission reduction efforts to jointly advance the achievement of carbon neutrality goals. Among this, interactive collaboration among carbon sink developers serves as the foundation for promoting coordinated coupling between terrestrial and marine ecosystems so as to increase the value of carbon sinks, and it is also the basis for these participants to enhance their economic returns. However, existing studies on terrestrial and marine carbon sinks are largely fragmented. In response, this paper incorporates stochastic disturbances and, based on differential game theory, constructs mathematical models involving terrestrial and marine carbon sink developers under four different decision-making modes, followed by numerical simulation and computational experiments. The results show that: (1) Closer cooperation between terrestrial and marine carbon sink developers increases both the expected value and the variance of carbon sink output, with actual output and returns fluctuating around their expected levels. (2) Joint carbon sequestration and revenue generation are more likely to be achieved when the developer with relatively weaker effort effectiveness among the two heterogeneous carbon sink developers takes the lead and shares part of the other party’s costs. (3) Under stochastic disturbances, the realized output of cooperative carbon sinks may deviate from expectations and even fall below that under non-cooperation; therefore, developers should leverage the respective advantages of land and sea in different stages, conduct cooperation flexibly, and seek to mitigate the impact of randomness.

To improve patrol coverage efficiency under limited police resources, this study addresses the joint routing and scheduling optimization of cooperative police vehicle-UAV patrols. A synchronized time-space network is constructed to model vehicle and UAV flows, with arc-based rewards introduced to quantify crime coverage. A 0-1 network-flow mixed-integer programming model is formulated to maximize cumulative coverage, incorporating practical constraints such as minimum vehicle patrol duration, UAV battery and recharging limits, patrol coverage requirements, and diminishing returns from repeated patrols. A path-encoding-based harmony search algorithm with a feasibility repair mechanism is proposed to efficiently solve large-scale instances. Computational experiments based on real-world cases demonstrate that the proposed method achieves near-optimal solutions for small instances and outperforms CPLEX on medium- and large-scale instances within limited computation time, showing strong stability and scalability.

Aiming at the situation that most of cloud model information aggregation operators neglect the density degree of data distribution, cloud density weighted arithmetic averaging (CDWAA) operator and cloud density weighted geometric averaging (CDWGA) operator are defined. Two novel operators utilize three numerical characters of cloud model to represent the fuzziness and randomness of linguistic information and use the density weights of density weighted averaging operator to denote the density degree of data distribution. The commutativity, idempotency, boundary, and monotonicity of the operators are investigated, based on which, a new multiple attribute decision making method is put forward. By taking an example with regard to the grain supplier selection to analyze, the results show that not only can this method effectively consider the fuzziness and randomness of linguistic information, but this method can also better consider the density degree of data distribution.

With the continuous increase of production costs in China, some electric vehicle manufacturers (EVMs) have begun to develop battery suppliers in Southeast Asia with lower costs, which involves cost uncertainty and information asymmetry. Based on this, combined with the characteristics of battery recycling in the electric vehicle industry, this paper considers a game of developing battery suppliers and studies the impact of key parameters on the decisions of EVMs to develop battery suppliers and battery procurement quantities. The study shows that: (1) Whether EVMs develop battery suppliers, that is, the main body selection of developing battery suppliers, mainly depends on market size, differences in battery recycling rates, and battery recycling benefits. (2) Reducing cost uncertainty in Southeast Asia or improving its signal accuracy may not necessarily attract EVMs to turn to Southeast Asia to develop battery suppliers. (3) The increase in production costs in China may lead to only one EVM developing the battery supplier in Southeast Asia.

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.

Public health emergencies have a serious impact on China's economy, social stability, and people's life safety, placing unprecedented stress on the emergency supply chain system. Drawing on social cognition theory and incorporating the mechanism of public opinion evolution, this study employs the WSR-DEMATEL method to identify crucial elements of the emergency medical supplies supply chain's capabilities. Furthermore, it analyzes the dynamic interplay between epidemic control measures and the allocation of essential medical resources, leading to the development of a dynamic model for the emergency medical supplies supply chain. Finally, contextualized within the backdrop of the Wuhan pandemic, a sensitivity analysis is performed on parameters such as government crisis management intensity, mobilization and procurement lead time, emergency policy enactment duration, exceptional production regulation timelines for medical resources and official news transparency. This multi-faceted investigation aims to uncover key optimization pathways for strengthening supply chain's capabilities. The results indicate that during the initial phase of epidemic prevention and control, emergency provisioning relied predominantly on the mobilization and collection of medical resources from the community. It is crucial to maintain a measured extent of governmental crisis management intensity, to avert shortages in the quantity of resource collection arising from either a surge in public sentiment or inadequate attention. Moreover, improving official news transparency steadies public attention and boosts social medical resource mobilization efficiency. Taking a longer-term perspective, bolstering governmental crisis management efforts, shortening the duration of emergency policy implementation, and reducing the adjustment time for exceptional medical resource production are all conducive to enhancing the rate of demand satisfaction. Unleashing the synergistic potential of systemic interconnection mechanisms to enhance overall coordination capabilities emerges as the pivotal factor for ensuring the provision of medical resources and optimizing epidemic control strategies.

Frequent emergencies pose a serious threat to human life and health. These events often trigger a sudden surge in drug demand, leading to serious supply shortages and unstable prices. Although governments have taken action through emergency supply and price caps, ensuring drug access and market stability remains difficult during emergencies, To address this, our study constructs a market game model comparing scenarios with and without emergencies. We analyze how the government should respond under demand surges, and examine how emergency supply and price cap policies help stabilize the market, ensure supply, and affect both drug prices and corporate profits. The results show that whether or not a price cap exists, the emergency reserve supplier does not charge excessively high prices. However, the price cap shifts the drug supplier’s strategy from “profit maximization through price increases” to “profit maintenance through output expansion” . Specifically, the government’s price cap effectively controls drug prices during emergencies, while emergency supply contributes to price stabilization and supply expansion in the market. Moreover, the government further curbs price hikes by selecting emergency reserve suppliers with larger market shares. Although the drug emergency supply improves consumer surplus and social welfare, a low price cap may weaken these benefits. This study proposes a coordinated strategy for market price and supply stability through strengthened government-enterprise collaboration and the integration of emergency supply with reasonable price caps. This approach is crucial for optimizing the allocation of government emergency resources, enhancing response effectiveness, and advancing the practice of emergency management systems.

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.

As China faces the arduous tasks of energy conservation, emission reduction and structural transformation, it is of great significance to study the drivers of digital transformation of heavily polluting firms. This paper analyzes the impact mechanism of environmental protection tax on digital transformation of enterprises from the perspective of strategic and substantive transformation, based on the panel data samples of A-share listed high-polluting enterprises in China from 2011 to 2021, and based on the accurate measurement of digital transformation index of enterprises, and from the perspectives of resource crowding and innovation forcing. The study finds that, firstly, environmental protection tax promotes the digital transformation of enterprises, and this transformation effect is mainly manifested as “strategic transformation” rather than “substantive transformation”, that is, the “innovation forcing” effect of environmental protection tax on strategic transformation is greater than the “innovation forcing” effect of environmental protection tax on strategic transformation. Secondly, environmental protection tax promotes strategic transformation mainly through external pressure (increased media attention and supervision) and internal drive (increased innovation consciousness of executives), while inhibits substantive transformation through resource crowding (digital investment crowding) and financial difficulties (increased financing constraints). Finally, the extent of the impact of environmental protection taxes on firms' digital transformation is stronger for firms in regions with higher levels of financial development, capital- and technology-intensive industries, and larger firms. This paper provides a new theoretical perspective for academics to understand the comprehensive impact of environmental regulation on enterprise digital transformation, thus helping to promote the deep integration of green low-carbon development and enterprise digital transformation.

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.

The deployment of carbon capture, utilization and storage (CCUS) technologies creates a supply chain in which upstream and downstream members can forge synergies through internal carbon trading, thereby establishing a viable foundation for on-chain financing cooperation. We investigate a scenario in which a capital-constrained manufacturer secures financing from an upstream supplier to implement emission reduction activities. By incorporating the opportunity cost of capital occupation, we construct a noncooperative-cooperative biform game model to analyze CCUS supply chain financing. Furthermore, the Minimax principle and the Shapley value are utilized to derive the equilibrium solutions. The results show that: 1) When the production cost savings from CCUS projects go beyond the price of carbon trading and the manufacturer's initial capital drops below a certain level, financing cooperation can enhance supply chain members' returns. This leads to a Pareto improvement at the supply chain level. 2) As production cost savings increase, financing rates tend to decrease. At the same time, carbon capture ratios rise, which lead to higher overall supply chain profits. However, these positive effects diminish significantly when opportunity cost rates are high. 3) Under the financing cooperation mechanism, as carbon trading prices rise, the financing rates increase significantly, while carbon capture ratios, output, and member profits remain relatively minor. Compared to the incentive effect of production cost savings, higher carbon prices show a much weaker influence on member decision-making and cooperation stability.

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.