Permutation polynomials have been widely used in cryptography, coding theory, combinatorial design, and other areas of mathematics and engineering. By applying the AGW criterion and determining the number of solutions to certain equations over finite fields, we propose five classes of permutation polynomials with special types. Compared to the known works, this paper not only characterizes more relaxed permutation conditions but also obtains new permutation polynomials. Specifically, we construct two classes of permutation polynomials with the form $\sum\limits_i(x^{2^m}+x+\delta)^{s_i}+x$ over $F_{2^{3m}}$ and three classes of permutation polynomials of the form $\sum\limits_i(x^{p^m}-x+\delta)^{s_i}+L(x)$ over $F_{p^{2m}}$, respectively. Finally, we formally prove that the permutation polynomials proposed in this paper are not quasi-multiplicatively equivalent to any currently known permutation polynomials.

The hull of a linear code plays an important role in determining the permutation equivalence of two linear codes and in characterizing the automorphism group of a linear code. Moreover, as an important class of self-orthogonal codes, the hull of a linear code can also be used to construct entanglement-assisted quantum error-correcting codes. Determining the parameters of the hull of a linear code is an important problem in coding theory. The paper investigates the hulls of negacyclic codes over $\mathbb{Z}_{2^a}$ of even length. The generator polynomials and the $2$-dimensions of the hulls of negacyclic codes over $\mathbb{Z}_{2^a}$ are given. The number of negacyclic codes over $\mathbb{Z}_{2^a}$ with a prescribed hull $2$-dimension is determined. An explicit formula for the average hull $2$-dimension of negacyclic codes of length $N$ over $\mathbb{Z}_{2^a}$ is derived. The upper and lower bounds for the average hull $2$-dimension are explored.

For linear discrete systems subject to deception attacks involving system perturbations, measurement noise, and unknown faults, a joint state and fault estimation method based on zonotopes is proposed. First, by analyzing the intrinsic characteristics of deception attacks, the zonotope boundary for deception attack signals is estimated, and this method can relax the non-negativity condition required in classical interval observer design. Second, based on the augmented system for state and fault estimation, a set of state variables for a Luenberger-type observer is formed, and through algebraic operations, an estimating set that envelops both the system state and faults is generated. Simultaneously, the optimal gain matrix for the ensemble estimation optimization criterion is obtained based on the minimum volume criterion of the zonotope. Finally, simulation results demonstrate that the proposed set-membership estimation algorithm accurately encapsulates the true state and system faults under attack conditions.

This paper proposes a novel adaptive control scheme for a one-dimensional unstable heat conduction equation with unknown control coefficients. Firstly, a new state observer is designed to estimate the system state, and a corresponding update law is constructed to estimate the reciprocal of the control coefficients. Unlike traditional state observers, the newly designed state observer in this paper relies on a specific control decomposition form, which eliminates the presence of both the unknown control coefficients and their estimates in the state observer. Consequently, the control design problem for the controlled object can be transformed into a control design problem for the state observer, effectively overcoming the challenges posed by the unknown control coefficients. The resulting closed-loop system is nonlinear, and its well-posedness and stability are proven mathematically. Additionally, some theoretical results are visually validated through numerical simulations. This paper is dedicated to commemorating the 90th birthday of Academician Chen Hanfu. We have selected this topic to celebrate Academician Chen's outstanding achievements in adaptive identification theory for stochastic systems.

Since Robbins and Monro proposed stochastic approximation algorithms in the 1950s, such algorithms have found wide applications in systems and control, statistics, machine learning, and other fields. This paper focuses on stochastic approximation algorithms with extended truncation developed over the past three decades. It first reviews the historical developments of centralized stochastic approximation algorithms, including the probabilistic methods and ordinary differential equation (ODE) approaches for convergence analysis of stochastic approximation, as well as the trajectory-subsequence method for stochastic approximation with extended truncation. An illustrative application of stochastic approximation with extended truncation to recursive principal component analysis is then provided. Finally, recent advances of such algorithms in networked and distributed settings, namely distributed stochastic approximation algorithms with extended truncation, are presented.

This paper investigates distributed online aggregative games with time-varying constraint sets. First, the one-way Hausdorff distance is introduced to characterize the variations of constraint sets between consecutive time instants. Second, a distributed online mirror descent algorithm is developed based on the Bregman divergence, where the effect of gradient noise is also considered. Under standard assumptions including joint connectivity of communication topologies and strong convexity of the mirror function, we further derive a sublinear upper bound on the expected dynamic regret for the proposed algorithm. Finally, numerical simulations are conducted to verify the effectiveness of the proposed algorithm.

Driven by the demands of driving safety, traffic efficiency, and energy conservation, tracking control for unmanned vehicle platoons has garnered extensive attention. In practice, complex road and airflow conditions expose vehicles to strong nonlinearities, rendering accurate modeling challenging. Existing approaches typically rely on linearized models or assume bounded lumped disturbances and their derivatives—assumptions difficult to verify in real-world scenarios. To address these issues, this paper proposes a longitudinal active disturbance tracking control scheme based on an extended state observer (ESO) and saturation constraints. The ESO is employed to online estimate and compensate for unmeasurable system states and lumped disturbances in the feedback control loop. A saturation mechanism is introduced to prevent system divergence induced by high-order nonlinearities under large ESO gains. Via proof by contradiction, the global uniform boundedness of the closed-loop system is established, and both observation and tracking errors can be made arbitrarily small by increasing the ESO gain.Finally, numerical simulations and comparative analyses with the adaptive control and sliding‑mode control methods are carried out to verify the effectiveness and superiority of the proposed method.

Against the backdrop of the national policy objective of ``effectively preventing and mitigating risks faced by high-quality leading real estate enterprises,'' this study focuses on two key issues: the rapid transmission of risks among real estate enterprises and the multi-channel diffusion mechanisms underlying such risk propagation. We constructed a high-dimensional dynamic risk spillover network covering 123 real estate companies listed on the Shanghai and Shenzhen A-share markets from 2007 to 2023. This network identifies its multi-risk-center structure and reveals the dynamic spatiotemporal patterns of risk-originating nodes. Our findings reveal: (1) Real estate network risk spillover exhibits both a one-month cycle of direct financial market shocks and an ultra-short chain transmitting through financial channels to the macroeconomy within three months; (2) The network displays a decentralized structure——rising spillover intensity coincides with a significant decline in network concentration, indicating systemic risk originates from dispersed contributions by non-hub nodes, fundamentally conflicting with traditional finance's ``center-periphery'' risk models; (3) Further integration of block models and the Fruchterman-Reingold algorithm identifies a key risk-originating mechanism: bidirectional risk spillover clusters (averaging 26% of total nodes) serve as risk-emitting nodes, exhibiting dual spatiotemporal dynamics——a 61.5% interannual turnover rate in node sequence and 22% of nodes distributed at network peripheries with cross-regional linkage; (4) Within-industry risk spillovers in both the real estate sector and financial subsectors are stronger than cross-industry spillovers, but bidirectional risk spillovers between the real estate sector and financial subsectors remain at relatively high levels during most periods, with the real estate sector acting as a net risk transmitter to the financial sector as a whole. Regression analysis confirms that the bidirectional risk-spillover cluster is the primary contributor to risk spillovers, generating multicenter concurrent diffusion of network risk through subsystem spatial decoupling, homogeneous node responses, and the external coupling field. In light of the ``dispersed outbreaks and convergent transmission'' mechanism of risk among real estate firms, this paper proposes four regulatory approaches for supervisory authorities: weekly risk monitoring based on the Elastic-Net-VAR framework, targeted supervision of bidirectional risk-spillover clusters, enhanced cross-regional coordinated risk prevention and response, and a differentiated risk-monitoring framework for the real estate sector and financial subsectors. The findings also provide empirical evidence for promoting a shift in real estate risk governance from scale-based control toward a prevention and control paradigm centered on network functions.

Jet engine turbine blades are responsible for converting high-temperature, high-pressure gas into mechanical energy, and their materials must be able to withstand extremely high temperatures. To analyze the cooling performance of turbine blades, existing methods typically construct finite element models of varying fidelity for numerical simulation. However, high-fidelity models are computationally time-consuming and expensive, and high-fidelity experiments can only select a small number of experimental points for constructing a surrogate model, so nested experimental designs are commonly adopted. In view of the fact that generalized Latin hypercube designs often provide better predictive performance in many cases, this paper proposes a generalized nested space-filling design for constructing finite element surrogate models. The proposed design places more design points near the boundary of the experimental region and further provides a corresponding construction algorithm framework. Results from both numerical simulation analysis and actual finite element simulations indicate that the proposed new design performs better in model prediction.

With the rapid development of the digital economy and the increasing complexity of the market environment, platform stratification has become a crucial strategy for platform enterprises to optimize resource allocation, precisely respond to user demands, and build competitive advantages. This study, based on the Technology-Organization-Environment (TOE) framework, employs the fuzzy-set Qualitative Comparative Analysis (fsQCA) method to conduct a configurational analysis of the stratification strategies of 199 platform enterprises. Through the analysis of multidimensional factor synergy mechanisms and dynamic evolutionary paths, platform stratification reveals three distinct paths: technology-organization driven, technology-environment driven, and technology-organization-environment driven. These paths form differentiated combinations that depend on the modularization of technological architecture, the enhancement of digital empowerment, and the dynamism of market competition. The study finds that the competitiveness of platform stratification stems from effective responses to user heterogeneity, technological architecture, and environmental uncertainty. Through niche stratification, it transforms refined customers, scaled suppliers, and long-tail markets into competitive advantages. The synergistic effects of multidimensional factors and nonlinear interactions enhance the precision of stratification and the resilience of the ecosystem, providing theoretical and practical guidance for platform enterprises to implement differentiated strategies in dynamic environments.

To evaluate the impact of the“East-Data-and-West-Calculation”Project on the dual transformation of digitalization and green development in target regions, this study constructs a dual-synergy system dynamics model integrating economic, demographic, technological, energy, policy, and environmental subsystems. Based on the national layout of the “4+4” computing-hub clusters, model parameters and governing equations were established, with the data-center migration scale and non-fossil energy share introduced as regulatory factors in the technology and energy subsystems. The model simulates the evolution of regional digitalization and green development from 2025 to 2060 under three scenarios: single computing-power scheduling, single power-system decarbonization, and their combined implementation. The results indicate that single computing scheduling yields limited emission reduction, while single decarbonization lowers emission intensity but proceeds slowly. In contrast, the integrated scenario achieves synergistic effects—advancing the carbon-peaking time by approximately 5 years relative to the baseline, while maintaining stable GDP and digital output growth. By around 2050, net CO₂ emissions peak and begin to decline, demonstrating coordinated progress in digital transformation, and green transition.

Amid growing tensions between the supply and demand of medical resources, healthcare payment schemes have become a critical reform measure to regulate medical practices and improve cost efficiency. However, they may inadvertently lead to hospitals selectively admitting patients. This study examines a specialized medical service system consisting of delay-sensitive patients, two heterogeneous hospitals, and a healthcare payer, addressing whether the payer should adopt bundled payment and how to design such a payment scheme to maximize social welfare. By constructing an integrated queueing——game-theoretic model, this study characterizes the trade-off among increasing service rates, reducing patient waiting costs, and rising subsequent medical costs in specialized healthcare services, analyzing hospitals' service rate strategies under bundled payment, and evaluate the impact on social welfare. The findings reveal that when the two hospitals are homogeneous in unit treatment cost, the payer can achieve maximum social welfare under bundled payment. However, this outcome is unattainable when hospitals are heterogeneous. Therefore, this study further proposes a bundled payment plus pay-for-performance (BP+P4P) coordination mechanism. By maintaining a uniform bundled payment while introducing performance-based incentives, the mechanism encourages hospitals with lower unit medical costs to serve a greater proportion of patients, thereby enhancing the accessibility of specialized healthcare services and reducing both patient waiting costs and total social costs.

This paper investigates the adaptive practical finite-time tracking control problem for a class of high-order nonlinear systems subject to full-state constraints and unknown time-varying powers. A nonlinear state transformation is constructed to handle the full-state constraints, through which the constrained system is transformed into an equivalent unconstrained one and state constraint violation is avoided. A new practical finite-time controller is designed by introducing parameters $\bar{p}$ and $\hat{p}$ to effectively compensate for the unknown powers. The adaptive fuzzy approximation technique is employed to identify unknown nonlinear dynamics, and nonlinear filters are introduced to avoid repeated differentiation of virtual control signals. In particular, the proposed filters are constructed with the aid of D-functions, enabling them to handle completely unknown parameters in nonlinear terms and effectively suppress filtering errors. To balance constraint safety and communication efficiency, a novel reset-dynamic event-triggered mechanism is developed to reduce unnecessary control updates while excluding Zeno behavior. By integrating the adaptive filtered backstepping technique with fuzzy logic systems, the proposed scheme compensates for system uncertainties and ensures that all closed-loop signals are semi-globally practically finite-time bounded. Furthermore, the developed practical finite-time control scheme drives the tracking error into an adjustable residual set within finite time while strictly respecting the predefined state constraints. Finally, simulation results demonstrate the effectiveness of the proposed control strategy and its advantage in saving communication resources.

In this paper, we focus on the reduction problems of two classes of multivariate polynomial matrices and their Smith forms, and establish the necessary and sufficient conditions for the equivalence of these matrices to their Smith forms. Furthermore, we extend these results to the scenarios of non-square and non-full-rank matrices. These conditions can be verified by computing the reduced Gröbner bases of the ideals generated by the relevant minors of the given matrix.

Preference relation is one of the most important and fundamental mathematical tools in multi-objective optimization. In this paper, we first present a quasi-order by using the idea of extended generalized Tchebycheff norm and establish the cone properties of this class of quasi-order. On this basis, we propose a new preference relation on the image set of a multi-objective optimization problem by utilizing the utopia point. Furthermore, we present the definitions of GT optimal solution and GT nondominated point for multi-objective optimization problems via the new preference relation, establish the relationships between GT optimal solutions and Pareto efficient solutions, and between GT optimal solutions and properly efficient solutions. Finally, we give two examples to illustrate the main results.

The resilience of regional industry-university-research innovation systems is crucial for their ability to withstand external impacts and maintain their own technological innovation capabilities. This paper focuses primarily on the network dimension of the regional industry-university-research innovation system, defining the network structural resilience of such systems based on their entity innovation relationship networks. Metrics and calculation methods for measuring network structural resilience are designed at both the overall system and subgroup levels. These measures are then applied to analyze the network structural resilience of the industry-university-research innovation system in the communication equipment manufacturing industry in the Beijing-Tianjin-Hebei region. The results indicate that the system's entity patent collaboration innovation relationship network would be significantly disrupted only when more than 90% of the nodes exit. The system's resilience strengthens as the intensity of the impact increases. The connectivity of the network is primarily sustained by entities in the Beijing region and corporate entities. In general, the damage to the overall network connectivity caused by the random exiting of nodes in Beijing is higher than that in Hebei and Tianjin. Additionally, the exiting of corporate entities causes more significant harm compared to universities, research institutions, and other organizations. It is advisable to minimize the occurrence of a large-scale exiting of university entities. In addition, the network structural resilience measurement method proposed in this paper can also address scenarios of non-random node exit. The comparative analysis reveals that the focused system possesses far weaker resistance against targeted node exit sorted by degree or betweenness than against random node exit. The conclusions drawn in this paper can assist administrators of regional industry-university-research innovation systems in effectively addressing the damage to the connectivity of their entity innovation relationship networks caused by the exiting of nodes resulting from impacts.

Low-carbon transition is not an isolated emission-reduction activity within a firm. Its effects can propagate through supply chains via input prices, production adjustments, and changes in green demand. This study develops a two-stage Stackelberg game involving an upstream supplier, a core producer, and a downstream demand market. Under demand uncertainty, the model incorporates the core producer's low-carbon transition investment, consumer green preference, carbon emission constraints, and green credit financing into a unified framework. We examine how a given level of low-carbon transition investment affects supplier profitability, production, downstream supply risk, and total supply-chain carbon emissions. We further introduce an emissions trading mechanism to investigate how carbon prices and allowance constraints regulate these spillover effects. The analytical results yield four main findings. First, low-carbon transition by the core producer can generate positive profit spillovers to the upstream supplier through expanded green demand and increased intermediate-input demand. However, the response of the wholesale price depends on whether the producer is constrained by its carbon allowance, indicating clear state dependence. Second, low-carbon transition does not necessarily improve environmental performance monotonically. The change in total supply-chain emissions is jointly determined by the reduction in emission intensity and the expansion in production. A carbon rebound occurs when the scale effect of production expansion exceeds the emission-reduction effect. Third, emissions trading increases the producer's effective marginal carbon cost and restrains production expansion. This reduces the positive profit spillover to the upstream supplier and increases the risk of downstream supply shortages, while simultaneously reducing total supply-chain emissions and narrowing the rebound region. Numerical simulations further show that emission-reduction technology endowment, consumer green-demand responsiveness, demand uncertainty, and carbon prices jointly determine the boundary conditions of these spillover effects. The findings suggest that low-carbon transition policies should account not only for the direct emission performance of core producers but also for the systemic consequences transmitted through supply-chain price and quantity adjustments.

Against the backdrop of the accelerating integration of digitalization and servitization in manufacturing, a rigorous evaluation of manufacturing firms' digital service innovation (DSI) is essential for identifying innovation bottlenecks and optimizing resource allocation. Drawing on the dynamic evolution of DSI, this study adopts the inputs-processes-outcomes (IPO) framework as its overarching logic and embeds technology-organization-environment-process (TOEP) drivers, initiation-development-implementation (IDI) innovation stages, and balanced scorecard (BSC) outcome dimensions into the I, P, and O components. On this basis, a DSI evaluation index system covering enabling conditions, innovation processes, and performance outcomes is developed. To address uncertainty in multisource evaluation information, unclear directions of indicator influence, the masking of critical weaknesses by favorable performance, and difficulties in capturing inter-indicator synergy, a progressive evaluation approach is proposed that integrates information preservation, directional weighting, gain-loss identification, and synergistic aggregation. First, hesitant fuzzy elements (HFEs) are used to preserve expert judgments and differences across data sources, while hesitant fuzzy transfer entropy is employed to determine directional information-contribution weights. Second, an asymmetric inverse-gamma gain-loss function separates advantages and disadvantages arising from deviations from reference levels, thereby highlighting the constraining effects of critical weaknesses. Finally, a combinatorial area-based aggregation method separately captures synergy among advantages and clustering among disadvantages, producing an overall DSI evaluation and bottleneck diagnosis. An empirical study of six manufacturing firms in Yunnan Province shows that the proposed approach can identify firm-specific strengths, transmission blockages, and improvement priorities across the input, process, and outcome stages. The approach provides methodological support for evaluating manufacturing firms' DSI, allocating resources, and selecting targeted improvement pathways.

Beck introduced two partition statistics $NT(r,m,n)$ and $M_{\omega}(r,m,n)$, which denote the total number of parts among partitions of $n$ with rank congruent to $r$ modulo $m$, and the total number of ones among partitions of $n $ with crank congruent to $r$ modulo $m$, respectively. Andrews proved two congruences on $NT(r,m,n)$ which were conjectured by Beck. Recently, Chern established more than 70 Andrews-Beck type congruences modulo 5, 7, 11 and 13 for $NT(r,m,n)$ and $M_{\omega}(r,m,n)$. Inspired by their work, we use congruence relations for rank and crank moments established by Atkin and Garvan to derive new Andrews-Beck type congruences modulo 23, 41, 43, 53 and 83 for $NT(r,m,n)$ and $M_{\omega}(r,m,n)$ in this paper.

Considering the dynamic evolutionary characteristics of DMUs in real-world settings and the objective interactions among them, this paper develops a dynamic DEA cross-efficiency model that accounts for both internal and external effects within alliances. First, carry-over variables are introduced to capture the interdependencies across consecutive periods. By integrating cross-efficiency with an intertemporal production frontier, a dynamic model is formulated that achieves vertical and horizontal comparability as well as intertemporal linkage. Second, based on this model, the Criteria Importance Through Intercriteria Correlation (CRITIC) method is employed to objectively measure the informational value of the results within the appraisal period and to derive differentiated weights. These weights are then utilized to perform a weighted integration of the highest internal and lowest external evaluations, thereby establishing a comprehensive approach that explicitly incorporates internal and external alliance effects. Finally, the Shapley value from cooperative game theory is adopted to aggregate and rank the efficiency scores. The proposed methodology is applied to the empirical evaluation of innovation efficiency for 44 listed "Specialized, Refined, Differentiated, and Innovative" (SRDI) enterprises in China from 2018 to 2022. A comparative analysis with alternative methods confirms the rationality and effectiveness of the proposed model, which systematically integrates internal-external alliance effects and weight configurations.

Given the significant differences in resource endowments and industrial structures across cities, the evaluation of carbon emission efficiency needs to account for both technological heterogeneity and the generation of pollutants as by-products. This paper integrates by-production technology with directional distance functions to develop an improved meta-frontier model incorporating sequential constraints. The model embeds the slack variables obtained from the group-frontier solution into the meta-frontier model as lower-bound constraints, thereby effectively avoiding anomalies of technology gap rate. Using the 16 prefectures of Anhui Province from 2006 to 2023 as a sample, this study conducts an empirical analysis by dividing them into high- and low-energy-intensity groups. Carbon emission efficiency is decomposed into economic output efficiency and carbon emission reduction efficiency. The results indicate: 1) carbon emission efficiency across Anhui's cities improved overall, although the pace of improvement varied across cities; 2) disparities in economic output efficiency were relatively small, whereas those in carbon emission reduction efficiency and technology gaps were more pronounced; and 3) for most cities, room for improvement in carbon emission reduction and economic output was concentrated within their respective group frontiers. Accordingly, differentiated low-carbon governance should be implemented in light of cities' energy intensity and industrial characteristics. This study provides methodological reference and decision support for efficiency evaluation in heterogeneous multilevel systems.

This paper investigates the two-agent scheduling problems in a permutation proportional flow shop based on the number of tardy jobs and the late work. Specifically, a tardy job refers to a job whose completion time exceeds its due date; the late work is defined as minimization of tardiness and processing time of a job; a permutation proportional flow shop means that all jobs are processed in the identical sequence on each machine, and the processing time of each job is machine-independent. The production system consists of two competing agents, denoted by $A$ and $B$, each having a disjoint set of jobs, and the processing of all jobs is non-preemptive. Agent $A$ takes the weighted number of tardy jobs or total late work as its optimization objective, while agent $B$ takes the number of tardy jobs as its optimization objective. It aims to minimize the objective function of agent $A$ under the constraint that the objective function value of agent $B$ does not exceed a given threshold. For the above scheduling problems, we show that the two problems are both NP-hard, and present dynamic programming algorithms and the time complexity analysis, respectively. Finally, numerical examples are used to verify the feasibility and effectiveness of the proposed algorithms.

This paper focuses on wireless sensor networks equipped with a capacitor-battery hybrid energy storage architecture and establishes an M/M/1 queueing-inventory system model with a standby inventory, where the energy consumption for a single data packet transmission (i.e., inventory demand) is assumed to follow a geometric distribution. If the total residual energy of the capacitor and battery is insufficient to transmit the current data packet, the data packet is dropped and the system runs out of energy. This model breaks through the limitations of traditional single-inventory systems and dual-supply shared-inventory frameworks by devising two independent replenishment mechanisms for the primary inventory and standby inventory, and introduces geometric batch demand to characterize the fluctuation of energy consumption during data packet transmission. Firstly, the steady-state distribution and key performance indicators of the system are obtained by utilizing the matrix-geometric solution method. Secondly, the system benefit function is constructed, and the optimal energy inventory strategy of the system and the corresponding optimal system benefit are obtained using the genetic algorithm. Subsequently, the influence of system-related costs on system benefits is analyzed through numerical examples. The study reveals that: when the waiting cost and the energy holding cost of the capacitor are high while the charging cost is low, the system equipped with a standby battery can achieve higher system benefits; conversely, when the waiting cost and the energy holding cost of the capacitor are extremely low while the charging cost is excessively high, the system equipped with a standby battery fails to attain higher system benefits. Finally, based on the results of optimization and comparative analysis, management recommendations for optimizing system performance are provided.

Secret sharing is an important method in cryptography for protecting information security. In a designated-participant threshold secret sharing scheme, the secret can be reconstructed only when the number of participants holding valid shares reaches the threshold and all designated participants are involved. During the secret reconstruction phase, the information exchange among participants is vulnerable to external attacks, and existing designated-participant secret sharing schemes mainly focus on sharing a single secret. In this paper, we propose a new designated-participant multi-secret sharing scheme based on bivariate polynomials. In the proposed scheme, session keys are established among participants based on the shares generated by the bivariate polynomial and the identity information of participants, which effectively prevents external adversaries from eavesdropping on secret information and mitigates internal collusion attacks.

The high insurance premiums for intelligent vehicles suppress consumer willingness to purchase and hinder the intelligent transformation of the automobile manufacturer. To address this issue, this study constructs a three-level supply chain game-theoretic model involving an automotive manufacturer, a dealer, and an insurance company based on a data-driven insurance (DDI) model. It compares the manufacturer's production decisions under both traditional insurance and data-driven insurance modes. The results indicate that (1) the insurance company offers premium discounts only when it possesses strong data value conversion capabilities. (2) Under the DDI model, the manufacturer opts to produce intelligent vehicles when the unit production cost is moderate; otherwise, it adopts a hybrid production strategy. (3) The DDI model can simultaneously enhance the AI technology level of intelligent vehicles, market demand, and the profits of supply chain members. Under certain conditions, it can resolve the conflict faced by automakers under traditional premium models between pursuing economic benefits and promoting technological upgrades, thereby achieving a coordinated improvement of both objectives. Furthermore, under the assumption that premiums are linked to vehicle price, the above conclusions remain robust.

We study an optimal investment and benefit-adjustment problem for a target benefit (TB) pension fund under a new class of utility functions. Existing studies typically use constant relative risk aversion (CRRA) or hyperbolic absolute risk aversion (HARA) utility functions to model such problems. To provide a more general framework, we move beyond the conventional HARA specification and adopt the generalized oblique bi-CRRA index (GOBI) utility proposed by Philip H. Dybvig, a 2022 Nobel laureate in economic sciences, and his coauthor Liu. We show that the Arrow-Pratt measure of absolute risk aversion under GOBI utility equals the corresponding HARA measure multiplied by an adjustment factor governed by an additional parameter. Using convex duality, we derive closed-form solutions for the optimal investment strategy, optimal benefit-adjustment strategy, and value function. Numerical illustrations show that the additional GOBI parameter significantly affects the optimal strategies and value function. Relative to HARA utility, GOBI utility leads to a larger allocation to the risky asset and thus provides a more flexible description of investors with lower risk aversion. This flexible utility specification also yields a novel closed-form framework for extensions to related problems.

Disaster assessment and verification are essential for the rational allocation of relief resources and the optimization of post-disaster governance. In practice, however, strategic misreporting by disaster-affected groups often coexists with the limited verification capacity of relevant authorities. Through automated cross-checking of multisource data, anomaly detection, and intelligent screening, artificial intelligence (AI) provides a new approach to improving verification efficiency and curbing misreporting. Using a tripartite differential game model that involves the government, enterprises, and the public and incorporates multidimensional information sources, this study systematically examines the effects of different decision-making modes and AI intervention on disaster assessment and verification performance and the system's net welfare. Four typical governance scenarios are established based on external technological conditions and internal decision-making structures, and their equilibrium outcomes are derived and compared. The results show that under traditional decentralized decision-making, independent actions by the parties tend to induce misreporting and distort verification results. Centralized decision-making can coordinate the interests of all parties and improve verification performance and the system's net welfare when coordination benefits exceed the corresponding costs and residual losses from misreporting. AI intervention improves verification efficiency by integrating authentic multisource information and using intelligent screening to reduce the profitability and disruptive effects of misreporting, but rigid algorithmic standards may also intensify procedural friction. Whether combining AI intervention with centralized decision-making creates a net advantage depends on the overall trade-off among the efficiency gains from information integration, the benefits of filtering misreporting, platform operation and maintenance costs, and social friction costs. These findings provide a theoretical reference for the digital transformation of governance and the design of intelligent information coordination platforms.

This paper investigates the adaptive constrained control problem for a class of multi-input multi-output (MIMO) underactuated nonlinear systems with both state delays and input delays. First, a standard state-space model is established for the considered underactuated system, where the effects of input delays are equivalently transformed into an input-delay-induced residual term. To guarantee that the tracking errors remain within prescribed bounds, a logarithmic barrier Lyapunov function is introduced in the first step of the backstepping design, and a virtual control law is constructed accordingly. Then, in the actual controller design, the unknown nonlinear dynamics, state-delay terms, and input-delay-induced residual term are integrated into a lumped unknown function, which is approximated by a radial basis function (RBF) neural network. Meanwhile, an adaptive estimation strategy based on the norm of the ideal weight matrix is employed instead of directly updating the neural network weight matrix, thereby reducing the complexity of online parameter adaptation. Furthermore, exponential-weighted Lyapunov-Krasovskii functionals are constructed for the state-delay and input-delay effects, respectively, so that the historical delay information can be retained and effectively handled in the stability analysis. By means of Lyapunov stability theory, it is proved that all closed-loop signals are uniformly bounded, the tracking errors always satisfy the prescribed constraints, and the closed-loop error system is uniformly ultimately bounded. Finally, simulation results are provided to illustrate the effectiveness of the proposed control scheme.

Collective intelligence arises from local interactions and adaptive behavioral updates among individuals, manifesting as a collective emergent cognitive capability derived from distributed behaviors. Evolutionary game theory provides a unified analytical framework for characterizing the transition from microscopic decision-making to macroscopic order. This paper first introduces the fundamental concepts of game theory, highlighting the limitations of the perfect rationality assumption and presenting the evolutionary perspective under bounded rationality. We then discuss replicator equations and evolutionary dynamics in structured populations. Building on this foundation, this paper surveys two representative lines of research that employ evolutionary game theory to study collective intelligence. The first focuses on the theoretical construction of collective estimation tasks, characterizing the emergence mechanisms of collective intelligence. The second emphasizes incentive mechanism, exploring how adjustments to payoff structures can effectively enhance group performance in prediction tasks. Finally, the paper summarizes the advantages of evolutionary game theory in integrating microscopic behavior with macroscopic outcomes and outlines directions for future research.

With the promotion of railway light-travel services, passengers can have their baggage picked up in advance through door-to-station services, allowing them to travel to the station without carrying heavy luggage. To ensure the timeliness and reliability of such services, efficient pickup scheduling must be achieved under the constraints of dynamic baggage requests, multi-trip vehicle operations, and synchronization with fixed train departure times. To address this problem, this paper aims to minimize vehicle operating costs by formulating a dynamic multi-trip vehicle routing optimization mixed-integer linear programming (MILP) model within a rolling horizon framework, capturing key constraints such as dynamically arriving pickup orders, service time windows, and train schedules. Considering the NP-hard nature of the problem and the requirement for real-time performance, an adaptive large neighborhood search (ALNS) algorithm embedded with a tabu mechanism is proposed, which is coupled with a rolling horizon framework to achieve rapid response and efficient solutions for dynamic demand. Computational experiments based on Beijing South Railway Station demonstrate that the proposed approach can generate cost-efficient pickup plans while satisfying timeliness requirements under dynamic demand scenarios. The results indicate that the optimization framework has strong practical potential and can effectively support intelligent scheduling for door-to-station baggage pickup in railway light-travel services.

With the deepening of medical insurance payment system reforms, some medical institutions engage in fraudulent practices by upcoding disease diagnosis codes to illicitly obtain medical insurance funds, seriously undermining the equity and sustainability of the fund. Existing methods suffer from insufficient utilization of heterogeneous textual data and limited model interpretability. To address these challenges, this study proposes an intelligent identification framework integrating three-way decision theory and hybrid supervised machine learning. For heterogeneous insurance data comprising numerical, textual, and temporal types, a multi-type feature construction strategy is developed: statistical aggregation captures cost distribution characteristics, Skip-gram and BioBERT models transform diagnosis codes and clinical texts into semantic vector representations, and sliding-window statistics encode temporal dynamics. Guided by the three-way decision framework, features are partitioned into acceptance, rejection, and boundary domains; granular-ball attribute reduction is subsequently applied to the boundary domain for refined feature selection. An improved osprey optimization algorithm (IOOA) incorporating chaotic mapping, elite opposition-based learning, Gaussian mutation, and adaptive nonlinear convergence factors is proposed to jointly optimize the Bayesian network (BN) structure and the regularization and kernel-width parameters of the least squares support vector machine (LSSVM). Prior and posterior probabilities derived from the BN are incorporated as augmented inputs to the LSSVM, simultaneously enhancing interpretability and classification performance. Experiments on a real desensitized medical insurance dataset comprising 28,231 records from 5,000 patients show that the proposed IOOA-BN-LSSVM model achieves an accuracy of 0.9565, recall of 0.9440, precision of 0.9557, and F1-score of 0.9498, outperforming six benchmark methods including logistic regression, random forest, and LightGBM. The proposed method offers medical insurance regulatory authorities an efficient, accurate, and interpretable intelligent audit tool with strong practical application value.

We study the problem of determining the nonnegativity of polynomials on a polytope $P \subseteq \mathbb{R}^n$. Every polynomial in $\mathbb{R}\left[x_1, \ldots, x_n\right]$ falls into one of three categories according to its behavior on $P$ : strictly positive, nonnegative with zeros, or not nonnegative. Using the $\mathcal{V}$-representation of polytopes, we establish an equivalence between the nonnegativity of polynomials on polytopes and that of their homogenizations on the standard simplex. Based on this equivalence, we combine Pólya's theorem with several new results to develop an algorithm that determines the category of a given polynomial.

In a distributed multi-project environment, information asymmetry and conflicting interests among sub-project managers make resolving global resource demand conflicts among projects a key challenge. In existing studies, the global resource supply is usually treated as a known and fixed constant, which fails to effectively respond to resource demand changes caused by the dynamic project environment (e.g., project entry/exit, resource disruptions) and leads to a disconnect between scheduling plans and actual needs. Therefore, this paper regards the global resource supply as a decision variable, and constructs a bi-level optimization model under uncertain environments by integrating the flexible resource supply mode: the upper-level model aims to minimize the total cost of multi-projects, while the lower-level model targets the shortest completion time of sub-projects. This model can not only reduce costs arising from inter-project resource demand conflicts but also effectively mitigate the negative impacts of uncertain environments. The paper designs a new negotiation mechanism based on genetic algorithms, and experiments verify the positive effect of the flexible resource supply scheduling method.

Dynamic clouds virtualize distributed computing for unmanned swarms, but edge nodes have limited capacity, and directly merging models fine-tuned on heterogeneous tasks causes parameter interference. Existing fusion methods target homogeneous NLP tasks and ignore sensitivity differences across heterogeneous tasks in swarms. To address this, we propose a lightweight heterogeneous task fusion method. First, we construct a sparse diagonal approximation of the Fisher Information Matrix from task vector magnitudes, computing parameter sensitivity only for core dimensions to reduce optimization variables. Second, we extract the shared feature subspace of multiple tasks via Singular Value Decomposition (SVD) and constrain global model updates to this subspace, preserving task-specific representations. Then, we formulate fusion as an optimization problem with fine-tuning offsets as variables, solving for a fused model with reduced interference under subspace constraints. A virtual-real simulation platform is built to test three heterogeneous tasks: task orchestration, path planning, and controller design. Results show that our method reduces parameter interference with low overhead, enabling rapid synchronization of heterogeneous capabilities across edge nodes.

The four-way shuttle storage and retrieval system (FSS/RS) is a core solution for modern high-density warehousing, and its parallel double-ended stack layout significantly improves space utilization and throughput efficiency. However, the operational scheduling of bi-directional storage and retrieval is highly complex, making the loading process a prevalent optimization challenge. Most existing studies adopt reactive approaches, focusing on alleviating blockages in pre-existing and potentially suboptimal storage layouts. They fail to fully exploit the proactive decision-making flexibility during the inbound stage to construct a physical topology with long-term outbound advantages and low blockage risks. To address this, this paper proposes a proactive prevention strategy by jointly optimizing pallet lane allocation and inbound direction decisions during the initial loading stage. We formulate an integer programming model aimed at minimizing the number of blocked pallets. Furthermore,

Urban high-quality development is reflected not only in the improvement of the overall development level but also in the coordinated operation of the five subsystems of innovation, coordination, green development, openness, and shared prosperity. Using 298 prefecture-level cities and above in China from 2004 to 2023 as the research sample, this study constructs a High-Quality Development (HQD) index and an internal coupling coordination degree (CCD). By employing the Dagum Gini coefficient, global Moran's I index, a modified gravity model, and social network analysis, this study examines their spatiotemporal evolution and the characteristics of the dual spatial association networks. The results reveal that 1) both HQD and CCD fluctuate within narrow ranges and are slightly lower at the end of the study period than at the beginning; their spatial inequalities are mainly attributable to net between-region disparities and transvariation density. 2) The spatial agglomeration of HQD generally weakens, whereas the spatial association of CCD continues to strengthen. 3) The dual spatial association networks exhibit a spatial pattern characterized by denser links in the east and sparser links in the west, along with polycentric linkages, while the positions of the core nodes remain relatively stable. These findings help identify internal structural imbalances and spatial network disparities in urban high-quality development and provide an empirical basis for implementing differentiated coordinated-development strategies across different types of cities.

Aiming at the problems of the traditional sentiment analysis model, such as the limited coverage of the sentiment knowledge base in specific domain and the failure to fully consider the semantic and syntactic information of sentences, an aspect-based sentiment analysis with semantic-syntactic enhancement and graph attention networks (SS-GAT) model is proposed, which combining semantic information, syntactic information and domain knowledge and using the graph attention networks (GAT) to conduct in-depth modeling, so as to effectively capture sentiment associations in text. To be specific, firstly, one-class support vector machine (One-Class SVM) is used to construct aspect-based domain knowledge by integrating prompt learning and large language model methods, so as to overcome the limitations of sentiment knowledge base in domain adaptability and enhance the model’s ability to capture sentiment information in a specific domain. Then, the aspect-based domain knowledge is used to enhance the syntactic graph, and the semantic graph is constructed with RoBERTa model, and perform element-wise addition of the syntactic and semantic graphs to generate a fused graph, so as to solve the shortcomings of traditional dependency tree in dynamic adaptation and information collaborative modeling. Finally, the hidden context representation obtained by the bi-directional long short-term memory (Bi-LSTM) network and the fused graph structure are used to input GAT, and a semantic-syntactic enhanced graph attention networks framework is designed. By masking non-target aspect words and using retrieval attention mechanism to generate more accurate aspect specific sentiment representation, and finally the sentiment analysis results are generated by the softmax classifier. The experimental results show that the proposed SS-GAT model achieves excellent performance on multiple datasets, and significantly improves the accuracy and Macro-F1 (MF1) value of sentiment analysis compared with the existing models, which verifies the effectiveness of the proposed model.

This paper investigates an oligopolistic market comprising a foreign firm (licensor) and two competing domestic firms (licensees). We consider a setting where the foreign firm and one domestic firm establish an R&D alliance to develop a cost-reducing technology. By constructing multi-stage dynamic game models under scenarios with and without transnational patent licensing, we analyze the foreign firm's joint decisions on R&D investment and licensing, alongside the alliance's impact on the equilibrium strategies and profits of all firms. The results indicate that the foreign product always commands a higher price than its domestic counterparts, regardless of whether a licensing agreement is reached. Furthermore, a lower initial technological level of the domestic firms increases the likelihood of licensing; however, such licensing also prompts domestic firms to adopt high-pricing strategies, thereby intensifying price competition in the market. Finally, the formation of an R&D alliance enhances the foreign firm's incentive to invest in R&D, ensuring its persistent motivation to establish the alliance. Nevertheless, this cooperative structure exacerbates the inequality in profit distribution between the licensor and the licensees.

With the rapid development of artificial intelligence (AI) technologies, AI-generated rumors have introduced new challenges to online rumor governance. This study aims to explore the spreading rules of traditional and AI-generated rumors and to identify effective governance strategies for different rumor types. Considering the strategic interactions between media and platforms in rumor dissemination, an SHIR evolutionary game model is developed by integrating rumor propagation dynamics with the behavioral evolution of relevant entities. The model is first applied to the traditional rumor case of ``Typhoon Ragasa is the strongest in history,'' where key event nodes are incorporated into simulation analysis for model validation. Subsequently, an AI-generated rumor case involving a fabricated fireworks factory explosion in Shangli County, Pingxiang City, Jiangxi Province, is selected, and comparative simulations are conducted by incorporating the distinctive characteristics of AI-generated rumors. The results show that regulating the strategic interactions between platforms and media and promoting responsible behaviors is an effective approach for rumor governance. For traditional rumors, increasing penalties on platforms can significantly improve governance effectiveness. However, for AI-generated rumors, governance outcomes depend more on reducing media traffic-driven incentives and lowering platform regulatory costs, while penalties mainly provide short-term deterrence. These findings reveal the differentiated governance mechanisms of traditional and AI-generated rumors and provide theoretical insights for developing targeted rumor governance strategies in the AI era.

The $\mu$-basis is an algebraic tool originating from the theory of moving curves and moving surfaces, and it is widely used in the study of rational curves and surfaces. It has extensive applications in implicitization, inversion formulas, and singularity computation. However, there are still few results concerning the explicit forms of $\mu$-bases. In this paper, we derive explicit formulas for the $\mu$-basis of planar quartic rational parametric curves based on redefined vector polynomials, with several illustrative examples provided. Meanwhile, we also discuss the corresponding cases for quadratic and cubic curves.