It is crucial to explore the propagation law of network rumors and provide scientific governance strategies for maintaining clear cyberspace. On the basis of the classic SEIR model composed of four groups: Susceptible(S) - Exposed(E) - Infected(I) - Removed(R), the infected people are further divided into rumor infecors (I) and fact clarifiers (C). Considering the government intervention and the heat of public opinion events, the SEICR rumor propagation model is constructed, and the propagation threshold $R_0$ is given. Focusing on the interactive transformation behavior of I and C, we introduces the Prospect Theory to construct the Bi-directional conversion model of IC, solves the five equilibrium points of the model, and explores the conditions that the system should meet when it evolves to a gradual stable point. Finally, based on the complex network environment, the SEICR model is simulated under the influence of the intensity of government intervention and the heat of public opinion events, and the case of “Cat One Cup” incident on TikTok platform is empirically analyzed through text mining and emotional analysis. The results show that the game between I and C can accelerate the evolution of public opinion; Effective government intervention can suppress the fermentation of rumors and reduce the scale of public opinion events; I and C have different sensitivities to the heat of public opinion events. When the heat of public opinion events is high, the government should pay more attention. Based on the research conclusions, some suggestions on rumor control are put forward from the perspective of government intervention means and intervention period.

The classical Bernoulli-Normal generalized linear mixed-effects joint model is commonly used to analyze data of mixed types including binary and continuous outcomes. Under the Bayesian framework, this paper incorporates the Pólya-Gamma distribution family into such mixed-effects joint models. To enhance computational efficiency, we employ the data-augmentation strategy in conjunction with the P?lya-Gamma distribution family to tansform the posterior distribution of regression parameters into a conjugate normal form. Also, the blocked Gibbs sampler is developed for drawing observations from the posterior distributions and producing the joint Bayesian estimates of unknown parameters and random effects. Furthermore, two goodness-of-fit statistics are proposed to evaluate the plausibility of the posited model, and the procedures for computing the deviance information criterion for model comparison are given. Finally, several simulation studies and a real example are presented to illustrate the proposed methodologies.

This study adopts a game-theoretic model to examine the strategic decisions of physical pharmacies regarding participation in a pharmaceutical platform that offers two delivery modes: traditional non-technical delivery (NTD) and technical delivery (TD). A benchmark model was established to analyze the operational choices of pharmacies before and after joining the platform, focusing on drug variety, logistics pricing, and profitability under each delivery mode. The research results show that when the logistics distribution cost is low, physical pharmacies will choose to join the pharmaceutical platform. At this time, the TD mode provides more drug types than the NTD mode, and the overall profit is higher, so the TD mode should be adopted; when the logistics distribution cost is at a medium level, any of them can be adopted; when the logistics distribution cost is high, neither mode will be chosen. In addition, the number of physical pharmacies will not affect the types of drugs before joining the platform, and when the number of pharmacies is small, there is no obvious difference in the optimal profit between the two modes. However, when physical pharmacies join the medical platform, as the number of pharmacies increases, the TD model will gain more profits, and when larger physical pharmacies join the platform, it will be beneficial to both parties and can achieve Pareto improvement. By further exploring the competition among platforms, it can be found that competition will intensify the contradictions between platforms, thereby reducing both their individual and overall profits.

Risk warning in the stock market is fundamental to maintaining the security and stability of a national economic system. Accurate stock market risk warnings are significant for investors, regulatory authorities, and related enterprises. This paper proposes a new graph neural network-based early warning model based on the stock relationship network. Compared with existing methods based on early warning indicator systems and traditional machine learning models, the proposed model in this article considers the graph structural features in the stock market interaction network and constructs a method for feature extraction and dynamic update of neighboring nodes in the network based on the multi-head attention mechanism, successfully capturing the structural feature information in the stock market linkage network. Firstly, we constructed a stock complex relationship network based on the dynamic time warping algorithm; secondly, the GARCH-VaR model was used to assess and classify stock market risks; thirdly, we proposed the construction of an integrated model combining multi-head graph attention networks and graph convolutional neural networks (mGAT-GCN) to establish a stock market risk warning model with the stock relationship network and stock characteristics as input variables. Empirical results from the stock markets of Shanghai, Shenzhen, and Hong Kong demonstrate that the proposed mGAT-GCN warning model has better warning performance on multiple datasets compared to other methods.

Genome-wide association studies (GWAS) commonly employ a two-stage analysis strategy, where results from the two stages cross-validate each other to reduce confounding factors and effectively lower the proportion of false associations. Existing literature on two-stage analyses primarily focuses on single diseases, with limited exploration of multi-disease scenarios. To address multiple diseases, this study proposes two two-stage analytical approaches: independent analysis and joint analysis. For both methods, we constructed quadratic test statistics for phenotype-single nucleotide polymorphism (SNP) association tests at different stages. Under the null hypothesis, we established that these statistics share the same asymptotic distribution as a weighted sum of mixed chi-square random variables. The approximate distribution was then utilized to calculate p-values. Numerical results demonstrated that both methods exhibit high statistical power across varying sample sizes and significance levels. When the minor allele frequency (MAF) is low, joint analysis outperforms independent analysis; conversely, independent analysis becomes superior at higher MAF values. Notably, statistical power increases with MAF for both approaches. Empirical results from a genotype-phenotype association study in mice revealed that both analytical methods effectively identified 48 SNPs with significant associations.

The emergence of missing data and high-dimensional spatial data has brought theoretical and computational challenges to spatial econometric modeling and estimation. This paper studies the variable selection problem of a partial linear spatial autoregressive model with autoregressive disturbance terms under the situation of randomly missing response variables. Combining the B-spline estimation method, a marginal penalized quasi-maximum likelihood variable selection method is proposed. Under appropriate regular conditions, the consistency and asymptotic normality of the estimator are studied. The block coordinate descent iterative algorithm is used to implement the calculation of variable selection. In the case of finite samples, the numerical performance of the proposed method under different sample sizes, missing proportions, and spatial weight matrices is compared through Monte Carlo numerical simulations. The superiority of the method is tested through the analysis of Boston housing price data.

Based on the master-slave game theory, the problem of coordinated security control and communication resource optimization of multi-regional power systems under multiple network attacks was studied. The attacker interfered with the transmission channel of the wireless network between regions, weakened the information interaction between subsystems, and thereby changed the synchronization coefficient of the regional interconnection line, threatening the overall stability of the system. Under the condition that both the system and the attacker had energy budget constraints, this paper took the energy allocation efficiency of the transmission channel as the core performance indicator and established a master-slave game model between the system and multiple attackers under incomplete information conditions. By solving the equilibrium solution of the game model, the optimal allocation scheme of the attack energy and the optimal energy allocation strategy of the system transmission channel were obtained respectively, which determined the system coefficient matrix of the subsystem. This further enabled the calculation of the control gain that ensured the asymptotic stability of the system. Finally, the correctness and effectiveness of the proposed method were verified through simulation experiments of actual power systems.

Responding to consensus-building in decision-making for large groups under social trust networks, this paper introduces the management idea of incentives, and proposes a new, large group decision-making incentive consensus model based on interval Fermatean fuzzy set under the social trust network. Firstly, a new social trust network is constructed by defining the professional competence trust relationship based on the similarity of experts' preferences, and the experts are clustered and grouped by the spectral clustering algorithm, and then the experts and criteria weights are obtained; Secondly, using the IVFFHWA algorithm to gather the initial comprehensive evaluation value, according to which the consensus and trustworthiness of large group decision-making experts are measured and divided into four different types of consensus feedback; Once again, incorporating the incentive means of "rewarding the good and punishing the bad" to build a more targeted incentive consensus model, and dynamically adjusting the feedback mechanism until consensus is reached, so that we can get the group-satisfactory contingency Finally, the feasibility and effectiveness of the method proposed in this paper are verified by the use of emergency decision-making examples and comparative analysis.

In this paper, we consider the optimal asset allocation problem for a defined contribution (DC) pension fund within a financial market where the risky assets exhibit pricing errors and stochastic volatility. We assume that the investment opportunity set as comprising a risk-free asset, a market index fund whose price follows the constant elasticity of variance (CEV) model, and a pair of mispriced risky assets (stocks). Employing the stochastic dynamic programming approach, we aim to maximize the expected hyperbolic absolute risk aversion (HARA) utility of participants’ pension fund accounts at retirement. Through this method, we derive analytical expressions for the value function and the corresponding optimal investment strategy. Additionally, we explore two special cases of the optimal investment strategy under exponential and power utility functions, respectively. Numerical analysis reveals that the optimal allocation to the index fund in the DC pension fund is directly influenced by the stochastic volatility of asset prices. When the two mispriced assets exhibit equivalent mispricing correction capabilities, their optimal investment strategy manifests as a symmetric long-short trading approach. Furthermore, a higher contribution rate to the DC pension fund leads to a more aggressive optimal asset allocation strategy.

Commodity derivatives are an important component of China's financial market, and their pricing effectiveness is related to the stability of China's financial system and the efficiency of resource allocation. The traditional models for pricing commodity derivatives are based on inventory theory, and their deficiency becomes more significant with the increasingly prominent trend of commodity financialization. By introducing a financialization discount factor to measure the impact of commodity financialization and a regime-switching mechanism to grasp the impact of economic changes from a macro perspective, a new model which is more in line with the actual commodity market is established for the pricing of commodity derivatives. This newly established model not only includes many stochastic factors, but also has a hidden Markov chain, which has made the pricing never an easy task either numerically or analytically. Although difficult, this paper derives semi closed-form analytical solutions for the prices of commodity futures and options. Numerical results demonstrate the validity of the closed-form solution while quantifying the effects of financialization and regime switching on the pricing dynamics, underscoring the model's superior performance in risk management applications. Finally, through an empirical study, the applicability of the current model to the Chinese commodity futures market has been clearly demonstrated.

Emotion, as a crucial driving factor in human behavior and decision-making, may impact the contagion of credit risk among businesses, with its processes and mechanisms yet to be clearly understood. This paper, based on complex network theory, establishes a dual-layer contagion model integrating entrepreneur emotions to explore the potential influence of emotions on the interrelated credit risks of businesses. The aim is to provide a comprehensive risk management perspective for governments. The research reveals that in the dual-layer networks of entrepreneur network A and business network B, as the probability of credit risk infection in network B's businesses and the connection probability between nodes in networks A and B increase, the effective transmission rate of pessimistic emotions in network A also rises. Conversely, a higher probability of pessimistic emotions shifting to optimistic emotions in network A leads to a lower effective transmission rate of pessimistic emotions. Moreover, as the immunity loss rate of businesses in network B, and the connection probability between networks A and B increase, the effective contagion rate of interrelated credit risks among businesses also increases. Additionally, a higher willingness of entrepreneurs to provide assistance results in a lower effective contagion rate of interrelated credit risks. When considering the interaction between the contagion of entrepreneur emotions and interrelated credit risks among businesses, if the random spread of entrepreneur pessimistic emotions dominates in network A, the thresholds for the contagion of entrepreneur emotions and interrelated credit risks depend only on the topological structure of network A and the probability of entrepreneur pessimistic emotion transmission. Conversely, if the random dominance of interrelated credit risks occurs in network B, the thresholds for the contagion of entrepreneur emotions and interrelated credit risks depend solely on the topological structure of network B, the willingness of entrepreneurs to provide assistance, and the rate of assistance provided by businesses.

To investigate the interaction between the manufacturers' risk-aversion information-sharing strategies and the retailers' store brand introduction decisions, this paper constructs a two-stage dynamic game involving a risk-neutral retailer and a risk-averse manufacturer. It examines how store brand introduction costs, product substitution rates, and the mean risk-aversion coefficient affect the manufacturer's information-sharing strategy under the retailer's endogenous introduction decision. Results indicate that when the retailer's store brand introduction costs are moderate and the product substitution rate exceeds a threshold, the manufacturer shares risk-aversion information to deter store brand introduction. Conversely, if the retailer introduces the brand ex ante, the manufacturer withholds such information to protect its utility. Furthermore, the threshold interval for information sharing widens with higher product substitution rates but narrows with a higher mean risk-aversion coefficient. Under certain conditions, the manufacturer's strategy may reduce its own utility while improving the supply chain's total expected utility, demonstrating its positive economic impact.

To address the challenges of missing incremental information in time-series data and data distortion caused by impact disturbances in dynamic multi-attribute decision-making, this paper proposes a dynamic grey relation TOPSIS evaluation method based on global improved normalization with weakened buffer operators. First, a second-order buffer processing is applied to raw data using the Average Weakening Buffer Operator (AWBO) to mitigate disturbance impacts. Subsequently, a global improved normalization method is integrated to eliminate dimensional differences among indicators while preserving temporal incremental information, thereby constructing a standardized matrix. Further, grey relational analysis is fused with an enhanced TOPSIS approach by introducing a vertical distance orthogonal projection method to establish grey relation orthogonal projection closeness, comprehensively incorporating both indicator discrepancy and growth trends. Finally, a dynamic comprehensive evaluation is achieved using a "recent-priority" quadratic weighting strategy. The proposed method is validated through a case study on the scientific and technological innovation capabilities of universities in 10 eastern Chinese provinces and cities from 2019 to 2023. The results demonstrate its effectiveness in resolving data distortion and retaining incremental information in dynamic evaluations, providing theoretical support for multi-dimensional temporal decision-making problems.

Since the production of decision-making units may show different patterns in different environments, the DEA-Malmquist index method is not able to analyze the risks and challenges that may arise due to environmental changes. To address this limitation, this paper proposes an enhanced DEA-Malmquist index method incorporating external environmental evaluation. This approach can analyze the technical feasibility, the change of internal driving forces, and the impact of external environment to some enterprises during cross-regional relocations. The proposed method is applied to study the cross-regional relocation of Chinese coal companies. Results show that this method can analyze not only the changes in internal drivers that may result from cross-regional transfers, but also the impact of changes in the external environment on the production activities of enterprises.

In view of the hierarchical medical system under the uneven allocation of high-quality medical resources, this paper considers the referral problem of price-sensitive heterogeneous patients. We analyze the dynamic decision-making process among price-sensitive heterogeneous patients, a community hospital, a tertiary hospital and the government by constructing the Stackelberg game model under the M/G/1 queuing framework, and propose two mechanisms for the community hospital to subsidize the tertiary hospital: A subsidy mechanism based on the referral rate of patients and a subsidy mechanism based on the sinking rate of service capacity. And then we give the referral rate of patients, the planning of the service capacity of the community hospital, the sinking rate of service capacity of the tertiary hospital, and the subsidy mechanism of the government. Furthermore, conduct a comprehensive appraisal of the influence that the subsidy mechanism exerts upon the decisions formulated by all parties concerned. It is found that the government should provide reasonable subsidies for the community hospital and the referred impoverished patients based on the total budget. When the total budget is tight, the whole budget should be subsidized to the community hospital and encourage the tertiary hospital to expand its service capacity, and the community hospital should not provide any subsidies to the tertiary hospital; When the total budget is abundant, the community hospital should be given balanced subsidies to avoid idling of resources, and a certain amount should be given to the referred impoverished patients according to their proportion. At the same time, the tertiary hospital should be restricted from expanding its service capacity so as not to jeopardize the utility of patients, in which case the community hospital should adopt a subsidy mechanism based on the sinking rate of service capacity. In regions with a moderate level of poverty or a large proportion of impoverished patients, the social welfare under the subsidy mechanism based on the referral rate of patients is greater. At this time, the government should try its best to narrow the difference in medical insurance reimbursement ratios between the two hospitals. In regions with a relatively low (high) level of poverty or a small proportion of impoverished patients, the subsidy mechanism based on the sinking rate of service capacity is more advantageous. Correspondingly, the government should adopt a differentiated medical insurance reimbursement strategy.

The data envelopment analysis (DEA) is an important method for evaluating the relative efficiencies of decision-making units (DMUS), which requires that the evaluated DMUs must meet the same policy environment. However, in reality, the policy environments confronted the evaluated DMUs are not uniform, so how to evaluate the relative efficiency of DMUs under multiple policy environments? How to optimize the evaluated DMUs’ production choices under different policy environments? The conventional DEA methodology encounters challenges. Firstly, this paper develops the production possible set under multiple policy environments and analyzes DEA efficiency meaning. Then, we present the efficiency evaluation model of the DMUs under multiple policy environments. Finally, with the government's new energy subsidy, the new methodology is applied to analyze the business performance and efficiency optimization paths of the automobile manufacturing enterprises under different policy environments. Through comparative analysis, the proposed methodology is more effective for solving the problem of evaluating the efficiency of DMUs under multiple policy environments, and also provides an effective analytical tool for DMUs’ efficiency improvement.

With the rapid development of the takeaway industry, the relay delivery model has emerged accordingly. The equitable distribution of riders' benefits is a critical factor affecting the sustainable development of this model. Based on the practical challenges of takeaway relay delivery, this study constructs a profit allocation model using Pythagorean fuzzy sets. By incorporating multidimensional indicators such as delivery distance, delivery time, and service density index, the model achieves optimized benefit distribution among riders. This research not only extends the application of Pythagorean fuzzy sets but also provides a novel approach to addressing benefit allocation issues in takeaway relay delivery systems.

To computationally characterize all extreme vertices and edge midpoints within a high-dimensional constrained mixture region, this paper proposes an Edge Cutting Algorithm, followed by a Combined Exchange Algorithm to select the optimal design point set. Numerical results demonstrate that the proposed algorithm achieves both high precision in identifying extreme vertices and computational efficiency across the constrained region.

In order to achieve $G^3$-smooth join at the joint points, a construction method is proposed for spatial quintic $G^3$ interpolating curves. Given two-point $G^3$ data, a quintic polynomial curve is the lowest-degree polynomial curve that can most possibly achieve $G^3$ interpolation. The interpolation problem reduces to solving a bivariate quartic polynomial system, then its optimal positive solution is obtained via the resultant method and the control points of the quintic Bézier curve are calculated subsequently. When such an interpolating curve does not exist in some cases, several $G^3$-joined interpolating curves are constructed by means of subdivision. Finally, an adaptive algorithm is proposed for converting parametric curves to quintic $G^3$ spline curves. Compared to previous quintic interpolation methods, numerical examples demonstrate that the new method has obvious advantages in fitting errors and the profiles of curvature and torsion.

Predicting the development of income inequality is important for understanding the gap between the rich and poor; it is particularly important for monitoring and forecasting the negative social impact caused by income inequality with more parsimonious model involving fewer variables but achieving higher prediction accuracy. For predicting the income inequality, we analyze the income inequality data set around the world with generalized linear mix-effects model. With this model, we propose a method for constructing candidate models and a novel criterion for choosing weights for achieving a parsimonious model averaging coefficient estimator. Numerical studies show that the criterion has satisfactory performance in parsimony and prediction accuracy. The real data analysis indicates that it will be of great significance to promote the openness and foreign investment, improve the level of human capital, total factor productivity and national income, and establish a flexible financial system and credit system to alleviate the problem of income inequality.

In-home services in the realm of daily living cater to the personalized, discrete, and diverse needs of consumers by directly delivering services to their residences or workplaces. This research centers on optimizing the staff scheduling and routing problem for in-home services offered by platforms, considering the order revenue heterogeneity, and the stochastic service times. This research incorporates the concept of the route operational feasibility and provides corresponding derivation formulas, which are integrated into problem constraints. Additionally, to ensure the feasibility and robustness of the service solutions, this research permits the postponement of the visits to certain customers and the heterogeneous characteristics of staffs are not currently considered. A novel approach is developed, involving an improved branch-and-price algorithm that integrates upper and lower bound predictions for precise solution finding. This algorithm leverages information from branch points, predicting bound values to expedite subproblem solving and enhance convergence speed. Experimental results using modified Solomon instances demonstrate that most instances yield precise solutions within an acceptable time. Sensitivity analysis was conducted on different revenue values and service duration distributions to explore the impact of these factors on path planning and customer access sequence. The precise solution of the in-home service scheduling and routing problem, which combines the randomness of service time and heterogeneity of benefits, can provide improvement solutions for subsequent response to order exchange and sudden orders, and provide decision support for the platform. It has practical application value and can be easily extended to other fields, thereby promoting the sustainable development of the service platform.

Aiming at the problems of multiple points and dispersed volume, high vehicle fuel consumption and carbon emission in cold chain logistics, an electric vehicle routing model and optimization algorithm for cold chain logistics considering split demand are proposed. Firstly, a mixed-integer planning model is established with the objective of minimizing the sum of fixed cost, transportation cost, refrigeration cost, time penalty cost and charging cost. Secondly, a variable neighborhood genetic algorithm is designed for model solving in response to the research problem, the greedy algorithm is used for population initialization, the crossover operation is improved on the basis of the traditional genetic algorithm, and the proportional splitting Principles is designed. Finally, the feasibility of the algorithm is verified by different scale cases and the actual distribution cases of an enterprise, and the simulation results of the cases show that the constructed model and the proposed algorithm can plan the vehicle route scientifically, reduce the total cost of logistics and distribution, and reduce energy consumption.

This study explores the enhancement of "first mile" logistics in the low-altitude economy, focusing on optimizing the harvesting and distribution of fruits and vegetables, which are characterized by seasonality, freshness, perishability, and regional specificity. We address the collaborative routing of trucks and multi-drones under time constraints by proposing a two-stage Mixed Integer Linear Programming model. The first stage minimizes the combined travel and activation costs for both drones and trucks, while the second stage reduces total transportation costs. Extensive numerical experiments validate the model's feasibility and effectiveness, and an empirical analysis using operational data from SF Express demonstrates its practical applicability. The results reveal that the model provides optimal solutions within specified time limits, significantly improving logistics efficiency while ensuring product maturity and freshness. This research offers valuable insights for modernizing agricultural supply chains and identifies new opportunities for applying low-altitude economy principles in agriculture.

In the presence of responses missing at random, this paper investigates the estimation and variable selection issues for the varying coefficient quantile regression model. By approximating the coefficient functions using B-spline basis functions, we propose a multiple imputation method to repeatedly impute missing response variables and estimate the unknown functions by minimizing the imputed quantile loss function. When there exist irrelevant variables in the model, the sparse estimators of the unknown coefficient functions are obtained by combining the basis function approximation technique with the one-step SCAD penalty method. Under certain regularity conditions, we prove that the estimators of the coefficient functions achieve the optimal global convergence rate. Additionally, by appropriately selecting penalty parameters, we establish the oracle property of the sparse estimators. Numerical results confirm the effectiveness and feasibility of the proposed methods.

The sustainable development of public transportation is inseparable from the government subsidy, to explore the rationality of the current government's subsidy allocation for public transportation operation, the game cross DEA model is used to analyze the bus enterprises in 30 provinces and cities in China (excluding Tibet, Hong Kong, Macao and Taiwan) in 2023. This model introduces, for the first time, the concept of scale grouping to accurately assess the subsidy differences among different regions. Firstly, the 30 provinces and cities are grouped according to their bus operation condition, ensuring that comparisons are made under similar circumstances. Subsequently, while keeping the total subsidy constant, the government subsidy and passenger volume are regarded as "income", the study takes the "income" per kilometer of bus operation as the core evaluation index to conduct horizontal comparisons between different scale groups based on the cross-evaluation mechanism in game theory, followed by mutual comparisons within the same scale group. The ideal "equilibrium" subsidy of bus enterprises in each region is then compared with the existing actual subsidy to identify future directions for subsidy adjustment. The results indicate that the scale of bus operation varies greatly in different regions. Excessively small and large-scale bus enterprises obtain relatively lower revenues. Moreover, even among provinces and cities with similar operational scales, subsidy allocation must be tailored to specific local conditions.

This paper focuses on a class of Stochastic Multiobjective Bilevel Programs(SMBP), considering the case that the objective function of the upper-level program is multi-objective while that of the lower-level program is single-objective. Under certain conditions, we apply the lower-level Mond-Weir duality to present a new reformulation, called SMMDP, and prove the equivalence of Pareto optimal solution in local sense and global sense respectively. In addition, due to the mathematical expectation in the objective functions and constraints of the model, which is difficult to be solved, this paper uses sample average approximation method and the penalty function method to propose the penalized sample average approximation problem of SMMDP to solve the problem. Finally, we give the global weak Pareto optimal solution of SMMDP penalized sample average approximation problem and the convergence results of Pareto stability points theoretically.

In the context of big data, optimizing portfolios for complex high-dimensional assets remains a major challenge for investors. This paper employs the Orthogonal Hierarchical Interaction Testing (Ohit) algorithm for dimensionality reduction, which effectively addresses the complex structure of error terms. This paper improves the Sample Average Approximation (SAA) model by incorporating regularization techniques, and proposes the cv-PBR model along with a corresponding Short Period Regularized Sparse Investment Strategy (SPOPBR). For parameter calibration, the study refines the performance-based k-fold cross-validation algorithm by extending portfolio evaluation metrics to a multidimensional framework. The applicability and effectiveness of the SPOPBR strategy are empirically evaluated. Case studies based on real market data show that the SPOPBR strategy outperforms other short-term high-dimensional asset allocation strategies in both returns and risk control. This research provides valuable insights into high-dimensional asset allocation and portfolio optimization.

With the increasing of end-of-life new energy vehicles, the recycling of retired power batteries faces dual challenges of environmental protection and resource reuse. This paper focuses on echelon utilization scenarios of power batteries by constructing a closed-loop supply chain model consisting of power battery manufacturers, new energy vehicle manufacturers, and consumers. It comprehensively analyzes the impact of blockchain technology on recycling mode decisions. Based on Stackelberg game theory, four recycling strategy models with/without blockchain technology are established respectively. The backward induction method is employed to solve equilibrium decisions, and numerical simulations reveal dynamic mechanisms of key parameters. Findings indicate that blockchain technology significantly reduces information verification costs through enhanced traceability levels, stimulating consumer demand growth. Consequently, the power battery manufacturer-led model demonstrates substantially faster profit growth than traditional models in high-echelon-utilization scenarios, while the new energy vehicle manufacturer-led model maintains competitiveness in medium utilization ranges through channel synergy advantages. Additionally, a critical threshold for traceability levels exists—beyond this threshold, technological synergy effects accelerate, but excessive investment leads to diminishing marginal returns.

The semi-parametric accelerated failure time (AFT) model holds a classical position in the field of survival analysis. Left-truncated and right-censored data, along with high-dimensional covariates, present significant challenges for fitting such models. We propose an estimation method based on rank theory for these models and data in this paper. We construct a rank-based variable selection procedure and designs a new coordinate descent algorithm to solve the penalized rank estimation. The related asymptotic theory for the proposed method are also provided. Finally, the effectiveness of the proposed method in finite sample situations is validated through simulation studies and empirical analysis.

In view of the problem of ``difficulty in seeing a doctor'' caused by the unreasonable allocation of medical resources, this paper considers the effect of point-to-point assistance on the cure rate of community hospitals based on the service model of medical consortiums, studies the strategies of assistance and government subsidies in first-class hospitals, and analyzes the effect of government subsidies on the allocation of medical resources and on the improvement of the cure rate of community hospitals. A tripartite game model involving the government, the first-class hospitals, and patients is constructed. By comparing the equilibrium strategies and their properties under different medical service environments, the comprehensive impact of patient perceived value, assistance efficiency, and patient concerns on the operation of the medical consortium is analyzed. It is found that whether top-tier hospitals can spontaneously provide assistance depends on patient concerns. The government needs to adopt different subsidy strategies for hospitals with different levels of patient concerns. The patient scale and assistance efficiency are important factors influencing the decision on subsidy intensity and assistance level. Numerical experiment results show that when the number of patients reaches a certain scale, the assistance levels of two types of top-tier hospitals vary with the patient scale under different assistance efficiencies. The government's subsidies for economically oriented hospitals increase with the expansion of the patient scale, while the subsidies for patient-oriented hospitals decrease with the expansion of the patient scale.

Based on reaction-diffusion equations and the sex structure of mosquitoes, this paper considers a mosquito model between wild mosquitoes and carrying Wolbachia. The optimal release problem for Wolbachia-carrying mosquitoes is discussed both theoretically and numerically. Theoretically, the paper employs the theory of optimal control for partial differential equations to derive the sensitivity system and adjoint system of the state equation, leading to the existence and characterization of the optimal control. Numerically, the forward-backward sweep method is used to illustrate different release strategies for Wolbachia-carrying mosquitoes. The results show that implementing optimal release strategy for Wolbachia-carrying mosquitoes can achieve population replacement; releasing only male mosquitoes carrying Wolbachia under a single optimal control strategy can achieve population suppression; the optimal control intensity in the diffusion scenario is less than that in the non-diffusion scenario. The conclusions can provide theoretical references for the prevention and control of mosquito-borne diseases such as dengue fever.

This study considers a supply chain composed of a supplier and an e-commerce platform under cyber-attack risks, where the government may impose penalties on the platform for failed defense. Game models are constructed under two sales modes (resale and consignment) and two scenarios (with or without government penalties) to explore the platform's defense effort level and analyze the government's optimal penalty strategy. The results show that: 1) When the commission rate is low, the e-commerce platform invests more in defense under the resale mode; conversely, it allocates higher defense effort under the consignment mode. 2) The supplier's preference for the consignment mode is not limited to low commission rates; its mode choice is also influenced by defense costs. 3) If the government penalizes platforms for failed defense, the fine amount under the consignment mode is higher than that under the resale mode, and the fine decreases as the commission rate increases. 4) From the perspective of maximizing social welfare, only when the government attaches sufficient importance to consumer surplus will the government's implementation of punishment increase social welfare, and the optimal punishment should be extremely heavy fines; otherwise, the government should not implement punishment.

At present, the technological achievements nurtured by a new round of global technological revolution and industrial transformation have reached the critical point of application and transformation, and disruptive and cutting-edge technologies have entered a window period of accelerating to transform them into real productive forces, thus more and more enterprises attach importance to the key role of enterprise digital transformation in obtaining sustainable competitive advantages. To explore the implementation mechanism of the edge-cloud system in assisting the digitalization process of the whole economy and society for various stakeholders, this paper constructs a dynamic game model among small and medium-sized enterprises, cloud service providers and edge operators based on evolutionary game theory, analyzes the final evolution direction under the mutual influence of the three parties and ideal state conditions of the system, and combines the system dynamics model to simulate and analyze the factors affecting the stability of the cooperative relationship and the impact of initial intention on the system evolution path. Research results show that the evolution process of the cloud-edge collaboration system is dynamic and complex, and the final evolution direction of each subject's strategy is the result of the systematic action. The task deployment strategies of small and medium-sized enterprises will have an impact on the operation mode of cloud-edge service system, and the initial state and external variables of the system will affect the final evolution results of the system. Reasonable adjustment of relevant parameters can effectively encourage the system to evolve into an ideal state, so as to promote the continuous development of cloud-edge collaboration system, provide effective technical support for enterprise digitization, accelerate the development of new quality productive forces in an adaptive manner, enhance new development momentum, and help to boost the high-quality development of China's economy and society.

This paper considers a two identical components warm standby repairable system where operating component has c failure modes. Applying the Markov renewal process theory, the Laplace transform and the Laplace-Stieltjes transform, we derive the analytical solutions of the distribution and the mean time to the first system failure, the system availability, and the rate of occurrence of failures of the system. Further, some numerical examples are provided to discuss the influence of system parameters on reliability measures.

This paper proposes an adaptive dynamic event-triggered control strategy for networked nonlinear systems with unknown dynamics and external distur-bances. Firstly, to address the communication resource limitation problem in networked systems and decrease unnecessary data transmission, the adaptive dynamic event-triggered control strategy is established between the controller and actuator channel. The triggering threshold is adjusted by a dynamic variable to conserve network resources. This strategy updates the control signal based on the system performance, which promotes network resource utilization. This approach aims to achieve bounded control of uncertain nonlinear systems and decrease the frequency of control signal updates. Next, an extended state observer is designed to estimate the unmeasurable states and generalized disturbances, including the system nonlinear term and external disturbances. At the same time, the introduction of a tracking differentiator avoids the problem of explosion of complexity when computing the derivative of the desired signal and virtual control laws. Moreover, this paper adopts an extended state observer adjustment technique with fewer parameters, which applies to a wider range of nonlinear system models. The adaptive dynamic eventtriggered control strategy is designed by applying backstepping with the extended state observer and tracking differentiator technique. Finally, based on the Lyapunov stability theory, the established control law can guarantee that all signals of the networked nonlinear systems are uniformly bounded without Zeno behavior.

In non-life insurance practice, to mitigate adverse selection and control premium levels, insurance contracts often incorporate claim payment ratios and deductibles, leading to partially censored claims data. To address this challenge, this study develops a risk-adjusted model that incorporates these policy-specific features, such as claim payment ratios and deductible thresholds. Within the framework of the exponential-variance premium principle, the study systematically explores Bayesian estimation methodologies for risk premiums, particularly in cases where the prior distribution is unknown. By applying a linear Bayesian approach, two innovative credibility estimators are proposed, and their statistical properties—such as asymptotic consistency and estimation efficiency—are thoroughly analyzed to assess the model's practical applicability. Through extensive numerical simulations, the convergence rates of the proposed credibility estimators are empirically validated, confirming the robustness and operational effectiveness of the model. The results demonstrate that this methodology enables accurate risk premium estimation in censored data settings, even with complex contractual structures. This research provides a novel theoretical framework for non-life insurance actuarial science, offering substantial value for pricing specialized insurance products that include risk-sharing mechanisms, such as proportional compensation clauses and deductible structures. The proposed model holds significant potential for improving actuarial fairness and enhancing market sustainability in heterogeneous risk pools.

This paper investigates a class of infinite-dimensional forward-backward stochastic evolution equations (FBSEEs) driven jointly by Brownian motion and a Poisson martingale measure. Under a general framework where the system coefficients depend on the state variable, the adjoint variable, the control variable, and the jump intensity, we establish the well-posedness theory for such FBSEEs with jumps. Based on a control-monotonicity condition, we construct a duality structure between the forward and backward stochastic evolution equations (SEE and BSEE) with jumps. By combining the method of parameter extension and Yosida approximation, we prove the existence and uniqueness of global solutions to the FBSEEs and derive corresponding a priori estimates. Furthermore, the developed theory is applied to an infinite-dimensional linear-quadratic (LQ) stochastic optimal control problem with jumps. By constructing a stochastic Hamiltonian system that satisfies the control-monotonicity condition, we obtain an explicit dual representation of the optimal control.

To address the issues of follower states being unavailable, slow asymptotic convergence, and limited communication resources in achieving consensus tracking for general linear multi-agent systems, this paper proposes a dynamic event-triggered finite-time tracking control algorithm based on a finite-time observer. First, utilizing output information and the Implicit Lyapunov Function method, a finite-time state observer is designed for followers to estimate actual states accurately within a finite time. Second, based on the relative observed states of followers, a distributed dynamic event-triggered finite-time tracking control protocol is developed by incorporating a sign function with fractional power into the control law. This protocol allows followers to update control inputs and broadcast state information to neighbors only when specific triggering conditions are met. By introducing internal dynamic variables into the triggering conditions, the number of triggering events is further reduced, thereby conserving communication resources. Finally, the general linear multi-agent system is proven to achieve finite-time output consensus tracking without Zeno behavior by algebraic graph theory and Lyapunov stability theory. Simulation results validate the effectiveness of the proposed algorithm.

With the acceleration of the digital transformation of the catering industry, users’ online evaluation information has shown explosive growth. Effective analysis of catering evaluation has dual value for consumer decision optimization and business service improvement. This study proposes a comprehensive evaluation method of catering stores based on user comments, which aims to quantify the fuzziness of user preferences and improve the accuracy of evaluation.Firstly, based on user comment data from Meituan and Dianping, the hierarchical evaluation index system including environment, service, taste, price and health is constructed by TF-IDF high-frequency word extraction and LDA topic model mining; Secondly, the multi-dimensional fuzzy evaluation of users is transformed into probabilistic language terms, and the language set representation model including probability distribution is constructed to quantify the uncertainty of comments; Finally, the index weight is calculated by entropy method, and the comprehensive score of catering stores is generated by weighted linear combination. Based on the empirical analysis of 8 catering stores in Jinshui District of Zhengzhou City, the score ranking of the model output is highly consistent with the actual user experience, which verifies its practical value in reducing consumer decision-making costs and guiding merchants to accurately optimize operation strategies.

New quality productivity itself is green productivity, and its key to development lies in improving green total factor productivity. How enterprises can adapt to and mitigate the risks brought by changes in trade policies by improving new quality productivity, especially green total factor productivity, is an urgent problem that needs to be solved. This article explores the relationship between trade policy uncertainty and new quality productivity from the perspective of enterprise green total factor productivity using the DID model, based on the merged data of Chinese industrial and commercial enterprises, customs, pollution, patents, US import tariffs from China from 1998 to 2014, and the Tariff Download Facility database of the WTO. Research has found that: 1) The growth rate of green total factor productivity of enterprises during the inspection period was 4.50%, mainly driven by technological progress.The regional growth rates are: Eastern>Central>Northeast>Western, and the industry dimensions are: High tech>Resource based>Medium tech>Low tech. 2) The significant reduction in trade policy uncertainty has significantly improved the green total factor productivity of enterprises, which is conducive to cultivating and developing new quality productivity. This conclusion remains robust after a series of robustness tests. This promoting effect is more significant in mixed trade, pure general trade, high export density, eastern regions, and high-tech industry enterprises. 3) The scale effect, technology effect, structural effect, and income effect generated by the decrease in trade policy uncertainty all exist. The scale effect is mainly achieved through the ‘quality’ of enterprise exports, while the technology effect is jointly achieved through the ‘quantity’ and ‘quality’ of enterprise patents.