中国科学院数学与系统科学研究院期刊网

29 September 2026, Volume 46 Issue 10
    

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  • SUN Wei, LI Jing, ZHANG Chaohui, XU Liangyu
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3127-3143. https://doi.org/10.12341/jssms241049
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    In this paper a bilateral boundary control strategy is developed based on the infinite-dimensional backstepping method for a linear $(1+1+1)\times(1+1+1)$ one-dimensional hyperbolic partial differential equation system in which one state exhibits zero transport speed. The proposed approach ensures the global exponential stability of the closed-loop system in the $L^2$ norm. Addressing the limitation that traditional backstepping fails in the presence of zero transport speed (potentially leading to unbounded controller gains), the Volterra transformation is introduced only in the subsystem with nonzero transport speed, while the zero transport speed state remains unchanged. The state with nonzero transport speed is treated as an external input to the subsystem with zero transport speed, thereby guaranteeing its input-to-state stability. Bilateral boundary control implies that actuators are installed at both ends of the spatial domain. Since the actuators act on both boundaries, the existing Lyapunov functionals are not directly applicable. To overcome this, a modified quadratic Lyapunov functional is constructed to rigorously prove the exponential stability of the target system. Numerical simulation results further verify the effectiveness of the proposed control strategy.
  • ZHU Chaoqun, WU Yichun
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3144-3163. https://doi.org/10.12341/jssms240481
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    This paper investigates the security control problem based on the predictive approach for discrete-time cyber-physical systems (CPS) under false data injection (FDI) attacks and denial of service (DoS) attacks. Firstly, considering the situation that communication networks are subjected to cooperative FDI and DoS attacks, the predictive model is introduced to address the impact of DoS attacks on system performance, and analyzes the upper bound of the predictive cumulative error that affects system stability. Secondly, a predictive scheme incorporating the termination step length is proposed based on event-triggered strategies, and the closed-loop switched system model with the mode characteristics of hybrid cyber attacks is established. Then, the design method of mode-dependent security control strategy is presented by utilizing Lyapunov stability theory and linear matrix inequality (LMI) techniques, and the theoretical feasibility of proposed termination step length prediction algorithm as well as the security performance of the switched system are demonstrated. Finally, the correctness and effectiveness of the proposed security control strategy are verified by simulation examples.
  • LI Zonggang, HU Yongkai, NING Xiaogang, CHEN Yinjuan
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3164-3183. https://doi.org/10.12341/jssms241023
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    To address the issues of follower states being unavailable, slow asymptotic convergence, and limited communication resources in achieving consensus tracking for general linear multi-agent systems, this paper proposes a dynamic event-triggered finite-time tracking control algorithm based on a finite-time observer. First, utilizing output information and the Implicit Lyapunov Function method, a finite-time state observer is designed for followers to estimate actual states accurately within a finite time. Second, based on the relative observed states of followers, a distributed dynamic event-triggered finite-time tracking control protocol is developed by incorporating a sign function with fractional power into the control law. This protocol allows followers to update control inputs and broadcast state information to neighbors only when specific triggering conditions are met. By introducing internal dynamic variables into the triggering conditions, the number of triggering events is further reduced, thereby conserving communication resources. Finally, the general linear multi-agent system is proven to achieve finite-time output consensus tracking without Zeno behavior by algebraic graph theory and Lyapunov stability theory. Simulation results validate the effectiveness of the proposed algorithm.
  • BAI Jinyan, CHAI Shugen
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3184-3191. https://doi.org/10.12341/jssms250050
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    In this paper, the authors study the exact controllability of strongly degenerate wave equations in one dimension, as the control acts on the degenerate boundary. By using the spectral analysis method, the hidden regularity and observability inequalities of the dual systems are established. The exact controllability of the controlled system is obtained by means of the equivalence between observability and controllability. Moreover, an explicit expression for the controllability time is given.
  • BU Yueying, YU Qiongxia, HOU Zhongsheng
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3192-3208. https://doi.org/10.12341/jssms250022
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    For control challenges of the difficulty in accurately modelling the actual unknown nonlinear system, the impact of external disturbances on the operation process, and the uncertain number of simulations and tests required to verify the control performance of the system, a finite-iteration adaptive fuzzy iterative learning control method is proposed to ensure convergence of the controlled system within a finite number of iterations. Firstly, a novel fuzzy system along the iterative domain is established to characterize the original unknown nonlinear system by utilizing historical operation data information of the system. A finite-iteration convergence condition is constructed based on a composite energy function, meanwhile an adaptive fuzzy iterative learning control method is designed and the required number of simulations and tests is determined according to the expected control accuracy requirements of the system, thereby enhancing the efficiency of system development. Additionally, an adaptive iterative learning control algorithm is designed to estimate and compensate for external disturbances during system operation, improving adaptability of the controlled system to the operating environment. Finally, the effectiveness of the proposed control method is verified through two sets of simulation examples and comparative simulations.
  • KELIMU Minawaer, WANG Hui, GONG Qiguo
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3209-3223. https://doi.org/10.12341/jssms250222
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    This study proposes a solution based on the newsboy model for the fruit supply chain problem in Xinjiang and other places far from the consumer market. The study finds that the choice of dealers to sell fresh fruit or processed products has a significant impact on the supply chain, and their decision depends on a key threshold: When the ratio of the value of processed products to the value of fresh fruit itself is lower than a certain threshold, processing is not recommended; Otherwise, processing is recommended to save transportation costs. Land transfer has transformed the original three-level supply chain into a two-level supply chain, improving operational efficiency. Further analysis of the study found that whether a repurchase contract or a revenue sharing contract is used for supply chain coordination, the threshold for the proportion of fresh fruit sales will be reduced, thereby expanding the feasible range of fresh fruit sales options.
  • ZHANG Jun, ZHANG Ning, DING Guangqian, JIANG Mengting
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3224-3240. https://doi.org/10.12341/jssms241059
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    The order batching problem (OBP) is often studied to improve the picking efficiency of the robotic mobile fulfillment system (RMFS). Most studies of OBP in RMFS focus on the robots' picking efficiency as the optimization objective and ignore the negative physiological impact of the pickers caused by the high-intensity picking operation. Ignoring human-robot collaboration may result in the decline of the comprehensive picking efficiency of RMFS. Thus, this paper proposes the order batching strategy by considering both pickers' energy expenditure and robots' picking efficiency. This paper evaluates the tasks and postures and model the expressions of the pickers' energy expenditure. After that, the dual-objective mixed-integer optimization model is formulated to minimize pickers' energy expenditure and robots' picking costs. The non-dominated sorting genetic algorithm (NSGA-II) is improved by providing the order batching strategy and the shelve selection strategy. To verify the effectiveness and efficiency of the proposed model and algorithm, the numerical experiments are conducted under seven different instances. The experimental results show that the improved NSGA-II algorithm can find the batching solutions with lower robots' picking costs and pickers' energy expenditure. The batch capacity is negatively correlated with the robots' picking costs and pickers' energy expenditure. The item storage strategy based on items' similarity and energy expenditure performs better in improving comprehensive picking efficiency. The order batching strategy proposed in this paper provides valuable enlightenment for decision-makers for planning, design, and scheduling management in RMFS.
  • REN Xiaohang, LU Qian, YUAN Li, LU Zudi
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3241-3264. https://doi.org/10.12341/jssms250011
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    Climate change is one of the major challenges for global green economic development. This paper, from the perspective of climate vulnerability, uses panel data from 150 economies (2010-2020) and combines the Green Solow Model with spatial econometric models to examine the spatial differences, convergence paths, and factors influencing global green economic growth. The results show: 1) Significant regional differences exist in green economic growth, with a strong positive spatial correlation. 2) Spatial convergence tests reveal significant absolute and conditional $\beta$ convergence, forming four convergence clubs. 3) The factor analysis reveals that climate vulnerability and the total amount of natural resource funds significantly promote the convergence of green economy. In contrast, per capita GDP, per capita wage level, and the share of goods trade have a significant inhibitory effect on the convergence of green economy. 4) The moderation effect shows that as the level of agricultural development increases, the impact of climate vulnerability on the convergence of green economy gradually weakens. Conversely, as per capita income rises, the influence of climate vulnerability on the convergence of green economy strengthens. This paper sheds light on green economic growth convergence trends under climate vulnerability and offers policy insights to address global development inequality driven by climate change.
  • WANG Zejun, FANG Siying, ZHANG Qi
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3265-3286. https://doi.org/10.12341/jssms251031
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    Driven by “dual carbon” goals and the rapid growth in computing demand, the energy consumption and carbon emissions of data centers have become increasingly prominent concerns, making deep integration with renewable energy a key pathway for green and low-carbon transition. This paper addresses the deferability of computing tasks and the intermittency of solar and wind resources. A queuing-theory-based model for deferred scheduling of computing tasks is developed and embedded within a planning and operational optimization framework for wind-solar-storage systems, yielding an integrated co-optimization model for computing-power and electricity systems. This model achieves simultaneous optimization of micro-level computing task scheduling and macro-level wind-solar-storage planning. The resulting mixed-integer programming problem is solved using the Benders decomposition algorithm. Numerical results across three scenarios demonstrate that incorporating computing task scheduling reduces energy storage capacity requirements by 15.6%-54.6%, indicating a significant substitution effect of flexible computing loads on physical storage. Compared with single-resource scenarios, the wind-solar complementary scenario reduces total system cost by 54.1%-65.7% without scheduling; introducing computing task scheduling reduces total costs by 15%-50.5% across all three scenarios. Sensitivity analysis reveals that computing task scheduling substantially alters the sensitivity structure of system costs, with the wind-dominated scenario exhibiting the most pronounced improvement in the temporal matching between renewable generation and load. The proposed integrated planning and operation optimization model provides a theoretical framework and decision-support tool for the low-carbon transition of data centers.
  • LIU Feng, GONG Yongchao, WANG Weiguo
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3287-3310. https://doi.org/10.12341/jssms240736
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    In recent years, China has actively pursued energy transition. As a key engine of economic growth, the industrial sector, which is also a major consumer of traditional energy, warrants examination regarding its susceptibility to energy transition impacts. This paper leverages China's new energy demonstration city (NEDC) pilot policy as a quasi-natural experiment and employs a differences-in-differences (DID) model with panel data from 155 prefecture-level cities from 2011 to 2021 to empirically examine the effects of energy transition on industrialization and its transmission mechanisms. The findings reveal that energy transition has an overall insignificant impact on industrialization levels but significantly enhances industrial benefits, a conclusion that remains robust across a series of rigorous tests. The mechanism analysis shows that the heterogeneous effect of green credit mechanism, the employment hedging and benefit superposition of enterprise innovation mechanism and government financial direct expenditure mechanism explain the above empirical results. Further research demonstrates that industrial scale strengthens cities' resilience to energy transition shocks but diminishes the extent of industrial benefits improvement. Unlike industrial scale, expanding energy demand enhances the stability of industrial employment, while economic agglomeration and shifts in employment structure exacerbate challenges to maintaining stable industrialization levels during energy transition. The study concludes that energy transition and industrial development exhibit strong compatibility. It emphasizes the need for region-specific energy transition policies and provides empirical evidence and policy insights for simultaneously advancing energy transition and high-quality industrial development in the new development stage.
  • ZENG Shouzhen, GAO Luhong, RONG Qiyu
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3311-3334. https://doi.org/10.12341/jssms250006
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    This paper addresses several issues in group decision-making under social network environments, such as low public participation, non-cooperative trust evaluation behavior, and insufficient trust information mining. A group decision consensus model considering non-cooperative behavior in dynamic social network environments is proposed. First, the TF-IDF algorithm is applied to mine user behavior data from social media to obtain the public-level criterion weights. These weights, combined with expert-level criterion weights based on intuitionistic fuzzy entropy, achieve a fusion of public and expert perspectives, thereby determining decision criteria and their corresponding weights in a scientific and reasonable manner. In the initial trust evaluation phase, a trust relationship based on intuitionistic fuzzy numbers is constructed. The uninorm operator is employed to quantify cooperative and non-cooperative features, identifying and addressing non-cooperative trust evaluation behaviors through a reward and punishment mechanism to adjust trust values. Furthermore, the concept of “directional trust” is introduced and its measurement algorithm is designed to capture the influence of opinion adjustment trends on trust, addressing the limitations of traditional similarity-based trust models. A dynamic trust network update algorithm is developed to incorporate initial trust, similarity trust, and directional trust in multiple decision rounds, accurately reflecting the dynamic evolution of trust relationships. In the consensus adjustment phase, expert consensus contributions and trust levels are integrated to select reference objects, guiding non-cooperative experts to adjust their opinions. Finally, the proposed method is applied to the decision-making process for the site selection of green small hydropower stations, demonstrating its effectiveness and superiority.
  • CHEN Yun, SHAO Xinyi, ZHOU Ligang
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3335-3348. https://doi.org/10.12341/jssms240713
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    This paper proposes a new criterion for forecasting accuracy, a group-individual effective measure of forecasting, by combining the continuous interval ordered weighted averaging (C-OWA) operator with the individual and group regret values. The interval values are transformed into the real numbers with parameters by using the new criterion and the C-OWA operator, and the positive ideal point sequences and the negative ideal point sequences are introduced. Furthermore, an interval combination forecasting model is put forward based on VIKOR method and the group-individual forecasting effective measure of forecasting. For the new model, some new concepts are defined, including a non-inferior combination forecasting method, a superior combination forecasting method, and a redundant combination forecasting method. Finally, through case analysis, the rationality and effectiveness of the proposed interval combination forecasting model are demonstrated, and sensitivity analysis of the parameters is conducted.
  • WANG Maida, WANG Yingming, CHU Junfeng
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3349-3368. https://doi.org/10.12341/jssms240962
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    Existing methods for resolving conflicts among experts in group decision making overlook the multiple social relationships among experts and the coupling relationships between multiple networks. This paper innovatively proposes a conflict elimination model based on trust-conflict multiplex network, aiming to effectively facilitate the elimination of conflicts among experts. Firstly, the sparse representation method is used to calculate the conflict degree among experts, and the concept of the trust-conflict multiplex networks and its construction method is defined. Secondly, the Uninorm operator is utilized to perform a nonlinear combination of weights in the trust layer and the conflict layer to calculate the comprehensive weight of experts. On this basis, this paper designs an evolution algorithm for conflict relationships and a development algorithm for trust relationships to simulate the interaction between the trust network and the conflict network. Finally, a case study demonstrates that the proposed model can effectively detect and eliminate conflict relationships among group members. Compared to traditional methods, the proposed method in this paper demonstrates significant advantages in handling the diverse social relationships among decision-makers and the coupling relationships between dual-layer networks.
  • REN Tinghai, LI Yuhao, WANG Dafei, ZENG Nengmin
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3369-3392. https://doi.org/10.12341/jssms260095
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    This study considers a data service supply chain “DSSC” consisting of a data provider, a data service provider, and users. Based on the unique characteristics of data such as infinite replicability and copyability and users' demand for data timeliness, we construct two profit decision game models: Pricing based on data timeliness “PB-DT” and pricing based on usage frequency “PB-UF”. By constructing profit decision game models based on two data asset pricing models, this study investigates the technology investment decisions of DSSC members, data asset pricing methods, and data asset and data service pricing decisions. Firstly, the study finds that under both pricing models, the decisions of DSSC members do not affect the sales volume of data services. Furthermore, the sales volume of data services under the PB-DT pricing model is greater than that under the PB-UF pricing model. However, this does not necessarily mean that the profits of DSSC members and user utility are greater under the PB-DT pricing model than under the PB-UF pricing model. Secondly, the study finds that the data supplier's choice of pricing method for data assets is solely related to the data service provider's valuation of the data's timeliness. For example, when the data service provider's valuation of the data asset is low (or high), the data supplier chooses the PB-UF (or PB-DT) pricing method. Finally, the study finds that the data pricing method actually chosen by the data supplier may be “consistent” with or “contradictory” to the data pricing method expected by the data service provider and users. Especially, when the DSSC members have consistent preferences regarding the data asset pricing method, the synergistic effects among DSSC members are maximized, and the DSSC performance can reach a Pareto optimal state.
  • NAN Jiangxia, LI Hefeng
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3393-3412. https://doi.org/10.12341/jssms240641
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    This study investigates the coexistence of recycling price competition and recycling technology cooperation in the closed-loop supply chain of retired power battery recycling. A noncooperative-cooperative biform game model is developed to examine both the recycling price competition among electric vehicle manufacturers, battery producers, and recyclers, as well as the recycling technology cooperation between battery producers and recyclers. By solving this biform game model, the optimal recycling prices and profits for all three participants are derived, along with the optimal cooperation strategies between battery producers and recyclers, including cost-sharing proportions and recycling technology levels. Furthermore, the impact of key parameters-such as the resale price of retired batteries and the ladder utilization rate-on optimal strategies and profits is analyzed. The results reveal that intense competition among recycling channels reduces the overall profit of the closed-loop supply chain. Additionally, when battery producers and recyclers engage in recycling technology cooperation, it not only significantly increases the recycling volume but also enhances the profits of both parties. Moreover, as investment difficulty rises, the recycling technology level declines, leading to a higher proportion of cost-sharing for recycling technology. The recycling price and profits of battery producers increase with the unit revenue from regenerated materials. Lastly, while recyclers' recycling prices decrease as the ladder utilization rate increases, their profits exhibit the opposite trend. This study provides valuable insights into pricing strategies and technology cooperation in power battery recycling, offering theoretical support for the sustainable development of the battery recycling supply chain.
  • WEN Limin, CHEN Guowu, ZHANG Yi
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3413-3432. https://doi.org/10.12341/jssms240944
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    In non-life insurance practice, insurance contracts often incorporate coinsurance rates and deductibles to mitigate adverse selection and reduce premium levels, causing claims data to exhibit special features such as zero-value concentration. To address this issue, this study develops a risk modification model incorporating coinsurance rates and deductibles, and investigates Bayesian estimation of risk premiums under the exponential-variance premium principle. Furthermore, when the prior distribution is unknown, two credibility estimators are proposed using a linear Bayesian approach, and their statistical properties are systematically analyzed. Numerical simulations are conducted to examine the convergence behavior of the proposed credibility estimators and to further illustrate the applicability and effectiveness of the model. The results show that, under the modified risk model with coinsurance rates and deductibles, the proposed method can accurately estimate risk premiums. This study provides a new theoretical framework and methodology for non-life actuarial science and has important practical value for pricing insurance contracts with coinsurance rates and deductibles.
  • QIN Yemei, ZHOU Fan, HU Boju, WANG Chen, ZHANG Liubo, ZHOU Xiancheng
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3433-3451. https://doi.org/10.12341/jssms240642
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    The strong stochasticity, nonlinearity, and non-stationarity inherent in financial markets pose significant challenges to stock price prediction. This paper proposes a stock price prediction model based on the sample convolutional interaction network (SCINet), which is structured with multiple SCI-Blocks arranged in a binary tree architecture. By splitting financial time series into even and odd subsequences and employing distinct convolutional kernels for feature extraction, the model effectively captures local patterns in stock price time series data, thereby enhancing prediction accuracy. Leveraging the price variation information derived from the SCINet prediction model, a hierarchical asset allocation strategy is designed and optimized using particle swarm optimization (PSO) to maximize investment returns while mitigating risks through adaptive threshold adjustments. Empirical studies are conducted on datasets including the S&P500 Index, Shanghai Stock Exchange Composite Index (SSEC), Shenzhen Stock Exchange Component Index (SZI), and eight constituent stocks of the S&P500. The results demonstrate that the SCINet-based prediction model outperforms SVR, CNN, LSTM, and CNN-LSTM models in accurately capturing price dynamics. Furthermore, the proposed asset allocation strategy informed by these predictions achieves superior returns, validating the effectiveness of the SCINet framework and its integrated approach to stock price forecasting and risk-aware asset allocation.
  • CHENG Yao, WANG Gaochao, NING Hanwen, LIN Jinguan
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3452-3470. https://doi.org/10.12341/jssms250955
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    This paper introduces a panel data structure containing firm-specific micro characteristics into the vector autoregressive model with exogenous variables (VARX) and thereby constructs a high-dimensional panel vector autoregressive (HPVAR) volatility forecasting model to characterize the dynamic features of realized volatility. First, to address the difficulty of lag-order selection in high-dimensional volatility series, an improved hierarchical own-other (IHOO) regularization method is proposed to achieve structured regularization and lag-order selection simultaneously in a high-dimensional setting. Next, a proximal gradient descent (PGD) algorithm with adaptive step sizes, together with Bayesian optimization, is employed for parameter estimation and hyperparameter selection. An upper bound for the in-sample mean squared forecasting error (MSFE) is further derived under regularity conditions. Finally, empirical analysis is conducted using high-frequency volatility data from the U.S. and Hong Kong stock markets. The results show that: 1) After firm-specific characteristics and external shocks are incorporated, HPVAR achieves higher forecasting accuracy than VAR and VARX; 2) IHOO produces better forecasting performance than hierarchical lag own-other (HLagO) and Lasso; and 3) Heatmaps of autoregressive lag coefficient matrices and estimated maximum-lag matrices indicate that the proposed model maintains both high forecasting performance and good interpretability under high dimensionality.
  • SHI Zhanwen, JIN Shaojia
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3471-3502. https://doi.org/10.12341/jssms250096
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    Generalized case-cohort (GCC) sampling is a classic design for controlling covariate measurement costs in large-scale cohort studies, and is widely applied in epidemiological studies with moderate to high incidence rates. Existing studies have largely focused on the large-sample asymptotic properties of variable selection methods under the GCC framework, while paying insufficient attention to estimation robustness in finite-sample settings with heavy censoring. Conventional inverse probability weighted estimators often suffer from degraded finite-sample performance and unstable variable selection results due to excessively large weight variance. This paper proposes a variance-shrinkage based robust weighted SCAD-penalized variable selection method. By constructing shrinkage-type robust sampling weights, the method substantially reduces weight variance with controllable bias, and mitigates estimation fluctuations induced by biased sampling in finite samples. Under a high-dimensional framework where the covariate dimension diverges with the sample size, we derive finite-sample uniform convergence bounds and explicit estimation error bounds of the estimator, establish the element-wise uniform boundedness and Frobenius norm bound of the Hessian matrix, and prove the oracle property of the proposed method. We also present the Berry-Esseen normal approximation bound and the explicit solution for the optimal shrinkage parameter, and quantify the impacts of sampling fraction, censoring rate and covariate dimension on estimation performance. Numerical simulation results demonstrate that the proposed method significantly outperforms the conventional weighted SCAD method in both estimation accuracy and variable selection stability under extreme scenarios with small sample sizes and heavy censoring. Finally, we apply the proposed method to data from the Busselton Health Study, providing practical guidance for GCC sampling design and variable selection across different research settings.
  • WANG Hongxia, ZHENG Cheng, HUANG Xingfang
    Journal of Systems Science and Mathematical Sciences. 2026, 46(10): 3503-3520. https://doi.org/10.12341/jssms240558
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    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.