This paper studies the equivalence theory between bivariate polynomial matrices and their Smith forms. For a class of bivariate polynomial matrices, by leveraging the special form of the greatest common divisor of the maximal minors of the matrix, we construct a homomorphism from the bivariate polynomial ring to a Euclidean domain. Subsequently, by applying Gaussian elimination, the matrix can be reduced to its Smith form. Consequently, we establish that the necessary and sufficient condition for such a type of matrix to be equivalent to its Smith form is that the reduced minors of each order generate the unit ideal.

Hotel occupancy rate forecasting is crucial for hotel management, impacting resource allocation, pricing, and revenue strategies. However, traditional methods often fail due to complex factors like seasonality, unforeseen events, and market dynamics, especially in multi-step and probabilistic interval predictions. This study proposes a novel hybrid forecasting model, NHITS-GMM, designed to improve the accuracy and reliability of occupancy rate predictions. By combining the multi-scale feature extraction of NHITS with the probabilistic modeling strength of Gaussian Mixture Models (GMM), the model decomposes time-series data using hierarchical interpolation and generates dynamic Gaussian mixture parameters. This enables both point and probabilistic interval forecasts for single-variable occupancy rates. Experimental results across four typical hotel scenarios show that NHITS-GMM significantly outperforms traditional and deep learning models in terms of stability and accuracy, particularly for multi-step and probabilistic interval forecasts. The proposed model offers hotel managers a more reliable tool for optimizing resource allocation and revenue management.

This paper investigates the inverse optimal control problems for continuous-time linear quadratic regulators over finite-time horizons, aiming to reconstruct the control, state, and terminal cost matrices in the objective function from observed optimal inputs. Previous studies have mainly explored the recovery of state cost matrices under the assumptions that the system is controllable and the control cost matrix is given. Motivated by various applications in which the control cost matrix is unknown and needs to be identified, we present two reconstruction methods. The first exploits the full trajectory of the feedback matrix and establishes the necessary and sufficient condition for unique recovery. To further reduce the computational complexity, the second method utilizes the feedback matrix at some time points, where sufficient conditions for uniqueness are provided. Moreover, we study the recovery of the state and terminal cost matrices in a more general manner. Unlike prior works that assume system controllability, we analyse its impact on well-posedness, and derive expressions for unknown matrices for both controllable and uncontrollable cases. Finally, we characterize the structural connection between the inverse problems with the control cost matrix either to be reconstructed or given as a prior.

Rumor propagation in social networks poses severe challenges to social stability. This study proposes a novel ILSDR rumor propagation model by introducing latents and debunkers within homogeneous networks, systematically elucidating dissemination mechanisms. First, theoretical stability proof is established through Lyapunov functions and the Poincaré-Bendixson property. Subsequently, to counteract rumor dissemination, a PID control strategy optimized via BP neural networks is developed, effectively mitigating rumor diffusion through intelligent control pathways. Compared with traditional static control models, this strategy provides an innovative technological pathway for rumor governance. Finally, leveraging Facebook data to construct network topology and the Erdős-Rényi algorithm to quantify average degree, three practical control strategies are proposed. Simulations validate their efficacy in curbing rumor diffusion. Overall, this work establishes a unified framework integrating dynamic modeling with intelligent control, laying methodological foundations for disinformation governance.

This paper addresses the leader-follower consensus control problem for multi-agent systems (MASs) with uncertainties. First, a fixed-time integral sliding mode (ISM) controller is developed to suppress uncertainties and achieve fixed-time consensus. Subsequently, a dynamic event-triggered mechanism (DETM) with an improved internal dynamic factor is proposed to dynamically adjust the triggering times. By incorporating full-state consensus errors into the error function, the DETM ensures the desired control performance while reducing the triggering times. Finally, a leader-follower consensus control strategy based on the fixed-time ISM control and the DETM is proposed to ensure that the system reaches the real sliding mode surface within a fixed time while reducing communication resource consumption. Theoretical analysis and comparative simulations validate the effectiveness of the proposed control scheme.

In this paper, a classical topic from computer science is reexamined from the perspective of modern control theory. Vector addition systems, first introduced in 1969, saw their first major results published in 1976. More recently, new developments have appeared in the computer science literature. Here, we study controllability, positive controllability, and reachability in detail, and establish necessary and sufficient conditions for each of these three concepts. While reachability has been the primary focus of the computer science works, those studies emphasize decidability-a topic not addressed in this paper. Instead, the main contribution of this work is the derivation of necessary and sufficient conditions for reachability expressed in terms of the system matrix.

This paper aims to investigate the secure synchronization control for complex dynamic networks (CDNs) under multi-channel deceptive attacks. Deceptive attacks compromise system synchronization by injecting false information to manipulate node states. Unlike existing related research, cyber attacks may exist in both the sensor and controller channels. To address the impact of cyber attacks on the detection channel, the purpose of an observer is to estimate the state information. Meanwhile, to ensure the dynamic performance of CDNs, an observer-based secure synchronization control method under deception attacks is proposed. By applying the comparison theory and Lyapunov stability theorem, some conditions for secure synchronization are derived, and an estimate is made of the maximum permitted synchronization error. Lastly, two computational simulation examples are provided to confirm the precision and potency of the suggested conceptual framework.

This study proposes a novel methodology for detecting change-points in time series risk measures based on support vector regression (SVR). For this, we first employ the FZ loss function to jointly model two key risk measures Value-at-Risk (VaR) and Expected Shortfall (ES), and then construct a LS-CUSUM statistic to test structural breaks in the resulting loss series. This can help us capture simultaneous changes both in VaR and ES. The asymptotic distribution of the LS-CUSUM statistic under the no change-point null hypothesis as well as its consistency under the alternative hypothesis are proved. To address the limitations of conventional parametric method in risk measurement estimation, we introduce a new SVR based estimation technique to estimate VaR and ES. This data-driven method effectively models the volatility processes in financial risk measures, overcoming the biases and underestimation issues inherent in parameter estimation. Simulation studies demonstrate the enhanced robustness of our proposed method when handling highly nonlinear time series, and show superior power performances when detecting change-point in high-frequency time series. Finally, we illustrate our method by a set of S&P 500 index data.

An off-policy reinforcement learning algorithm is proposed to solve the optimal control problem for discrete-time switched linear systems with both infinite and finite time horizons. The proposed algorithm does not require access to system dynamics and requires less computational effort to obtain the optimal policy for discrete-time switched linear systems while minimizing the performance function. In this work, reinforcement learning is used to fit the switched Riccati set and Q-functions via a least-squares algorithm. The complexity of the Q-function is reduced by combining it with the matrix pruning algorithm. It can be guaranteed that the algorithm will obtain the optimal solution with sufficient training data. Finally, the effectiveness of the algorithm is verified via simulation.

The Smith form of matrices plays a significant role in the reduction of multidimensional systems and the equivalence of matrices. In this paper, we investigate the equivalence problem for two classes of multivariate polynomial matrices and their Smith forms. We derive some criteria on reducing these matrices to their Smith forms. Additionally, we provide an example to illustrate the main results.

Although considerable progresses have been made in fuzzy or neural decentralized adaptive control, most of them only guarantee the closed-loop system to be semi-globally stable. This article concentrates on the globally fuzzy decentralized adaptive fault compensation control problem for a class of large-scale stochastic nonlinear time-delay systems subject to input nonlinearities. Compared with the existing results, the main features of this study include three aspects: (i) By virtue of a function replacement strategy, the input of the fuzzy logic systems becomes bounded reference signals, thereby ensuring that the closed-loop large-scale system is globally stochastically stable. (ii) The mismatched delayed interactions are not assumed to be upper bounded by any specific functions, and no extra growth assumption is imposed on them except for the global Lipschitz condition. (iii) Markovian jump faults of multiple nonlinear actuators are compensated in each control loop, in which the control gains are state-dependent functions rather than constants. By means of a novel Lyapunov-Krasovskii functional, it is shown that the closed-loop large-scale system is globally stable in probability, and the tracking error can converge into a tunable residual set in the sense of mean quartic value. Simulation studies are provided to demonstrate the validity and superiority of our proposed method.

This paper studies consensus of linear multi-agent systems with binary-valued measurements and switching topologies. Unlike the existing consensus of multi-agent systems with binary-valued measurements, Markovian switching topology is considered in this paper. A new algorithm is proposed to improve the consensus speed of multi-agent systems, with constant gains in both estimation and control, instead of time-varying gains. By analyzing the estimation error and the expected consensus error simultaneously, we prove that the proposed algorithm can make agents achieve consensus in a bounded range, and the consensus speed is negative exponential under certain conditions, which is faster than that in existing literature. Finally, simulation results are given to demonstrate the theoretical results.

Network data typically contain sensitive relational information, where direct release or sharing may lead to non-negligible privacy violations without proper statistical safeguards. While differential privacy has emerged as a powerful framework for privacy-preserving network data analysis, theoretical understanding remains limited particularly for models incorporating both network structure and nodal attributes. This paper bridges this gap by investigating a directed β-model with covariates under differential privacy constraints. Our model accounts for both node-level heterogeneity (via 2n-dimensional degree parameters θ) and covariate-driven homogeneity (via a p-dimensional parameter γ). To protect privacy, we introduce a joint Laplace mechanism for releasing network statistics while satisfying differential privacy constraints. Leveraging moment-based estimation techniques, we estimate the parameters of both degree heterogeneity and homogeneity and derive the consistency and asymptotic normality of the differentially private estimators as the network size tends to infinity. Our theoretical findings are validated through numerical simulations and real-world case studies, demonstrating the validity of our theoretical results.

This work investigates prescribed-time flocking control with collision avoidance for Cucker-Smale systems. We propose a novel control framework that guarantees prescribed-time flocking, with convergence time that are both independent of initial conditions and control parameters. Within the framework of Lyapunov stability theory, we derive sufficient conditions guaranteeing both flocking convergence and collision avoidance in Cucker-Smale systems. In addition, an upper bound for the energy required to achieve flocking is theoretically derived. The results indicate that parameters α and β significantly affect the system’s flocking dynamics. Specifically, parameter α exhibits a nonmonotonic relationship with convergence speed and energy cost, revealing a fundamental performance trade-off. In contrast, reducing parameter β simultaneously improves convergence speed and decreases energy cost. Furthermore, the prescribed time T_p and system size N are critical factors that substantially affect energy consumption. The results provide theoretical foundations for designing efficient flocking controllers and balancing the trade-off between convergence speed and energy cost.

In the real world, interactions are often subject to disruption due to imperfections and uncertainties. In this paper, we investigate the designing method of zero-determinant (ZD) strategies for repeated games on homogeneous networks. First, for each player, the set of his neighbors is regarded as a whole player, called the fictitious opponent player, then the corresponding algebraic model is proposed for repeated prisoner’s dilemma game on homogeneous networks. Moreover, the influence of implementation errors on designing ZD strategies is explored. Finally, the 3-degree homogeneous networked game is given to illustrate the theoretical results.

In this article, we demonstrate the construction of a small-disturbance input-to-state stabilizing output feedback saturation controller for a chain of integrators subject to measurement and external disturbances. More generally, we demonstrate that the saturation controller for a chain of perturbed integrators remains robust even when the measurement disturbances are eventually bounded. Futhermore, as an application, the proposed robust controller design approach is used as a design tool in solving robust output-feedback event-triggered saturation control problems in chains of integrators.

In this paper, a novel barrier function-based adaptive controller is proposed for an n-link flexible-joint (FJ) robotic system to accomplish the task of accurate trajectory tracking control in the presence of system model uncertainties, unknown external disturbances, and nonsmooth nonlinear inputs. Firstly, the traditional n-link robot system expressed by the Lagrangian dynamic function is remodeled as a fourth-order fully-actuated system by introducing the fully-actuated system theory. It results that the problems of complex controller design and computational explosion triggered by backstepping control method are solved successfully. Furthermore, under relaxed assumptions on system uncertainties, i.e., the upper boundary of the lumped system uncertainties is unknown, a barrier function-based adaptive sliding mode controller is designed, then the trajectory tracking errors of system are ensured to converge into a neighborhood of zero in the presence of nonsmooth nonlinear control inputs. Particularly, the convergence errors independent of the upper boundary of system uncertainties can be determined in advance based on practical engineering application. Meanwhile, the closed-loop stability of the FJ robot system under the proposed adaptive controller is rigorously proved based on the Lyapunov stability theorem. Finally, the superior performance of the proposed control approach is demonstrated by the simulation results of a two-link FJ robot system and a comparison study.

In this paper, we focus on the effective approximation ($N\to\infty$ then $\epsilon\to 0$) of stochastic interacting particle systems with fast regime-switching networks on digraph measures (DGMs). DGMs provide a robust approach to capturing sparse, intermediate, and dense network or graph interactions in the mean field, extending beyond traditional methods like graphons. The model can be used to simulate a vehicle's trajectory under different traffic signal states. The main goals are to derive the simplified system (9) as $\epsilon\to 0$ and to capture a class of mean-field limits under the assumption that the switching process tends to a stationary state as time evolutions. Using the martingale method and validating the continuity of the underlying graph heterogeneity, we establish the convergence in law of (1) to a probability measure $\bar{\mu}_t$, which satisfies semi-linear Vlasov-Fokker-Planck equation.

This paper focuses on studying an adaptive neural network predefined-time fault-tolerant control problem for high-order nonlinear systems. The considered plants include external disturbances, unknown nonlinear functions, quantized input signals, actuator, and sensor faults. Radial basis function neural networks (RBF NNs) are employed to address uncertainty in nonlinear systems, simplifying the difficulty of designing the state variable functions by using their structural properties. By employing the backstepping approach combined with the predefined-time Lyapunov stability theory, an adaptive predefined-time fault-tolerant controller is presented. In particular, a novel predefined-time filter is applied to avoid repeated differentiation of virtual control functions. It is proven that the proposed control strategy ensures that all signals in the closed-loop systems remain bounded and the tracking error converges within a predefined settling time in the presence of sensor and actuator faults. Ultimately, numerical and practical examples are provided to validate the effectiveness of the presented control strategy.

In this paper, a model-free inverse reinforcement learning (RL) algorithm based on static output feedback control (OPFB) is proposed to solve the problem of expert trajectory imitation in discrete-time (DT) systems with antagonistic disturbance. In detail, based on the expert-learner framework, the learner uses only the expert and its own input-output data to reconstruct an unknown cost function with antagonistic disturbance, producing the same control gain as the expert to thereby imitate the expert’s trajectory. It is worth noting that the model-free off-policy inverse RL algorithm for static OPFB control proposed in this paper adopts single-loop form and does not require knowledge of system dynamics. At the same time, the convergence of the algorithm is analyzed in detail. The results show that the probing noise added to maintain the excitation condition does not affect the algorithm, and the cost function is not unique when the algorithm converges to the optimal value. Finally, the effectiveness of the algorithm is verified by taking the F-16 aircraft autopilot as an example.

This paper is dedicated to studying the event-based consensus tracking control problem of leader-following multi-agent systems under hybrid attacks. First, different from conventional eventtriggered mechanisms, a dynamic memory event-triggered mechanism is designed to decrease the frequency of communication between agents, which relies on historical error data and instantaneous error data and considers the cumulative impact of historical data on the system. Then, an improved asymmetric Lyapunov-Krasovskii function is presented. Based on the integral inequality and Lyapunov theorem, some stability conditions of multi-agent systems under hybrid attacks are obtained by solving linear matrix inequality. Finally, two simulation examples are given to verify the feasibility and superiority of the proposed method.

This article studies attack detection problems for the secure distributed state estimation of multi-sensor networks with intermittent observation. The Kalman consensus filter is equipped to develop the minimum mean-square error estimation of the process. Due to the vulnerability of the communication network, an attack scenario is considered where both the sensor-to-estimator channels and the estimator-to-estimator channels are attacked. The attackers would intercept and modify the measurement based on a linear attack strategy. Meanwhile, the false data is injected into the prior state estimates sent to other nodes. The χ² detectors fail to identify the well-designed linear and false data injection attacks. To overcome this drawback, the watermarking-based attack detection strategy is proposed. The effectiveness of the proposed scheme for stealthy attacks is analyzed. Furthermore, the presence of intermittent observations prevents the residuals from reflecting false data injection attacks in estimator-to-estimator channels. This problem is effectively addressed by employing a stochastic detection strategy integrated with watermarking. Based on effective attack detection, the malicious data can be mitigated by using the Kalman consensus filter to avoid performance degradation. Finally, a numerical simulation validates the effectiveness of the proposed method.

The AB/BA trial design is the simplest crossover design for comparing the effects of two treatments. It is widely applied in practice because it enables the direct comparison of two treatments for each individual while effectively controlling for inter-subject variability. However, unmeasured carryover effects can compromise the validity of the results, and this paper proposes the equivalence evaluation method for two treatment effects that account for carryover effects. A novel nonparametric statistical method is developed to quantify the treatment effect and the carryover effect, namely the win probability that a subject receiving one treatment or sequence achieves a better outcome (or "wins" against) compared to a subject receiving the other treatment or sequence. Five simultaneous confidence intervals for these two win probabilities are considered to evaluate the effectiveness of the two treatments, including those based on the normal distribution, t distribution, adjusted t distribution, logit transformation, and inverse-hyperbolic-sine transformation. Simulation results demonstrate that confidence interval procedures based on logit and inverse hyperbolic sine transformations perform well in terms of coverage and average interval width, even for small sample sizes, and hence are recommended for practical applications. Two AB/BA crossover trials involving continuous and ordinal outcomes are utilized to illustrate the proposed methods.

Multi-dimensional arrays are referred to as tensors. Tensor-valued predictors are commonly encountered in modern biomedical applications, such as electroencephalogram (EEG), magnetic resonance imaging (MRI), functional MRI (fMRI), diffusion-weighted MRI, and longitudinal health data. In survival analysis, it is both important and challenging to integrate clinically relevant information, such as gender, age, and disease state along with medical imaging tensor data or longitudinal health data to predict disease outcomes. Most existing higher-order sufficient dimension reduction regressions for matrix- or array-valued data focus solely on tensor data, often neglecting established clinical covariates that are readily available and known to have predictive value. Based on the idea of Folded-Minimum Average Variance Estimation (Folded-MAVE: Xue and Yin, 2014), we propose a new method, Partial Dimension Folded-MAVE (PF-MAVE), to address regression mean functions with tensor-valued covariates while simultaneously incorporating clinical covariates, which are typically categorical variables. Theorems and simulation studies demonstrate the importance of incorporating these categorical clinical predictors. A survival analysis of a longitudinal study of primary biliary cirrhosis (PBC) data is included for illustration of our method.

Within the sufficient dimension reduction framework, research on nonignorable missing data remains relatively scarce, primarily due to the associated identifiability issues. This paper considers the problem of sufficient dimension reduction when the response is subject to nonignorable missingness. By adopting a flexible semiparametric missingness mechanism to ensure identifiability, we construct three classes of estimating equations based on inverse probability weighting, regression imputation and augmented inverse probability weighting. The novel aspects of our methods also include the incorporation of sufficient dimension reduction techniques in the implementation of these estimating equations to mitigate the high-dimensional effect, and the construction of the estimator for the conditional expectation of the estimating functions given both the covariates and the missingness indicator. We prove that the resulting three estimators are asymptotically normally distributed. Comprehensive simulation studies are conducted to assess the finite-sample performance of our methods, and an application to PM2.5 concentration data is also presented.

This paper proposes a novel Relaxed Total Generalized Variation (RTGV) model for image restoration under Gamma noise, which integrates a convex fidelity term and an RTGV regularization term. The convex fidelity term is designed to balance the regularization intensity between dark and bright regions, while the RTGV regularization term aims to reduce computational complexity in contrast to the traditional Total Generalized Variation (TGV) regularization. The Alternating Direction Multiplier Method (ADMM) is employed to solve the proposed model, and the regularization parameter is adaptively updated at each iteration by incorporating the Generalized Cross Validation (GCV) technique. Numerical experiments demonstrate that the proposed approach outperforms traditional methods in terms of both restoration quality and computational efficiency.

This paper investigates the exponential synchronization problem for a class of nonlinear directed networks with time delays and general unknown transition rates. The considered model incorporates time-delays, directed topological structures, and uncertain transition rates, where the transition rates can be either completely unknown or only partially estimated. A distributed controller is designed within a novel pull-based event-triggered sampling framework, ensuring that the closed-loop system achieves exponential synchronization while significantly reducing the update frequencies of sensors and controllers with performance guarantees. By estimating a positive lower bound for event intervals, the proposed event-triggered schemes effectively exclude Zeno behavior. Event-triggered parameters are systematically designed based on the feasibility conditions of associated matrix inequalities. Numerical simulations are provided to validate the theoretical findings, demonstrating the effectiveness and practical applicability of the proposed approach.

Attack defense and privacy protection are critical for secure consensus control of multiagent systems (MASs). While prior studies have addressed these threats individually or jointly, this paper proposes a novel encoding-decoding-based consensus control strategy for discrete-time MASs under denial-of-service (DoS) attacks, leveraging a buffer-based switching mechanism and dynamic quantization to ensure both information availability and confidentiality. Based on the uniform quantizer, we first perform an encoding-decoding-based algorithm with a dynamic quantization factor. Thus, the information to be transferred to neighbors is encoded by the encoder and the received data from neighbors is decoded by the decoder, which can prevent information from being directly exposed. Furthermore, the problem of information interruption caused by DoS attacks can be solved by introducing a buffer that can save the latest state information when DoS attacks occur. A distributed controller with a switching mechanism is proposed by employing the stored and decoded state information. The linear matrix inequality (LMI) and the Lyapunov function are also used to get the switched control gains and sufficient conditions of the system’s stability. Finally, a numerical simulation example is provided to demonstrate the effectiveness of the developed control strategy.

Drawing on industry convergence theory, this study develops an evaluation index system to quantify cultural-tourism integration. It applies the entropy weight method and a multiple-linear comprehensive index approach to measure both the levels and the spatiotemporal dynamics of culture-tourism integration in 31 Chinese provinces (municipalities and autonomous regions) from 2010 to 2022. A staggered Difference-in-Differences model is then used to estimate the driving effects of integration policies and to uncover the pathways. The results show a steady upward trend in integration, marked regional disparities consistent with a Matthew effect, and a significant overall policy effect on integration levels, with notable heterogeneity across regions. Pathways analysis indicates that policies primarily enhance resource and market integration and that the pathways of policies also influence differ by region. This study advances understanding of how policy drive cultural-tourism integration and provides guidance for promoting high-quality, balanced regional development of culture-tourism.

The operation of a microgrid (MG) system with multiple nodes not only needs to solve the optimization problem of economic dispatch but also has to consider the optimization goals of the safe and environmentally friendly operation. Therefore, the purpose of each node with renewable resources is to collaborate to achieve the optimization of multiple objectives. In this paper we shall design a deep reinforcement learning (DRL) algorithm to perform the multi-objective optimization which can handle continuous action space and determine the specific output power of each device. Unlike the existing algorithms that learn policies with holistic reward signals, the proposed algorithm decomposes the reward into multiple parts and trains multiple critic networks for sub-objectives to get the Pareto optimal solutions. The proposal of single-actor multi-critic architecture not only can avoid task-specific local optimal policies but also does not need to set weight values. The effectiveness of the algorithm is verified by case studies on a modified IEEE-30 bus system and a modified IEEE-118 bus system. After training, the DRL agent can adapt to the high uncertainty of the photovoltaics and exploit the capacity of battery energy storage stations safely, which is more practical in a real system.

The precision matrix is an essential tool for studying the conditional relationships among large groups of variables. This paper develops a Distributed Refitted Cross-Validation (DRCV) procedure to estimate a large precision matrix in distributed settings, whose communication complexity is proportional to the number of non-zero entries in the precision matrix. The proposed method designs two rounds of communication. The first round selects non-zero positions of the precision matrix via node-wise regressions, while the second round constructs a global-debiased estimation for the precision matrix. To address the overfitting issue regarding this inference-after-selection strategy, the proposed method splits observations at each machine into two parts, one for position selection and the other for parameter estimation. DRCV achieves the global estimation consistency with respect to the total sample size under certain conditions and allows the number of machines in distributed settings to increase as the total sample size increases. Numerical studies on simulated datasets and a real high-frequency stock dataset show that DRCV has good estimation performance and a low communication cost.

This paper investigates the Pareto-Nash equilibria for multicriteria normal games and multicriteria networked evolutionary games (MCNEGs) using the semi-tensor product of matrices. Firstly, an easy-to-verify matrix criterion is provided to calculate the Pareto-Nash equilibria of multicriteria normal games. Secondly, an algorithm is established to convert the dynamics of an MCNEG into an algebraic form. Thirdly, based on the algebraic form, a necessary and sufficient condition is presented to verify whether a profile is a Pareto-Nash equilibrium, and the asymptotic stability of an MCNEG to the Pareto-Nash equilibrium set is studied. Finally, an illustrative example is given to demonstrate the correctness of the new results.

In this paper, we analyz the uniform exponential stability of a semi-discrete scheme for a coupled system derived from a one-dimensional wave equation, which is subject to boundary feedback with noncollocated observation. This system was previously studied in [IEEE TAC, 52(2007),371-377], where the Riesz basis methodology was utilized. However, it is critical to acknowledge that the Riesz basis approach is inadequate for addressing the uniform exponential stability of discrete schemes. In contrast, the Lyapunov function offers a more straightforward alternative approach. Therefore, we first establish exponential stability by constructing a global Lyapunov function for the closed-loop system. Subsequently, employing the order reduction method, we derive the semi-discrete finite difference (FD) scheme of the system. Analogous to the demonstration for the continuous case, we construct discrete Lyapunov functions and utilize them to demonstrate that the discretized scheme exhibits uniformly exponential decay as the step size approaches zero.

Advances in high-throughput technologies have vastly expanded our ability to dynamically characterize disease states and associated biomarkers, which play a crucial role in the prevention, detection, and treatment of diseases. In the field of precision medicine, pinpointing patient subgroups that stand to gain the most from specific treatments is of paramount interest. This study explores the challenge of identifying such subpopulations, characterized by disease outcome-biomarker relationship. This complexity is due not only to the dynamic nature of disease outcomes and biomarker profiles but also to the intricate and often nonlinear—interactions between them, necessitating careful consideration. This study employs methods from reproducing kernel Hilbert space (RKHS) to model the complex interactions between outcomes and biomarkers. By utilizing RKHS distance metrics, we identify clusters according to varying patterns in the estimated subject-specific outcome-biomarker relationship functions. Comprehensive numerical simulations were conducted to validate the superior efficacy of our approach in comparison to existing methodologies. Additionally, the utility of our method is further exemplified through its application to real-world datasets.

With the advancement of modern information technology, the collection and analysis of multi-source time series data play an important role in decision-making and process management. However, due to the complexity of capturing the dynamic features for spatio-temporal information, multisource time series forecasting remains a challenging problem. Previous spatio-temporal models usually overlook the integration of physical and spatial dependencies between multivariable data features, as well as the effects of dynamic diffusion. To address these challenges, we propose a Spatio-Temporal Information Dual-layer Diffusion Network (STIDDN) for multi-source time series collaborative forecasting. STIDDN employs residual LSTM networks for temporal dependency modeling of internal features at each station, while the Dual-layer Diffusion Graph Convolutional Network (Dual-DGCN) focuses on capturing both physical and spatial dual-layer dependencies between stations, along with the dynamic diffusion process. By integrating spatio-temporal information through a skip-connection and multi-head attention mechanism, STIDDN achieves effective collaborative forecasting across multiple stations. Extensive experimental results demonstrate that our model consistently outperforms advanced baseline models on two different spatio-temporal prediction task datasets.

Data censoring is a common problem during the process of survival data collection. To maximize the usable information in dataset with censoring, Cox model has been proposed and becomes of a benchmark model in censoring data modelling. However, as data size grows, challenging raises on learning Cox model and its modern extensions. Existing algorithms for training Cox model facing the problems of insufficient sample pair usage and control sample unbalance. In this work, we introduce the batch recombination algorithm : a chain-based method that better uses sample pairs while keeping control sample balance. We show that, under mild conditions, parameter estimates from stochastic gradient descent using our recombinated batch are consistent. Confidence interval can also be established using asymptotic distribution. Extensive numerical experiment both on simulated data and real data, linear and neural network Cox model show efficiency and accuracy of the proposed method.

NMDS codes and MDS codes have critical theoretical and practical value. In this paper, we develop a general construction of 3-dimensional NMDS codes of lengths from $2^m$ to $2^m+2$ by selecting suitable generator matrices and determine their weight enumerators, where $m\geq2$ is an integer. In particular, we construct two types of 3-dimensional MDS codes and analyze the properties of the subfield codes of one of them. Then we derive some optimal locally recoverable codes via the NMDS codes. It is worth noting that all the NMDS and MDS codes are near Griesmer and Griesmer codes, respectively. Furthermore, the duals of the NMDS codes achieve length and dimension optimality, and of the MDS codes achieve distance optimality under the sphere packing bound. Finally, we use some of the codes constructed to build $s$-sum sets (where $s>1$ is odd), strongly regular graphs and $3$-designs.

To estimate physical parameters in a grey-box model with linear regressions, a two-step approach with much reduced computational complexity is developed. First, the parameters of the linear regression model are estimated via the simple linear least square method, before they are fed into a nonlinear optimization problem of a much reduced dimension. It is discovered that the right formulation of the optimization criterion depends on the input-output data, and can be expressed in terms of the singular value decomposition of the data matrix. It is also found that the estimated physical parameters can be fed back to improve the parameters of the linear regression model. This improvement is a consequence of exploiting the structural information of the system contained in the grey-box model, and thus overfitting to the limited training data can be avoided. Numerical examples are presented to demonstrate the effectiveness of the approach.

This paper investigates a finite-time optimal bipartite containment control problem for multiagent systems (MASs) with input saturation. Firstly, a command-filtered technique is applied to filter the virtual control signals to avoid the problem of “explosion of complexity”. Then, the filter and saturation losses are compensated simultaneously by skillfully constructing auxiliary systems, whose signals converge in finite time. Due to the strong nonlinearity of the Hamilton-Jacobi–Bellman equations and system dynamics, the modified identifier-actor-critic reinforcement learning (IAC-RL) algorithm is employed to approximate the unknown functions and train the optimal controller. Specifically, the cost function in the traditional IAC-RL algorithm is modified to ensure its convergence over a long time. With the help of a correction term, the updating laws of the IAC-RL neural networks are also improved to avoid premature termination during training optimal controllers. Finally, the MASs are proved to be semiglobally practically finite-time stable. The effectiveness of the proposed protocol is proved through numerical and practical examples.

According to the Expected Utility with Uncertain Probabilities (EUUP) proposed by Izhakian and Yermack (2017, 2020), this paper measures market uncertainty of the Chinese stock sectors. The cross-sector uncertainty connectedness is explored using a TVP-VAR based connectedness approach. The results suggest that most of the stock sectors have strong connectedness with each other. Their relationships are heterogeneous under different market states, as well as before and during the emergency events, including the COVID-19 pandemic and the Russia-Ukraine conflict. Three external uncertainty indices, including economic policy uncertainty, climate policy uncertainty, and trade policy uncertainty are employed to investigate their quantile effects on the market connectedness. Most of them have significantly negative effects on the connectedness under bear state, while they are insignificant under bull state. Moreover, their relationships have been changed greatly during the emergency events, compared with the results before. This study highlights the effects of market states and emergencies on the transmission mechanisms of cross-sector uncertainty.