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.

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.

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 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.

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.

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.

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.

Addressing the price transmission issue between the supply and demand sides in virtual power plants (VPP), this paper takes into account the uncertainty of renewable energy output, grid electricity purchase prices, and operating costs of various units. The authors propose a dynamic time-of-use pricing strategy within the VPP and, considering the comprehensive demand response from the load side, introduce a two-layer economic dispatch model for VPP with EV (electric vehicle) integration to ensure low-carbon economic operation of the VPP. The upper layer focuses on the energy side costs, aiming to minimize the supply costs for VPP operators. It also introduces the carbon capture system (CCS) as a flexible resource, proposing an operational mode for the carbon capture device that maximizes the use of renewable energy and off-peak grid electricity. The lower layer considers the energy consumption costs of the demand side, including EVs, with the objective of minimizing these costs. Finally, the effectiveness of the proposed strategy is validated through numerical examples. The results show that, compared to the grid’s time-of-use pricing mechanism, the proposed dynamic time-of-use pricing mechanism can save 51.8% of energy supply costs and reduce CO₂ emissions by 81.62%, effectively enhancing the economic and low-carbon performance of the VPP.

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.

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.

This paper is concerned with the robust feasibility for a class of support vector machine problems with uncertain data. Firstly, a robust counterpart problem of the uncertain support vector machine problem is introduced in terms of robust optimization. Then, a reformulation of the robust counterpart problem of the uncertain support vector machine problem is given. Finally, by using this reformulation and the so-called epigraphical set, an exact formula for the radius of robust feasibility of the uncertain support vector machine problem is obtained.

In the field of equipment fault diagnosis, text data such as operation instructions and maintenance records have great application value, thus fully mining and utilizing text data can significantly improve the efficiency of fault diagnosis. Semantic feature extraction and unsupervised clustering methods are commonly used to mine text data for the purpose of assisting in fault location, but such methods are not able to explain the cause of faults and give reasons for providing corresponding repair solutions. Furthermore, repair solutions generated by those methods are not easy to understand. Based on the existing mature pre-trained language model BERT (bidirectional encoder representation from transformers), this paper proposed a BERT-based short text classification model combined with knowledge graph for fault location, in order to fully explore and utilize the knowledge and laws contained in the text data of CIR equipment. Firstly, fault modules were determined by functional hierarchical relationships of CIR equipment. Then, this paper used BERT-based text classification model to obtain the preliminary fault location. Finally, causes and other information were further recognized with the assistance of knowledge graph to assist in fault diagnosis. Proving fault repair solutions based on the fault diagnosis knowledge accumulated by the knowledge graph makes solutions easy to be understood by maintenance personnel, and helps in knowledge management and engineering efficiency. In terms of text classification techniques, this paper used fault maintenance ledger records of CIR equipment to do experiments, and results proved that the performance of our BERT-based model had been greatly improved compared with traditional classification models. In terms of fault diagnosis, the proposed fault location method combining text classification and knowledge graph also provided support for rapid fault diagnosis by inexperienced equipment maintenance personnel, as well as obtaining certain practical significance.

This paper considers the problem of preview saturated control for uncertain periodic discrete-time systems with actuator saturation. The classical difference operator method in preview control theory can not be applied due to the existence of time-varying uncertain matrix and input saturation. The state auxiliary variable is introduced and the usual state difference is replaced by the the difference between the state vector and the state auxiliary variable. Therefore, the augmented error system of uncertain discrete system with input saturation is successfully constructed. By constructing the augmented model, the problem of designing the preview saturation controller of the original system is transformed into the problem of stabilization of the augmented error system. A sufficient condition for the asymptotic stability of the closed-loop system is derived by using the improved sector condition to deal with the saturation nonlinearity and the LMI technique. Finally, a simulation example is given to illustrate the validity of the results.

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.

Transient behavior, steady-state precision, regulation time, and convergence rate are the four key indicators for evaluating closed-loop control system performance. In this paper, the authors propose a tracking control design scheme that simultaneously satisfies the above four indicators for unmatched uncertain pure feedback nonlinear systems. This scheme ensures that the system output signal always stays within the envelope range formed by the performance function by setting the performance function. At the same time, under a novel error transformation mechanism control, the steady-state precision and regulation time of the closed-loop system can be pre-set. The authors use neural networks to approximate completely unknown nonlinear functions, where the weights of the neural network can be updated online by adaptive laws. In addition, the authors add the σ-correction term in the adaptive law to avoid parameter estimation drift phenomenon. Finally, simulation results validate the effectiveness of the proposed control method and its superiority in control performance.

In reflexive Banach spaces, the time optimal control problem for linear control systems is considered. By virtue of nonsmooth analysis, the properties of the minimal time function which has two variables with the initial point and the size of control set are studied such as continuity. The results that the target point should be the origin are generalized to be an arbitrary point.

Traveling salesman problem (TSP) is a typical problem in combinatorial optimization, and the relevance of solving the TSP is significant. Using deep reinforcement learning (DRL) models to automatically design learning algorithms has become a recent research hotspot as DRL is widely used in industry. In order to enhance the generalization ability of the DRL model on the large-scale TSP, this paper proposes a hybrid model of dynamic graph convolutional network to encode and spatial attention mechanism to decode for tackling the large-scale TSP. Dynamic graph convolution module can dynamically encode node information so as to efficiently update the hidden layer state of each node. Spatial attention facilitates capturing the global connections between nodes, and then calculating and extracting key features by weighting all local features. Experimental results show that our model outperforms the previous DRL model for optimization when generalizing the training strategy of TSP50 to TSP250/500/750/1000, and the test results on the standard dataset of TSPlib also show the improvement of the model for optimization performance.

An adaptive dynamic programming (ADP) algorithm is proposed for a class of model-free stochastic linear quadratic (SLQ) optimal tracking problem with time-delay. Firstly, the equivalent system of the original time-delay system is derived using the double causal coordinate transformation. A new augmented system consisting of the equivalent system and the command generator is constructed, and then the stochastic algebraic equations of the augmented system are given. Secondly, in order to solve the SLQ tracking control problem, the stochastic problem is transformed into deterministic problem. Then the ADP algorithm is proposed and its convergence analysis is given. For the purpose of realizing the ADP algorithm, three neural networks are designed, which approximate the optimal cost function, the optimal control gain matrix and the system model respectively. Finally, the effectiveness of the algorithm is verified by a numeric example.

The prescribed-time bipartite consensus control problem for linear cooperative-competitive multi-agent systems (MAS) based on the event-triggered mechanism is studied considering the possible external disturbances. Firstly, a disturbance observer is designed to estimate the external disturbances to the system, and an event-triggered condition is given for each agent to reduce the communication frequency between agents and save the limited communication network resources, while proving to avoid the Zeno phenomenon. Secondly, in order to explicitly pre-allocate the settling time, a prescribed-time event-triggered control protocol in a cooperative and competitive topology is designed in conjunction with the estimated value of the disturbance observer to ensure that all agents achieve bipartite consensus despite external disturbances. Finally, the feasibility and effectiveness of the proposed method are verified using simulation examples.

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.

For the purpose of comparing the development level of multiple objects to be evaluated at different times and the overall development level in a certain period of time, dynamic evaluation is required. In order to overcome the shortage of Euclidean distance calculation of closeness in traditional TOPSIS, this paper introduces the idea of set-pair analysis connection degree into TOPSIS, uses connection vector distance instead of Euclidean distance to calculate closeness, adds time dimension, and proposes a dynamic TOPSIS evaluation method based on connection degree. This method can not only obtain the evaluation value and the ranking result reflecting the difference degree of the evaluation index value, but also obtain the evaluation value and the ranking result reflecting the increase degree of the evaluation index value, and the comprehensive evaluation value and the ranking result considering the above two situations at the same time. Finally, an empirical analysis of green development level of the Yangtze River Economic Belt is used to verify the effectiveness of the proposed method.

As the core of coordinating urban traffic, intelligent transportation system (ITS) is developing rapidly, as well as, the traffic flow prediction is an important part of ITS, which is regarded as the key factor for successful deployment of ITS. Because of the complex spatial topological structure of the traffic network, the traffic flow shows higher-order nonlinearity and dynamic spatial-temporal complexity. In order to better predict the traffic grid data, this paper proposes a new spatial-temporal network model DCSTGCN, which has the following characteristics: 1) The Chebyshev polynomial (Ch) is applied to the graph convolutional neural network, and the traditional fixed traffic topology is converted with self-diffused convolution to make it more random and dynamic; 2) The spatial Transformer model is added. While considering the data heterogeneity, the multi head self attention mechanism is used to consider the multi attribute problems of nodes, local neighbors, and non local nodes, and the hidden feature information between nodes is considered from the high-dimensional subspace; 3) Combining the temporal transformer with a 1 × 1 2D convolutional neural network (Conv2d). Multiple weights are assigned to the traffic flow time series information to obtain important time features, and the Conv2d network is used to predict the output. The experimental verification shows that the method model is better than a variety of comparative baseline models.

Along with the rise of Internet public welfare, e-commerce platforms represented by Alibaba and JD have injected a strong impetus into the development of Chinese public welfare. However, the public practices of platforms and merchants often contain both public welfare and profit motives. In this paper, three differential game models are constructed for platforms and merchants to discuss their cooperation question about carrying out joint cause-related marketing (CRM), considering the government’s subsidy policy for platforms and the characteristics that engaging in social welfare is multi-cycle and dynamic. Our main results are as follows: 1) The government subsidies can incentivize platforms and merchants to provide more investments for social welfare, and motivate platforms to be willing to share more CRM costs for merchants. 2) Under certain conditions, platforms share a certain percentage of CRM costs for merchants can not only enhance its social welfare investment, but also achieve Pareto improvement of profits for both. 3) Government subsidies can improve the Pareto effect of CRM cost-sharing contracts on the profits of platforms and merchants, but platforms may retain some of the government subsidies and will not invest them all in social welfare. 4) In the joint CRM case, the benefits of platforms, merchants, and the whole system as well as the consumer surplus and social welfare are all optimal. Finally, our main results are verified via numerical simulation, hoping to provide a theoretical basis and reference for the joint CRM of platforms and merchants.

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.

This paper studies the robust optimal reinsurance and investment problem under the ambiguity aversion and inflation risks are considered, simultaneously. The surplus process of an insurance company is defined by the diffusion approximation model, and the financial market consists of a risk-free asset and a risky asset. The insurance company can reduce the risk of claims by adopting proportional reinsurance and increase his wealth by investing in the financial market. The price of the risky asset is converted by inflation, and then the influence of inflation on investment is obtained. By using Radon-Nikodym derivative and Girsanov theorem, the wealth process of the insurance company under ambiguity aversion is obtained. With the goal of maximizing expected utility, the analytical solution of robust optimal reinsurance and investment strategy is obtained. Finally, the influence of model parameters on the theoretical results is discussed through numerical experiments, and the research results can effectively guide the reinsurance and investment decisions of the insurance company.

The region constrained consensus of flexible-joint robot manipulators is studied. A consensus control torque for flexible-joint robot manipulators is proposed based on the regional potential functions, which can effectively guarantee the range of the synchronization state of flexible manipulators without calculating the final synchronization state, so it is suitable for cooperative control and application of multiple flexible-joint manipulators in the task space. Further more, a sufficient condition for solving region consensus problems is presented based on the structure of network topology. Finally, the effectiveness of the obtained theoretical results is verified by numerical simulations.

In the context of carbon trading mechanism, considering the low carbon preference of consumers, this paper studies the selection of the optimal emission reduction technology authorization strategy for innovation-oriented enterprises by constructing a competitive duopoly market, analyzes the three authorization modes of fixed fee, franchise fee and two-system fee, and explores the impact of technology authorization strategy on the environment. The results show that: 1) The two-part licensing strategy is always the best for the technology owning enterprises, and the advantages and disadvantages of fixed-fee licensing and licensing fee licensing are determined by the substitution degree and emission reduction rate between products; 2) Regardless of the degree of innovation, fixed-fee authorization has the greatest impact on the environment. When the emission reduction rate is very small, the total carbon emission generated by the two-part fee authorization is the minimum; Otherwise, the total carbon emission generated by the license fee authorization is the minimum.

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.

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 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.

If the level changes of some factors are very difficult or expensive, or if there is a time trend in the experiment, it is very important to arrange the experiment in a reasonable order so that it has the minimum or maximum level changes. Based on Hamming distance and Manhattan distance, this paper studies the run order with the minimum,(maximum) number of level changes in the experiment, the optimal run order and search algorithm are discussed for isometric designs and cyclic designs. These results are of great significance for saving the experiment cost or ensuring the steady trend of time. The examples show that the search algorithm in this paper is very effective.

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.

In view of the problems of asymmetric information, high operating costs, low management efficiency, and difficult supervision in the carbon trading system, applying blockchain technology to the carbon trading market is conducive to sharing information among manufacturers with different emission reduction efficiencies, and promoting manufacturers' cooperation to improve emission reduction level. This paper uses the cooperative game method to study the cooperation between two competing manufacturers in a low-carbon supply chain based on blockchain technology, and obtains the optimal production strategy, emission reduction strategy, and profit distribution of manufacturers after cooperation under the cooperative situation. A comparative analysis is conducted with traditional competitive emission reduction models. The impact of blockchain costs, emission reduction efficiency and degree of competition on optimal decision-making and social welfare was further discussed. The results show that: 1) Through the sharing of emission reduction information on the blockchain carbon trading platform, carbon trading efficiency is improved. However, higher blockchain operating costs will reduce the willingness of manufacturers to enter the platform; Manufacturers' production decreases as emission reduction efficiency of their competitors increases, and increases as their own emission reduction efficiency increases; An increase in degree of competition will lead to a decline in manufacturers' profits and social welfare, as well as a reduction in carbon emissions. In addition, higher carbon prices are conducive to reducing carbon emissions and improving social welfare. 2) In the cooperative situation, when the transfer agreement price is at a certain threshold, it is profitable for both manufacturers to conduct carbon emission quota transactions in the form of transfer agreement. Otherwise, as the transfer agreement price changes, it will harm the profits of a certain manufacturer. 3) Compared to competitive situations, cooperation between competing manufacturers based on the blockchain carbon trading platform can achieve higher returns while generating lower carbon emissions. Therefore, from both environmental and economic perspectives, cooperation is a win-win strategy for both environment and manufacturers.

Manufacturers often disclose product quality information to reduce consumers' valuation uncertainty before launching innovative products. Nevertheless, introducing store brand by e-platforms has changed the cooperation between manufacturers and platforms. This paper investigates the impacts of the platform's store-brand introduction on the manufacturer's quality disclosure strategy and the profitability of supply chain members. The results show that: 1) If the manufacturer's market share and disclosure cost are both relatively low, the platform's store-brand introduction will induce the manufacturer to disclose more quality information and improve the information transparency in the supply chain; otherwise, the platform's store-brand introduction will lead the manufacturer to disclose less quality information. 2) The manufacturer's quality disclosure threshold varies in an inverted “U” shape with the platform's imitation capability. 3) If the manufacturer's product quality is lower than a particular level, the platform's store-brand introduction will benefit himself but hurt the manufacturer; otherwise, the platform's store-brand introduction will hurt the profitability of both parties.

According to the city sanitation management total process is divided into infrastructure construction and facility operation two aspects, and the practical problems of harmless treatment and garbage transfer treatment should be carried out at the same time in facility operation. In this paper, a parallel two-stage DEA efficiency evaluation model based on two-stage DEA and parallel DEA is proposed. This model systematically analyzes the governance efficiency of infrastructure construction and facility operation in the sanitation management. At the same time, it fully analyzes the governance efficiency of the two subsystems of harmless treatment and garbage removal, and finally obtains the overall efficiency of the sanitation management. Through the analysis of the efficiency of urban appearance and environmental health governance in 30 provinces and cities (except Xizang; Hong Kong, China; Macao, China; Taiwan, China) in China from 2011 to 2020, it is concluded that: From 2011 to 2020, the average efficiency of all provinces and cities in China in the infrastructure construction stage is 0.92, the average efficiency of infrastructure operation stage is 0.75, the average efficiency of harmless treatment is 0.82, the average efficiency of garbage collection, transportation and treatment is 0.67, and the overall average efficiency of the two stages is 0.90. In most provinces and cities, overall efficiency of city sanitation management and governance efficiency in infrastructure construction phase are in the middle and upper reaches, the governance efficiency of the facility operation phase is in the middle and lower reaches, and the governance efficiency in infrastructure construction stage is greater than that in facility operation stage, and the efficiency of harmless treatment subsystem is greater than that of garbage collection, transportation and treatment subsystem.

The improper use of credit funds for fiscal purposes is an important problem facing China, which should be effectively handled to prevent the outbreak of systemic financial risk. Based on the unique utility function of urban commercial banks, this paper constructs a theoretical framework to explore the mechanism of different types of local government fiscal revenue on excess credit expansion and liquidity risk of urban commercial banks through implicit guarantee or financing substitution, and conducts an empirical analysis using data of 104 Chinese urban commercial banks from 2012 to 2019. The empirical results show that: First, the general fiscal strength of local governments encourages urban commercial banks to excessively expand credit and thus increase their liquidity risks through implicit guarantee. Second, there is a significant substitution relationship between land-transferring fees and credit funds of urban commercial banks, so it can reduce the liquidity risk of urban commercial banks. As an implicit guarantee index, local government bond will improve the liquidity risk of urban commercial banks, but it can also lower the liquidity risk as a financial instrument. Finally, the excess credit financing of local government financing vehicles plays a major mediating role, and the financing constraints of local government financing vehicles, listed state-owned enterprises and listed non-state-owned enterprises play a decreasing positive moderating role in the improvement of liquidity risk of urban commercial banks by general fiscal strength. This paper sheds light on the transformation mechanism of credit funds into fiscal funds during the period of credit expansion and provides insights for strengthening the countercyclical supervision of excess credit expansion of urban commercial banks.

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.

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.

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.

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.