In the context of global climate warming, China is experiencing increasingly frequent extreme high-temperature events, which leads to a rising trend towards climate risks and severe losses of crops. In this paper, the deep learning algorithm N-BEATS model is used to iteratively forecast the future evolution trend of temperatures. Based on the intensity and duration of extreme high temperatures during a day, a novel extreme heat index and corresponding weather derivatives contracts are constructed. These contracts are used to hedge the extreme weather risks faced by crops. The results demonstrate that the proposed model significantly improves the prediction accuracy of future temperature changes, and the newly developed weather derivatives provide an effective hedging tool for extreme high-temperature risks.

We discuss the maximum information subspace of square integrable functional data in L² in order to find a suitable m dimensional projection subspace, which reserves the most information of the original functional data in all of the same dimension subspace to achieve dimensionality reduction while preserving important information. In this paper, the existence of the subspace is proved by the convex optimization method, it was further proved that the subspace with the eigenfunctions corresponding to the first $m$ largest eigenvalues of the sample covariance operator of the functional data as base functions is the maximum information subspace. Then, from the perspective of information reconstruction, it is proved that the subspace is the most powerful space for reconstructing the original functional data. Finally, the 2 dimensional maximum information subspace for functional data of 35 weather stations in Canada is studied. It is found that the cluster analysis results in this space are consistent with those based on discrete data. This shows that projecting functional data onto the maximum information subspace not only dynamically presents the overall characteristics of each category from the perspective of the function, but also ensures the reliability of the clustering results by retaining the maximum information of the original data.

In response to the fact that existing environmental performance evaluation methods are mostly based on the optimistic frontier constituted by efficient decision-making units, this study introduces the concept of double frontier evaluation into the directional SBM model, proposes a new double frontier directional SBM model considering undesirable output, and develops its super efficiency expression to improve the model's ability to distinguish decision-making units. This method evaluates environmental performance from both optimistic and pessimistic frontier perspectives, while simultaneously accounting for potential biases introduced by improvement directions and slacks, effectively strengthening the recognition of the evaluation results among all participants. On this basis, a global Malmquist index satisfying the circular test based on the double frontier directional SBM model is constructed to accurately measure the dynamic evolution of environmental performance across provinces in China from 2011 to 2021. The results indicate that China's green total factor productivity shows a fluctuating upward trend, with technological progress identified as the principal driver. Significant regional heterogeneity is observed in technological efficiency changes among different economic zones. This study is important for the continuous improvement of green total factor productivity in regions according to local conditions, as well as for the orderly advancement of the carbon peaking and carbon neutrality goals.

Under the carbon cap-and-trade mechanism, in order to solve the problem of renewable energy cooperative investment strategy, this paper constructs a two-level power supply chain composed of power generators and electricity sellers, considers the intermittently of renewable energy, and studies the problem of renewable energy investment decision-making between power generators and electricity sellers under three different cooperation modes: no cooperation, semi-cooperation and full cooperation. Through the analysis of the equilibrium solution, the following main conclusions are drawn: (1) When the carbon emission per unit of traditional energy power is small, the total renewable energy investment of the supply chain in the non-cooperation model is the largest, while when the carbon emission per unit of traditional energy power is large, the total renewable energy investment in the supply chain in the semi cooperation model is the largest; (2) The supply chain profit under the complete cooperation model is higher, the supply chain profit under the semi cooperation model is lower, and the supply chain profit under the non-cooperation model is the lowest; (3) The increase in carbon emissions per unit of power from traditional energy sources will increase the amount of renewable energy investment and electricity prices, and reduce the electricity demand and total supply chain profits when renewable energy is intermittent.

The rapid development of the e-commerce economy and the upgrading of eco-consumption demand have made e-commerce platforms one of the main driving forces for the sale of green products, which also brings about a diversification of logistics service strategies, along with some new challenges such as delivery delays.Due to uncertain market environment caused by intense competition, there is insufficient sample data to infer demand for new green products.Therefore, considering the consumers' perception of the time difference between the actual and promised delivery time, uncertainty theory is applied to study the scenario selection problem under four combination scenarios consisting of different e-commerce sales modes (resale mode or agency mode) and logistics service strategies (logistics outsourcing or logistics sharing) in the green supply chain. It is assumed that supply chain members seek to maximize profits under uncertain demand with a certain confidence level, from which four Stackelberg decentralized game models are constructed.Furthermore, an effective delivery time reward-penalty mechanism for non-self-supporting logistics strategies is designed.The results show that the green investment cost coefficient, the maximum delivery cost and the promised delivery time have a negative impact on supply chain behavioral performance.Moreover, the logistics sharing strategy outperforms the logistics outsourcing strategy, and the win-win-win equilibrium can be achieved under the logistics outsourcing strategy within a certain range of commission rate and decision-maker confidence level in different e-commerce sales modes.More importantly, the delivery time reward-penalty mechanism has a positive impact on supply chain members and society as a whole, and the relationship between the optimal profitability of the actual incentivized party and the promised delivery time depends on the incentive strength when consumers and the product owner implement equal reward-penalty incentives for delivery time.

In the context of information asymmetry, how to stimulate third-party logistics service providers to provide the optimal logistics service level is the key issue which restricts the development of e-commerce enterprises. Based on above, according to the multi-agent problem on the logistics outsourcing for e-commerce enterprises and the double moral hazard problem of hidden effort for e-commerce enterprises and third-party logistics service providers, combining the specific features of logistics outsourcing activities for e-commerce enterprises, the principal-agent theory was adopted to establish an incentive contract model considering consumer behavior (i.e. consumer preference, consumer evaluation and consumer refund). Results show: 1) Guided by consumer behavior, e-commerce enterprises and third-party logistics service providers can effectively mitigate moral hazards stemming from their own limitations in capabilities and costs. 2) With the increase in the benefit-sharing coefficient and consumers' preference for logistics services, the effort of third-party logistics service providers will be improved, leading to a reduction in the cost ratio associated with discrepancies in consumer evaluations. 3) E-commerce enterprises do not intensify their cooperation and supervision efforts solely because of revenue sharing. However, the sensitivity of consumers to logistics service levels drives e-commerce enterprises to enhance their cooperation and supervision efforts.

This paper considers the supply interruption of a supply chain composed by two suppliers and one retailer, where one supplier is an integrated supply and marketing supplier and the other supplier is a pure supplier, and the retailer makes replenishment from the latter supplier and makes and emergency order from the former when the supply is interrupted. For this system, we mainly investigate the retail price decision and the emergency replenishment from the supply and retailing integrated supplier in the case of a supply interruption with a random end time from the second supplier. Based on maximizing the benefits of each member in the supply chain, we establish an optimization model, and its solution is obtained via a theoretical analysis which gives the optimal decision for each member of the supply chain. Some numerical experiments are made which gives the impact analysis of main parameters on the optimal decision of each member of the supply chain and their benefits for the supply interruption period.

This article aims to improve estimated precision of total number of the population and net census error by means of triple system estimator on the basis of the census list, post-enumeration survey list, and administrative record list. In order to realize this goal, the triple system estimator and its related questions are studied through mathematical model. The research shows that the triple system estimator can not be constructed and used in the population directly; the triple system estimator is a biased estimator, its sample variance, bias, and squared error should be calculated. The triple system estimator will produce main role in the future of net census error estimation, which will gradually replace the widen used dual system estimator including correlation bias.

To address the stability challenges faced by Industrial Cyber-Physical Systems (ICPS) under non-periodic Denial-of-Service (DoS) attacks, this research investigates an adaptive event-triggered sliding mode control strategy based on observers. A mathematical model is developed for DoS attacks constrained by attack frequency and duration, accompanied by the construction of an observer to estimate the system state. A sliding mode controller is designed to mitigate the effects of DoS attacks, and an adaptive event-triggering mechanism is employed to conserve communication resources. The stability criteria and conditions are solved using techniques involving piecewise Lyapunov functions and H_∞ theory, which also guide the coordinated tuning of observer and controller gains. With a batch processing reactor system as the target of control, simulations carried out on the MATLAB platform confirm that the proposed control strategy effectively ensures system stability amidst non-periodic DoS attacks, simultaneously reducing communication resource consumption.

This paper studies the mean square consensus problem of linear discrete multi-agent systems under the simultaneous influence of communication delays and packet losses. The objective is to establish conditions based on delay information, packet loss rates, and communication topology, under which an effective control protocol exists that can achieve mean square consensus for the multi-agent system over channels characterized by both delays and packet losses. First, sufficient conditions for achieving mean square consensus in multi-agent systems are derived using optimization theory and the stability conditions of stochastic systems, considering two scenarios: one with only packet loss during communication and the other with both communication delays and packet losses. Second, to mitigate the effects of delays and packet losses on the mean square consensus of the multi-agent system, feasible state control protocol design algorithms are proposed by solving the positive definite solution of the modified Riccati inequality. Compared to existing results, this algorithm is easy to implement with low computational complexity. Finally, numerical simulations are conducted to verify the feasibility of the obtained results.

This paper discusses a type of online time series prediction problem where data arrives in batches in a streaming fashion. Traditional time series prediction models typically assume a static dataset, often resulting in lower prediction accuracy when dealing with dynamically changing data streams. To address this issue, this paper proposes an improved time series prediction model based on the Transformer architecture. Firstly, the paper improves upon the traditional Temporal Convolutional Network (TCN). By adjusting the connection structure and embedding the temporal convolution module at the front end of the encoder and decoder, the proposed model can not only capture the relationships between elements in the sequence data but also capture local features in the time dimension through temporal convolution, thereby expanding the model's "receptive field." This improvement enhances the model's understanding of time series data without significantly increasing computational complexity. Secondly, the paper introduces the experience replay strategy from reinforcement learning into model training. This strategy allows the model to be trained more fully on a limited dataset, thereby improving the model's generalization ability and prediction accuracy. Finally, the proposed model is validated on multiple datasets. The results show that, compared to the original Transformer model, the proposed model achieves performance improvements to varying degrees. The performance improvement is particularly significant on larger, more complex datasets. Additionally, the paper provides detailed proofs and supplementary materials in the appendix to further support the rationale behind the model design and performance improvements. In summary, this paper combines the advantages of Temporal Convolutional Networks and the Transformer architecture to propose a new online time series prediction model. This model significantly improves prediction accuracy while maintaining computational efficiency, providing an effective solution for the prediction of dynamic data streams.

Inspired by the Routh-Hurwitz stability criterion for planar linear systems, we investigate in this paper the stability of a class of planar nonlinear systems with unknown parameters. Drawing upon the framework of homogeneous system theory, we study the stability of a nonlinear system, which is inherently a homogeneous system, under various conditions of unknown parameters. The analysis employs both Lyapunov's method and the particular solution method to derive insights into the system's stability characteristics. As a result, several sufficient conditions, and necessary and sufficient conditions for stability are derived. The particular solution method adopted in this paper can be effectively applied to analyze the instability of the system, thereby enriching the methods available for the stability analysis of nonlinear systems. Furthermore, the results obtained in this paper have practical applications in the controller design of certain nonlinear systems. To demonstrate this, specific examples are provided to illustrate how the results can be utilized in practice.

The construction of battery swapping stations supports the promotion of the "vehicle-electricity separation" model for new energy vehicles, and it is crucial to design a contract mechanism to encourage supply chain enterprises to jointly participate in the investment of battery swapping stations. This article studies the joint decision-making problem of investment and product pricing in new energy vehicle supply chain enterprises under different power structures, designs two models about battery price discount contracts and battery price concession contracts based on the number of battery swapping stations invested, and analyzes the impact of correlation coefficients on the decision-making of all parties. Research has shown that both battery price concession contracts and battery price discount contracts can make the supply chain achieve Pareto improvement; Under different power structures, either battery enterprise or car enterprise investing in the construction of battery swapping stations is beneficial for promoting the battery swapping model and increasing the profits of both enterprises; The construction cost of battery swapping stations significantly affects the investment willingness and pricing decisions of battery and car enterprises. The research results provide cooperative ideas and new contractual mechanisms for enterprises to make investment decisions in replacement power plants.

Individual selection preferences and the abuse of recommendation algorithms have trapped the public in an information cocoon dilemma. It would trigger differentiated collective behavior, exacerbate the formation of opinion polarization, and even have a serious impact on social public order. In this paper, we systematically analyze the effects of differences in public behavior within the information cocoon on the interaction between heterogeneous opinion groups, including the intra-group homogeneity restriction weakening-strengthening effect and the inter-group inhibition-promotion combination interaction effect. Then, based on the Lotka-Volterra modeling approach, the opinion polarization dynamic model with the interaction of heterogeneous opinions is constructed. Besides, the equilibrium points and their stabilities are estimated, too. Moreover, we also explore the law of opinion polarization through numerical simulations and empirical analysis. The results show that under the influence of the information cocoon, the weaker the intra-group homogeneity restriction and the stronger the inter-group promotion effect, the faster and the larger the expansion of the two groups, and the more likely to generate binary polarization situation. What's more, when the inter-group inhibition effect is stronger and the intra-group homogeneous restriction of heterogeneous opinion is weaker, the expansion rate of the group would slow down and the size would decrease and even disappear after reaching the peak, and generate single polarization situation. In addition, the potential diffusion range positively affects the expansion rate and final size of the group itself. Furthermore, the potential diffusion range would also slow down the expansion of the heterogeneous group under the inter-group promotion effect, but does not affect its final size.

Based on the Chinese herbal medicine supply chain where the medicinal farmers have the adulteration behavior, this paper studies the governance strategy selection of Chinese herb enterprises against the adulteration behavior of medicine farmers under the quality sampling inspection mechanism. We construct the supply chain Stackelberg game models for four scenarios, namely, without governance strategy, return penalty governance strategy, liability cost-sharing governance strategy and combined governance strategy. The operational differences in the Chinese herbal medicine supply chain under different governance strategies are comparatively analyzed. Governance strategy choices for Chinese herb enterprises are revealed. The findings of this paper are as follows: Under the return penalty governance strategy and combined governance strategy, when the unit penalty is higher than a certain level, it can effectively eliminate the adulteration of medicinal farmers. In contrast, the liability cost-sharing governance strategy is unable to eliminate adulteration. The increase in the return penalty parameter benefits the governance of adulteration and the profits of Chinese herb enterprises, but not the profits of medicinal farmers. The increase in the liability cost-sharing parameter benefits the profits of both parties, but not the governance of adulteration. The medicinal farmers prefer the Chinese herb enterprises to choose the liability cost-sharing governance strategy, and they least prefer the Chinese herb enterprises to choose the return penalty governance strategy. From the perspective of governing adulteration, the Chinese herb enterprises should choose the return penalty governance strategy. From the perspective of gaining profits, the Chinese herb enterprises should choose the combined governance strategy and set a higher unit penalty.

Currently, most studies on predator-prey models with slow-fast effect focus on temporal dynamics, while relatively fewer investigations address the influence of slow-fast effect on spatial pattern evolution in predator-prey systems. This paper establishes a slow-fast modified Leslie-Gower predator-prey model incorporating time-delay and reaction-diffusion. We investigate the conditions for Turing instability and Hopf bifurcation, derive analytical expressions for bifurcation thresholds using time-delay as the bifurcation parameter, and explore how slow-fast effect impacts spatial patterns and stability region. The study reveals that reaction-diffusion drives Turing instability, with different diffusion coefficients inducing distinct spatial patterns. Time-delay can trigger Hopf bifurcation near bifurcation threshold. Both slow-fast effect and time-delay significantly alter pattern morphology, generating rich spatial configurations. Furthermore, slow-fast effect nonlinearly modulate stability region of system. These findings demonstrate that slow-fast effect plays a crucial role in spatial pattern evolution and stability regulation in predator-prey systems.

The water rights trading mechanism is a market-oriented institutional arrangement for promoting the construction of water ecological civilization and realizing national water-saving actions. Exploring how it affects the green transformation decisions of high water consuming enterprises and promotes green technology innovation is of great significance for practicing high-quality development. Our article establishes a quasi-natural experiment and explores the impact and mechanism of the water rights trading policy on green innovation based on the samples of high water-consuming enterprises. The results show that the water rights trading mechanism can drive the "incremental improvement" of green technology innovation in high water-consuming enterprises, and this conclusion is still reliable and effective after robustness testing. Heterogeneity analysis shows that water rights trading mechanisms are more conducive to stimulating green technology innovation in state-owned, large, western regions,regions with low water resource endowment and highly competitive enterprises. The mechanism indicates that the water rights trading mechanism mainly enhances green technology innovation through channels such as increasing executives' green attention and R&D investment in high water-consuming enterprises;institutional investors' shareholding has promoted enterprises' green innovation, but the equity financing cost has a hindering effect. The results provide useful insights for promoting water rights trading mechanisms and enterprises' green innovation.

Optimizing the business environment has been a significant initiative continuously promoted by our country in recent years, aiming to drive the rapid development of new productive forces by enhancing resource allocation and stimulating market innovation vitality. This study takes the 2021 business environment innovation pilot city construction as a quasi-natural experiment to investigate the impact of the business environment on corporate innovation. The findings reveal that the pilot policies effectively stimulate local corporate innovation, and the promotion effect is more prominent among firms that are non-state-owned, with high institutional transaction costs, low degree of digital transformation, and high degree of development of the factor market in the host city. Mechanism analysis shows that the policies promote innovation through increasing market competition, alleviating financing constraints, and activating intellectual property trading markets in the pilot cities. Further results indicate that the promoting effect of the business environment on corporate innovation is mainly reflected in the "intensive margin" rather than the "extensive margin," meaning that enterprises with prior patent applications are better positioned to leverage policy opportunities to enhance their innovation output. These findings contribute to the understanding of how the business environment influences micro-level enterprises and provide valuable insights for future policy optimization.

The carbon quota allocation mechanism is one of the core institutional designs for constructing a carbon emission trading system. On the one hand, free allocation may weaken market efficiency and distributive fairness; on the other hand, a direct transition to a full-auction mechanism could lead to a sudden surge in corporate compliance costs and exacerbate transformation risks. However, existing research has been mostly confined to the binary opposition paradigm of "free allocation-full auction," and there is a lack of systematic research on institutional designs under incremental transformation paths, resulting in a theoretical gap for exploring phased transformation paths in China's carbon market. This study breaks through the traditional analytical framework by innovatively constructing a multi-market linked carbon emission trading model that integrates the primary carbon market, secondary carbon market, product market, and intertemporal corporate strategic adjustments into a unified system. It simulates the impacts of three quota allocation methods—free allocation, consignment auction, and auction—under different paid allocation ratios on carbon market effectiveness. Simulation research based on Chinese data shows that in the early stage of carbon market construction, adopting a small-scale consignment auction can activate market vitality while controlling transformation costs, but caution is needed regarding incentive distortion effects from revenue return mechanisms as policy stringency increases. As the carbon emission trading system matures, a high-proportion auction remains the optimal allocation method, as it significantly promotes long-term technological progress and carbon reduction. This finding provides a critical path for the incremental transformation of carbon emission trading systems: through dynamically adaptive institutional design, it ensures market stability during the transition period while achieving deep emission reduction goals in the maturity stage.

In response to the scenario of a two-stage production structure that includes undesirable outputs and shared input factors, a two-stage data envelopment analysis (DEA) model has been developed. This model not only enables the rational allocation of shared resources between the two stages but also addresses undesirable outputs by applying the weak disposability theory, which aligns with real-world production dynamics. Furthermore, drawing on the concept of non-cooperative games, the model decomposes the efficiency of subprocesses by considering scenarios in which either the first or second stage is dominant, thereby establishing subprocess efficiency models. Ultimately, we employ the proposed model to evaluate the innovation efficiency of Specialized, Refined, Distinctive, and Innovative (SRDI) small and medium-sized enterprises in Fujian Province. By conducting a thorough analysis of both the overall efficiency and the subprocess efficiency of these enterprises, more accurate and comprehensive evaluation results can be obtained. Additionally, comparisons with various models further enhance the rationale and feasibility of the model presented in this paper.

Based on Nash non-cooperative game theory and variational inequality theory, this paper constructs a supply chain network equilibrium model under the combination of historical emission method and industry benchmark method, aiming at the production decision of different carbon emission manufacturers under different carbon quota allocation strategies. By comparing the effects of single carbon policy and complex carbon policy on supply chain network equilibrium, the implementation conditions of the optimal carbon quota allocation policy are proposed and its effect is verified. Secondly, it expands the supply chain network equilibrium model in which the government is a participant, and reveals the double leverage effect of the linkage between carbon quota allocation ratio and carbon price when the government is an endogenous player, which provides a quantitative decision-making tool for the design of “precise carbon control” policy. Finally, the model is simulated by projection shrinkage algorithm. The conclusion is as follows: Under the historical emission method, compared with expanding production scale, the two manufacturers with different carbon emissions are more inclined to achieve the optimal profit through carbon quota trading, while retailers are faced with the risk of profit compression. Under the industry benchmark method, when the unit carbon quota is greater than the unit carbon emission, the profit advantage of the emission reduction manufacturer over the ordinary manufacturer will gradually decrease with the increase of the carbon trading price; when the unit carbon quota is less than the unit carbon emission, the profit of the two types of manufacturers will decrease with the increase of the carbon trading price, and the profit of the retailer is generally stable in both cases. Under the composite carbon quota policy, when the unit carbon quota is greater than the unit carbon emission, the industry benchmark method accounts for a large proportion, and the profits and social welfare of the two types of manufacturers are the best, but the profit growth rate of the ordinary manufacturers is higher than that of the emission reduction manufacturers. When the unit carbon quota is smaller than the unit carbon emission, the larger proportion of historical emission method is more advantageous to the profits and social welfare of the two types of manufacturers. The profit of retailers gradually decreases with the increase of the proportion of historical emission method. After the government is included in the decision-making body, the increase in carbon price significantly increased the income of emission reduction manufacturers through cap-and-surplus trading, while ordinary manufacturers could only pass on the cost due to technology locking, resulting in a negative imbalance in social welfare. This study provides theoretical support and decision-making basis for the government's carbon quota allocation policy and supply chain network response strategy.

With the rapid development of the platform economy, e-commerce platforms' store brands have been presented with opportunities for swift growth. Digital traceability technology, as an effective measure to enhance consumer trust in store brands, has become a key to strengthening brand credibility. In view of this, this paper constructs four e-commerce supply chain decision models with and without the introduction of digital traceability technology, considering both the competition between national brand products and store brand products, and the two sale modes of reselling and agency selling. It deeply explores the impact of different sale modes on the decision-making of e-commerce platforms to adopt digital traceability technology. The study shows that high product substitutability and high consumer trust can both lead to higher profit levels for manufacturers and e-commerce platforms, and the introduction of digital traceability technology can create greater profit margins for both manufacturers and e-commerce platforms. By comparing the profits of both parties under different sale modes for national brand products, it is found that for manufacturers, when the investment cost of digital traceability technology is low and the commission rate is low, the profits under the reselling mode are higher than under the agency selling mode. Conversely, if the investment cost is high, regardless of the commission rate, the agency selling mode is the best choice. For e-commerce platforms, when the commission rate is high, the profits under the agency selling mode are higher than under the reselling mode; if the commission rate is low, then the profits under the reselling mode are higher. Finally, this paper further explores the corporate decision-making when sharing the cost of digital traceability technology. It is always the best strategy for manufacturers to choose the reselling mode to sell their national brand products, and when the commission rate for national brand products and the investment cost of digital traceability technology are both low, the profits of e-commerce platforms under the agency selling mode for national brand products will be higher.

This study explores in depth the impact mechanism of state-owned institutional investors' shareholding on corporate investment efficiency, especially in the context of mixed ownership reform. Combining theoretical analysis and empirical testing, it reveals the key role of state-owned institutional investors in improving corporate investment efficiency. Research has shown that an increase in the shareholding ratio of state-owned institutional investors has a significant promoting effect on improving the investment efficiency of enterprises. In addition, factors such as corporate governance level, enterprise size, industry competition level, and cash flow volatility also have a direct impact on the investment efficiency of enterprises. Further research has found that digital transformation and green innovation of enterprises play an important intermediary role between the shareholding of state-owned institutional investors and the efficiency of enterprise investment. State owned institutional investors accelerate the process of digital transformation and green innovation by providing financial support, strategic guidance, and resource allocation. Digital transformation can improve information processing capabilities and optimize resource allocation efficiency, while green innovation can indirectly enhance the investment efficiency of enterprises by improving resource utilization efficiency and enhancing market competitiveness, enabling state-owned institutional investors to hold shares can indirectly improve the investment efficiency of enterprises. This article not only enriches the relevant research on the economic consequences of state-owned institutional investors, but also provides a new theoretical perspective for understanding the mechanism of improving investment efficiency of enterprises. At the same time, it provides important theoretical basis and policy inspiration for deepening the reform of state-owned enterprises, optimizing the layout of state-owned capital, and enhancing the overall competitiveness of enterprises in the new era.

This study investigates risk contagion mechanisms and driving factors in the smart grid industry chain under major event shocks using a DCC-GJR-GARCH-MES model. By integrating complex network theory, event breakpoint analysis, and MST algorithms, we examine network evolution across upstream, midstream, and downstream sectors during crises like the COVID-19 pandemic, OPEC production adjustments, Russia-Ukraine conflict, and stock market crashes. Machine learning combined with SHAP values identifies risk drivers and enables early warnings. Key findings reveal: (1) Upstream sectors show greater stability than mid/downstream counterparts during shocks, with enhanced local clustering in risk networks. Systemically important enterprises act as risk transmitters while peripheral firms exhibit weaker linkages. (2) Public health emergencies exert a greater impact on tail risk contagion networks compared to other events, with drivers showing significant time-varying characteristics across different shock types and industry segments. (3) Firm size, interconnectedness, and profitability consistently emerge as critical drivers, with XGBoost models demonstrating strong systemic risk prediction capabilities. These insights reveal sector-specific vulnerabilities and response mechanisms under external shocks, offering strategic guidance for optimizing risk management in smart grid supply chains.

In response to the noise problem, the article adopts a controller design method to attenuate the sound wave equation and achieve the effect of controlling noise. Time delay is considered in the controller design, and a differential controller is designed using the idea of system equivalence. The specific steps are as follows: Firstly, we need to identify the exponentially decaying system and use it as the target system. Secondly, based on the form of integral feedback control, we establish equivalent transformations between systems to ensure that the studied system is equivalent to the target system. The appropriate parameter function is determined during the calculation process to obtain the expression of the controller. Thirdly, we considered the solvability of parameter functions and the boundedness of transformations. Finally, numerical simulations were conducted and the conclusion was drawn that under the action of the controller, the original system exhibited exponential decay Therefore, this method can effectively control noise.

Double cyclic codes are an important class of error correcting codes, which not only have good algebraic structures that are easy to encode and decode, but also contain numerous optimized linear code classes. The paper studied the Hermitian hull of non-separable cyclic codes over finite fields, and determined the explicit polynomial of Hermitian hull. Then based on the construction method of entanglement-assisted quantum error-correcting codes, we construct some entanglement assisted quantum error correction codes with good parameters. Comparing with known entanglement assisted quantum error correction codes, our code has new parameters.

With the aim of maximizing any objective payment of populations, the concept on strong Pareto-Nash equilibrium of multi-objective population game is introduced. By utilizing the Ky Fan section theorem, under the continuity of the vector payment function and a cone properly quasi-concave assumptions, the existence theorem of the equilibrium is obtained. Meanwhile, the equivalent relationship between the strong Pareto-Nash equilibrium of multi-objective population games and the solutions of vector strong variational inequality problems is established. Applying the equivalent relationship of the equilibrium, the stability of the strong Pareto-Nash equilibrium in multi-objective population games is studied. Finally, corresponding examples are presented to explain results obtained in the paper in detail.

Optimal subset selection can accurately and efficiently mine important information from high-dimensional data to build a reduced regression model. In recent years, it has been used more and more in machine learning, image processing and biomedicine. However, most of the existing optimal subset selection methods are based on least squares or maximum likelihood, resulting in insufficient robustness when dealing with heterogeneous data. In order to effectively deal with the heterogeneity of high-dimensional data and comprehensively analyze the conditional distribution of response variable, a robust optimal subset selection algorithm based on $\ell_{0}$ penalty and smoothing quantile loss function is designed in this paper. In practice, the real number of important variables is usually unknown. In this paper, a truncated sequential search algorithm is proposed for efficient and accurate selection of the number of important variables. In the simulation, comparing with the existing variable selection methods, it is found that the proposed method has more advantages in variable selection and parameter estimation accuracy. Finally, the new method is used to analyze the gene data related to the production of riboflavin by Bacillus subtilis. The experimental results show that the new method has a smaller quantile prediction error in estimating the riboflavin production rate.

For multi-objective switching constraint optimization problems, the presence of switching constraints can render the Karush-Kuhn-Tucker (K-K-T) conditions potentially invalid at feasible points. Therefore, it is necessary to investigate weaker stability concepts and applicable optimality necessary conditions. This paper first defines the generalized Guignard constraint qualification for such problems. Under this constraint qualification, we then construct and prove the necessary conditions for optimality. Due to the possible discontinuity of the feasible region in switching constraint programming problems, traditional nonlinear programming methods are difficult to apply directly. Finally, we propose a relaxation model for this problem and prove that, under certain assumptions, The Pareto efficient solution set and the Pareto weakly efficient solution set of the relaxation model converge to the Pareto efficient solution set and the Pareto weakly efficient solution set of the original problem in the sense of Kuratowski-Painlevé. respectively. Additionally, the Pareto KKT set of the relaxation model converges upwards to the set of Pareto weakly stable points of the original problem.

Taking a green supply chain consisting of a single manufacturer and a single retailer as the research object, this study examines the impact of channel demand transfer and manufacturers' social responsibility on manufacturers' channel selection under three channel strategies in the context of uniform retail pricing. The findings are as follows: (1) When the level of social responsibility assumed by the manufacturer and the channel demand transfer coefficient are low, it is optimal for the manufacturer to open both retail channel and direct channel; (2) As the level of social responsibility assumed by the manufacturer and the consumer demand transfer coefficient increase, opening only direct sales channel surpasses opening both retail channel and direct channel to become the optimal strategy, and opening only traditional retail channel is not the optimal strategy under any circumstances; (3) When the channel demand transfer coefficient is high, the total demand for the product increases, the greenness level improves, and the retail price of the product rises. At the same time, consumer surplus increases, and the manufacturer's overall profitability improves.

Open-ended questions within surveys, devoid of predetermined response options, afford respondents greater latitude in articulating individual perspectives, thereby facilitating researchers' comprehension of respondents' stances on intricate matters and fostering the exploration of novel avenues for inquiry. Consequently, undertaking systematic investigations into these questions is deemed essential. Currently, the research method of open-ended questions in academia relies on manual coding based on Grounded theory. However, the preliminary stage of summarizing and sorting materials is laborious and time-consuming. Although there are guiding coding standards, there is no mature method to automate the process, which limits the scope of academic research. To address this challenge, our research proposes a new topic model method inspired by BERTopic to automate the coding of open-ended questions in questionnaires. We use Sentence BERT to embed documents, hierarchical clustering to cluster them, and Text Rank and PEGASUS to extract keywords and automatically summarize them. Our method can conduct hierarchical topic modeling on the input open-ended answer text, and achieve classic three-level coding. It can also obtain different numbers of themes at different levels to suit various needs. After applying our method on the open-ended question dataset of the government environmental impact assessment questionnaire, it can identify hierarchical themes with clear meanings, showing excellent results and significantly improving the efficiency of manual coding.

In the context of major natural disasters with multiple affected areas, it is crucial not only to respond quickly to rescue needs but also to comprehensively consider the efficiency, effectiveness, and fairness of assistance. This study proposes two optimization objectives for emergency aid across multiple affected regions: minimizing unmet demand and minimizing the maximum arrival time. A multi-objective nonlinear programming model is established for multi-supply-point collaborative assistance, incorporating the collaborative effects among supply points into the optimization model. The model is solved using the Non-dominated Sorting Genetic Algorithm II (NSGA-II), which optimizes multiple objectives under complex constraints, generating efficient and practical resource scheduling solutions. Numerical analysis validates the effectiveness of the proposed model and algorithm in improving the efficiency of emergency resource allocation, ensuring fairness, and reducing response time, providing scientific evidence and practical application references for resource distribution in multi-affected-area scenarios.

With the increasing demand for rural delivery in mountainous areas, the routing problem of rural delivery logistics in mountainous areas(RPRDLMA) has become an academic hotspot. Based on the background of rural passenger, cargo and postal integration development, the RPRDLMA under the cooperative distribution of bus-electric vehicle-drone(RPRDLMA-CDBEVD) is studied in this paper. Firstly, the village service points are divided into type TC and type FC, meaning that they are served by EVs or by drones, according to their geographic location, distribution characteristics and volume of cargo delivered or mailed. Next, a continuous function of bus idle capacity is established based on the tidal rural passenger flow characteristics. Then, the RPRDLMA-CDBEVD model is constructed with the goal of total cost minimization. Specifically, the total cost includes commissioning cost, capacity-based cost, distance-based cost, time-based cost and electricity consumption cost. In order to solve the model, a hybrid algorithm of multi-constraint modified clustering algorithm and improved adaptive genetic algorithm (MCDCA-IAGA) is designed. The experimental results and case studies show that the collaborative delivery mode of passenger shuttle bus electric vehicle unmanned aerial vehicle effectively reduces delivery costs by 2.9% and delivery time by 8.6%, providing a feasible solution for logistics path planning in mountainous and rural areas.

This study aims to delineate an integrated evolutionary game model for the smart elderly care service system by constructing an integrated evolutionary game model. The model encompasses four key stakeholders: government agencies, smart elderly care service providers, digital platform operators, and the elderly user group. Employing the game model approach that scrutinizes the interactive dynamics and strategic choices among these stakeholders, we unveil the collaborative mechanisms within the smart elderly care service sector. The research findings suggest that strengthening cooperation among the government, enterprises, digital platforms, and the elderly population can effectively promote the development of smart elderly care services, thereby improving the quality of life for the elderly. Under effective policies and regulatory mechanisms, the smart elderly care industry can achieve a certain level of stability. The results of this study contribute to the advancement of the smart elderly care sector and provide a critical theoretical foundation for the construction of a smart elderly care service system.

In this paper, considering the limitations of traditional noise processing methods, a novel approach for handling noisy datasets based on the concept of feature subspace interpolation is proposed, termed RELIS (Robust Equidistant Linear Interpolation Synthesis).First, the original feature space is divided into multiple feature subspaces with approximately equal samples through unsupervised clustering. Second, based on the clustering results, the concept of the Traveling Salesman Problem (TSP) is introduced to order the feature subspaces. Next, by combining a soft parameter sharing mechanism, linear fitting is applied to samples in adjacent subspaces. Finally, an innovative multi-stage minimum weight matching method is proposed to obtain an optimal interpolation matching strategy. This paper theoretically demonstrates the optimization effect of the RELIS method for noise of different distributions and further validates it through simulation experiments.

Focusing on the supply side of vehicle charging service, this study proposes two differential game models for charging pile operation decision-making, with the government, operator, and third-party platform (hereinafter referred to as the platform) as the participants. The two differential game models are decentralized (i.e., operators and platforms aim to maximize their own interests) and centralized (i.e., operators and platforms aim to maximize the overall interests of both). The results show that under the equilibrium state with fixed revenue distribution ratios between operator and platform, compared with the decentralized decision-making mode, the centralized decision-making mode can improve the efforts of operator and platform, service quality and social benefit. When the platform is relatively weak and has a lower share of revenue, adopting the centralized decision-making mode can achieve a Pareto improvement in the revenues of both operator and platform; conversely, when the platform is relatively strong and has a higher share of revenue, adopting the decentralized decision-making mode can increase the revenues of both operator and platform. This indicates that as platform develops from weak to strong, the decision-making mode of the charging service market may shift from centralized to decentralized. At this time, the proportion of government policy support will increase, and social benefit and service quality may decrease.

To effectively address and alleviate the trust uncertainty crisis faced by cloud service providers (CSPs) and cloud service consumers (CSCs) during the formation and adoption of cloud alliances, and to avoid incurring additional trust costs, it is essential to monitor and constrain the trust levels within these alliances in real time. For this reason, a dynamic trust evaluation approach for cloud alliances based on the flexible ideal solution ($FIS$) and reflecting reward-penalty mechanisms is proposed. The approach employs hesitant fuzzy elements (HFE) to integrate the different trust performances of CSPs in the alliance, providing a comprehensive and accurate characterization of the trust levels. Additionally, it introduces the COWA operator and hesitant fuzzy linguistic quantifiers to construct the $FIS$ and carries out the evaluation based on the idea of two $FIS$ as the theoretical basis. Furthermore, three distinct measurement approaches that reflect dynamical rewarding and penalizing for alliance trustworthiness (i.e. $TD$ and $UD$) are provided to meet practical decision-making needs. Finally, the applicability of the proposed dynamic evaluation method is validated through its application to a case study involving the selection of alliance partners for an internet company. Discussion on the impact of the varying absolute-relative inclination coefficients on the generation of FIS is presented, demonstrating the method's flexibility and superiority.

The aggregate dimension reduction (Wang et al. ^[1]; Wang & Yin^[2]) is a class of important approaches of sufficient dimension reduction, which have competitive advantages in handling complicated models. It conducts the dimension reduction in the $k$ neighborhood of each sample point and aggregate their results. In this article, we try to adjust the distributions of data in the local areas to make them close to elliptical contoured distribution, which can improve the results of the local dimension reductions and enhance the accuracy of the final aggregate inverse mean estimate. However, because the sample size of the local areas cannot be large, the existing reweighting method based on the Voronoi weights (Cook和Nachtsheim^[3]) may be faced with two problems: Firstly, it may be difficult to construct the objective distribution fitting the data well; Secondly, it may be also difficult to obtain the weights of the data points. To solve these issues, we propose an adaptive reweighting method, which obtains the weights of the data points in each local area based on the result of an initial sufficient dimension reduction on it. We deduce several properties, revealing the relationship between the initial dimension reduction directions and the subspace on which the projection of the predictor vector does not satisfy the linear design condition, to illustrate the reasonableness of the proposed method. The proposed method is illustrated by simulations and a real data analysis.

Under the framework of classical neighborhood rough set, various fast attribute reduction algorithms based on fast positive region calculation have the following characteristics: 1) Neighborhood is the basic perspective of algorithm design; 2) Label information of datasets is not fully utilized; 3) Neighborhood and positive region are calculated by traversal method. These characteristics mean that these algorithms have redundant and inevitably repeated distance calculations and adopt inefficient calculation modes, which leads to low efficiency in calculating attribute reduction results, especially on large-scale datasets. In addition, these fast algorithms have good acceleration effects only when the dependency degree is used as the attribute evaluation function, which may lead to low classification ability of the attribute subset in the attribute reduction result. Therefore, we design an accelerated algorithm for attribute reduction from the basic perspective of heterogeneous neighborhood relationships and propose the inconsistency degree as the attribute evaluation function based on heterogeneous neighborhood relationships. The experimental results on 11 standard datasets show that the proposed method can save 88.0% of the total average computing time compared with the best-performing comparison algorithms(GRRS), and 97.1% of the total average computing time compared with the worst-performing comparison algorithm(EasiFFRA) while ensuring or improving the classification ability of the attribute reduction results.

The volatility and nonlinear characteristics of time series have made modeling and prediction difficult and have attracted widespread attention from scholars. This study combines the decomposition and integration framework to achieve effective information extraction and modeling to improve prediction accuracy. Correspondingly, our proposed methodology involves four main steps: data decomposition via complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN); component grouping via sample entropy (SE); prediction of the reorganized low-, mid-, and high-frequency component groups through persistence (PER), convolutional neural networks (CNN), gated recurrent unit (GRU), and ensemble prediction via weighted addition using ant lion optimization (ALO). Taking the hourly PM_2.5 concentration of Xi’an as the sample, experimental results showed that our proposed hybrid decomposition-group-ensemble forecasting framework (i.e., ALO-CEEMDAN-SE-(PER-CNN-GRU)) significantly outperformed the benchmarks, and the final prediction error obtained the lowest value (2.53%). This validates the superiority of the decomposition integration framework with excellent neural network models for PM_2.5 prediction.