Yard cranes (YCs) are the primary loading and unloading equipment in container terminal yards, and their scheduling efficiency is a critical factor influencing the overall operational efficiency of the terminal. This paper studies YC scheduling in multi-crane and partitioned zones, based on task priority and YC occupancy level. Firstly, the execution priority of YC tasks is defined, and YC occupancy level is introduced to characterize the balance of YC operations. It is worth noting that most existing literature measures YC balance solely based on the number of tasks, while YC occupancy level depends not only on the quantity of tasks but also on their difficulty. Secondly, considering different types of tasks, a mixed-integer programming model is constructed with the objective of minimizing the sum of YC idle time and the variance of YC occupancy level, based on the concepts of task priority and YC occupancy level. Finally, a genetic algorithm is employed to solve the proposed model, and a case study is provided to demonstrate the effectiveness of the proposed method. Compared to existing research, the YC scheduling method based on task priority and YC occupancy level proposed in this paper is applicable to more general operational scenarios, while also improving the parallelism and efficiency of YC operations.

To better investigate practical research and development scenarios where responses are simultaneously influenced by mixture component proportions and their order of addition, this study employs optimality criteria for designs within mixture design regions defined by basic and additional constraints. We systematically examine saturated design problems covering no interaction, first-order interaction, and second-order interaction cases between component proportions and order-of-addition variables. Explicit closed-form solutions are derived for the D- and A-optimality criterion functions, the corresponding saturated optimal designs, and their associated D- and A-efficiencies under the order-of-addition-dependent q-component secondorder Scheffé centroid polynomial models. Analysis of these efficiencies reveals that A-optimal designs consistently demonstrate superior robustness compared to D-optimal designs when evaluated under combined optimality criteria. Case studies validate the theoretical findings.

In view of the limitations of classical probabilistic models in dealing with complex decisions and the interference of overlapping communities on decision-making, a group decision-making method based on quantum cognitive theory considering the overlapping community division is proposed. Taking consumers’ multiple social identities as the breakthrough point, we reveal the mechanism of preference formation and group preference integration under the interference effect. Firstly, a fuzzy C-means clustering algorithm is used to divide overlapping communities based on the differences in decision-makers’ preferences, and the membership degree of an individual in different communities is obtained and quantized to reflect the individual’s superposition state of multiple community belongings. Then, in the framework of quantum-like Bayesian networks, the belief entropy method is used to quantify the interference effect between communities, modify the weight of decision makers and integrate group preferences. Finally, the method is used to analyze the online reviews to verify the influence of the interference effect between communities on the group decision results. The study shows that the quantized overlapping community division method can effectively capture the complex belonging relationship of individual consumers to multiple communities. And the quantum-like Bayesian network has stronger explanatory power in predicting consumer preferences under the interference of overlapping communities.

Consider a system consisting of an electric automaker (EA) with the ability to produce batteries and an EA without the ability to produce batteries, who build extra charging stations. This paper constructs a Cournot competition model, and respectively constructs a co-opetition model with independence-based pricing and a co-opetition model with negotiation-based pricing through Stackelberg game and Nash negotiation game. This paper investigates the optimal strategy choice and decisions of building extra charging stations for EAs. It is shown that: 1) The optimal strategy choice (i.e., competition, co-opetition with independence-based pricing and co-opetition with negotiation-based pricing) depends on the bargaining power of the EAs, the degree of electric vehicle substitution, the network efficiency of charging stations and the battery cost difference. And whether the wholesale price of batteries is determined through bargaining mainly depends on bargaining power. 2) When the EA with the ability to produce batteries has relatively high bargaining power, compared with bargaining, the EA with the ability to produce batteries can always benefit from the pioneer advantage in the Stackelberg game, but the Stackelberg game undermines the overall profits of the two EAs during cooperation-competition.3) Compared with the competitive strategy, when co-opetition strategies realize the Pareto improvement of EAs, the electric vehicle prices are also lower than the competition strategy. 4) When the co-opetition strategy is implemented, co-opetition strategy will make the EA without the ability produce batteries to build more charging stations, while it will cause the EA with the ability to produce batteries to build less charging stations. And co-opetition contracting can also affect decisions of building extra charging stations for EAs.

Addressing the issue of battery strategy selection in the production and R&D of new energy vehicles by traditional automakers, a two-tier and three-tier automotive supply chain model is constructed, led by manufacturers and involving suppliers and dealers. Utilizing differential games and optimal control theory, the study examined the impact of various battery selection strategies on the optimal emission reduction trajectory for fuel vehicles, the optimal goodwill trajectory, and long-term profits under scenarios where fuel consumption targets are met or not met. The results reveal that: First, as time progresses, there is an observable increase in the emission reduction and fuel efficiency levels of fuel vehicles, as well as an enhancement in their brand goodwill. In the long term, the in-house battery development strategy demonstrates superiority over the external procurement strategy in terms of emission reduction, brand goodwill trajectories, and stable revenue values. Second, the credit price exhibits a threshold effect across various strategies. At low credit prices, the in-house development strategy offers a significant advantage in reducing carbon emissions. In contrast, at high credit prices, the purchased strategy responds more quickly under fuel efficiency compliance conditions. Thirdly, under the in-house development strategy, an increase in credit price effectively incentivizes manufacturers to allocate more resources to enhancing the range capabilities of new energy vehicles.

This paper studies the time-consistent non-zero-sum stochastic differential game strategies for n competitive insurance companies. Insurance companies adopt the proportional reinsurance, and the risk process follows a compound Poisson risk model. Considering the stochastic correlation between risky assets, a multivariate 4/2 stochastic covariance model is introduced to characterize the price processes of two risky assets. The objective of each insurer is to find the optimal investment-reinsurance strategy so as to maximize the expected value of its terminal relative wealth while minimizing the variance of the terminal relative wealth. By introducing an auxiliary deterministic process, this paper obtains a modified mean-variance objective function, and constructs an alternative time-consistent mean-variance control problem. Then, by solving the HJB equation, the time-consistent equilibrium investment-reinsurance strategies for insurers are obtained. Finally, some numerical examples are provided to analyze the effects of important parameters on the equilibrium strategies. The results show that the intensification of competition between insurers will prompt them to adopt more aggressive investment and reinsurance behaviors; and at the same time, the correlation between risky assets in financial markets will also influence the decision-making of insurers.

As a non-parametric Bayesian regression approach, Bayesian Additive Regression Trees (BART) model combines the precision of likelihood-based inference with the flexibility of machine learning algorithms. It provides superior predictive performance when there is a nonlinear relationships or complex interaction scenarios among the response variables and covariates. Longitudinal data, widely presents in fields such as medicine, economics, and environmental science, holds important research significance. To improve the predictive accuracy of longitudinal data analysis, this study proposes a new method for longitudinal data analysis based on BART, in which utilizes BART to estimate non-parametric parts in the semiparametric mixed-effects model. In numerical simulations, this study compares the new method with four other methods: mixed-effects gradient boosting method (MEGB), stochastic mixed-effects regression tree method (SMERT), stochastic random effects expectation-maximization regression tree method (SREEMtree), and stochastic mixed-effects random forest method (SMERF). The simulation results consistently show that the new method outperforms the other four methods. To illustrate its practical application, this study applies it to two real-world datasets.

To address the challenges of digital healthcare services and meet the personalized needs of diverse patient types, this study investigates the optimization of scheduling and routing for home healthcare workers. Unlike previous studies, in the problem, both doctor and patient bilaterally have personal preferences, heterogeneous patients can choose three service modes: outpatient, door-to-door, and online services, healthcare workers have fatigue perception, and healthcare workers’ scheduling and routing decisions are reflected in hybrid scheduling and routing multi-objective optimization decision-making with the fusion of online and offline multi-service modes. A bi-objective mixed-integer programming (MIP) model is proposed to maximize the satisfaction of both healthcare workers and patients, subject to constraints such as shift limitations and worker-patient matching. To address the characteristics of the model, an improved Strength Pareto Evolutionary Algorithm-II (ISPEA-II) is developed. Using metrics such as HV, Spacing, and GD for algorithm evaluation, numerical experiments demonstrate that the proposed ISPEA-II outperforms traditional Strength Pareto Evolutionary Algorithm-II (SPEA-II), Non-Dominated Sorting Genetic Algorithm-II (NSGA-II), Non-Dominated Sorting Genetic Algorithm-III (NSGA-III), Differential Evolutionary Algorithm (DE), and Immune Algorithm (IA). Finally, sensitivity analyses on key parameters, including skill levels of healthcare workers, shift lengths, and maximum consecutive working days, yield managerial insights, providing theoretical guidance for scheduling and routing decisions in home healthcare.

This paper addresses several issues in group decision-making under social network environments, such as low public participation, non-cooperative trust evaluation behavior, and insufficient trust information mining. A group decision consensus model considering non-cooperative behavior in dynamic social network environments is proposed. First, the TF-IDF algorithm is applied to mine user behavior data from social media to obtain the public-level criterion weights. These weights, combined with expert-level criterion weights based on intuitionistic fuzzy entropy, achieve a fusion of public and expert perspectives, thereby determining decision criteria and their corresponding weights in a scientific and reasonable manner. In the initial trust evaluation phase, a trust relationship based on intuitionistic fuzzy numbers is constructed. The uninorm operator is employed to quantify cooperative and non-cooperative features, identifying and addressing non-cooperative trust evaluation behaviors through a reward and punishment mechanism to adjust trust values. Furthermore, the concept of "directional trust" is introduced and its measurement algorithm is designed to capture the influence of opinion adjustment trends on trust, addressing the limitations of traditional similarity-based trust models. A dynamic trust network update algorithm is developed to incorporate initial trust, similarity trust, and directional trust in multiple decision rounds, accurately reflecting the dynamic evolution of trust relationships. In the consensus adjustment phase, expert consensus contributions and trust levels are integrated to select reference objects, guiding non-cooperative experts to adjust their opinions. Finally, the proposed method is applied to the decision-making process for the site selection of green small hydropower stations, demonstrating its effectiveness and superiority.

New energy vehicle power batteries are gradually entering the end-of-life phase, and the number of decommissioned batteries is increasing day by day, which has already shown a large-scale trend. To avoid environmental pollution and increase the recycling rate of used power batteries, it is particularly important to study the recycling problem of used power batteries. First, according to different government supervision intensity, a consumer utility function influenced by consumers’ environmental awareness and government subsidies is constructed, and a game model including the competition between formal and informal recycling enterprises is established. The optimal recycling prices and recycling rates under different government supervision intensities are obtained, and the impacts of government supervision intensity, subsidies, recycling cost coefficient, and consumers’ environmental awareness on the optimal decisions of these two types of enterprises are analyzed. Second, the social welfare functions under different supervision intensity are constructed, and the optimal government supervision intensity is obtained through numerical analysis, and the impacts of consumers’ environmental awareness on social welfare and the recycling rate of formal recycling enterprise are further analyzed. The results show that: (1) It is effective and feasible for the government to regulate the market in order to standardize the recycling market. (2) Consumers’ environmental awareness has a greater impact on enterprises’ decision-making than government subsidies. Government subsidies are more effective when consumer environmental awareness is high. (3) Consumers’ environmental awareness is positively correlated with the government’s regulatory strength, and the improvement of consumers’ environmental awareness promotes the government to strengthen the regulation of informal enterprise. (4) In order to increase the recycling rate of formal recycling enterprise, the government needs to sacrifice a certain amount of social welfare.

In this paper, the dynamic event triggering control problem is studied in Lur’e networks under denial-of-service (DoS) attacks. In order to tackle DoS attacks, a dynamic event-triggered control protocol is firstly designed, in which the coefficients of the dynamic parameters can be automatically adjusted according to whether the network is attacked or not, reducing the impact of DoS attacks on the network synchronization and also ensuring the dynamic adjustment capability of the control protocol. By using the Lyapunov stability and linear matrix inequality methods, a sufficient condition for the synchronization of the Lur’e network under DoS attacks is derived. Furthermore, it is proved that the proposed event-triggered protocol is free of Zeno behavior. Finally, the effectiveness of the control protocol and the theoretical results are verified by simulation results.

The digital economy has increasingly become a core engine driving highquality economic development in the new era, but it still faces challenges related to unbalanced and insufficient development across regions and industries. Drawing on input-output tables for China.s provincial digital economy industries and relevant data from 2007, 2012, and 2017, this article provides an in-depth analysis of the dynamic evolution of regional value chain positions and their underlying formation mechanisms, aiming to reveal the structural development patterns of China.s digital economy across regions. The study finds that industrial digitization in China continues to accelerate. However, the production capacity of the communications manufacturing industry remains overly concentrated in Guangdong and Jiangsu, while its share is steadily declining in some northern regions. The penetration of digital technologies in traditional industries remains limited in most central and western regions, especially in the agricultural sector. As digital transformation deepens, the industrial digitalization sector has played a leading role in driving socio-economic development, characterized by a diminishing influence coefficient but a growing propagating effect. In contrast, the digital industrialization sector demonstrates a stronger driving effect, with a steadily rising influence coefficient, particularly in the central and western regions. However, development in the northeastern region remains relatively slow. Further analysis reveals that the strengthening of the digital economy.s industrial linkage is primarily driven by the rapid growth of internal consumption and distribution) reflecting an expanding intra-industrial cycle. However, this also contributes to a weakening connection with traditional sectors, especially agriculture, which has become a notable weak point in the current development of the digital industry.

In the context of the rapid development of e-commerce, but the return and exchange rate remains high, resulting in a large amount of wasted resources, online retailers use augmented reality and other technologies to provide consumers with a "virtual showroom" service in order to reduce the operating costs arising from a large number of returns and exchanges. To address the impact of consumer free-riding behavior on the pricing and service decisions of supply chain members when virtual showrooms are introduced into the online dual-channel supply chain, this paper constructs a dual-channel supply chain model consisting of the manufacturer’s online direct sales channel and the online retailer’s distribution channel based on the Stackelberg game theory, and analyzes the impact of the consumer’s free-riding behavior on the optimal profits of the supply chain members, as well as the strategic game between the online retailer and the manufacturer. We analyze the impact of consumer free-riding behavior on the optimal profits of supply chain members and the strategic game between online retailers and manufacturers. The study finds that, firstly, consumer free-riding behavior harms the profitability of online retailers and affects the sensitivity of the optimal profitability of manufacturers and online retailers to the return rate of products. Second, online retailers can eliminate the effect of consumer free-riding behavior through price matching, but this strategy is effective only when the channel competition intensity is high and the product return rate is low. Finally, manufacturers also have sufficient incentives to open virtual showroom services when product return rates and channel competition intensity are high.

In this article, we consider three types of agents: policyholders, insurers, and reinsurers. From the perspective of the insurer and the reinsurer, we measure the risk through the distortion risk measures. When the premium principle is the distortion premium principle, we obtain the optimal form of the loss function of the policyholder and the insurer respectively. The result shows that in some cases, the risks of the policyholder and the insurer need to be fully borne by the insurer and the reinsurer. In some cases, the risks of the policyholder and insurer do not need to be borne by the insurer and reinsurer. When the distortion risk measures is designated as value at risk (VaR) and tail value at risk (TVaR) risk measure, and the distortion premium principle is designated as the expected premium principle, we analyze the optimal reinsurance problem in detail, and give the optimal form of the loss function of the policyholder and insurer respectively under different circumstances.

Investors’ risk perception has a key impact on asset pricing. We use the change in book-to-market ratio (△BM) of a firm between two consecutive months, to measure investors’ risk perception, and explore its relationship with expected stock returns. We find a positive and significant correlation between investors’ risk perception and expected stock returns, which cannot be explained by existing asset pricing models. We further show that the predictive ability of △BM on expected stock returns is driven by investors’ risk perception rather than firm’s future financial information, mispricing, or investor sentiment. Additionally, we find significant heterogeneity in the predictive effect of risk perception under different market conditions and firm characteristics, indicating that this effect is more pronounced during bear markets, and among small firms and firms with low liquidity. After a series of tests, our findings remain robust.

This article aims to construct a dual-source estimator with complete theory, sampling registration, and population movement, in order to improve the precision of estimating the net error of population census. To achieve the goal, a combination of mathematical models and on-site surveys is used to study the dual-source estimator and its related issues. It is found that the dual-source estimator cannot be directly constructed in the population, but should be established at the population stratum with equal probability; when calculating the sampling variance of the dual-source estimator of the population, the co-variance between equal probability population strata cannot be ignored, otherwise the sampling variance of the dual-source estimator of the population will be underestimated or overestimated; although the dual-source estimator is widely used, measures should be taken to meet its assumptions; the innovation lies in clarifying the inherent logical relationship between the Peterson-Lincoln estimator and the dual-source estimator; constructing sampling variance estimator, bias estimator, and mean square error estimator for dual-source estimator based on stratified jack-knife method; comparing the estimation results and precision between non-population movement and population movement dual source estimators from a data perspective. The significance of this study is to elaborate the dual-source estimator from its origin, construction, variance and bias estimation, and specific operation, so as to provide theoretical methods and practical basis for the scientific use of dual-source estimator.

Combinatorial designs have attracted significant attention due to their wide applications in coding theory, finite geometry, and statistics. This paper constructs a class of extended primitive cyclic codes of length $q$. By using the $2$-transitivity of the affine transformation group, we prove that the supports of the nonzero codewords in this code support 2-designs. In particular, when $q=3^m$, by an investigation of the properties of certain special symmetric polynomials, we demonstrate that the constructed code is an A$^2$MDS code with parameters $[q, 6, q-7]$, and its dual code is an AMDS code with parameters $[q, q-6, 6]$. Meanwhile, utilizing the $2$-transitivity of the affine transformation group, we prove that the codewords of minimum weight $6$ in the dual code also support $2$-designs. The design parameters are verified via the Magma program, and experimental results show that the constructed $2$-designs possess new parameters, thereby providing new instances for the theory of 2-designs.

In the current era of rapid development in quantum information technology, the construction of quantum maximum distance separable (MDS) codes has become a crucial research topic in the field of quantum error-correcting codes. By establishing necessary and sufficient conditions for generalized Reed-Solomon (GRS) codes to be self-orthogonal, this paper first presents explicit constructions of two classes of Hermitian self-orthogonal GRS codes. Subsequently, employing the Hermitian construction method and utilizing the aforementioned codes, we further develop two new classes of quantum MDS codes. Notably, the minimum distances of both classes of quantum MDS codes constructed in this work exceed $\frac{q+1}{2}+2$. Furthermore, comparative analysis with existing codes demonstrates that our constructions achieve larger minimum distances while maintaining the same code lengths.

In order to improve the control performance of active suspension and save communication resources, an aperiodic sampling fault-tolerant controller is proposed. The active suspension system is reconstructed by the input delay method. Using Lyapunov-Krasovskii (L-K) stability theory, the looped-functional is constructed and then stability criterion is established. Based on linear matrix inequalities (LMIs), the controller gain and the maximum sampling period satisfying the given $H_\infty$ performance index are solved. Finally, the effectiveness of the designed controller is verified by numerical simulation.

Battery suppliers face a choice between independent R&D and cooperative R&D with new energy vehicle manufacturers when improving battery technology. To address this issue, we consider a two-echelon supply chain consisting of a single battery supplier and a single new energy vehicle manufacturer to examine the selection of battery R&D strategies under different power structures (the battery supplier-led and the new energy vehicle manufacturer-led) by using game theory. The results show that regardless of who dominates the supply chain, the cooperative R&D strategy is always favourable for the new energy vehicle manufacturer. When the battery supplier dominates the supply chain, the cooperative R&D strategy is the dominant strategy for the battery supplier. However, when the new energy vehicle manufacturer is the leader, the battery supplier prefers the cooperative R&D strategy only if the new energy vehicle manufacturer’s R&D cost coefficient is relatively small; otherwise, the battery supplier tends to choose the independent R&D mode.

In the comprehensive evaluation, the current research lacks sufficient consideration of the equilibrium level of the development of the evaluated object. Especially in the process of dynamic incentive evaluation under the new development pattern of high-quality development, full attention should be paid to the development equilibrium level of the evaluated object, while considering timing gain and balanced development level, to reflect its development situation more comprehensively and accurately. To optimize the traditional static evaluation method, the idea of contact vector distance is introduced to improve the traditional Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method. In terms of indicator weighting, the improved G$_1$-Entropy combination weighting method is used to assign indicators, and the difference of information entropy between decision-makers’ subjective opinions and objective indicator data is considered. In the dynamic evaluation method, considering the incentive factors of the development trend of evaluation indicators and the equilibrium level, the vertical temporal gain and horizontal equilibrium development of the evaluated object are integrated into the dynamic evaluation process from both external and internal perspectives, and an improved TOPSIS dynamic evaluation method considering the dual incentive characteristics is proposed. Finally, the model is used to carry out dynamic evaluation and analysis on the development performance of 300 A-share listed SRDI SMEs in 2019-2021, and put forward targeted suggestions for promoting high-quality development of SRDI SMEs.

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.

To investigate the strategic choices of supply chain enterprises when engaging lead users in marketing, this study constructs a supply chain system comprising a manufacturer and a retailer, where the retailer collaborates with a lead user to promote the product. Three marketing strategies are proposed: full retailer-dependence, partial retailer-dependence, and full consumer-dependence. A Stackelberg game framework is developed to analyze the strategic interactions. Furthermore, to enhance the marketing efficiency of lead users, a refined partial retailer-dependence strategy is introduced based on the lead user’s marketing efforts. The results show that: retailers should select appropriate marketing strategies based on the lead user’s conversion rate and the presence of the eclipsing effect; the eclipsing effect of lead users influences supply chain decision-making outcomes; cooperating with lead users who exhibit strong social responsibility can significantly improve the effectiveness of marketing strategies; a slotting fee scheme based on the lead user’s marketing effort level can increase supply chain profits and product innovation; consumer heterogeneity does not undermine the positive impact of lead users’ social responsibility on supply chain innovation.

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.

This study investigates the staggered replenishment problem of multiple products in vending machines with limited storage capacity, using a two-product scenario as an example. The replenishment quantity, replenishment cycle, and the time interval between the staggered replenishments of the two products are treated as decision variables. A nonlinear programming model is formulated with the objective of minimizing the sum of replenishment costs and inventory holding costs. The necessary conditions for the optimal solution are analyzed and proven, and an analytical expression for the optimal solution is derived. Based on this, a method is developed to determine the optimal replenishment strategy for two products sharing a common, limited storage space. To validate the effectiveness of the proposed staggered replenishment strategy, numerical experiments are conducted using a representative case. Sensitivity analyses are performed on key parameters including demand rate, unit holding cost, maximum storage capacity, and unit storage space per product. The effects of these parameters on the replenishment cycle, staggering interval, and minimum total cost are examined. Practical guidelines for inventory management decisions under storage constraints are provided from a managerial perspective. This study offers theoretical support for developing optimal replenishment strategies for multiple products sharing constrained storage space.

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.