The importance of discovering significant variables from a large candidate pool is now widely recognized in many fields. There exist a number of algorithms for variable selection in the literature. Some are computationally efficient but only provide a necessary condition. The others are computationally expensive. The goal of the paper is to develop a directional variable selection algorithm that performs similar to or better than the leading algorithms for variable selection, but under weaker technical assumptions and with a much reduced computational complexity. It provides a necessary and sufficient condition for testing if a variable contributes or not to the system output.

Accurate forecasting of urban traffic flow across different time horizons is crucial in intelligent transportation systems. Due to the spatiotemporal aliasing of traffic emissions, traditional spatiotemporal graph modeling methods often suffer from cascading error amplification during long-term inference. It remains a challenge to balance short-term fluctuations with long-term trends and ensure long-term evolution patterns aren’t overshadowed to enhance the forecasting reliability. To address it, we propose a Scale-Disentangled Spatio-Temporal Modeling (SDSTM) framework for long-term traffic emission forecasting. It enhances data separability by lifting data from the non-linear raw space into a higher-dimensional linear space, leveraging predictability differences to decompose and fuse multi-scale features remaining independent yet complementary. Specifically, SDSTM introduces a dual-stream feature decomposition strategy based on the Koopman theory. It lifts the scale-entangled spatiotemporal dynamics into an approximate linear space via Koopman operators and delineates the predictability boundary using gated wavelet decomposition. Furthermore, rigorous theoretical justifications validate the framework design, showing that the product terms induced by the dual-stream decomposition are approximately orthogonal, and the gated dynamic component is stable and non-expansive. Experiments on a road-level traffic emission dataset within Xi’an’s Second Ring Road demonstrate that SDSTM achieves state-of-the-art performance, with an average improvement of 11.65% for long-term forecasting.

Realized probability has been proved to be more effcient than traditional 0-1 binary index for return directions forecasting. This paper proposes a Conditional AutoRegressive Beta (henceforth CARB) model for realized probability to forecast return directions. An empirical study is employed on the U.S. stock market to evaluate its performance relative to the dynamic probit model, and the results confirm that the CARB model yields better in-sample and out-of-sample forecasts. Economic analysis shows that an investor would like to pay an annual return of 2.84% to access the CARB forecasts relative to the simple market portfolio, while investors using dynamic probit model only would like to pay an annual return of 2.43%.

Polynomial multiparameter eigenvalue problems (PMEPs) arise in various applications, such as aeroelastic flutter problems, delay differential equations, and ARMA models. The existing methods for solving this problem linearize them as multiparameter eigenvalue problems (MEPs). However, this method is only applicable to specific problems. To the best of our knowledge, there is no method for solving the general PMEPs. This paper presents a homotopy continuation method to find all solutions to PMEPs. The convergence of the method is proved using techniques from algebraic geometry and numerical linear algebra. An acceleration technique for path tracking is also proposed, and numerical results show the effectiveness of our homotopy method.

Zero-one biochemical reaction networks are widely recognized for their importance in analyzing signal transduction and cellular decision-making processes. Degenerate networks reveal nonstandard behaviors and mark the boundary where classical methods fail. Their analysis is key to understanding exceptional dynamical phenomena in biochemical systems. Therefore, we focus on investigating the degeneracy of zero-one reaction networks. It is known that one-dimensional zero-one networks cannot degenerate. In this work, we identify all degenerate two-dimensional zero-one reaction networks with up to three species by an efficient algorithm. By analyzing the structure of these networks, we arrive at the following conclusion: if a two-dimensional zero-one reaction network with three species is degenerate, then its steady-state system is equivalent to a binomial system.

Financial time series are often characterized by conditional heteroscedasticity, and the ARGARCH model has been a widely used method to capture such dynamics by simultaneously modeling the conditional mean and variance. Most existing studies about AR-GARCH model estimation focus on single-frequency data, particularly low-frequency observations such as daily, weekly or monthly stock returns. However, it is well recognized that high-frequency data contain rich information that reflects the fine-grained characteristics and temporal evolution of financial markets, thereby offering the potential to enhance time series modeling. Therefore, this paper proposes a high-frequency augmented estimation approach that incorporates intraday high-frequency data into the daily AR-GARCH models. We also establish the asymptotic properties of the obtained estimators, and evaluate their finite-sample performance by simulation studies. Finally, we apply our method to three major stock indexes, to demonstrate both the practical advantages and the superiority of high-frequency augmented estimation.

Computing the intersection between B-spline curves/surfaces is a fundamental task in computer-aided design and geometric modeling. It remains challenging especially when the input data is subject to manufacturing or sensing errors. In this paper, we propose a tolerance-controlled framework for intersecting B-spline curves. Each curve is modeled as a disk B-spline curve (DBSC), forming a ribbon that encloses all admissible geometries. A subdivision-based algorithm is presented to compute the intersection directly on DBSCs with provable error bounds. Accelerated by oriented bounding boxes, our method achieves speedups as high as several hundredfold compared with classical techniques while ensuring high accuracy especially for high-degree, ill-conditioned, and overlapping configurations. Examples are provided to illustrate the effectiveness of the proposed algorithm.

In practice, data often contain outliers, which can significantly distort the results of traditional statistical methods. Meanwhile, in some practical problems, our objective is to precisely identify outliers. Therefore, it is necessary to perform outlier detection before or in data analysis. The use of auxiliary information generally improves the performance of statistical methods. Building on this idea, a ratio estimator for the Median Absolute Deviation (MAD) is constructed, and its consistency is proven. Based on this estimator, we develop novel outlier detection methods that incorporate auxiliary variables into the MAD framework. Simulation results demonstrate that the proposed method outperforms some commonly used outlier detection techniques. An application to the “Body and Brain Weight” dataset also shows the merit of our method.

Zero-one biochemical reaction networks are widely recognized for their importance in analyzing signal transduction and cellular decision-making processes. Degenerate networks reveal nonstandard behaviors and mark the boundary where classical methods fail. Their analysis is key to understanding exceptional dynamical phenomena in biochemical systems. Therefore, we focus on investigating the degeneracy of zero-one reaction networks. It is known that one-dimensional zero-one networks cannot degenerate. In this work, we identify all degenerate two-dimensional zero-one reaction networks with up to three species by an efficient algorithm. By analyzing the structure of these networks, we arrive at the following conclusion: if a two-dimensional zero-one reaction network with three species is degenerate, then its steady-state system is equivalent to a binomial system.

This paper investigates the data-driven event-triggered control problem for unknown continuous-time linear systems. To reduce unnecessary data transmissions, a topology-aware dynamic event-triggered mechanism is proposed. Unlike strategies that rely solely on the magnitude of the measurement error, the proposed design incorporates the topological relationship between measurement errors and system states by integrating the Lyapunov-function matrix into the triggering condition. By identifying when the directional state-error interaction is favorable, the mechanism automatically decelerates the decay of the dynamic threshold, thereby extending inter-event intervals. A robust design framework is established using noisy offline data, where both the controller gain and triggering parameters are jointly determined via linear matrix inequalities (LMIs). Theoretical analysis guarantees exponential input-to-state stability (ISS) and excludes Zeno behavior. Simulation results validate the effectiveness of the method.

This article addresses the prescribed-time bipartite output consensus problem for linear heterogeneous multi-agent systems under a directed signed graph. Firstly, an improved prescribedtime convergence lemma is developed through the introduction of an auxiliary function, facilitating relaxed constraints on relevant parameters. Secondly, a prescribed-time distributed observer is proposed for locally known leader states by leveraging cooperative and competitive interactions among agents. Furthermore, this paper designs both continuous and event-triggered control protocols, whereby some sufficient conditions for achieving prescribed-time bipartite output consensus are obtained by using the proposed convergence lemma. Finally, several numerical simulations are presented to verify the validity of our theoretical results.

This paper studies the online noncooperative game problem, where each player aims to find the Nash equilibrium in a distributed manner. In particular, we consider the scenario where the gradient of the cost function is not directly accessible, and there exists communication noise among the players. In this case, each player is only able to obtain the noisy gradient of its individual cost function and the set of local decisions. Communication noise affects the estimation of other players’ strategies, while the noisy gradient remains an unbiased estimate of the true gradient. An online distributed Frank-Wolfe algorithm is proposed, where the consensus tracking protocol is designed and the dynamic regret is introduced to measure the performance. Specifically, under the assumption that the communication noise follows a martingale difference sequence and the gradient noise diminishes over time, we establish a sublinear upper bound on the dynamic regret. The results show that if the cost function changes at a certain rate, the regret increase sublinearly, and the variance of the communication and gradient noise affects the increase. Finally, we conduct simulation experiments to verify our theoretical results.

We propose a measure termed the kernel Pearson correlation coefficient, which can be conceptualized as a nonparametric extension of the traditional Pearson correlation coefficient within the framework of a reproducing kernel Hilbert space. This methodology offers several desirable benefits including eliminating the necessity for model assumptions, being well-suited for high-dimensional data, and being adaptable to diverse data structures with a suitable kernel. We validate its robust statistical properties through simulations and demonstrate its effectiveness through a practical application involving the host transcriptome and microbiome data.

In this article, we propose an innovative life-cycle planning model with behavioral considerations in a realistic financial market. Specifically, the wage earner invests in one risk-free asset and one risky asset whose price dynamics follow the constant elasticity of variance (CEV) model. The performance functional of the wage earner is defined as maximizing the expected utility derived from the intertemporal consumption, bequest, and terminal wealth across an uncertain lifespan. Hyperbolic absolute risk aversion (HARA) utility preference is considered because it is more general and encompasses the commonly used power utility, logarithmic utility, and exponential utility as special cases. Applying the dynamic programming principle and the Legendre transform-dual approach, we have derived explicit formulae for optimal investment, consumption and life insurance purchase decisions and the value function. Numerical demonstration have also been provided to illustrate the influence of several momentous parameters on the optimal strategies.

With the rapid deployment of Cyber-Physical Systems in industrial and infrastructure sectors, ensuring their security has become a pressing challenge. In this paper, the challenge caused by data tampering is examined within the system identification framework using binary observations. An identification algorithm is first developed for the attack-free scenario, and the consistency of the estimated parameters is established. The convergence of parameter estimation under data tampering attacks is then analyzed, followed by the formulation of an optimal attack model with constraints, where absolute error is adopted as the performance metric. From the attacker’s perspective, the problem of achieving maximal attack impact with minimal energy is investigated, and both analytical and numerical solutions for optimal attack strategies under varying conditions are derived. Extensive simulation results validate the effectiveness of the proposed strategies.

Optimization and decision-making problems in the planning and scheduling of power systems, and more generally of engineering systems, are subject to high levels of uncertainty, must accommodate multiple (often conflicting) objectives, and involve complex competitive and cooperative interactions among different decision makers. Such problems are representative in engineering design and are difficult to address using conventional optimization methods. Inspired by Qian Xuesen’s development of engineering cybernetics from Wiener’s feedback-based cybernetics, our group has proposed engineering game theory, whose core idea is to reconcile conflicts via game-theoretic equilibrium, opening a new avenue for optimal decision making in complex large-scale systems. This paper presents the fundamental principles, mathematical models, and engineering applications of engineering game theory, aiming to provide a general paradigm and reference for decision-making problems encountered in engineering practice.

Leveraging a general framework adapted from symbolic integration, a unified reductionbased algorithm for computing telescopers of minimal order for hypergeometric and q-hypergeometric terms has been recently developed. In this paper, we conduct a deeper exploration and put forth a new argument for the termination of the algorithm. This not only provides an independent proof of existence of telescopers, but also allows us to derive unified upper and lower bounds on the order of telescopers for hypergeometric terms and their q-analogues. Compared with known bounds in the literature, our bounds, in the hypergeometric case, are exactly the same as the tight ones obtained in 2016; while in the q-hypergeometric case, no lower bounds were known before, and our upper bound is sometimes better and never worse than the known one.

This paper is concerned with a kind of linear-quadratic (LQ) optimal control problem of backward stochastic differential equation (BSDE) with partial information. The cost functional includes cross terms between the state and control, and the weighting matrices are allowed to be indefinite. Through variational methods and stochastic filtering techniques, we derive the necessary and sufficient conditions for the optimal control, where a Hamiltonian system plays a crucial role. Moreover, in order to construct the optimal control, we introduce a matrix-valued differential equation and a BSDE with filtering. Under the assumption that the cost functional is uniformly convex, we present explicit forms of the optimal control and value function. Furthermore, we present some verifiable sufficient conditions that guarantee the uniform convexity of the cost functional. Finally, the relationship between the backward problem and its corresponding forward problem under partial information is considered, and a numerical example is provided to illustrate both this relationship and the main results of the paper.

This paper develops two subgradient-based algorithms for solving distributed constrained non-smooth optimization problems under a H${\ddot {\bf o}}$lderian growth condition (HGC) with $\theta\in (0,1]$. Firstly, we propose a projected subgradient method with a fixed step size and demonstrate that it linearly converges to a suboptimal solution. Moreover, for $\theta\in (0,\frac{1}{2}]$, we improve the projected subgradient method with diminishing step sizes to find the an $\varepsilon$-solution in terms of decision variables in ${\mathcal O}_{x}^{}(\varepsilon_{}^{-\frac{2(1-\theta)}{\theta}})$ iterations, which is faster than that of the conventional distributed subgradient methods. Furthermore, for $\theta\in [\frac{1}{2},1]$, we design an epoch-based projected subgradient method and demonstrate its ${\mathcal O}_{x}^{}({\varepsilon}^{-\frac{4\theta^{2}-2\theta+1}{2\theta^{2}}})$ iteration complexity to find the $\varepsilon$-solution, which is better than existing subgradient methods. Finally, we present two examples to illustrate the effectiveness of the proposed algorithms.

This paper presents a comprehensive review and synthesis of recent advances in learning-based resilient control methods for uncertain systems subject to denial-of-service (DoS) attacks. Across discrete-time and continuous-time settings, these frameworks integrate techniques from reinforcement learning (RL), adaptive dynamic programming (ADP), output regulation, switching-systems theory and small-gain analysis to achieve stability and robustness under cyberattacks and model uncertainties. The reviewed works demonstrate that active and data-driven control policies can be learned directly from input–state data, without requiring prior system knowledge, even in the presence of adversarial DoS attacks. Critical DoS attack duration and frequency bounds are characterized to ensure closed-loop stability. Moreover, these bounds are shown to be learnable using input-state data. Together, these advances highlight a unified perspective on resilient control—where learning, robustness, and security are jointly addressed to guarantee stable performance of cyber-physical systems under adverse network conditions.

In this paper we propose an algebraically motivated modification of the power method via matrix iterations. The advantage of the new one is that the convergence is always guaranteed and is not affected by the choice of the initial matrix. Moreover, this method can compute the principal eigenvalues of complex matrices even when their algebraic multiplicities and geometric multiplicities do not coincide. Finally, we present several numerical examples demonstrating convergence rates consistent with theoretical analysis.

Orthogonal Latin hypercube design, as a useful class of Latin hypercube designs (LHDs), play a significant role in computer experiments. In this paper, we propose two general methods to construct group-orthogonal LHDs, whose columns can be partitioned into groups such that the columns from different groups are orthogonal. All column pairs of the generated designs can achieve stratifications on $s\times s$ grids when projected onto any two dimensions. Moreover, the designs generated by the second method can achieve stratifications on $s\times s\times s$ grids in some three dimensions. The second method is further extended to construct group-orthogonal designs and the resulting designs enjoy good stratifications in two and three dimensions. Simulation studies are presented to demonstrate the effectiveness of the constructed designs in data collection. Many new designs with good stratifications are constructed and tabulated.

Finite-population games (FPGs) provide a unified paradigm for modeling strategic interactions among anonymous players, where interactions depend on other players only through their aggregate distribution. However, as the population size increases, computing Nash equilibria of FPGs becomes computationally intractable. As the limiting framework of FPGs when the population size tends to infinity, mean field games (MFGs) constitute a viable method for tackling this challenge. This review summarizes recent progress in the study of FPGs with a focus on MFG-based theoretical connections. First, the fundamental concepts of static and dynamic FPGs are introduced. Then, attention is devoted to the construction of their MFG counterparts. This review of recent research leads to the following conclusion: the mean field equilibria of the MFGs correspond to the ε-symmetric Nash equilibria of the associated FPGs. Finally, to demonstrate the foundation of a physical application with MFG-based approaches, a decentralized charging/discharging mode decision problem for large-scale electric vehicles influenced by collective behaviour is taken as an illustration. It will be shown that the formulation is carried out in the fashion of a multi-valued logical system using the semi-tensor product framework.

This paper investigates the optimal time-varying formation tracking control (TVFTC) problem for a heterogeneous swarm of hypersonic flight vehicles (HFVs) with a non-cooperative leader. Conventional approaches often fail to achieve both precise TVFT and optimal performance under multiple uncertainties. To address these limitations, a novel integrated control scheme, incorporating an adaptive neural network and an Extended State Observer (ESO), is proposed. First, an ESO enhanced by an adaptive neural network is designed to accurately estimate and compensate for the aggregated uncertainties in real time. Second, based on this observer, a distributed optimal TVFTC protocol is constructed, which eliminates the need for intermediate control laws. Then, by leveraging the Lyapunov stability theory, it is rigorously proven that the closed-loop system can achieve the predefined formation tracking objectives while maintaining optimal control performance, despite the presence of uncertainties. Finally, numerical experiments were performed to verify the efficacy of the developed control scheme.

The interbank market is essential for liquidity allocation but also a major conduit for systemic risk. This paper develops a dynamic network game that models how financial institutions, acting as borrowers, lenders, or intermediaries, form and adjust bilateral exposures while optimizing liquidity decisions subject to balance-sheet and trust. The equilibrium structure of the lending network is characterized through a dynamic game-theoretic analysis based on best response dynamics and fixed-point conditions, showing how strategic complementarities and balance-sheet feedback generate stable configurations. Building on this framework, we analyze how exogenous shocks propagate through the network using a control-theoretic formulation. For asymptotically stable equilibria, we give an upper bound for the peak deviation following such a shock. In unstable scenarios, we establish sufficient conditions for structural stabilizability using policy interventions. Finally, a constructed case study simulates the dynamic generation of the endogenous equilibrium.

We study the efficient subsampling estimating equation for massive data sets. A two-step procedure is proposed: (i) design a subsampling probability (SP) to draw a subsample from the full data set, and (ii) construct an estimating function based on the subsample. To improve estimation efficiency, the SP in step (i) is allowed to be informative, i.e., to depend on the response. However, informative subsampling typically induces bias in the estimating function used in step (ii). To correct this bias, three approaches are developed to modify the estimating function: inverse probability weighting (IPW), generalized IPW (GIPW), and projection (PJT), yielding three subsampling estimators. IPW is widely applicable but may inflate variance. GIPW adds a non-informative weight to mitigate this issue. PJT relies on likelihood information and is often the most efficient. Asymptotic properties are then established, based on which we propose data-driven methods for selecting the SP and weights by minimizing the estimated asymptotic variances. Numerical results support our theoretical findings.

In this paper, we consider the steady state classification problem of the Allee effect system for multiple tribes. First, we reduce the high-dimensional model into several two-dimensional and three-dimensional algebraic systems such that we can prove a comprehensive formula of the border polynomial for arbitrary dimension. Then, we propose an efficient algorithm for classifying the generic parameters according to the number of steady states, and we successfully complete the computation for up to the seven-dimensional Allee effect system.

This paper addresses the sampled-data boundary stabilization problem of a cascaded system comprising an ordinary differential equation (ODE) and two coupled reaction-diffusion partial differential equations (PDEs), and in particular, tackles challenges arising from the spatial interconnections among PDE states and arbitrarily large but bounded distributed delays in the input channel. Initially, a continuous-time control law is developed using a backstepping-forwarding transformation, with the global exponential stability of the closed-loop system established. Subsequently, a sampleddata control strategy is obtained by applying a sample-and-hold mechanism to the continuous-time signal. The stability analysis for this digital implementation integrates spectral analysis of the discretized target system with input-to-state stability (ISS) estimates for the infinite-dimensional dynamics. It is demonstrated that global exponential stability is preserved, provided that the sampling period meets a specified spectral radius condition. Numerical simulations confirm the effectiveness of the proposed control strategies and validate the stability bound on the sampling period.

A distributed observer design is proposed for continuous-time linear time-invariant (LTI) systems, in which the precise estimation is achieved in prescribed (user-defined) time. Unlike most existing research results that analyze the distributed observer via the Lyapunov theory, we construct an equilibrium relationship between the estimated state and the real state by introducing a delay term. By doubling the dimensions of the estimated state from the original, it is ensured that there exist transformation matrices that convert the estimated state to the real state. Therefore, two local observers are created for each node, whose parameter design is based on resolving basic linear matrix inequalities. Two groups of observer systems consisting of local observers are capable of prescribed-time state estimation under the omniscient condition, and the omniscient condition is satisfied by the distributed discrete communication algorithm. By choosing an appropriate observer gain matrix, initial communication moment and communication interval, each observer node can estimate the system state within the prescribed convergence time. In contrast to the existing works, we propose a general approach of distributed prescribed-time observer for state reconfiguration, where the prescribed convergence time is independent of the initial state of the system and the local observer parameters. The simulation results validate the effectiveness of the distributed prescribed-time observer.

Censored quantile regression (CQR) has become an essential tool in survival analysis due to its ability to characterize heterogeneous covariate effects under censoring. However, existing CQR methods typically rely on a single dataset, overlooking the abundant and diverse auxiliary datasets increasingly available in modern applications. To address this limitation, we propose a flexible model averaging-based parameter-transfer framework that improves prediction accuracy for a target CQR model by effectively incorporating information from multiple related source models. The method avoids negative transfer through fully data-driven weight assignment across source models. We prove that the proposed method achieves asymptotic optimality when the target model is misspecified, and it automatically excludes all misspecified source models asymptotically if the target model is correctly specified. Extensive simulations and a real-data analysis on a cirrhosis study demonstrate that our approach outperforms existing alternatives, providing a robust and computationally efficient transfer learning for multi-domain censored quantile regression.

In this paper it is shown how a recent enhancement of a method for asymptotic stabilization of a MIMO nonlinear system via state-feedback suggested by Liberzon in the early 2000s can be profitably used to solve a problem of robust output regulation. The proposed method requires assumptions weaker than those proposed earlier in the literature and yields a simpler structure of the controller.

In this paper, the issue of resilient event-triggered asynchronous control is concerned for Markov jump systems subject to replay attacks. Both jump law and event-triggered data are considered to be inflected by replay attacks. When attacks affect jump law, the asynchronous behavior among subsystems, controller and event-triggered mechanism (ETM) occurs and the Markov jump closed-loop system is constructed under asynchronous control. In order to exclude Zeno sampling resulted by replay attacks, a positive constant is fixed in ETM in advance. According to replaying interval, a new triggering inequality is built with the help of iteration method. On basis of the new triggered inequality and multiple Lyapunov functions method, sufficient conditions along with the event-triggered asynchronous controller design are given to guarantee the stochastic stability of the Markov jump closed-loop system. At last, numerical examples are provided to show the validity of the proposed results.

This article proposes a dual-loop forward backward sweep method (DL-FBSM) for solving constrained time-optimal control problem. The conventional forward-backward sweep methods face difficulties in handling the first-order necessary conditions for time optimization, particularly in the presence of terminal equality and inequality constraints. To address this issue, the proposed DL-FBSM algorithm integrates an inner loop and an outer loop to solve the optimality conditions derived using the calculus of variations. The inner loop performs the forward-backwards sweep operations, updates the control numerically according to the Armijo condition, and employs Anderson acceleration to enhance convergence. The outer loop reformulates the terminal function, derives the first-order terminal optimality conditions based on the interior-point method, and constructs a vector function, of which zero point is sought using the numerically approximated Jacobian matrix. This strategy effectively alleviates the Jacobian singularity issue associated with the terminal function. A rigorous convergence analysis is conducted for both continuously integrable and discretized systems, providing solid theoretical support for the proposed algorithm. Two numerical examples demonstrate that the DL-FBSM achieves comparable accuracy and performance to the benchmark algorithm GPOPS, thereby verifying the computational accuracy and effectiveness of the algorithm.

In this paper, the problem of tracking a given reference output trajectory is investigated for the class of Boolean control networks, by resorting to their algebraic representation. First, the case of a finite-length reference trajectory is addressed, and the analysis and algorithms first proposed in [19] are extended to be able to deal with arbitrary initial conditions and to identify all possible solutions. The case of delayed tracking is also investigated. The approach developed for the finite-length case is then adjusted to cope with periodic reference output trajectories. First, exact tracking of periodic output trajectories from all possible initial states is considered and shown to be equivalent to exact tracking, from all possible initial states, of the finite length trajectory obtained by restricting the original one to a single period. Then, delayed tracking (both with an arbitrary delay and with a delay that is a multiple of the period) is explored. Several algorithms support the analysis and the numerical implementation of the necessary and sufficient conditions derived in the paper for the solvability of the various problems. The results of the paper are illustrated through examples.

This paper presents a primal-dual prediction-correction (PD-PC) method for solving linearly constrained time-varying convex optimization problems, which frequently arise in control, signal processing, and online learning applications. The proposed method establishes a novel integration of primal-dual gradient dynamics with a discrete-time prediction-correction structure, specifically designed for problems with time-dependent linear constraints. A tunable memory parameter is introduced in the prediction phase to perform linear extrapolation using past iterates, enabling a flexible trade-off between the amount of historical information stored and the computational cost of correction. In the correction phase, primal and dual variables are updated via gradient descent-ascent iterations, thus maintaining the computational efficiency of a first-order method without requiring Hessian or high-order derivative computations. Theoretical analysis shows that the method achieves $\mathcal{O}(h^2)$ asymptotic tracking accuracy for both primal and dual variables, matching the state-of-the-art performance among first-order methods even in unconstrained settings. Numerical experiments on problems with both time-invariant and time-varying constraints validate the theoretical findings and demonstrate the method's effectiveness.

Autonomous decision-making in continuous-time systems involves determining both which action to take and when to execute it. It remains challenging due to the curse of dimensionality and limitations of existing methods. In this paper, we propose a novel modeling framework for continuous-time decision problems, termed Continuous-Time Monte Carlo Tree Search (CT-MCTS), which addresses these issues by jointly optimizing action and time as decision variables. Furthermore, an efficient continuous-time MCTS algorithm with theoretical support is present. The algorithm introduces time-action pairs as fundamental decision units and incorporates a dynamic tree reconstruction mechanism with a modified temporal Upper Confidence Bound (UCB) formula during the selection phase. This design effectively overcomes the coarse decision granularity and discretization distortion inherent in conventional methods, while preserving computational efficiency. We provide theoretical guarantees for the algorithm, proving its asymptotic convergence and evaluating the efficiency of its dynamic branching strategy. Simulation experiments on benchmark reinforcement learning environments demonstrate that the CT-MCTS achieves superior performance compared to conventional MCTS and its variants, particularly in sparse reward scenarios.

Optimizing refined oil secondary distribution can substantially reduce logistics costs. The distribution problem involves two interrelated decisions: managing the inventory of each petrol station and planning vehicle routes under multiple operational constraints. In this study, the problem is formulated as an inventory routing problem with a continuous planning horizon. We first develop a flow-based mixed integer programming model and then decompose it into a set-covering master problem and a pricing subproblem. The pricing subproblem is formulated both as a mixed integer program and as a dynamic program. To solve the problem, we design column generation algorithms based on a labeling approach and investigate two alternative methods for solving the pricing subproblem. Extensive computational experiments are conducted to evaluate the efficiency of the proposed algorithms. The results show that the improved column generation algorithm (ICGA), which combines both pricing strategies, performs best overall. For small-scale instances, ICGA solves 80% of the cases to optimality within the allotted computation time, while for medium-scale instances, ICGA attains the largest number of best solutions among the compared methods.

This paper presents a study on decomposition algorithms for singular toric surfaces and introduces a novel method for transforming singular points based on toric degeneration theory. Traditional algorithms often fail when applied to the surface containing one or more singular points. To address this challenge, we establish a conversion method from singular to non-singular toric surfaces. This method involves two key steps: extending the lattice polygon to convert singular points into non-singular ones, and integrating the degeneration theory of toric varieties to design a decomposition strategy that preserves the geometric features of the surface. Then the proposed algorithm is applied to computing accurate offset surfaces of singular toric surfaces. Numerical experiments on several typical singular toric surfaces demonstrate that the proposed algorithm is efficient.

Floater-Hormann barycentric rational interpolation is a family of interpolation methods with high approximation precision. Based on Floater-Hormann barycentric rational interpolation, researches have provided algorithms for solving ODEs. Since barycentric rational interpolation function has one uniform expression r(x) on the entire interval, when there are local changes in interpolation data, r(x) changes globally. When solving ODEs, the coefficient matrix of linear equations obtained based on r(x) is dense, which brings complexities for solving equations. To overcome these problems, a weighted piecewise barycentric rational interpolation method is established in this work. Regarding the interpolation case, when there are local changes in data, the interpolation function obtained by the proposed method only changes locally. When solving two-point boundary value problems based on weighted piecewise barycentric rational interpolation method, number of non-zero elements in the obtained coefficient matrix reduces with the increase of ``pieces''. Especially, under specific conditions for dividing pieces, the coefficient matrix reduces to a 3-diagonal matrix. Experiments show that, this kind of weighted piecewise barycentric rational interpolation method has some advantages for both interpolation and solving two-point boundary value problems.

This article investigates the issue of data-based adaptive resilient optimal consensus control for a class of nonlinear multi-agent systems (MASs) under denial-of-service (DoS) attacks. Within the framework of control design, integral reinforcement learning (IRL) is adopted as a model-free approach for approximating the Hamilton-Jacobi-Bellman (HJB) equation in real time when system dynamics are not explicitly known. Combining IRL and critic neural networks (critic NNs), an adaptive resilient optimal consensus control scheme is developed by designing a dynamic event-triggered (ET) mechanism. Through the Lyapunov-based stability theory, the developed optimal control method can ensure that the signals of the closed-loop system is uniform ultimate boundedness (UUB). In addition, the closed-loop system can achieve Nash equilibrium and Zeno behavior can be avoided. Finally, a simulation example is given to illustrate the effectiveness of the developed resilient optimal control strategy.