As competition among platform enterprises intensifies and development accelerates, introducing private labels and supporting small and medium-sized merchants have emerged as key strategic initiatives for platforms seeking new sources of profit growth. Accordingly, under a hybrid marketplace, this study employs the Spokes model to characterize an online sales system comprising a brand manufacturer, a small and medium-sized merchant, and an e-commerce platform. It further examines how factors such as product substitutability and perceived quality influence the platform's motivation to introduce private labels, as well as the subsequent effects on the decision-making and profitability of supply chain members. The results show that: (1) When product substitutability is high and consumers' perceived quality of the private label is low, introducing a private label increases both wholesale and retail prices of the brand manufacturer's and the small and medium-sized merchant's products. (2) Even when the seller's products are highly substitutable with the private label, introducing a lower-perceived-quality private label can still enhance sellers' profits. (3) When product substitutability is high and the private label's perceived quality is low, the platform still has strong incentives to introduce a private label, and doing so can achieve a win–win–win outcome for all three parties.

Aiming at the modeling problem of integer-valued time series data with limited value range, correlated counting events and hysteretic characteristics, this paper proposes a class of self-exciting hysteretic generalized binomial autoregressive models. Firstly, the strict stationarity and ergodicity of the model is proved, and the probabilistic and statistical properties of the model, such as conditional expectation, conditional variance and transition probability, are studied. Secondly, in both the cases where the threshold parameters and the initial values of the state indicators are known and unknown, the conditional least squares estimation and conditional maximum likelihood estimation methods of the model parameters are studied, and the asymptotic properties of the estimators are given. Among them, when the threshold parameters and the initial values of the state indicators are unknown, an algorithm capable of estimating the two threshold parameters is constructed. In addition, the testing method for the nonlinear structure of the model is studied. Subsequently, the effectiveness of the parameter estimation algorithms and the testing method for the nonlinear structure of the model are verified through simulation studies. Finally, the model is applied to the analysis of the number of precipitation days every two weeks in the Berleburg station of Germany and the Honolulu area of the United States. The results of the empirical analysis show that the model performs well in both fitting and prediction.

In this paper, linear Bayesian estimator for parametric vector of linear model with interval constraints is considered. Firstly, linear Bayesian estimator is constructed based on the interval-constrained least-squares estimator of parametric vector. Secondly, the dominance properties for proposed estimators are analyzed by mean square error matrix. Finally, a simulation study and real data analysis are performed to illustrate the theoretical results. It is shown that linear Bayesian estimator dominates the interval-constrained least-squares estimator and approaches Bayesian estimator.

To address the challenges of high-dimensional state spaces, the infeasibility of exhaustive enumeration, and the difficulty of discrete-state modeling in power system reliability assessment, this paper proposes a two-stage reliability evaluation method that integrates a branch search algorithm with a Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP). In the first stage, the entire system is decomposed into two subsystems: generators and transmission lines. Potential critical states are efficiently identified through prefix expansion, upper-lower bound criteria, and logical pruning, thereby avoiding the need to evaluate all system states as required by traditional enumeration methods. To account for transmission constraints, a maximum-flow-based evaluation algorithm is developed for the line subsystem, which can rapidly determine system supply capability without relying on power flow equations, significantly improving state evaluation efficiency. In the second stage, high-value samples obtained from the state space via the branch search algorithm are used to train a WGAN-GP generative model. By combining the Wasserstein distance with gradient penalty, stable continuous relaxation training is achieved, enabling sample augmentation and diversity generation within the critical region. Experimental results demonstrate that, for the RBTS system, the proposed method achieves a 98.5% coverage rate with only 535 evaluation analysis in 6.75 s. For the RTS-79 system, 2,070,564 critical states are identified within 15.82 s. Moreover, compared with traditional Monte Carlo simulation (MCS), the proposed method yields reliability indices LOLP and Expected Demand EDNS that are highly consistent with MCS results. The relative error is approximately 1.1016% for LOLP and 1.4064% for EDNS, fully validating the proposed model's high efficiency, stability, and accuracy.

This paper investigates the time-optimal control problem for the one-dimensional heat equation. The objective is to drive the system state into a given target set in the shortest possible time. A direct deep learning-based approach is proposed, where the differential evolution algorithm is employed to optimize network parameters, and we obtain the optimal time and the time-optimal control. In order to verify the rationality of the obtained results, the Pontryagin's Maximum Principle is used as a consistency check. Numerical results show that the computed control exhibits an explicit Bang–Bang structure, which is in high agreement with the necessary conditions. The optimal time and the control profile remain stable under different perturbed initial values, demonstrating strong robustness. The results in this paper indicate that deep learning provides an effective implementation approach for the optimal control of distributed parameter systems.

In classification tasks, accuracy serves as a core metric for evaluating the predictive performance of models. However, a single predictive model often suffers from model uncertainty, and directly maximizing classification accuracy leads to an NP-hard optimization problem. To address these challenges, this paper proposes an Accuracy-maximizing Model Averaging prediction method (AccMA). Based on a classification-calibrated surrogate loss function, AccMA assigns weights to candidate models by minimizing the $K$-fold cross-validation criterion of the sample surrogate loss, and the weight selection process is completely data-driven. Theoretical analysis shows that the proposed method is asymptotically optimal in the sense of minimizing classification error risk, which is equivalent to maximizing prediction accuracy. Numerical simulation experiments verify the effectiveness of AccMA, and applications to three real-world datasets (machine predictive maintenance data, sonar detection data and AIDS clinical trials group study 175 data) demonstrate that AccMA has a distinct advantage over competitive methods in improving classification accuracy.

The Twin Support Vector Quantile Regression model (TSVQR) not only exhibits good generalization performance but also captures the heterogeneity characteristics within datasets. When addressing nonlinear problems, this model initially requires mapping input features into a high-dimensional feature space before fitting a linear quantile model within that space. Given that there may be numerous redundant features in the high-dimensional feature space, TSVQR is susceptible to biased parameter estimates influenced by these redundant features, which further affects the predictive performance of the model. In this paper, we propose a Hybrid Twin Support Vector Quantile Regression (HTSVQR) model that incorporates both $L_1$ and $L_2$ regularization terms into the objective function. This integration endows the HTSVQR model with the smoothness of the $L_2$ regularization term while also achieving sparsity through the $L_1$ regularization term. Consequently, it enables sparse estimation, enhances generalization performance, and improves robustness of the model. Finally, the effectiveness of the proposed model and method is validated through numerical simulations and analysis of air quality data from Jiangxi Province. The analysis results show that HTSVQR exhibits better robustness and generalization performance than other models for different distributions of noise.

Given the substantial global manufacturing transformation that promotes servitization in manufacturing, service-oriented manufacturing(SOM)-a new industrial paradigm that combines manufacturing and services-is crucial to enhancing industrial chain resilience and reaching carbon peaking and carbon neutrality targets. Although multi-scale synergies spanning micro-enterprises, meso-industrial networks, and macro-policies are essential to SOM's effectiveness, current research faces enduring obstacles such as fragmented innovation efficacy evaluation frameworks, underdeveloped modeling of technology-organization-institution dynamic couplings, and multi-source heterogeneous data integration. This paper creates a collaborative measurement framework that combines multi-scale optimization, causal inference, and hypernetwork modeling to close these gaps. In order to quantify cross-scale transmission dynamics, we build a tripartite "service-industry-policy" hypernetwork model in conjunction with differential equations. We introduce two metrics: dynamic viscosity for meso-resource allocation efficiency and collaborative entropy for micro-interaction stability. The framework incorporates asymmetric evolutionary game strategies to resolve SME-LE collaboration imbalances and leverages federated tensor decomposition for cross-modal data alignment. Empirical analyses substantiate the model’s validity, demonstrating significant policy multiplier effects and operational feasibility of service module assembly patterns. Collectively, this work establishes rigorous theoretical and methodological underpinnings for SOM’s digital transformation, enabling integrated stability monitoring, adaptability optimization, and resilience enhancement across manufacturing ecosystems.

Longitudinal data are widely used in critical fields such as medicine and genomics, with complexities primarily arising from within-subject correlations and potential heteroscedasticity. Most existing feature screening methods are designed for cross-sectional data and are not directly applicable to longitudinal data. This paper proposes a feature screening method for ultrahigh-dimensional longitudinal data based on generalized estimating equations and expectile regression, termed GEEES. By incorporating a working correlation matrix to account for within-subject correlations and utilizing expectile regression to capture heteroscedasticity, the proposed method offers broad applicability. Theoretical analysis shows that, as the sample size tends to infinity, GEEES can select all important variables with probability approaching one, even when the working correlation structure is misspecified. Numerical simulations under both standard longitudinal data and heteroscedastic longitudinal data settings demonstrate the superiority of GEEES. Finally, the proposed method is applied to an ophthalmology longitudinal dataset, further illustrating its practical applicability.

In this paper, strict co-radiant separation theorems in vector optimization are established on locally convex spaces using the normlike-base, that is, a cone and a co-radiant set can be separated by a Bishop-Phelps type normlike-linear separating function. Meanwhile, by using the concept of the augmented $\varepsilon$-dual co-radiant sets, a sufficient optimality condition for the $(C,\varepsilon)$-Benson proper efficient solution of vector optimization problem is proposed, and the nonlinear scalarization characterization results for $(C,\varepsilon)$-Benson proper efficient solution are obtained by applying the strict co-radiant separation theorems.Finally, considering the uncertain vector optimization problem, the results of linear and nonlinear scalarizations for $(C,\varepsilon)$-robust Benson proper efficient solution are respectively established.

Effectively reducing the impact of estimation errors has always been a critical challenge in constructing high-dimensional portfolios using the mean-variance model. From a perspective that emphasizes both the mitigation of estimation risk and the control of suboptimality risk, this paper investigates the problem of regularized high-dimensional portfolio construction. It introduces generalized position constraints that can incorporate investors' personalized preferences and based on these, establishes a regularized model framework for high-dimensional portfolios. This framework aims to mitigate estimation risk while controlling suboptimality risk, thereby reducing the impact of estimation errors more effectively. Furthermore, the solution algorithm for the new model and recommendations for selecting tuning parameters are provided to facilitate its application. Simulation experiments using generated data and empirical analyses on real-world data from several major domestic and international financial markets demonstrate that the new model outperforms existing regularized high-dimensional portfolio models not only in reducing portfolio risk and turnover rate and improving the Sharpe ratio but also in achieving portfolios with a more flexible and diverse sparsity pattern. Simultaneously, the study provides new empirical evidence that can inform the development of portfolio management strategies

With the increasing prominence of interdependencies among insurance businesses, how to balance investing in loss prevention and purchasing reinsurance for limited capital, has become a core issue in insurers' risk management. The current research on joint dynamic optimization of loss prevention and reinsurance under dependent risk is insufficient. This paper investigates an optimal risk control decision-making problem for an insurer under dependent risks, where two risk management measures of loss prevention and reinsurance are considered and the objective is to maximize the terminal expected utility. By constructing Thinning model to characterize the dependent claim processes of insurance businesses and establishing the Hamilton-Jacobi-Bellman (HJB) equation based on stochastic control theory, closed-form expressions of the optimal strategy and value function are obtained. The study reveals that the optimal fund allocation strategy of insurers highly depends on their risk aversion level: when risk aversion is low, priority is given to investing in loss prevention; when risk aversion is high, the proportion of reinsurance is increased to transfer risks. Meanwhile, the scale of prepared funds and the claim probability also significantly influence the decision-making: abundant funds for a high risk-averse individual enhance the marginal benefit of loss prevention, while high claim probability increases the cost of reinsurance, prompting insurers to prefer proactive risk management through preventive measures. This research provides a theoretical basis and decision-making reference for insurers in managing dynamic risks under dependent businesses.

This study addressed omnichannel inventory and order fulfillment problem with the decision maker's risk aversion and customers' time preference under uncertain environment. To handle the ambiguity in the probability distribution of uncertain parameters and satisfy customer's service level requirement, a distributionally robust optimization model with joint chance constraints is developed. Based on the ambiguity sets, the proposed distributionally robust optimization model can be transformed into equivalent mixed-integer linear programs, and a conservative CVaR is adopted to transform the chance constraints. Numerical experiments are performed to illustrate the effectiveness of the proposed model and solution. The results demonstrated that distributionally robust optimization model shows superior out-of-sample performance compared with the traditional stochastic optimization model; WMQD criterion has a better performance in risk measurement; the lengthening of popular period and the increasing of short-term and long-term factors increase the objective function values; adopting both SFS and BOPS is not always better than a single fulfillment strategy; the service level have significant impacts on operational performance of retailers.

Green Total Factor Productivity (GTFP) is a core indicator of regional green transformation, and the synergy of innovation, industrial, and capital chains (the “Triple Chain”) is key to its improvement. Based on panel data from 30 Chinese provinces (2011-2022, with Tibet excluded due to data unavailability), this paper employs the composite system synergy degree model, super-efficiency SBM-DEA, and fsQCA to explore the configurational paths and regional heterogeneity of Triple Chain synergy driving GTFP growth, resolving the paradox of inverted regional rankings-the eastern region has the highest synergy but not the fastest GTFP growth, while the opposite holds for the western region. Findings reveal that GTFP improvement relies on the systemic configurational effect of Triple Chain synergy, exhibiting a configurational non-linear relationship where synergy quality outweighs quantity. Four equivalent driving paths are identified, including the Triple Chain synergy type, the innovation-capital dual-drive type, the industry-capital dual-drive type, and the innovation-industry dual-drive type. Triple Chain integration driving GTFP evolves dynamically from “scale-driven” to “innovation-led”, with significant path heterogeneity across China's four major regions. This paper reveals the configurational logic of Triple Chain synergy driving GTFP, offering differentiated policy implications for regions to optimize their Triple Chain integration models.

Leveraging large language models for disease diagnosis can effectively improve diagnostic accuracy, lower technical barriers, and reduce diagnostic costs, and their effectiveness largely depends on prompt engineering. However, due to strong reliance on clinical diagnostic experience, high similarity of symptoms across different diseases, and complex diagnostic decision-making paths, existing mainstream prompting methods are unable to meet the medical requirements of precise diagnosis. To address these issues, this paper proposes a Multiagent Knowledge-enhanced Prompting (MKP) method for disease diagnosis. MKP proposes a knowledge retrieval strategy to address reliance on clinical diagnostic experience, a multi-perspective reasoning strategy to handle similar symptom presentations, and a decision fusion strategy to manage complex diagnostic decision paths. Experiments on three real-world disease diagnosis datasets demonstrate that MKP significantly outperforms current mainstream prompting methods on disease diagnosis tasks, providing new techniques and methodological guidance for intelligent healthcare. Additionally, a robustness analysis is conducted on the key parameters of MKP to identify optimal parameter settings, providing practical support for its clinical deployment.

Under the background of green and low-carbon transition, there is a research gap concerning the dynamic characteristics of regional low-carbon innovation network resilience. Based on low-carbon patent data of enterprises and academic institutions across 31 provinces in China from 2016 to 2023, this paper constructs a network and quantifies resilience from three dimensions—resistance, recovery, and innovation—by incorporating a cascading failure model. The study employs Kernel density estimation, standard deviation ellipse, Gini decomposition, and $\sigma$ and $\beta$ convergence methods to analyze spatiotemporal evolution, and constructs a random forest model to reveal the influence mechanisms under two failure scenarios. The results show that: (1) Under both scenarios, resilience exhibits a three-stage evolution of "adjustment–stabilization–improvement", with regional heterogeneity forming a "core–periphery" four-echelon structure; (2) Spatially, both types of failures display agglomeration characteristics, yet their geographical patterns differ significantly; (3) The influencing factors show a dual-wheel differentiated driving force of "element–structure": under random failure, internal structural variables dominate, while under intentional failure, external environmental variables are key. Accordingly, policy recommendations are proposed, including scenario-specific measures, differentiated spatial governance, and the establishment of a dual-dimensional support system.

The application of blockchain technology has enhanced the traceability of power batteries in new energy vehicles and stimulated consumer demand; however, it has also intensified consumer concerns over the risk of privacy leakage. A supply chain model, consisting of a power battery supplier, a new energy vehicle manufacturer, and consumers, was constructed in this paper. The optimal pricing decisions of blockchain adopters were analyzed and compared under different types of consumer behavior. The findings were as follows: (1) When consumers were risk-neutral, although the adoption of blockchain technology by battery suppliers was found to increase battery recycling volume, it was not conducive to an increase in market demand. Moreover, it was found that only when the demand gain and recycling volume gain brought by blockchain technology simultaneously met the corresponding threshold conditions could the profit of the firm adopting blockchain technology be increased; (2) When consumers were risk-averse, the advantages of blockchain technology adoption by all parties were found not to be affected by consumers' risk aversion. Moreover, the conditions for their profit growth were shown to be influenced by the proportion of risk-averse consumers in the market; (3) Regardless of the proportion of consumer types, an increase in the degree of loss caused by risk aversion was shown to systematically suppress market demand and recycling volume across all models. Furthermore, corporate profits were observed to exhibit a U-shaped trend-decreasing initially before increasing-as the degree of loss caused by risk aversion intensified.

This study investigates a non-zero-sum reinsurance-investment game for an insurer and a reinsurer with common shock dependence. It is assumed that the insurer buys proportional reinsurance from the reinsurer to diversify risks, and the claim business of the insurer and the reinsurer has common shock dependence. In addition, both the insurer and the reinsurer are allowed to invest in the same risk-free asset and risky asset, where the price process of the risky asset is described by the square root factor model. The objectives of both the insurer and the reinsurer are to maximize the expected exponential utility of their relative wealth at the terminal time. Relying on dynamic programming principle, we establish the coupled Hamilton-Jacobi-Bellman equations in the framework of non-zero-sum games. Furthermore, we obtain the explicit solutions of the Nash equilibrium reinsurance and investment strategies. Finally, some numerical examples are given to illustrate the impacts of model parameters on the optimal strategies. The results show the competition coefficient exerts a significant influence on the reinsurance decisions of both parties. The common shock intensity parameter has a negative effect on the reinsurer's underwriting willingness, yet it has a positive impact on the insurer's reinsurance demand.

The high default rate in the 'company-farmer' order model severely restricts the healthy development of agricultural modernization in China, with the fundamental reason being insufficient coordination in the agricultural product supply chain. This paper establishes a two-level agricultural product supply chain Stackelberg game for the 'company-farmer' type and considers the company's service level to analyze the impact of cost-sharing contracts under the company's altruistic preference on supply chain performance and social welfare. Secondly, through theoretical analysis and numerical simulation, the specific conditions for achieving coordination in the agricultural product supply chain are determined, compensating for the shortcomings of purely altruistic preferences or purely cost-sharing contracts in coordination, and demonstrating the synergistic effect of combining the two. The following conclusions are drawn: (1) The company's altruistic preference behavior achieves dual improvements in 'supply chain efficiency' and 'social welfare' through price adjustment and service optimization; (2) Cost-sharing contracts under altruistic preference can improve the company's service level and stimulate market demand for agricultural products; (3) Cost-sharing contracts with altruistic preference can achieve effective coordination in the agricultural product supply chain. Finally, based on the research conclusions, three implications are proposed for companies, farmers, and the government, respectively, providing new theoretical perspectives and practical guidance for the coordinated development of the 'company-farmer' agricultural product supply chain.

This paper studies the reinsurance contract making problem under the leader-follower stochastic differential game between two competitive insurers and two competitive reinsurers. The claim process of the two insurers satisfies the compound Poisson process, and the dependence between the insurance businesses of the two insurers is reflected through the common Poisson process in the claim process. Based on the relative wealth, this paper quantifies the competition between two insurers and two reinsurers, respectively. Based on the mean-variance criterion, we respective establish two kinds of non-zero-sum stochastic differential games between two insurers and two reinsurers, and then establish two kinds of leader-follower stochastic differential games between two insurers and two reinsurers. These two kinds of non-zero-sum stochastic differential games are nested in the two kinds of leader-follower stochastic differential games. Based on the theory of stochastic control and the idea of game theory, the optimal time-consistent claim risk sharing strategy of insurers and the optimal time-consistent reinsurance pricing strategy of reinsurers are obtained, furthermore, the optimal time-consistent reinsurance contract is obtained. Finally, the influence of the degree of competition, risk aversion degree and the dependence of insurance business of two insurers on the theoretical results is explored through numerical experiments, and some new enlightenment is obtained.

In view of the current trend of rapidly promoting the electrification of ride-hailing in many parts of the country and the background of differences in the process of electrification of ride-hailing between different regions. Based on the strategy of differentiated subsidies for different types of vehicles on the platform, taking into account the competition between ride-hailing and cruising taxi, the service supply of drivers and the bounded rationality of passengers, the optimal supply of different types of drivers is solved by using Kuhn Tucker theorem. Aiming at maximizing platform revenue and minimizing ride-hailing carbon emissions, a three-level programming model of " ride-hailing platform-driver-passenger" is established to optimize the platform reward ratio, unit mileage price and subsidies, and the existence of Nash equilibrium price is demonstrated. In terms of model solving, the optimization variables are processed hierarchically, the genetic algorithm is used to optimize the reward ratio and subsidy, the sensitivity analysis method is used to describe the derivative relationship between the demand of different travel modes and the price change, and the relaxation method is used to solve the equilibrium price. The study shows that: (1) Promoting the electrification of ride-hailing vehicles can achieve a lower equilibrium transportation service price in competition;(2) When the proportion of pure electric vehicles in the market is stable, the platform will increase the reward ratio allocated to all drivers, which will help to increase the platform revenue;

This paper focuses on the core issue of how the quantification of data assets acts on corporate credit risk in the era of the digital economy. Aiming at the biases and distortions that may arise in estimation and statistical inference from traditional model selection methods, we adopt the model averaging method to construct a more robust econometric analysis framework, so as to systematically identify the impact mechanisms and heterogeneous manifestations of data assets on credit risk. For this purpose, we use the panel data of China's A-share listed companies from 2012 to 2024 and employ the model averaging method based on smooth penalty, which effectively alleviates the problem of model uncertainty and ensures the reliability of statistical inference. The empirical findings show that: First, data assets exert a robust and significant negative impact on corporate credit risk, indicating that they have a distinct risk mitigation effect. Second, the heterogeneity analysis reveals that this effect is more prominent in non-state-owned enterprises, high-tech industries, manufacturing industries, and mature enterprises. Third, the mechanism test demonstrates that data assets reduce corporate credit risk by enhancing information transparency, boosting total factor productivity, and strengthening executive incentives. The contributions of this paper are mainly reflected in the following two aspects. Empirically, it provides systematic empirical evidence for the credit enhancement effect of data assets and uncovers their applicable contexts and impact channels. Methodologically, by introducing an econometric framework of model averaging that can effectively address model uncertainty and heteroscedasticity, it improves the robustness and inferential reliability of research on relevant topics. The conclusions offer theoretical insights and practical reference value for deepening the assessment of data elements and improving corporate credit risk management.

In treatment effect estimation, practical constraints such as imbalanced study populations and the costs of data collection, annotation, and computation often result in substantially fewer treated units than controls, which undermines the stability and precision of inference. Within the conformal prediction framework, we investigate the impact of imbalanced treatment assignment on the construction of prediction intervals for treatment effects. Simulation studies reveal that increasing imbalance can substantially inflate interval width. Motivated by these findings, we introduce random under-sampling and probability-based sampling strategies for propensity score estimation, thereby alleviating the adverse effects of treatment imbalance on the construction of conformal prediction intervals. Results from simulation experiments and semi-synthetic data analyses demonstrate that both sampling strategies can significantly reduce interval width without sacrificing empirical coverage, with probability-based sampling yielding the most pronounced improvements in interval efficiency.

In view of the problem of information sharing in emergency collaboration for emergencies, this study constructs a network evolution game model of information sharing between emergency response decision-makers, and analyzes the influence of factors such as the capability heterogeneity of decision-making entities, sustainable interests and network structure on the evolution of information sharing strategy. The results show that: 1) When the sustainable benefit is too small (or too large), all decision-making entities do not share (or share) emergency information.; when the benefit is in a certain range, if the difference in the ability to obtain emergency information is larger, it is trapped in an inefficient “half-sharing” dilemma; the difference is small or even the same, the result of “full sharing” or “not sharing at all” appears. 2) The network structure effect leads to equilibrium “drift”. 3) The impact of key factors such as information sharing costs, sustainable interests, group size, external environmental uncertainty, number of neighbors, and probability of random rewiring on the choice of sharing strategies is interfered with by the heterogeneity of decision-makers' capabilities. 4) In the context of homogeneous decision-making capabilities, a higher proportion of groups choose the “information sharing” strategy.

In this paper, taking the data of some component stocks of Shanghai Stock Exchange 50 index, combined with fractal theory, return-risk ratio, and multiple realistic constraints, an optimal asset allocation model with maximizing return-fractal risk ratio as the investment goal is constructed. In order to obtain the optimal asset allocation ratio, an improved teaching and learning optimization algorithm combining multiple "learning" operators is proposed to solve the portfolio model. The empirical results show that the returns of single component stocks themselves and between two component stocks have fractal characteristics, and fractal theory is suitable for the construction of stock portfolio. Whether in a bull or a bear market environment, the return-fractal risk ratio model with different adjustment periods, different levels of volatility and time scales are generally better than traditional portfolio models such as Mean-Variance and Mean-VaR in terms of average rate of return and Information ratio.

In the highly interconnected information environment shaped by social media, rumor propagation exhibits greater complexity and suddenness. To more accurately characterize the positive reinforcement mechanism of social media in the rumor diffusion process, this study develops the ISDR-M (Ignorant—Spreader—Debunker—Removed—Media) model, incorporating both the activation of social media by spreaders (activation rate $\eta$) and the amplification of rumor diffusion by social media (transmission rate $\beta$). The basic reproduction number $R_0$ and the existence conditions for four types of equilibria are derived analytically. Furthermore, the Routh—Hurwitz criterion is employed to investigate the local stability of each equilibrium. By applying the global asymptotic stability criterion and transcritical bifurcation theory proposed by Castillo-Chavez et al., this study systematically characterizes the global dynamics and bifurcation structure of the model as key parameters vary. Comparative analysis with the traditional ISDR model reveals that the positive reinforcement mechanism of social media significantly enlarges the scale of rumor diffusion and weakens the dominant role of traditional contact-based transmission pathways. Finally, numerical simulations are conducted to validate the theoretical findings. This study provides a theoretical foundation for understanding the nonlinear mechanisms and key regulatory factors of rumor propagation in the context of social media, and offers mathematical support and policy implications for the design of effective intervention strategies, such as platform governance and anti-rumor information dissemination.

With the rapid development of China's financial sector, the number of bank branches has grown steadily, leading to a significant increase in bank density around firms. As an intuitive signal of financial service accessibility, changes in the density of nearby banks may exert profound influences on information transmission and investment behavior in securities markets. Using data from A-share listed companies over the period 2007-2023, this paper takes stock idiosyncratic volatility as a representative indicator of stock market microstructure characteristics, and examines the effect of neighboring bank density on idiosyncratic volatility and its underlying mechanisms. The empirical results demonstrate that greater neighboring bank density significantly reduces stock idiosyncratic volatility, thereby mitigating the noise embedded in firm-specific information. Mechanism analysis reveals that improved financing conditions and enhanced corporate information environments serve as important transmission channels. Furthermore, heterogeneity analysis indicates that this effect varies significantly across firms with different ownership structures, regional locations, industries, and sizes. This study extends the literature on the spatial distribution of bank branches and firm-level microstructural characteristics, and offers policy implications for deepening supply-side structural reform in the banking sector, improving resource allocation efficiency, and strengthening banks' capacity to serve the real economy.

Unlike standard least squares methods that only consider observation errors, the total least squares (TLS) methodology accounts for perturbations in both the dependent variable and the system matrix, offering enhanced practical relevance. Inspired by recent advances in subsampling-improved randomized singular value decomposition, we develop an accelerated randomized algorithm for truncated total least squares (ARTTLS) problems, specifically tailored to large-scale ill-posed matrices. The algorithm employs a dual strategy of row-space subsampling and random projection to explicitly approximate the dominant spaces of the augmented matrix. We establish an upper error bound for the proposed algorithm and perform numerical experiments. The results show that ARTTLS algorithm maintains a comparable or superior solution accuracy while significantly reducing computational time. This study presents an efficient and robust solution to TTLS problems in large-scale scenarios.

Against the backdrop of the digital economy emerging as a key engine driving high-quality regional development, this paper focuses on provincial-level digital economies. It constructs a measurement and forecasting framework tailored to provincial data characteristics, categorizing the digital economy into foundational and integrated types. By incorporating substitution and spillover effects into growth accounting theory, it quantifies the contribution of digital technologies to traditional industrial growth. To address data gaps, a combined forecasting method integrating the GM(1,1) model with node interpolation is proposed. Empirical results using Shaanxi Province's data from 2002 to 2020 demonstrate: (1) The framework exhibits strong feasibility and effectiveness at the provincial level, with a forecast error of only 0.78% for the 2022 digital economy share—outperforming traditional single models; (2) During the estimation period, Shaanxi's digital economy expanded from RMB 17.766 billion to RMB 412.601 billion, with its GDP share rising from 8.21% to 30.22%; (3) Digitalization outcomes exhibit significant sectoral heterogeneity, with secondary and tertiary industries serving as core contributors; (4) Projections indicate Shaanxi's digital economy will exceed RMB 1.12 trillion by 2027, surpassing 50% of GDP. The proposed analytical framework enables continuous measurement and trend forecasting of provincial digital economy scale, providing quantitative references for establishing provincial digital economy accounting systems, identifying key industrial digitalization sectors, and formulating differentiated digital economy policies.

Hazardous chemical safety is crucial for people’s life and property, and it is of great importance for governments and policy makers. With the rapid development of China's national economy and chemical industry, chemical accidents have also shown an escalating trend on its occurrence. Therefore, there is an urgent need to assess potential chemical accident risks to support decision making on accident prevention and disposition. To this end, this paper proposes a novel approach, called RAG-Risk, to utilize RAG (Retrieval Augmented Generation) with large language model to predict the root causes of potential risks for given chemical production enterprises. Specifically, this paper constructs the context for retrieval-augmented generation of large language model using the collected 716 chemical accident cases, and refines the context of the given chemical production enterprise by using deep learning to improve the performance of root cause prediction for chemical accidents. Experimental results on the collected 716 real cases show that, compared to the baseline methods, RAG-Risk can effectively improve the precision and recall of root cause prediction for chemical accidents, with average improvements as 30.16% and 48.81% in terms of micro-F1 and macro-F1, respectively. This research provides great management insights for chemical accident risk management and emergency decision-making.

Global commodity prices are a key common factor influencing inflation in the open economies. Investigating the dynamic transmission paths of commodity price shocks to major economies is of great significance for understanding inflation formation mechanisms and formulating effective economic policies. This paper selects inflation indicators and commodity price indices for China, the United States, and the Eurozone over the period from 2000 to 2023. It constructs a multi-region time-varying parameter vector autoregressive (TVP-VAR) model and applies the generalized forecast error variance decomposition method to quantitatively evaluate the heterogeneous spillover effects of commodity price shocks on inflation in these three regions and their transmission paths. Monetary policy variables, including money supply growth and the U.S. dollar index, are incorporated as control variables in the model specification. Furthermore, a series of robustness tests—including tests for variable selection rationality, model specification validity, cross-country spillover effects, and core variable substitution—are designed to verify the appropriateness of the model design and the reliability of the empirical results through comparative analysis. The results indicate that commodity prices exert significant spillover effects on inflation in China, the United States, and the Eurozone. However, the transmission efficiency and direction exhibit pronounced regional dynamic characteristics and are closely related to the monetary policy environment.

Against the background of digital-real integration, digital platforms have continuously expanded their market power into the real economy through vertical integration. How to evaluate the welfare effects of such behavior and implement scientific regulation has become an urgent issue to be addressed. Based on the traditional two-sided market model, this paper integrates the Cournot model and the Stackelberg model in industrial organization theory, and constructs a two-tier two-sided market model that can simultaneously characterize the equilibrium of both the platform market and the real economy market. The results show that when focusing on a single real economy industry, mild vertical expansion may help improve total social welfare. However, when the equilibrium of related real economy industries and the platform market are incorporated into the model for an overall investigation, it is found that monopolistic platforms tend to extend their monopoly power into the real economy, while competitive platforms may use vertical expansion as a competitive strategy to engage in cut-throat competition. Without effective regulation, such behavior will intensify and lead to a decline in total social welfare. Finally, combined with the model analysis, this paper discusses how to regulate the vertical expansion of platforms in the new stage of platform economy development.

Against the backdrop of accelerating digital and intelligent transformation in the current economy and society, cybersecurity has become a critical strategic issue with far-reaching implications. This paper constructs a combined risk management framework of “direct defense + cybersecurity insurance” to investigate optimal cybersecurity investment strategies for centralized and decentralized enterprises under uncertain losses. Breaking from existing research reliant on fixed loss distributions, this study adopts a data-driven approach. It constructs a high-dimensional loss uncertainty set based on Laplace kernel density functions and derives optimal solutions through robust optimization methods. Findings reveal: The strategies derived from this model exhibit greater robustness than traditional models; Compared to decentralized enterprises, centralized enterprises face fewer investment constraints and enjoy greater decision flexibility, with distinct investment strategies emerging between the two; When budgets are constrained, firms should select strategies aligned with their risk aversion levels. As budgets increase, firms exhibit a pattern of rising direct defense expenditures, insurance premiums, and wealth utility followed by stabilization. With ample budgets, firms should proactively opt for full insurance coverage. This research provides theoretical foundations and practical guidance for firms to develop scientifically sound, practical, and effective cybersecurity defense strategies.

Acceptance sampling is a critical strategy in quality control for determining whether to accept or reject an entire product lot through inspection of randomly selected samples. However, existing variables sampling plans have two main limitations: First, they ignore the variation of the process fraction defective and fail to effectively incorporate prior process information, resulting in excessive sample sizes and therefore low inspection efficiency; Second, the most commonly used process capability index, $C_{pk}$, lacks a precise correspondence with the actual fraction defective, which makes it impossible to accurately evaluate the real process risks, thus resulting in lot misjudgments and significant economic losses. To address these issues, this paper first develops a Bayesian statistical model based on the process yield index $S_{pk}$, aiming at minimizing the inspection sample size. Subsequently, a Bayesian economic loss model is established with the objective of minimizing expected total loss by introducing an exponential consumer loss function that captures “threshold effect” behavior. Comparison results show that the proposed statistical model can significantly reduce the required inspection sample size while maintaining the same producer's and consumer's risks as existing plans, and the proposed economic model can further lower the average expected total loss.

The rapid growth of the new energy vehicle industry has accelerated the optimization of energy structures and promoted sustainable economic development. Improving the resource utilization efficiency of retired power batteries requires careful consideration of quality differences during the remanufacturing process. At the same time， the integration of blockchain technology has provided new momentum for the green and low-carbon transition. Against this backdrop， this paper develops a closed-loop supply chain Stackelberg game model involving battery manufacturers， vehicle manufacturers， and third-party recyclers. The model examines the optimal strategies and profits of each participant under centralized and decentralized decision-making， taking into account the effects of battery quality grades， battery traceability levels， and investments in blockchain technology on recycling decisions. The results indicate that centralized decision-making is optimal for both maximizing total supply chain profits and enhancing consumer benefits. However， when the quality grade of remanufactured batteries is either too high or too low， the recycling price decreases， leading to a lower recovery volume. The adoption of blockchain technology significantly improves battery traceability. Moreover， when the reduction in recycling prices and the increase in recovery volume together offset the cost of blockchain implementation， the use of blockchain by

A green supply chain network that integrates carbon trading, carbon reduction investment, carbon pledge financing, and consumer green preferences was designed to address the operational, financing, and carbon reduction needs of capital-constrained supply chains. A mixed-integer linear programming model was established with the objective of maximizing supply chain profits, and the NP-hard of the problem was proven. A decomposition-based two-stage heuristic algorithm was developed to efficiently solve large-scale problems. In addition, a genetic algorithm with a greedy decoding strategy is proposed as a benchmark for performance comparison. Numerous test results indicated that the genetic algorithm can obtain feasible solutions with average gaps of 9.07% and 5.20% for small- and large-scale instances in 0.24 seconds and 32.28 seconds on average, respectively. The two-stage heuristic algorithm could obtain near-optimal solutions within 1 second, with an average gap of less than 1% in small-scale instances. For large-scale instances, the algorithm achieved satisfactory solutions with an average gap of less than 1% compared to the upper bound in an average of 520.38 seconds, where CPLEX failed to find a solution. Sensitivity analysis showed that increases in carbon price and consumer preferences positively impact the total profit of the supply chain. Carbon emissions increase with the improvement of consumer preferences, while first increase and then decrease with the rise in carbon prices.

This paper quantifies climate transition risk in China using 28,600 text entries from mainstream Chinese news media between 2010 and 2022. By applying the Latent Dirichlet Allocation (LDA) model, a topic classification technique in machine learning, it measures the exposure of listed companies to climate transition risks and further investigates the relationship between this exposure and stock price crash risk. The study finds that exposure to climate transition risks positively impacts the risk of stock price crashes. Mechanism analysis suggests that higher exposure to climate transition risks triggers more short-term speculative behavior in companies, thereby increasing the likelihood of stock price crashes. The positive effect of climate transition risk exposure on stock price crash risk is more pronounced in firms with lower information transparency, higher stock price bubbles, high-polluting industries, and less government focus on climate issues. This paper provides new evidence on the relationship between corporate risk exposure and stock prices in the context of climate transition.

Green electricity consumption is the primary pathway to achieving low-carbon on the residential side. Exploring the evolutionary trajectory of investment behavior in green electricity consumption and identifying guiding mechanisms constitutes a vital means of propelling society towards dynamic green development. To achieve this objective, we develop a mixed-game model grounded in prospect theory, taking into account both the residents' heterogeneity and the operational characteristics of micro-grid. This model analyzes the strategic evolution of both parties and undergoes numerical simulation testing. Subsequently, we construct a cooperative investment revenue distribution model based on inequality aversion theory, examining revenue allocation strategies under various scenarios. The results show that for distributed photovoltaic investment projects, the ultimate strategy evolution for both residents and micro-grid converges upon cooperative investment and participation under the prevailing circumstances. This approach actively promotes efficient green electricity consumption on the residential side, enabling both residents and micro-grid to maximize their respective benefits. Risk response mechanisms, investment costs, and shared energy storage exert a significant influence on the strategic evolution of both parties. Heterogeneous residents generate cooperative value through collaborative efforts rather than independent investment. Benefit distribution strategies grounded in inequality aversion theory can effectively safeguard the returns of diverse resident groups, and maximize residents' perceptions of equitable gains from Behavioral Economics.

This study examines how alternative green financing mechanisms influence the operational decisions and emission-reduction behaviors of a capital-constrained supplier within a two-echelon manufacturing supply chain operating under a carbon emissions trading scheme. A Stackelberg game model is developed to incorporate capital constraints across three financing modes—green credit financing, carbon allowance repurchase–based financing, and internal equity financing—and analytical results are complemented with numerical experiments to investigate the determinants of financing-mode selection and emission-reduction levels. The findings show that repurchase-based financing offers suppliers the lowest financing cost when the repurchase price spread is small, while green credit financing becomes more advantageous at medium or high carbon price levels due to its cost stability; the attractiveness of internal equity financing increases with a widening repurchase price spread. For manufacturers, guiding suppliers to adopt green credit financing maximizes supply chain profits when the repurchase price spread is low to medium, whereas high carbon prices motivate manufacturers to promote repurchase-based financing. Internal equity financing yields the highest emission-reduction level, whereas green credit financing provides the weakest incentives. These insights clarify the mechanism linking carbon prices, repurchase price spreads, and financing modes, offering targeted theoretical and managerial guidance for manufacturing firms making financing and emission-reduction decisions under the “dual-carbon” policy context.

With the continuous expansion and deepening of the knowledge system, disciplinary boundaries are gradually dissolving, and cross-disciplinary integration has become an irreversible trend. This paper proposes the Cross-Disciplinary Latent Dirichlet Allocation model (CrossLDA) to investigate the integration and mutual influence between disciplines. The CrossLDA model can automatically identify shared and discipline-specific topics from two sets of domain-related texts (e.g., research articles), and track the dynamic evolution and development patterns of these topics, thereby uncovering the patterns of interdisciplinary integration and interaction. Taking statistics and computer science as examples, we model the content of articles published over the past decade in ten representative statistics journals and the AAAI Conference on Artificial Intelligence. We extract shared topics such as machine learning and intelligent decision-making, and examine the shifts in their research focus as well as the development trends of both disciplines in these shared areas. The findings reveal a close connection and mutual influence between the two disciplines. This study not only demonstrates the effectiveness of CrossLDA in uncovering the patterns of disciplinary integration but also provides data support and methodological references for academic exchange and cross-disciplinary innovation.