Factor analysis (FA) is a popular statistical technique that is used to identify the latent common factors among a set of variables. Nevertheless, it is only applicable to vector-valued data, where observations are vectors. To apply FA to matrix-valued data, where observations are matrices, one common solution is to first vectorize the matrix observations. However, the vectorization may cause FA to suffer from two problems: Poor interpretability and curse of dimensionality. To solve the two problems, the authors utilize the inherent matrix data structure and propose bilinear factor analysis (BFA) in this paper. The novelties are that BFA uses a bilinear transformation, which greatly reduces the model parameters and thus can overcome the curse of dimensionality; Moreover, it can simultaneously identify the interesting common row, column factors among the row, column variables, respectively. The authors develop two efficient algorithms for finding the maximum likelihood (ML) estimates. The authors give the theoretical property of the ML estimator and derive explicitly the closed-form expression of Fisher information matrix to evaluate the estimator's accuracy. The authors then discuss the model selection issue. Unlike the traditional FA, where the factor score is a vector, the factor score in BFA is a matrix. The authors further develop the approaches for calculating the matrix factor scores and visualizing them. Empirical studies are constructed to understand the proposed BFA model and compare with relevant methods. The results reveal the superiority and practicability of BFA in matrix-valued data analysis.

The "fundamentals" that determine expected stock returns consist of three components: The expected return component that is rationally compensated for systemic risk, the cash flow news generated by changing expectations of future cash flows, and the discount rate news generated by changing expectations of rational future discount rates. Of these, cash flow news that are not driven by fundamentals are the component most likely to reverse in the short term. In this paper, for the first time, we use analyst forecast revisions to measure cash flow news and construct a short-term reversal strategy based on residual returns to study the short-term reversal effect in the Chinese Stock Market. The empirical results find that the strategy generates higher risk-factor-adjusted returns compared to the standard reversal strategy. Further, the methodological test based on isolating cash flow news finds that liquidity shocks rather than investor sentiment can explain the short-term return reversal phenomenon in the Chinese Stock Market from both the long and short leg of the portfolio. This paper examines the short-term reversal strategy of A-shares from a new perspective of residual returns, which not only enriches the research in the area of financial anomalies in asset pricing, but also provides international evidence on understanding the theory of short-term return reversal in emerging markets, with China as an example.

Innovation and entrepreneurship is an effective choice to shape a new engine of development. As a new development form, the digital economy can provide new opportunities for enhancing the entrepreneurial vitality of the region. First, based on the panel data of selected 30 provinces in China from 2010 to 2020, this paper constructs the fixed-effects model, mediation model, and threshold model. Second, the models are applied to analyze the impacts and mechanism of the digital economy on entrepreneurial vitality from the perspectives of the labor and data factors. Third, this paper explores the boundary effects of intellectual property protection. The study shows that: 1) The development of digital economy has a significant positive effect on the entrepreneurial vitality, among which it improves the entrepreneurial vitality in the two aspects of Internet application and digital finance, while the role of the basic dimension of informatization is not obvious. 2) Digital economy can promote entrepreneurial vitality through two paths: “Labor factor allocation” and “data factor utilization”. 3) In the southeast half of the “Hu Huanyong Line”, the digital economy has a significant impact on the entrepreneurial vitality. 4) As an important institutional guarantee, intellectual property protection plays a threshold role in regulating the relationship between digital economy and entrepreneurial vitality, and can play the maximum effect when its level is in the optimal range. Accordingly, to stimulate the entrepreneurial vitality, all regions need to further improve the information infrastructure and the application level of digital technology, and optimize the allocation of regional elements. Besides, based on location characteristics, adopt the different strategy of independent innovation, and cooperation to create an entrepreneurial environment that is compatible with the development level of the digital economy.

In this paper, to address the challenges of semantic granularity and limited flexibility in effective portfolio investment caused by the inadequate perception of stock price fluctuations in portfolio return prediction models, the authors propose a comprehensive system prediction model for stock returns by integrating the sentiment situation evaluation score model (SESTM) and graphical lasso (GLASSO). Firstly, the authors introduce quantile regression to model stock price volatility, defining volatility width sequence and volatility mean sequence to identify vocabulary related to positive return fluctuations. Next, the SESTM model is employed to extract perception vocabulary related to stock price volatility from news announcements and generate news sentiment scores based on closely related themes and matching dictionaries associated with policies, valuations, and market sentiments. Finally, by combining the GLASSO method, the authors construct a network structure of interdependence among stock prices and develop individual stock portfolio strategies based on this network. Empirical experiments are conducted using stocks from the biotechnology vaccine sector during the epidemic period to compare network interdependence and sentiment situation evaluation models. The results show that firstly, investment strategies constructed based on perception vocabulary are more suitable for short-term predictions; Secondly, incorporating information the reflected partial correlations in the interdependent network, the average daily logarithmic returns of the investment portfolio reached 1.6%, which is a 14.3% improvement by 14.3% compared to not considering partial correlations, and it is twice the average daily logarithmic returns of a random combination 0.7%. Moreover, the highest return increased from 3.117 for a random combination to 3.605, showing a significant improvement of 15.6%. These results indicate that the combination model of SESTM+GLASSO provides an efficient and superior system prediction model through a comprehensive approach that can analyze the network interdependence among stock prices and accurately predict stock returns for formulating corresponding investment strategies. It has positive implications for advancing statistical research in dynamic price perception and deepening generation-based cross-modal tasks within large language models.

Bayesian quantile regression can well estimate the parameters in the linear mixed effect model. Gibbs sampling is commonly used in Bayesian parameter estimation. In order to obtain accurate estimation results, Gibbs sampling method requires multiple sampling. When the model parameter dimension is high, the Gibbs sampling will be very time-consuming. Therefore, we use variational inference to approximate the posterior distribution of parameters. Variational inference uses unconditional distribution to approximate the conditional distribution obtained by Gibbs method, thus making the calculation more efficient. In this paper, a priori assumption of the parameters of the model is normal distribution, and the variation inference of the parameters of the unpunished linear mixed effect model is carried out. Considering the high dimensional situation, we assume the prior distribution of the model parameters as Laplace distribution, and make variational inference for the parameters of the double penalty linear mixed effect model. From the simulation results, although the accuracy of variational inference for model parameter estimation is slightly less than that of Gibbs sampling, it runs faster. In the case of high dimension, the improvement of operation efficiency is more obvious. In the era of big data, the consumption of time and resources is the first factor we need to consider. Therefore, the method proposed in this paper can be applied to the high-dimensional linear mixed effect model.

By virtue of the vector order structure, the concepts of Nash equilibria and cooperative equilibria for set payoff population game are introduced. Due to Ky Fan section theorem and generalized Scarf theorem, the existence theorems of Nash equilibria and cooperative equilibria for set payoff population game are obtained with the assumption of upper semi-continuity of set payoff function, respectively. Finally, an example is given to verify the feasibility of the conclusion and illustrate the difference between Nash equilibria and cooperative equilibria.

The COVID-19 pandemic brings a crisis to China’s stock market, and investor’s choice of safe haven assets is increasingly attracting attention. This paper uses the DCC-GARCH t-copula model to test the safe haven property between gold and bitcoin in China’s stock market during the COVID-19 pandemic. The results show that gold is a better safe haven asset than bitcoin on average, because gold has a lower average hedging ratio than bitcoin, provides a cheaper hedge, and requires a lower proportion of gold than bitcoin in a portfolio with the same stock industry index. The dynamic volatility of optimal hedging ratios and portfolio weights also further points to the need for investors to actively rebalance their portfolios rather than adopt a static approach.

Hopf bifurcation is a kind of simple but important dynamic bifurcation problem, which means that when the system parameter changes past the critical value, the equilibrium point changes from stable to unstable and a limit cycle is generated. Based on Hopf bifurcation, this paper proposes a time-delay reaction-diffusion rumor propagation model with saturated control, which better reflects the characteristics of rumor propagation in real life, and studies the Turing instability and Hopf bifurcation. Meanwhile, the time delay is selected as the bifurcation parameter, and the analytic expression of the bifurcation threshold is given. Finally, the correctness of the theoretical results is verified by numerical simulation. The results show that both diffusion and time delay are the causes of the system instability. The traditional rumor propagation model only considers the time evolution, while the model depicts the traditional rumor propagation model from the two dimensions of time and space, making it more appropriate to reflect the law of rumor propagation in real life, and providing new ideas for the governance of rumor propagation.

In the process of achieving high-quality development, enhancing regional economic resilience is one of the important guarantees for promoting economic development and driving overall regional development. This paper analyzes the mechanism of digital finance influencing regional economic resilience from a theoretical perspective, and measures and analyzes the level of regional economic resilience of each province by constructing a regional economic resilience evaluation index system. Based on panel data of selected 31 provinces (autonomous regions, municipalities) in China from 2011 to 2021, a benchmark regression model, a mediating effect model, and a panel threshold effect model are further constructed to empirically test the theoretical analysis. The research shows that:1) There are still a large number of regions with relatively low levels of regional economic resilience, and there is a large disparity in the development level of economic resilience between provinces, which exhibits an imbalanced pattern of "high in the East and low in the West"; 2) Digital finance has a significant positive impact on regional economic resilience, with a regional heterogeneity of "eastern region$>$ central region$>$ western region"; 3) Digital finance has a significant positive mediating effect in the relationships of "digital finance $\rightarrow$ industrial structure upgrading $\rightarrow$ regional economic resilience", "digital finance $\rightarrow$ narrowing the urban-rural income gap $\rightarrow$ regional economic resilience", and "digital finance $\rightarrow$ social security level $\rightarrow$ regional economic resilience"; 4) The promotion effect of digital finance on regional economic resilience can be more significant when crossing the threshold of internet penetration, and the acceleration threshold effect in eastern coastal regions is significantly higher than that in central and inland regions and western remote areas. Therefore, by developing digital finance in line with local conditions, giving full play to the positive effects of industrial structure upgrading, narrowing the urban-rural income gap, and improving social security, and accelerating the construction of modern information technology, it can effectively enhance the resilience of the regional economy.

The optimization of revenue management is one of the effective ways to improve retailers' economic returns. Pricing is the engine and core technology of revenue management, which plays an important role in improving retailers' revenue. Considering the complexity of forecasting and optimization problems in the practical application of revenue management, the steps of forecasting product demand first and then optimizing revenue are usually adopted. When forecasting product demand, there are usually multiple candidate models, that is, facing the uncertainty of the model. At this time, the final model is generally determined by model selection. However, traditional model selection criteria, including Akaike information criterion(AIC) and Bayesian information criterion(BIC), usually only consider the impact of model selection on prediction accuracy, without considering how the prediction model will affect the next optimization decision objectives. This paper first proposes the focused information criterion(FIC) model selection criterion in the optimization of commodity income management, uses the FIC model selection criterion to select the product demand forecasting model, considers the structure of the optimization model, and selects the prediction model with the goal of minimizing the decision-making error rather than prediction error. The numerical simulation results show that, in most cases, compared with AIC and BIC model selection criteria, FIC model selection criteria considering decision objectives performs best. Meanwhile, the empirical research results also verify the superiority of the FIC model selection criteria considering decision objectives.

This paper presents a Euler-Maruyama,(EM) method for Riemann-Liou-ville fractional stochastic differential-integro equations, and analyzes the strong convergence of the presented EM method. Specifically, the considered fractional stochastic differential-integro equations are transformed into their integral forms, and then the left rectangle rule is used to construct the EM method. The strong convergence with order $(1-\alpha)\wedge(0.5)$ of the presented EM method is established, where $\alpha$ is the order of Riemann-Liouville fractional derivative with $0<\alpha<1$. Finally, numerical experiments are demonstrated to support the theoretical results.

This paper presents a comprehensive comparison of various models for predicting cryptocurrency volatility. The findings highlight that the rough volatility model demonstrates robust and reliable performance in forecasting out-of-sample volatility across multiple periods. Conversely, the heterogeneous autoregressive(HAR) model shows relatively weaker results. However, the log-transformed HAR model exhibits superior predictive capabilities. Additionally, the study emphasizes the significance of selecting appropriate time zone divisions, considering the impact of different time zones on cryptocurrency market volatility. To address model uncertainty in volatility modeling, the paper introduces the method of model averaging using least squares. The results indicate that model averaging outperforms alternative approaches by effectively balancing the strengths and weaknesses of different models, ultimately enhancing the credibility and stability of predictions in the cryptocurrency market. The study underscores the importance of considering the unique characteristics and historical performance of cryptocurrency volatility when selecting suitable volatility models. Furthermore, it emphasizes the need for careful evaluation of model performance across diverse datasets and prediction targets to mitigate uncertainty arising from blind application.

MOOC comments contain a wealth of user opinions and emotional information, reflecting the quality demands and satisfaction from the user's perspective. This study constructs a model for the quality characterization of MOOC based on the "Theme-Emotion" coupled analysis of user comments. Specifically, it utilizes LDA to extract thematic information from comment texts, representing dimensions for assessing MOOC quality. Furthermore, it employs BERT for emotion classification to characterize user satisfaction and attention towards MOOC quality. The study takes "Chinese University MOOC" as an example to analyze the MOOC quality characterization results. The findings reveal that the quality assessment dimensions vary in MOOCs of different subject areas, user satisfaction and attention towards each dimension differ for different MOOCs, and the quality assessment dimensions have varying significant impacts on MOOC quality. The proposed MOOC quality characterization model can be generalized to various online course platforms with user comments, offering a fine-grained representation of course quality. This model provides precise criteria for builders to design and improve courses and for learners to select courses, contributing to the optimization of MOOC development and user experience.

A variety of hot topics lists released by social media platforms serve as a convergence and showcase for hot topic information, which provides significant insights toward our understanding of current popular discussions. However, due to vocabulary sparsity and short text length in hot list texts, traditional LDA and neural network-based topic mining models face poor performance in topic aggregation. To address these challenges, the paper proposes a topic modeling framework enhanced by a large language model—STAB, which combines the generative capabilities of large language models for text data with the excellent performance of document embeddings in topic modeling, enabling the extraction of meaningful topics from short text datasets. Experimental results on multiple datasets show that our framework outperforms existing topic modeling methods in terms of general objective evaluation metrics and applications in downstream tasks.

With the accelerated advancement of digital government construction, online administrative inquiry plays an indispensable role in social governance of China. In order to explore the key factors affecting the effectiveness of online administrative inquiry, this study focuses on the relevant data from the Luzhou online administrative inquiry platform "Please Speak Up". This study adopts a text data mining method combining various machine learning and deep learning models to identify characteristic variables in online administrative inquiry texts, construct two public satisfaction classification models. And multiple explainable methods are used to explain the model results from both structural and semantic features. The research finds that variables such as administrative inquiry sentiment, length of administrative inquiry text, type of appeal, response sentiment, type of response agency, length of response time all have varying degrees of influence on public satisfaction. In addition, the explainable framework constructed by this study can also effectively identify key content in online administrative inquiry, such as time, location, and organization names.

To solve the dilemma of information-sensitive e-waste recycling under incomplete information, this paper constructed an evolutionary game model composed of government, consumers and recyclers based on prospect theory, and discussed the main factors affecting system game strategy. The results show that the government's increased supervision can promote the standardization of the recycling market. The negative credit evaluation of consumers is conductive to the informal recyclers. The high negative credit evaluation encourages the normalization of the informal recyclers, while the low negative credit evaluation promotes the informal recycling treatment of the recyclers. In the recycling process, if consumers suffer information leakage losses, they tend to distrust strategies, and the greater the information leakage loss, the deeper the degree of distrust. In addition, the loss factors in prospect theory have an impact on the strategies of consumers and recyclers, while the return factors have almost no effect, indicating policymakers pay more attention to loss aversion in the game.

Under the major public health emergency, the accurate prediction and rational allocation of emergency medical supplies are of great significance to curb the development of the COVID-19 outbreak. This paper focuses on the optimization of the allocation path of emergency medical supplies to ensure that emergency medical supplies reach the demand nodes quickly and accurately. Firstly, the Bayesian sequential decision-making model is used to predict the infection rate of the COVID-19. On this basis, the demand of each demand node is calculated according to the relationship between the number of infected people and the quantity of emergency medical supplies. Secondly, the emergency medical supplies allocation model is established based on to the number of emergency medical supplies required by the demand nodes. Thirdly, a particle swarm optimization-adaptive large neighborhood search,(PSOALNS) algorithm is developed to solve the proposed model, and then the validity and accuracy of the algorithm are verified through several sets of numerical examples. Finally, taking the outbreak stage of the COVID-19 in Wuhan as an example, this paper considers eight types of emergency medical supplies and predicts their demands, the designated medical institutions in Wuhan are selected as the demand nodes, and the path optimization is solved and the optimal configuration route is obtained. By predicting the demand for emergency medical materials in advance and optimizing the emergency medical supplies distribution route accordingly, this study can achieve the optimal allocation of emergency medical supplies more accurately and efficiently.

Starting from the physical mechanism and data-driven, based on the consistent representation of different causal modalities such as Bayesian causal graph network, dynamic intervention and counterfactual hypothesis, we have constructed a new paradigm of multi-game, multi-drive, multi-dimensional competitive causality learning. From intervening to change the flow of causality, relying on the causal relationship between the abstract variables of the graph network, and the reuse of causal mechanisms based on counterfactual assumptions, this paper combines different mechanisms and variables in a brand-new way in order to closely link causes and effects. Therefore, a better understanding about how the world works is formed from the perspectives of causality, predictability, and intelligence. Finally, we reintegrated the causal knowledge of multi-modal learning to form a hybrid orthogonal neural causal network, making full use of the actions, forces and interventions in the causal relationship and reusable causal mechanisms to greatly improve the prediction of the neural causal network ability. This paper has important guiding significance for giving existing deep learning in inductive reasoning and stronger interpretability of neural networks.

On the basis of the soft parameter sharing model, the authors set the adaptive regular term coefficient $\lambda^{*}$ and adaptive parameter decay ratio $\theta$ by the similarity between tasks and the relationships between parameters. In this paper, the authors propose an adaptive soft parameter sharing method based on multi-task deep learning. On the basis of $L_{2}$ norm based on the mean constraint, the effect of removing information with low similaritities between tasks can achieve by adaptively removing the number of terms in the regular term of the loss function. The approach in this paper dynamically transforms soft parameter multi-task learning into joint soft parameter multi-task and single-task learning. Compared with soft parameter multi-task learning methods, this method reduces the impact of negative migration phenomena. Compared with single-task learning method, this method can greatly reduce the risk of local minimum solution. Both simulation studies and case analyses have confirmed the effectiveness of this approach, demonstrating that its achieves superior predictive accuracy compared to traditional multi-task learning and single-task learning methods.

The randomized controlled trial,(RCT) is widely used in clinical trials, and sample allocation for the RCT is an important issue in practical applications. However, for the RCT under the causal inference framework, traditional sample allocation methods did not consider the correlation of potential outcomes. To solve this problem, we propose a sample allocation method considering the sensitivity parameter, and combine it with a response-adaptive randomization design to estimate causal effects. Simulation studies have verified that our method can obtain more accurate estimators of causal effects than other commonly used allocation methods when the independence assumption does not hold.

Considering a second-order nonlinear multi-agent systems with time-delayed, this paper investigates the leader-following consensus problem for this system under a fixed directed topology. In order to save the communication and computation resources of the system, a distributed consensus control protocol based on event triggering mechanism is presented. A corresponding event triggering condition is designed for each agent, and the agent updates the controller only when the triggering condition is satisfied, the frequency of updating information among the agents is effectively reduced. Some sufficient conditions for the multi-agent system with time-delayed to achieve leader-following consensus are given using graph theory, matrix theory and Lyapunov stability theory, and the Zeno behavior of the system is strictly excluded. Finally, the feasibility and effectiveness of the proposed control protocol are verified by simulation results.

The hydrodynamic characteristics of USV are highly nonlinear and time-varying. In order to facilitate the control of the yaw, a nonlinear parameter-varying (NPV) model based on the surge velocity is proposed. Firstly, a nonlinear mechanism model with three degrees of freedom is established by introducing Ross damping model from the hydrodynamic mechanism. Secondly, on the basis of the mechanism model, the nonlinear term is implied in the linear structure to make the model form a linear structure. Then, the sway damping term with small value is ignored, and the surge velocity is taken as the variable parameter to establish the NPV model based on the surge velocity. The NPV model has a simple structure with nonlinear and variable parameter terms, which is an extended form of the Norrbin nonlinear model and linear parameter-varying (LPV) model. Finally, simulations and experiments show that the NPV model can well describe the nonlinear and time-varying characteristics of the yaw motion of the USV.

This paper explores how retailers can choose the best retail mode for multi-channel retailing based on consumers' channel preferences. It compares the pricing and profit of a retailer under dual-channel, showrooming, and BOPS modes. Results show that as consumers' online channel preference increases, the optimal profit under dual-channel mode decreases then increases, while the optimal profit under BOPS and showrooming modes increases. Dual-channel is best when consumers' online channel preference is low or high enough, but BOPS and showrooming modes are more profitable for moderate online channel preference. BOPS has an advantage over showrooming as online channel preference increases. Showrooming and BOPS are expected to have more advantages as online channel preference continues to fluctuate. Our results suggest that retailers in specific industries can select the best model based on showrooming and drainage effects.

Promoting new energy vehicles is an important measure to effectively reduce the carbon footprint of the transportation system. Based on the consumer utility theory, we construct a decision model for both charging and switching modes of new energy vehicles. This model enables a comparative analysis of pricing and promotion mechanisms for the two service modes. Additionally, we examine the impacts of battery production cost, switching model technology level, driving range, and energy prices on the promotion of both modes. Our main results are as follows: 1) Compared to the charging mode, the switching mode effectively alleviates consumer charging anxiety, albeit at the expense of a premium for switching services; 2) The production cost of power battery and the level of power change technology are important dimensions that affect the adoption of the two service modes; 3) There exists a divergence in the influence of battery production costs and driving range on the promotion of the two modes; 4) Decreasing battery production costs prove more beneficial for the promotion of the switching mode, while an extended driving range is more advantageous for the promotion of the charging mode. Changes in electricity or fuel prices exert similar effects on the promotion of both modes, accelerating their application by establishing operational cost advantages for new energy vehicles.

A large amount of evidence suggests that companies with good ESG performance have a lower risk of collapse and stakeholder risk, thereby diluting systematic risk. However, compared to fundamental financial indicators, ESG as a non-financial indicator has not yet reached a consistent conclusion on its mechanism, dynamic variability, and heterogeneity of impact on stock systematic risk. Based on this, this paper selects data from January 2009 to November 2023 in the A-share market for empirical research. Based on the conditional CAPM model, the systematic risk $\beta$ is dynamically characterized as a linear function of ESG performance (non-financial characteristics) and company fundamental characteristics (financial characteristics). Then, the MCMC Bayesian estimation method is used to obtain time-varying estimates of $\beta$ for results analysis. The research results are as follows: First, there is a negative correlation between ESG performance and stock systematic risk, which has become increasingly strong and significant in recent years. Second, the impact of ESG performance on stock systematic risk shows heterogeneity across industries. For industries that are more affected by energy or national policies, good ESG performance helps to reduce systematic risk. Third, although ESG performance can affect stock systematic risk, investors respond less to ESG risk than to fundamental risk, leading to asymmetric investor reactions. Therefore, ESG risk can be considered a secondary risk, and its impact on systematic risk is moderated by fundamental characteristics such as market value and book-to-market ratio.

In the context of the digital economy, the monopolistic behavior of platform enterprises and the design of antitrust mechanisms have become hot and difficult problems in current research. To solve this problem, a tripartite evolutionary game model among government, platform enterprises and the public was established under both static and dynamic reward & punishment mechanisms. In terms of model analysis, the possibility of mixed strategy Nash equilibrium (MNE) as an evolutionary stability strategy (ESS) under the two reward & punishment mechanisms and its system evolution characteristics were mainly discussed. It was proved that MNE under dynamic reward & punishment mechanisms may be the system ESS, and confirmed through system simulation. The simulation results indicate that under the static reward & punishment mechanism, all parties in the game will exhibit periodic strategy selection patterns, while under the dynamic reward & punishment mechanism, the system gradually stabilizes to MNE. This indicates that the existence of the dynamic reward & punishment mechanism is indeed a stability improvement compared to the static reward & punishment mechanism. Finally, it is suggested that government should develop dynamic reward & punishment mechanism, while increasing the intensity of punishment on platform enterprises and gradually reducing the intensity of rewards for the public. This approach can significantly increase the probability of compliance operation of platform enterprises and improve the expected utility of government and the public.

Information asymmetry is the main reason that prevents manufacturers from actively participating in carbon market trading and investing in emission reduction technologies. Based on the carbon trading mechanism, this paper studies the choice of manufacturers' emission reduction and retailers' information sharing strategies under the condition that retailers hide consumers' low-carbon preference information. In this paper, Stackelberg model is used to investigate the optimal decisions of each member of the supply chain, in which retailers have private information (consumers' low-carbon preferences) and decide whether to share this information with manufacturers. By using game theory and static comparative analysis, it is found that retailers' sharing of information is beneficial to the supply chain, and under the condition of asymmetric information, manufacturers and retailers can improve their own profits by formulating revenue sharing contracts. When the manufacturer's risk aversion is low, retailers are willing to share information; When consumers have high low-carbon preferences and are insensitive to product prices, the emission reduction rate of manufacturers will increase; For products with high emission reduction costs and low consumer preference for low-carbon emission reduction, increasing carbon quotas will reduce the price of products, thereby reducing manufacturers' incentive to reduce emissions. Therefore, manufacturers can appropriately reduce their risk aversion behavior to attract retailers to share information. In addition, it is beneficial for the supply chain to establish revenue sharing contracts between manufacturers and retailers; In order to strengthen the manufacturer's investment in emission reduction technology, retailers can give priority to the promotion and promotion of low-carbon products to non-price sensitive users.

This paper studies the controllability of the multi-agent systems based on equipotential nodes, and proposes a method of constructing controllable graphs. Firstly, the relationship between the eigenvalues of the Laplacian matrix and the controllability of the multi-agent system with multi-signal inputs is provided. Secondly, it is found that there are differences between the controllability of the system with single-signal input and that of the system with multi-signal input. It is easier to realize the controllability of the system with multi-signal inputs than the case with single-signal input. In addition, the relationship between the topological structures with equipotential nodes and the eigenvectors of Laplacian matrix is provided, and a leader selection method is proposed to ensure controllability. Then, we analyze how to construct controllable graphs based on equipotential nodes for the multi-signal inputs system, and present a necessary and sufficient condition for controllability. Finally, a numerical example is given to verify the effectiveness of the method of constructing controllable graphs.

With the rapid development of the platform economy, more and more manufacturers sell the products through their own channels (i.e., the direct channel) besides the retailers (the indirect one), i.e., the dual-channel supply chain. Traditional wisdoms also refer to the dual-channel as the manufacturer encroachment, endowing manufacturers with absolute control over prices. Intuitively, one finds the manufacturer can have more carbon emission, which increases the manufacturer's purchase cost of carbon emissions (i.e., carbon cost) because of the increasing sales with channel competition, especially under the carbon cap-and-trade, namely channel competition effect. On the other hand, the research and development (R&D) cost per the unit product of the carbon reduction can be alleviated due to channel competition, which results in the lower unit carbon mission and wholesale price, namely, spillover effect. Motivated by the observations, we employ a Stackelberg game between a manufacturer (she) and a retailer (he) to explore the manufacturer's channel decisions under carbon cap-and-trade. It shows that the manufacturer always has an incentive to develop the direct channel. Counterintuitively, whether the manufacturer's carbon emissions in the dual-channel supply chain are higher than that in the single channel one depends on the manufacturer's reduction cost in carbon emission. To be specific, when the manufacturer's reduction cost in carbon emission is low, her carbon emission in the dual-channel supply chain is lower than that in the single channel; Otherwise, her carbon emission in the dual-channel supply chain is higher. For the retailer, he can benefit from the manufacturer encroachment. When the carbon price is high and the manufacturer's reduction cost in carbon emission is low, the retailer benefits from the manufacturer encroachment; Otherwise, his profit in the dual-channel supply chain is lower. In addition, we identify the region in which the retailer's profit is higher and the carbon emission is lower in the dual channel supply chain than those in the single one.

The digitalization of cross-border trade motivates the development of cross-border e-commerce (CBEC). To inspire the small and medium-sized companies to participate in the innovative CBEC practice, 165 CBEC comprehensive pilot zones have been established in different batches and the so-called “no-ticket exemption” policy has also been introduced. In this paper, the integrated optimization of the CBEC supply chain network design and the tax-declaring strategies are studied, and both the comprehensive experimental zones and the “no-ticket exemption” policy are taken into account. A two-stage nonlinear stochastic programming model is developed, in which, uncertain demands and exchange rates are involved. To optimally solve it, the proposed model is linearized and an optimally dedicated L-shaped algorithm is designed. The case study shows that the “no-ticket exemption” policy can significantly decrease the tax burden of the CBEC companies, and then, attract the CBEC companies to deploy their hubs in the comprehensive pilot zones. Moreover, the introduction of the “Regional Comprehensive Economic Partnership” agreement would alleviate the difference between overseas warehouses and domestic warehouses and inspire the CBEC companies to concentrate cargo logistics to a few overseas warehouses with geographical superiority. Both of the two policies can reduce the layout cost of supply chain network of the CBEC companies.

To solve the problems of high subjectivity of "self-confidence" and lack of correspondence moderation mechanism in the self-confident double hierarchy linguistic, proposing a new decision-making term based on the self-confidence double hierarchy linguistic and a multi-attribute group decision-making method based on the preference relationship of the duality-confident double hierarchy linguistic preference relation is developed. Firstly, using the social network method to acquire the "trust-relationship" between experts is completed by considering the OWA operator and the shortest link principle, coupling the "trust-relationship" and the self-confidence double hierarchy linguistic to create the duality-confident double hierarchy linguistic, expanding the duality-confident double hierarchy linguistic preference relation, and study its consistency and consensus indicators. Secondly, the feedback adjustment mechanism of the duality-confident double hierarchy linguistic is constructed. Then a new expert empowerment model is constructed for the adjusted "self-confidence" and "credibility" indicators in the duality-confident double hierarchy linguistics. Finally, combined with the feedback moderation mechanism and expert empowerment model, a multi-attribute group decision-making method is proposed based on the duality-confident double hierarchy linguistic preference relationship. Through the analysis of renewable energy investment projects in Hunan Province, the applicability and effectiveness of the method are verified.

To analyze the cooperation behavior from the perspective of doctors and patients in the smart medical information platform, this paper constructs a random evolutionary game model and introduces random interference factors to represent the information uncertainty in the information platform. Afterward, this paper transforms the stochastic evolutionary game model of doctors and patients into a cusp catastrophe model through the limit probability density function, proving that the sudden change mechanism is implied in the behavior evolution of doctors and patients. Finally, the simulation method is used to analyze the evolution and sudden change mechanism of the behavior selection of doctors and patients in the diagnostic information platform and the interactive information platform. This paper finds that: In the smart medical information platform, the behavior selection of doctors and patients may change drastically due to factors such as perceived value and random interference; When the initial cooperation probability between doctors and patients is high if the security and reliability of information platform are poor, doctors and patients tend not to cooperate; When the initial cooperation probability is low if the information platform security and reliability are good, doctors and patients tend to cooperate; When the initial cooperation probability is at a moderate level, the behaviors of doctors and patients in the information platform are more susceptible to the additional benefits of non-cooperation, sudden changes of behavior selection are more probable. This paper analyzes the cooperation mechanism between doctors and patients in the smart medical information platform by combining evolutionary game theory and cusp catastrophe theory. It explains the reasons for sudden discontinuous changes in the behavior state of doctors and patients. The conclusion provides enlightenment for the research on doctor-patient cooperative behavior in the information platform and the development of the smart medical platform.

In order to study the nature of chaos and make use of chaos better, chaos in a three-dimensional generalized Rabinovich system is studied in this paper according to Lyapunov stability theory and bifurcation theory, including dissipation, the equilibrium point and local asymptotic stability, Lyapunov exponent, Lyapunov dimension, bifurcation diagram, global attractive domain, etc. According to the result of global exponential attractive set of this chaotic system and Dini derivative, a suitable controller is designed to realize global exponential synchronization for two identical chaotic systems. A linear feedback controller is designed to achieve global exponential synchronization for two identical chaotic systems in order to make it easier to achieve fast synchronization for chaos synchronization scheme in practical applications. The innovation of this paper is that the boundedness of the chaotic system is obtained firstly, then the precise mathematical expression of the controller of this chaotic system is obtained by using the boundedness of this chaotic system. Finally, the numerical simulation of the synchronization process is carried out and the simulations confirm the feasibility of the theoretical results.

Cylindrical algebraic decomposition is a basic tool in semi-algebraic system solving and real quantifier elimination. In the actual solving process, the choice of a variable ordering may have a significant impact on the efficiency of cylindrical algebraic decomposition. At present, the existing heuristic or machine learning ordering selection methods are basically based on the implicit assumption that the support set of a polynomial system is the determinant for affecting the variable orderings. In this paper, we first test this hypothesis by designing an experiment with the support set fixed but the coefficients varying. The experimentation shows that the support set is indeed an important factor, though not the only factor, determining the optimal variable ordering. Aiming at selecting the optimal ordering for computing cylindrical algebraic decompositions for systems with the same support set but different coefficients, this paper designs an ordering selection scheme via reinforcement learning. The experimentation on four variables shows that this scheme can surpass the accuracy limit of existing methods on selecting the optimal variable ordering that rely solely on the support set. In addition, experiments on systems owning up to 20 trillion of possible orderings show that the scheme is much more efficient than traditional heuristic methods. In contrast to the existing supervised learning methods for selecting the variable ordering of a few variables, this reinforcement learning scheme overcomes the difficulty of obtaining high-quality labeled data when the number of variables increases, which may lead to the combinatorial explosion of the number of variable orderings.

In this paper, we adopt the spatial error model to describe the network structure relationship between individuals, and propose both estimation and imputation methods of the varying-coefficient partially linear spatial error model with missing responses. We firstly construct the estimator of the model parameter through profile maximum likelihood method and a matrix blocking technique. We prove the asymptotic normality of the parametric estimators and show the convergence rate of the nonparametric estimator. We then propose imputation estimators of missing response based on this model. Finally, we conduct Monte-Carlo simulation studies to detect the infinite sample performance of the estimator and analyze the QQ data set using the proposed method.

In this paper,synchronization of complex networks with cyber attacks and output coupling is investigated.In the case of deception and denial-of-service attacks between controller and actuator,an output feedback proportional-integral-derivative (PID) controller is designed.By employing Lyapunov stability theory and linear matrix inequalities,a sufficient criterion is acquired to satisfy both mean square asymptotically stability for the synchronization error system and strictly $(\mathcal{Q},\mathcal{S},\mathcal{R})$-$\gamma$-dissipativity.Finally,the feasibility and effectiveness of the obtained theoretical results are verified through simulations.

This paper studies boarding probabilities of metro passengers at platforms. Under several reasonable assumptions, we prove a stochastic queueing model for passengers' boarding probabilities, which extends the deterministic queueing model (first-come-first-serve principle) in the research of Grube, et al. (2011) and Mo, et al. (2020). We present a simplified version of the stochastic queueing model that reduces to the deterministic queueing model when the parameter of the version is set to be zero. Based on the stochastic model, we construct a passenger flow simulation on a typical route. With the train schedule, passengers' tap-in times, and walking time distributions being inputs, the simulation yields each passenger's movement and tap-out time as outputs. Combining real data and simulation outputs, we provide a parameter calibration method. Real data analysis on Changping line of Beijing Metro illustrates advantages of the proposed stochastic model over the existing deterministic model.

This paper mainly focuses on the prediction variance when one data is missing in the Box-Behnken design, and derives the mathematical formula of the relative prediction-variance inflation. The relative prediction-variance inflation not only depends on the length of given vector and the length of the missing observation vector, and the angle between the two vectors, but also the sum of the squares of the inner products of the two vectors. Subsequently, the distribution of the relative prediction-variance inflation within 5% and 10% of the variable range is given.

A three-stage Stackelberg game model consisting of government, manufacturer and equity-concerned retailer was established. From the perspective of consumer utility, dynamic game theory and nonlinear consumer utility function were used to construct three models, namely government non-subsidy model, government subsidy manufacturer model and government subsidy consumer model. The optimal decision results under different subsidy strategies were solved and compared. The influence of retailers' fair concern and channel competition on optimal decision-making, consumer utility and social welfare of dual-channel green supply chain under different government subsidy strategies is studied. The results show that when the government does not subsidize and subsidize consumers, the retailer's equity concern will reduce the wholesale price, sales price, greenness and consumer utility. When the government subsidizes manufacturers, the product's greenness is the highest, and the retailer's equity concern will not affect the product's sales price, greenness, social welfare and consumer utility. Government subsidies will increase the wholesale price and sales price. When the government does not provide subsidies, the online direct selling price of products is equal to the wholesale price and lower than the offline retail price; after the government subsidies, the online direct selling price is higher than the wholesale price and lower than the offline retail price. When consumers are subsidized, the wholesale price and sales price of products are the highest. When the fairness concern coefficient of retailers is constant, channel competition will also reduce the greenness of products, and the wholesale price will increase with the enhancement of channel competition when the government does not subsidize or subsidize manufacturers.

The rumors breed and spread in the complex social network. In order to control rumors effectively, we explore the influencing factors of rumor forwarding behavior based on the game theory on the graph by introducing the elaboration likelihood model (ELM) and cognitive theory of emotion. Then, from the perspective of information content differentiation, an evolution game model for rumor spreading behavior of social network users is established. The simulation results illustrate that:1) Increasing users' interest in rumor/anti-rumor information directly affects whether they forward the rumor or refute the rumor; 2) The release strength of information has a direct effect on the dissemination of the information; 3) Users are more willing to forward the information of the close nodes, when they receive the information with uncertainty; 4) Rumors are more likely to be spread when they contain positive contents and when the user's personal emotions are unstable. Accordingly, this paper puts forward relevant suggestions to control the spread of rumors in social networks, and provides some theoretical support for relevant departments to formulate effective rumor control strategies.