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.

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.

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.

Interval-censored data are common in many fields. When the failure event is relatively rare and covariate collection is costly, researchers often adopt the case-cohort design. However, for interval-censored data arising from the case-cohort design, existing studies typically rely on the assumption of linearity in modeling covariates, which may not capture the complex nonlinear relationships. To address this limitation, we consider a class of transformation models with unspecified covariate-dependent functions and propose a sieve maximum weighted likelihood approach. The method employs deep neural networks to flexibly represent the covariate-dependent function and uses Bernstein polynomials to approximate the cumulative baseline hazard function. We establish the consistency and convergence rate of the proposed estimator and show that the resulting nonparametric deep neural network estimator attains the minimax optimal rate of convergence (up to a polylogarithmic factor). Simulation results demonstrate good finite-sample performance of the proposed method. We further apply the proposed method to a real dataset, in which the Shapley Additive Explanations (SHAP) approach is employed to interpret the model’s predictions and provide insights into how covariates influence the outcomes.

Community detection is a fundamental task in network analysis, aiming to partition nodes into groups with similar connectivity patterns. Traditional methods often rely solely on edge information, neglecting other sources that can provide complementary insights. To fully utilize accessible information, a community detection method has been proposed, which integrates edges, triangle motifs, and node covariates, into a unified similarity matrix. The similarity incorporates two hyperparameters to adaptively balance the contributions from topology and covariates. Under the weighted stochastic block model, a spectral norm bound for the estimated similarity matrix and the consistency of community recovery have been established. Extensive simulations under various network regimes demonstrate that our proposed Higher-order Spectral Clustering method with node Covariates (HSCwithCov) outperforms the existing methods that use only subsets of the available information. Applications to the Lazega lawyers network and the Weddell Sea food web further confirm the practical utility and interpretability of the proposed method.

Sanitizable signature is a special type of signature which allows designated sanitizers to update authorized sensitive data blocks in the signed data, then produce a valid signature corresponding to the modified data. The existing definitions of accountability, however, do not meet some legal and application requirements, such as government management and e-healthcare. Strong accountability overlooks the possibility that both the signer and the sanitizer could be dishonest. Non-interactive public accountability, while resolving this issue, conflicts with transparency. Moreover, the existing lattice-based sanitizable signature schemes do not satisfy the requirement of unlinkability. In this paper, we concentrate on refining the formal framework of sanitizable signatures eliminating this imperfection, and the revised accountability is called as full accountability. Full accountability handles dishonest signers and sanitizers simultaneously. Finally, we present the first sanitizable signature scheme from lattices, which meets transparency, unlinkability and full accountability. Our work bridges critical gaps in accountability while delivering a post-quantum framework for legally compliant data governance.

Resource allocation plays a crucial role in the reliable operation of large-scale multi-agent systems, particularly when the operating environments and the optimization goals are time-varying. This paper investigates a distributed real-time resource allocation problem over a directed communication network. The global objective is to minimize the sum of time-varying local costs subject to a time-varying resource allocation constraint. The time-varying nature of both the local cost functions and the resource allocation constraint is modeled by an exosystem. To address the combined difficulties of time-varying optimization and directed information flow, we design a distributed algorithm for each agent that only utilizes the information of its own cost function and the information obtained through a network represented by a strongly connected and weight-balanced digraph. The distributed algorithm contains a distributed estimator that estimates global information involving all agents. We prove that the proposed method achieves exponential convergence of all agents’ decisions toward the time-varying optimal solution with any pre-specified level of accuracy. Simulation studies involving distributed energy resources in a virtual power plant further demonstrate the practical effectiveness of the algorithm.

The semi-tensor product (STP) of matrices is a powerful mathematical tool that has developed rapidly, owing to its successful applications not only in engineering but also in algebraic theory. This survey summarizes the engineering applications of STP, which mainly include those in logical systems, finite games, nonlinear feedback shift registers, compressed sensing, fuzzy systems, as well as practical implementations in combustion engines and hybrid electric vehicles. In this regard, several unsolved problems and research directions concerning the further applications of STP are proposed, which can help explore how engineering applications drive the development of STP.

Conventional Transformer models for multivariate time series (MTS) rely on fixed-dimension inputs, necessitating explicit masking or pre-filling strategies when handling missing data. These strategies can distort observational distributions, underestimate predictive uncertainty, and introduce bias, particularly in scenarios characterized by dynamic dimensionality and unknown missing patterns. To address these challenges, we propose VarDim-Transformer, a novel architecture that natively supports variable input dimensions without requiring padding or channel identifiers, leveraging the Semi-Tensor Product (STP) of matrices. The core mechanism, the PiRegistry, dynamically projects arbitrary-length observation vectors into a unified latent feature space, enabling interaction via VarDim-Attention and VarDim-FFN before inverse projection. We evaluate the model under a rigorous "Random Dynamic Two-Level Missingness" protocol, which simulates long-term sensor failure and transient packet loss under privacy constraints. Experiments on the C-MAPSS FD001 remaining-useful-life prediction task demonstrate that VarDim-Transformer significantly outperforms imputation-based baselines. Notably, in a "Top-K" worst-case error analysis, VarDim-Transformer reduces the penalized error score by 21.28 % compared to baselines and achieves a 77.1 % win rate on the most critical samples. This confirms its superior robustness and generalization capability in extreme, privacy-sensitive missingness scenarios.

This paper addresses the synchronization of hyperbolic complex spatio-temporal networks described by semilinear wave equations, with a focus on intermittent and pinning control strategies under spatially sampled state measurements. Specifically, sensors provide spatially distributed state measurements (pointwise or averaged) over sampling intervals. Stability criteria for differential inequalities with aperiodiclly intermittent control and delays are rigorously proven via mathematical induction. Sufficient conditions are derived for exponential synchronization between homogeneous networks of semilinear damped wave equations with delays via the Lyapunov method. These conditions explicitly incorporate the number of pinned nodes, the magnitude of the control rate, and upper bounds on spatial sampling intervals. Furthermore, analogous results are extended to heterogeneous networks of semilinear damped wave equations with delays. Two numerical examples validate the theoretical findings and demonstrate the practical applicability and effectiveness of the proposed synchronization strategies.

Uncertainty is ubiquitous in natural and engineered systems, influencing both individual decisions and collective dynamics. While robust control theory has provided powerful tools for analyzing how uncertainty affects engineered systems, the study of robustness in game theory remains limited. This paper introduces three fundamental models to capture distinct sources of uncertainty: environmental stochasticity affecting the payoff structure, demographic fluctuations arising from stochastic reproduction, and perceptual uncertainty shaped by noisy observation and subjective risk preference, extending the concept of robustness to strategic and evolutionary systems. Together, these models reveal how uncertainty at different levels—external, internal, and cognitive—can reshape evolutionary outcomes, alter stability, and generate complex dynamical patterns such as coexistence, multistability, and oscillations. Based on these theoretical foundations, we further study the evolution of cooperation in variable-sized populations with mutation. The analysis shows that when the population is divided into multiple subpopulations, migration among subgroups can effectively protect cooperators from the invasion of defectors and sustain cooperation even under mutation. This result demonstrates how robustness concepts can elucidate the emergence and persistence of cooperation in uncertain and heterogeneous environments.

Sanitizable signature is a special type of signature which allows designated sanitizers to update authorized sensitive data blocks in the signed data, then produce a valid signature corresponding to the modified data. The existing definitions of accountability, however, do not meet some legal and application requirements, such as government management and e-healthcare. Strong accountability overlooks the possibility that both the signer and the sanitizer could be dishonest. Non-interactive public accountability, while resolving this issue, conflicts with transparency. Moreover, the existing lattice-based sanitizable signature schemes do not satisfy the requirement of unlinkability. In this paper, we concentrate on refining the formal framework of sanitizable signatures eliminating this imperfection, and the revised accountability is called as full accountability. Full accountability handles dishonest signers and sanitizers simultaneously. Finally, we present the first sanitizable signature scheme from lattices, which meets transparency, unlinkability and full accountability. Our work bridges critical gaps in accountability while delivering a post-quantum framework for legally compliant data governance.

In the multiple change-points detection problem, accurately estimating both the number and locations of change-points poses significant challenges. This paper proposes a novel data-driven method based on symmetry for the multiple mean change problem. The core idea involves constructing two independent sets of samples based on the CUSUM statistic. Under the null hypothesis, these statistics exhibit symmetry around zero. Leveraging this symmetry, we approximate thresholds for large positive CUSUM values using the negative part of the distribution. These thresholds are then employed to screen for candidate change-points, and the maximum property of the CUSUM statistic is utilized to refine their locations. We demonstrate the effectiveness of the method under the mean change-points model. Through theoretical analysis and simulations, we show that the proposed approach exhibits reduced sensitivity to noise distributional assumptions, enhancing its applicability. Moreover, the method delivers robust performance in real-world applications.

This paper investigates a formation maintenance control problem of fixed-wing UAVs with collision avoidance and limited communication range, subject to wind disturbances and unmodeled dynamics. The challenge arises from the fact that strong wind disturbances may induce passive displacement of UAVs that exceed effective communication range between UAVs, thereby causing link disruptions and formation mission failures. Moreover, insufficient space resulting from converging displacement increases collision risk of inter-UAVs. To tackle this challenge, fixed-time disturbance observers (FTDOBs) are designed to estimate external disturbances and unmodeled dynamics. Then, a formation maintenance controller, based on prescribed performance control (PPC) and FTDOBs, is proposed to achieve predefined transient and steady-state performance. Additionally, a zeroing control barrier function utilizing local position information is constructed to guarantee the safety formation requirement. Thus, a quadratic programming problem is formulated to optimize the control strategy, effectively yielding a prescribed performance formation maintenance controller with collision avoidance. Finally, numerical examples are conducted to validate the effectiveness of the proposed algorithm.

This paper studies the optimal leader-follower consensus control problem of nonlinear multiagent systems (NMASs) with input saturation and error constraints. Since some followers may not receive the leader's signals, an error-guaranteed estimator is designed to estimate the leader's trajectory. Moreover, the prescribed performance control technique is applied to constrain system errors. Note that a large control input is required when the system errors approach the constraint boundaries, which cannot be satisfied under input saturation. Therefore, an elastic performance function (EPF) is designed to achieve elastic constraints on errors under saturation. Subsequently, an elastic optimal control strategy is proposed by integrating the estimator, EPF, and reinforcement learning, which not only ensures system stability through elastic relaxation of constraint boundaries, but also optimizes control costs. Finally, the effectiveness of the proposed control strategy is verified via a practical example.

No-regret learning has been widely used to compute a Nash equilibrium in two-person zero-sum games. However, there is still a lack of regret analysis for network stochastic zero-sum games, where players competing in two subnetworks only have access to some local information, and the cost functions are subject to stochastic uncertainty. Such a game model can be found in network interdiction problems, when a group of inspectors work together to detect a group of evaders. In this paper, we propose a distributed stochastic mirror descent (D-SMD) method, and establish the regret bounds $O(\sqrt{T})$ and $O(\log T)$ in the expected sense for convex-concave and strongly convex-strongly concave costs, respectively. Our bounds match those of the best known first-order online optimization algorithms. We then prove the convergence of the time-averaged iterates of D-SMD to the set of Nash equilibria. Finally, we show that the actual iterates of D-SMD almost surely converge to the Nash equilibrium in the strictly convex-strictly concave setting.

This paper presents a systematic comparative study of three major axiomatic set theory systems: Zermelo-Fraenkel system with "the Axiom of Choice" (ZFC), von Neumann-Bernays-G?del system (NBG), and Morse-Kelley system (MK). The research begins by tracing the historical development and motivations behind these three axiomatic frameworks, followed by a detailed analysis of their axiom structures and fundamental concepts. The systems are then compared across several dimensions: expressive power, metamathematical properties, and practical applications. The significant contribution of this study lies in introducing the Coq proof assistant as a formal verification tool to implement and compare MK, NBG, and ZFC, systematically investigating their differences within a formalized environment. Research findings indicate that the three axiomatic systems present distinct advantages and challenges during formalization, providing new perspectives for understanding the essential characteristics of axiomatic set theory and its position in mathematical foundations. This comparative analysis helps clarify the relationships between these three axiomatic systems and provides a theoretical reference for future formal verification work in set theory.

We extend the marginal coordinate test for predictor contribution (Cook, 2004) to the case with multivariate responses. Instead of explicitly specifying the link functions between the responses and the predictors, an asymptotic test is proposed under the normality assumption of the predictors as well as an asymmetry assumption about the unknown regression mean function. When these assumptions are violated, the asymptotic test with elliptical trimming and clustering is still valid with desirable numerical performances.