Bilevel Optimization recently became a very active research area. This is mainly due to its important applications from machine learning. In this paper, we give a gentle introduction to algorithms, theory, and applications of bilevel optimization. In particular, we will discuss the history of bilevel optimization, its applications in power grid, hyper-parameter optimization, meta learning, as well as algorithms for solving bilevel optimization and their convergence properties. We will mainly discuss algorithms for solving two types of bilevel optimization problems: lower-level problem is strongly convex and lower-level problem is convex. We will discuss gradient methods and value-function-based methods. Decentralized and federated bilevel optimization will also be discussed.

The fundamental question in exploring the path of economic growth is how emerging industries gain and maintain their comparative advantages.This paper investigates the impact of knowledge spillovers and policy interventions on the emergence and sustainability of comparative advantages,using big data from 1.33 million registered enterprises across provinces from 2010 to 2020.It conducts various heterogeneous analyses at the industry and provincial levels to explore this issue in depth.The study finds that knowledge spillovers contribute to the emergence of new industry comparative advantages.However,only knowledge spillovers among related industries within a province facilitate the maintenance of existing comparative advantages.National-level industrial policies do not increase the probability of the emergence of supported industry comparative advantages but enhance the share of targeted industries.Regarding the development of comparative advantages,industries with high knowledge intensity and geographic concentration receive lower benefits from knowledge spillovers.Provinces in the central and western regions and those with higher specialization rely more on inter-provincial knowledge spillovers during industry development.Further analysis reveals that a developed highway system enhances the promotion effect of inter-provincial knowledge spillovers on industry development,while provinces with a high net inflow of population act as knowledge spillover sources.Inter-provincial knowledge spillovers positively moderate the effectiveness of development policies for targeted industries.This research provides empirical evidence for enhancing industry diversity.

This paper considers the impact of operation activities and financial hedging in constructing the exchange rate exposure faced by the Chinese enterprises.Using various databases to calculate and calibrate the exchange rate exposure in their operations for the first time,this paper discusses the determinants and solutions of exchange rate exposure in a comprehensive framework.This paper concludes three reasons for lower exchange rate exposure in their operations among Chinese enterprises:Low foreign production cost,low import penetration rate and low foreign revenue.Combined with the actual exchange rate exposure,we find exchange rate pass-through,operational hedging,foreign debt and foreign exchange derivatives reduces exchange rate exposure by 31.86%,3.76%,11.15% and 39.25%,respectively.This paper further expands the theoretical model to simulate the potential changes in the exchange rate exposure under two circumstances:Foreign countries promote the localization of the industrial chain and China continues to opening up.This paper explores exchange rate exposure from the perspective of micro-mechanism,which is of great value to the development of the foreign exchange market,resolving enterprises' exchange rate risk,and the formulation of related policies.

In the era of digital economy,the competition pattern of China's banking industry is undergoing tremendous changes,and various digital technologies affect the business model and development level of banks.Based on the perspective of the integration of big data and traditional data,this paper uses factor analysis to measure the digital finance development level of 120 commercial banks in China from 2009 to 2019.Then,the kernel density estimation and the spatial panel Dubin model are used to investigate the temporal and spatial variation characteristics of the digital finance development for banks in China from two perspectives of time and space,and the evolution feature of regional differences and sources of bank digital finance is analyzed.Finally,the interactive relationship between the digital finance development level of banks and regional digital inclusive finance is examined.It is found that the digital finance level of Chinese commercial banks shows polarization differences over time.In the eastern region,there is a mutual promotion effect between bank digital finance and regional digital inclusive finance,while in the northeast region,there will be a suppression effect.In the central and western regions,there is no obvious interaction between them.This paper enriches the construction system of digital finance level measurement,and provides important reference experience for revealing the differences in the development of digital finance.It also explores countermeasures for synergistic improvement with regional digital inclusive finance.

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.

In this paper, the problem of identifying autoregressive-moving-average systems under random threshold binary-valued output measurements is considered. With the help of stochastic approximation algorithms with expanding truncations, the authors give the recursive estimates for the parameters of both the linear system and the binary sensor. Under reasonable conditions, all constructed estimates are proved to be convergent to the true values with probability one, and the convergence rates are also established. A simulation example is provided to justify the theoretical results.

The scheduling problem in surgery is difficult because, in addition of the planning of the operating rooms which are the most expensive resources in hospitals, each surgery requires a combination of human and material resources. In this paper, the authors address a surgery scheduling problem which arises in operated health care facility. Moreover, the authors consider simultaneously materiel and human resources. This problem is a three-stages flow shop scheduling environment. The first stage (ward) contains a limited number of resources of the same type (beds); The second stage contains different resources with limited capacity (operating rooms, surgeons, nurses, anesthesiologists) and the third stage contains a limited number of recovery beds. There is also a limited number of transporters (porters) between the ward and the other stages. The objective of the problem is to minimize the completion time of the last patient (makespan). The authors formulate this NP-Hard problem in a mixed integer programming model and conduct computational experiments to evaluate the performance of the proposed model.

Curve interpolation with B-spline is widely used in various areas. This problem is classic and recently raised in application scenario with new requirements such as path planning following the tangential vector field under certified error in CNC machining. This paper proposes an algorithm framework to solve Hausdorff distance certified cubic B-spline interpolation problem with or without tangential direction constraints. The algorithm has two stages: The first stage is to find the initial cubic B-spine fitting curve which satisfies the Hausdorff distance constraint; the second stage is to set up and solve the optimization models with certain constraints. Especially, the sufficient conditions of the global Hausdorff distance control for any error bound are discussed, which can be expressed as a series of linear and quadratic constraints. A simple numerical algorithm to compute the Hausdorff distance between a polyline and its B-spline interpolation curve is proposed to reduce our computation. Experimental results are presented to show the advantages of the proposed algorithms.

Commodity is an important part of industrial production and financial investment, and accurate commodity price forecasting is of great significance to safeguard industrial production and help investors avoid risks. However, most of the existing commodity price forecasting models are point-value models based on closing prices, which ignores the volatility information. Therefore we propose a heteroskedasticity threshold autoregressive interval model with exogenous variables (HTARIX) and apply it to the commodity markets. We also construct a test statistic based on interval-valued data to test whether there is conditional heteroskedasticity in the model, and propose a generalized minimum $D_K$ distance estimation. The advantage of our model is that it can capture the conditional heteroskedasticity and nonlinear features of interval-valued time series models. Compared with the point-valued models, our method contains more information of the data. The empirical results imply that HTARIX model performs better than other comparative models in interval-valued commodity price forecasting.

This paper studies how environmental regulation affects the sustainable economic development through an angle of soft constrains of environmental regulation. We first develop a theoretical model, based on the threshold effect of innovation investment, to introduce the role of soft constrains of environmental regulation into the theoretical framework of Porter hypothesis, and analyze how the soft constraints of environmental regulation affect enterprise competitiveness. Using policy change of the SO₂ emission charges from 2007 to 2014, we examine the Porter hypothesis by adopting a DID estimation. We find evidence that state owned enterprises have more significant soft constraint problems than non-state owned firms, which weaken incentives for innovation investment, and then hurt enterprise competitiveness. However, we find strong evidence of the existence of Porter hypothesis for no-state owned firms.

To implement the instructions from General Secretary Xi Jinping regarding "enhancing the effciency of funding for the National Natural Science Foundation, " the Department of Management Sciences conducted a series of research activities, systematically analyzing the funding effectiveness of the distinguished young scholars and outstanding young scholars talent projects. A total of 556 survey questionnaires were designed and distributed, and 233 experts participated in the discussion. Utilizing statistical methods such as the coeffcient of variation, the difference-in-differences, and the natural language processing, the survey data were quantitatively analyzed. The statistical analysis of the survey data showed the following key findings: First, compared to other talent projects like outstanding young scholars, the comprehensive funding effectiveness of distinguished young scholars is relatively higher. After approval, there is a significant improvement in both academic achievements and academic influence. Second, there is heterogeneity in the funding effectiveness among talent projects like distinguished young scholars and outstanding young scholars. Third, scholars who receive distinguished young scholars funding before the age of 42 experience a greater improvement in comprehensive funding effectiveness. Based on these analysis, recommendations are proposed, emphasizing the need to "strengthen process management and project closeout management" for talent projects.

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 authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger operator. The proposed approach combines a newly developed loss function with an innovative neural network architecture that incorporates prior knowledge of the problem. These improvements enable the proposed method to handle both high-dimensional problems and problems posed on irregular bounded domains. The authors successfully compute up to the first 30 eigenvalues for various fractional Schrödinger operators. As an application, the authors share a conjecture to the fractional order isospectral problem that has not yet been studied.

In this paper, the authors propose Neumann series neural operator (NSNO) to learn the solution operator of Helmholtz equation from inhomogeneity coefficients and source terms to solutions. Helmholtz equation is a crucial partial differential equation (PDE) with applications in various scientific and engineering fields. However, efficient solver of Helmholtz equation is still a big challenge especially in the case of high wavenumber. Recently, deep learning has shown great potential in solving PDEs especially in learning solution operators. Inspired by Neumann series in Helmholtz equation, the authors design a novel network architecture in which U-Net is embedded inside to capture the multiscale feature. Extensive experiments show that the proposed NSNO significantly outperforms the state-ofthe-art FNO with at least 60% lower relative L²-error, especially in the large wavenumber case, and has 50% lower computational cost and less data requirement. Moreover, NSNO can be used as the surrogate model in inverse scattering problems. Numerical tests show that NSNO is able to give comparable results with traditional finite difference forward solver while the computational cost is reduced tremendously.

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.

Based on the theoretical framework of multiple competing platforms, two forms of exclusive contracts are investigated: Traditional exclusive contracts and “pick one of two” contracts. We distinguish the differences in the incentives of the dominant platform to use these contracts, and analyze the impact of the different forms of exclusive contracts on market competition and the revenues of market participants. Our study shows that the degree of differentiation between platforms and between sellers are the core factors in determining the incentives for the dominant platform to use different forms of exclusive contracts and the impact on market participants. When the degree of differentiation between platforms and between sellers are both small, the dominant platform uses traditional exclusive contracts, while when the degree of differentiation between sellers is large, the dominant platform uses “pick one of two” contracts. Although both exclusive dealings reduce consumer surplus and social welfare, the impact on profits of other competing platforms and sellers is uncertain. Traditional exclusive contracts can reduce the profits of all competing platforms, whereas “pick one of two” contracts can reduce the profits of all sellers. This study provides a theoretical explanation for the use of different forms of exclusive dealing of platforms.

Based on the two-dimensional Hotelling model, this paper builds a game model that simultaneously considers the differentiation of platforms and merchants, to explore the adoption of different exclusive strategies by dominant platforms and the impacts of such strategy. The results show that, there are two types of exclusive strategies, namely monopoly-driven and differentiation-driven exclusivity. The monopoly-driven exclusivity can be promoted by low commission rates of strong platform, low horizontal differentiation between platforms, high vertical differentiation between platforms, and high horizontal differentiation between products; Otherwise, the differentiation-driven exclusivity will be strengthened. Second, the differentiation-driven exclusivity is also beneficial for weak platforms. To avoid the monopoly-driven exclusivity, weak platforms can increase horizontal differentiation between platforms and reduce vertical differentiation or commission rates. Finally, fierce competition among merchants can stimulate the differentiation-driven exclusivity implemented by dominant platforms, which in turn reduces competition among merchants and improves their profits. Overall, the research clarifies the drivers of exclusivity strategy of dominant platforms and distinguishes the influences of different exclusivity strategies on both platforms and merchants, providing strong policy implications for the regulation of dominant platforms and anti-monopoly in the platform industry.

Complex decision analyses are often faced with the high-level uncertainty beyond the normal range of common understanding, which is so-called “deep uncertainty”. Generally, the system characterized with deep uncertainty cannot been or has not been known well, and it usually has many components and mechanisms that would interact in a variety of ways and change over time. Deep uncertainty brings unexpected difficulties to system simulation and forecast. In recent years, the research on the simulation approach under deep uncertainty has been becoming one of the important directions in the field of system science. This paper firstly investigates the state of the art in the concept understanding and its cognition development from uncertainty to deep uncertainty, and then summarizes the key features and constraints for system simulation under deep uncertainty. The current mainstream simulation approaches including their modeling thoughts and implementations are also elaborated by systematically classifying the published literature and outlining main trends in modelling uncertain system. On this basis, a dynamic exploratory simulation approach based on data-and-model hybrid is proposed and applied into traffic simulation and forecast. Simulation experiment results show that this approach is a useful pathway to enhance computing system's adaptability to uncertainties and complex changes of real system.

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.