This paper investigates the stability and robustness of a class of recurrent neural network controllers (RNNCs) for nonlinear uncertain systems. For the cases of \(n=1\) and \(n\geq 2\), the conditions for setting the parameters of RNNCs, rather than training, to ensure the states of the closed-loop systems convergence to the target values are provided. Meanwhile, the quantitative relationships between the RNNC parameters and the range of the initial state, target value, plant uncertainty and external disturbance are presented. Moreover, a fundamental limitation for RNNCs is proved: RNNCs with bounded activation functions cannot globally stabilize even linear uncertain plants. Finally, numerical simulations are provided to verify the theoretical results.

This paper integrates the ``control design'' idea to develop some iterative methods for the solving of linear algebraic equations (LAEs), which brings a new perspective to establish the connections between mathematics and control such that the applicability of iterative methods may be improved. A control system related to the LAE is first constructed, where the output controllability and the state observability of this control system are disclosed to have the equivalent relations with the solvability and the solution uniqueness of the LAE, respectively, from a unified viewpoint. Based on these equivalent relations, an iterative method is further proposed under the error-based feedback controller by exploiting the relation for the solving problem of the LAE and the output reference tracking problem of its induced control system. As a consequence, all (least squares) solutions can be obtained in an analytical form for any (un)solvable LAE, which depends linearly on the initial condition. As an additional benefit, it is shown that the general solution and the particular (least squares) solution for any (un)solvable LAE coincide with the unobservable state and the observable state of its induced control system, respectively.

The LOL algorithm is a stream cipher with extremely high throughput, proposed by Feng et al. recently to meet the high-throughput demands of 6G communications. It contains two main variants: LOL-MINI and LOL-DOUBLE. This study focuses on the permutation property of the initialization round function $\mathcal{F}$ in LOL-MINI. Our results show that $\mathcal{F}$ is not a permutation. Specifically, we first reduce $\mathcal{F}$ to a simpler mathematical function $\mathcal{G}$, then apply differential analysis together with MILP tools to find a valid collision for $\mathcal{G}$ within minutes on a personal computer. Exploiting the relation between $\mathcal{G}$ and $\mathcal{F}$, any single collision of $\mathcal{G}$ immediately yields $2^{128}$ distinct collisions of $\mathcal{F}$. It shows that the LOL-MINI round function possesses a huge number of valid collisions. The above approach also applies to the initialization round function of LOL-DOUBLE. Despite the existence of this large class of collisions, we have not yet found a method to translate this structural property into a practical weak-key attack.

Existing research on distributed dynamic optimization typically focuses on single-objective or static scenarios and often assumes that system dynamics are negligible at the optimal solution, making it challenging to achieve an effective trade-off between multiple objectives while ensuring theoretical convergence. To address the dynamic optimization problem characterized by conflicting bi-objectives in multi-agent networks, we propose a hierarchical decoupled cooperative control framework based on virtual leaders. Unlike the limitations of existing weighted-sum methods that require globally consistent weights, or distributed evolutionary algorithms that suffer from slow convergence and lack theoretical guarantees, the proposed method delegates the multi-objective optimization task to virtual leaders for centralized processing. Consequently, agents are only required to track the states of these leaders, thereby significantly reducing computational and communication burdens. Targeting two typical scenarios where system dynamics are either zero or non-zero at the optimal solution, we design distributed controllers and an estimation-based compensation mechanism, respectively. Furthermore, explicit conditions for gain design are derived based on the Lyapunov analysis, providing a rigorous proof of the convergence of the closed-loop system. Simulation results demonstrate that the proposed method not only achieves a tunable trade-off between conflicting objectives but also effectively handles non-zero dynamic perturbations, exhibiting superior adjustability and robustness.

This paper investigates demand information sharing in agency channels across four supply chain structures defined by upstream competition (common vs. independent manufacturer) and downstream competition (monopoly vs. duopoly agent). Incorporating endogenous sales effort and heterogeneous signal accuracy, we characterize the equilibrium sharing decisions of all supply chain members and evaluate their social welfare implications. We show that information sharing is always a Pareto improvement under the Monopoly/Common structure, while the agent optimally shares with at most one manufacturer under the Monopoly/Independent structure when competition is sufficiently intense. Under the Duopoly/Common structure, asymmetric signal precision introduces endogenous free-riding incentives that may shift the equilibrium from full sharing to partial sharing, a result that cannot arise under symmetric accuracy assumptions. The Duopoly/Independent structure uniquely achieves full sharing as the dominant equilibrium, with private incentives perfectly aligned with the social optimum. A cross-structure welfare analysis further reveals that supply chain organizational form is a first-order determinant of system efficiency, while the efficiency improvement from information sharing is remarkably uniform across all structures regardless of organizational configuration. These findings provide actionable guidance for agency operators: structural configuration should precede information policy design, and targeted interventions are warranted only in structures in which private and social incentives diverge.

This paper investigates the sampled-data output-feedback group consensus problem for strict-feedback nonlinear multi-agent systems based on the gain control method. It is noteworthy that the considered system is subject to packet losses, which has not been addressed in existing studies. To address this challenge, a distributed sampled-data output-feedback control protocol is proposed. Specifically, the update of the controller relies on successful data transmission, effectively coping with the performance degradation caused by packet losses. Subsequently, by dividing the time interval into sampling intervals and packet loss intervals, as well as combining Lyapunov stability theory and Lyapunov-Krasovskii functionals, it is proved that the desired group consensus can be achieved by the proposed control protocol. Further, the results are extended to the scenario where the system simultaneously suffers from packet losses and communication delays, establishing the relationship between the packet loss rate, communication delay, sampling period, and control gain. Finally, the effectiveness of the proposed control scheme is verified through simulation examples.

This paper investigates the event-triggered consensus problem of linear multi-agent systems (MASs) under distributed denial-of-service (DDoS) attacks from multiple attackers that target different communication channels. The joint connectivity of the physical topology induced by the DDoS attacks is analyzed, which is shown to be a necessary yet insufficient condition for the joint connectivity of the communication topology induced by the interaction between DDoS attacks and event-triggered communication. To ensure the joint connectivity of the resulting communication topology, we design a dynamic secure controller with a novel consensus protocol and a novel event-triggered mechanism that includes a communication recovery detection strategy. Then, asymptotic consensus is theoretically established, with a guaranteed exclusion of Zeno behavior. Finally, the effectiveness of the proposed approach is verified through numerical simulations.

Visual localization systems rely on local image descriptors to enable pose estimation and loop closure, yet face a critical trade-off between accuracy and efficiency in resource-constrained settings. High-dimensional floating-point descriptors provide strong matching performance but impose significant communication and storage overhead, especially in distributed or embedded applications. Conversely, compact binary descriptors reduce resource demands but suffer from notable performance degradation under challenging conditions. To bridge this gap, we propose a geometry-aware selfsupervised distillation framework that converts pretrained floating-point descriptors into compact binary codes while preserving their geometric structure. Our method formulates the quantization process as a Semi-Orthogonal Procrustes Problem, ensuring that pairwise descriptor similarities are retained during binarization. A lightweight single-layer MLP is then used to perform the transformation, maintaining compatibility with existing pipelines. Experiments demonstrate that our approach preserves the accuracy of state-of-the-art floating-point descriptors while leveraging the efficiency of binary representations, establishing a new state-of-the-art for binary descriptors in visual localization systems.

This paper investigates the parameter identification problem of Takagi-Sugeno (T-S) fuzzy systems under quantized output measurements. In contrast to conventional identification theories that rely on continuous-valued observations, quantization mechanism introduces nonlinear and non-smooth error structures, which fundamentally alter the statistical properties of the identification problem and render classical analytical methods inapplicable. To address this issue, we first consider the case where the membership weights are known. By constructing a periodic structure involving the input and the membership functions, a parameter identification algorithm based on periodic excitation is developed, and the strong consistency of the parameter estimates is rigorously established. Subsequently, for the case with unknown membership weights, a set of nonlinear equations incorporating the parameters of the membership functions is formulated. The identifiability and local solvability conditions of this system are analyzed, and a data-driven approach is proposed to achieve joint identification of the local model parameters and the membership function parameters. Finally, numerical simulations are conducted to validate the effectiveness and convergence performance of the proposed methods. This work systematically reveals the underlying principles of T-S fuzzy system identification under quantized observations, and provides a generalizable theoretical foundation for the identification and analysis of nonlinear systems with finite-precision measurements.

How to derive optimal control strategies for preventing the spread of two-strain competing epidemics in complex networks is a significant challenge. This paper first establishes two-strain epidemic models with mutations and imperfect immunity in a single-layer network, which incorporate control measures in the infection compartment to find optimal control strategies. Then, the equilibrium states of the system are analyzed by classifying them into three different types, and the stability conditions are derived. Next, we design an optimal curing strategy that globally minimizes both epidemic severity and control costs in the network. Furthermore, the predictability of epidemic spread is demonstrated by establishing structural insights into its existence and uniqueness. The strategy's effectiveness is evident in the consistent severity of epidemics, which aligns with the applied curing efforts. Meanwhile, a gradient descent algorithm is proposed to find the optimal curing strategy, which is based on a fixed-point iterative scheme. Finally, to corroborate the theoretical analysis, a series of numerical simulations are conducted. The current results are useful in helping us to understand how multi-strain epidemics behaviors.

With the continuous advancement of computer technology and information storage systems, data structures have become increasingly voluminous and complex, posing significant challenges to data analysis. In practical tasks such as classification and clustering, it has been gradually recognized that while the category information relevant to task objectives typically exhibits concise characteristics, the associated data variables may encompass multiple subclass structures unrelated to current objectives. Conventional methods often neglect these subclass information patterns, resulting in unnecessary information loss. To comprehensively explore the subclass structures within the data, this study proposes a robust t_ν,p distributional factor model (T-DFM) for cluster analysis framework using mixture of Student-t distributions. The proposed T-DFM employs Student-t distribution as clustering factors while emphasizing robustness and interference resistance. T-DFM utilizes a stabilized approach to estimate proportional vectors of distributional factors for observed samples through EM algorithm, enhancing efficiency and accuracy in cluster analysis. Theoretical analysis confirms the algorithmic convergence and robustness of the proposed method. Moreover, extensive experiments conducted on simulated datasets, along with real-world applications of loan approval dataset and air pollution dataset, demonstrate the superior effectiveness and computational efficiency of T-DFM compared to conventional approaches.

This study employs mathematical modeling to analyze the role of combined intervention strategies integrating social distancing and vaccination in epidemic control under Intensive Care Unit (ICU) capacity constraints. Conventional Susceptible–Infected–Removed (SIR) models typically assume a constant total population and often fail to adequately capture the joint effects of viral mutations and demographic dynamics. To address this, we propose an extended SIR model with a Markov-modulated mechanism that accommodates a variable total population and incorporates both deterministic dynamical switching triggered by the emergence of dominant variants and stochastic jump events arising from demographic changes. Within this framework, two stochastic models are developed, differing in how rare events are classified within the jump mechanism. For each model, we first establish mathematical well-posedness, including normalization of population dynamics and proof of positivity for all solution components. The second one is of qualitative and quantitative nature, providing a mathematically rigorous description of regular herd immunity zones with social distancing control when ICU constraints are enforced. The results demonstrate that controlled intervention can sustainably maintain infection levels below the ICU threshold, offering a theoretical basis and policy insights for epidemic management under variant-driven uncertainty.

Feedback serves as a fundamental mechanism that adjusts system input based on measurable information, thereby attenuating the influence of plant uncertainty on system performance. This paper investigates the intrinsic limitations of feedback control for a class of high-order uncertain nonlinear systems. By developing an improved analytical approach, a new difference iteration is derived, whose asymptotic behavior is rigorously shown to govern the divergence properties of the closed-loop system. In contrast to existing results, new quantitative limits on the capability of the feedback mechanism to handle structural uncertainties are then derived based on this iteration. These findings contribute to a deeper understanding of the fundamental capability boundaries of feedback.

We study dataset labeling with inexpensive but unreliable sources, such as AI models or non-expert annotators, aiming to produce labels whose error rate is controlled with high probability. We propose MSPAC, a multi-source labeling procedure that allocates error and confidence budgets across sources and learns an uncertainty threshold for each source. Each source labels only samples with uncertainty below its threshold, and samples that no source considers reliable are sent to experts. We formulate allocation as a cost-reduction problem relative to full expert labeling and theoretically show that MSPAC attains this error guarantee and is asymptotically cost-efficient. Comprehensive experiments confirm that MSPAC is empirically valid and achieves superior cost reduction compared with existing approaches.

Existing studies on the bidding dilemma in electricity markets mostly adopt mandatory participation and rarely integrate reputation effects. To fill this gap, this paper proposes reputation-driven Q-learning as a solution to the bidding dilemma between heterogeneous generation groups, developing a coupled evolutionary model of reputation, strategy, and voluntary participation. We examine $256$ social norms under low, medium, and high demand scenarios. Results show that the synergy of reputation and voluntary participation significantly outperforms mandatory participation: it supports more social norms and promotes cooperative high-bidding by rewarding good-reputation generation companies (GENCOs) and punishing bad-reputation ones, whereas mandatory participation only works under limited norms and often relies on unfair reward-punishment rules. We further reveal the phase-transition patterns of cooperative high-bidding under different social norms, which provides clear guidance for designing low-cost market mechanisms. The proposed reputation-driven Q-learning mechanism can achieve spontaneous market cooperation without heavy administrative intervention, thus reducing regulatory costs and improving market efficiency.

In markets subject to institutional or compliance constraints, optimal execution under monotone constraints, which requires that the inventory trajectory must remain continuously monotone over the trading horizon, constitutes an important problem, directly affecting trading efficiency and market stability. A representative example arises from China’s T+1 trading rule, which prohibits investors from selling stocks purchased on the same day. Under a signature-based framework, enforcing such time-continuous monotonicity leads to a nontrivial structural difficulty: pathwise feasibility must hold for all times, which induces a stochastic semi-infinite constraint. To address this difficulty, we propose a two-step approach: First, we robustify the pathwise stochastic constraints over time, yielding a deterministic semi-infinite program. Second, by exploiting the temporal structure of the uncertainty sets and the prefix structure of signatures, we derive an exact finite-dimensional reformulation of the resulting deterministic semi-infinite problem. We establish the consistency of the solution in the proposed framework, obtained from sample-based approximation of both the objective function and the feasible set, thus providing theoretical performance guarantees. Experiments on real market data show that the proposed framework strictly maintains pathwise monotone feasibility while achieving improved execution performance relative to standard benchmarks.

Collective cooperation drives practical complex systems, and although the public-goods game serves as a prominent framework for studying its evolution, standard models often assume closed environments with infinite horizons. This paper investigates cooperation dynamics in open environments by introducing a novel overlapping generations (OLG) public-goods game with a macro exit mechanism, serving as a foundational toy model for cooperation evolution. By analyzing the simplest case that preserves essential system features, we completely characterize the Nash equilibrium (excluding the critical case). This reveals how players' optimal choices—dynamically switching between cooperation and speculation—depend on cost thresholds and remaining lifespans. Furthermore, for the general case, we rigorously establish a threshold-type sufficient condition guaranteeing the existence of a Nash equilibrium wherein at least one player cooperates. Finally, an illustrative example is provided to validate the theoretical findings and demonstrate the resulting cooperation dynamics.

This work is concerned with a class of discrete-time linear quadratic mean field game, in which the diffusion coefficient of each agent can depend on the state, the control and the average of the state. The decentralized strategies contribute an $\varepsilon$-Nash equilibrium which are obtained by the discrete-time consistency condition system. As an application, a discrete-time interbank credit problem is investigated.

High-dimensional functional data, characterized by multiple curves observed over a common domain, are increasingly prevalent in modern applications. Extracting low-dimensional latent structures from such data is essential for effective dimension reduction and interpretable modeling. While existing Multivariate Functional Principal Component Analysis (MFPCA) successfully captures domain-varying local variations, it often overlooks domain-invariant global patterns that frequently coexist within the data. To address this limitation, we propose Semiparametric Functional Principal Component Analysis (Semi-FPCA). This novel framework decomposes the variation of latent processes into two distinct components: a global parametric component governed by scalar loadings (representing domain-invariant structures) and a local nonparametric component governed by functional loadings (representing domain-varying dynamics). This dual representation simultaneously models static patterns that remain constant across the domain and dynamic features that evolve over it. To ensure accurate parameter estimation, we develop an iterative algorithm based on covariance structures and residual updates. Under mild regularity conditions, we establish the consistency of the estimated loading spaces and the identified model dimensions. Extensive simulations demonstrate that our proposed Semi-FPCA substantially outperforms MFPCA in reconstructing latent processes. Furthermore, an application to heart sound data reveals distinct global and local physiological patterns differentiating normal and pathological subjects, achieving markedly lower reconstruction errors with fewer components than MFPCA.

This paper addresses the parameter identification problem for nonstationary autoregressive and moving average (ARMA) systems with a low-rank noise process and without the strictly stable assumption for the AR polynomial matrix. The noise process's low-rank property stems from the tall moving average polynomial matrix $C(z)$, of dimension $n \times l$ with $n \geq l$. When the zero-order coefficient matrix $C_0$ of $C(z)$ is known and full column rank, a recursive algorithm is developed by alternating between recursive least-squares and posterior noise estimation. Under mild assumptions, asymptotic error bound and strong consistency of the parameter estimates are theoretically established. When $C_0$ is unknown but full column rank, for the system with the first $l$ rows of $C_0$ normalized to an identity matrix, a recursive global parameter identification algorithm is constructed by integrating least-squares estimation for the remaining $n-l$ rows parameters of $C_0$ with recursive estimation of other system parameters, and the same theoretical results as the known $C_0$ case can be obtained. Furthermore, a comparative analysis demonstrates that the system with a low-rank noise process achieves a smaller asymptotic variance for the parameter estimates (excluding $C_0$), indicating superior estimation efficiency. Simulation results confirm the effectiveness and performance of the proposed algorithms.

In this paper, we investigate the existence of one-term quadratic complementary $m$-sequences. They correspond one-to-one with one-term quadratic $m$-sequences. Their feedback functions contain constant term $1$, linear terms, one quadratic term. We first give two necessary conditions for the existence of such feedback functions. Then we generate all such functions for orders $n$ up to $24$ and fit a quadratic curve between the quantities and the order. We also give a heuristic discussion showing that their quantities should be with the size of $n^2$, coinciding with the fitting result. Finally, we propose a search algorithm and find such feedback functions up to order 31.

This work considers a stochastic epidemic model with general incidence rates incorporating an Ornstein-Uhlenbeck driven transmission rate. We establish the uniqueness of the global solution. We then prove the model’s geometric ergodicity, and provide a mild condition under which the model converges to a unique stationary distribution around the equilibrium. Because the transition density of this system is analytically intractable, we employ a stationary Gaussian pseudo maximum likelihood estimation approach and profile likelihood methods for parameter estimation and confidence intervals. A subsampling method for sampling near-independent observations from time trajectories is proposed. The theoretical reliability of this subsampling method is established through rigorous proof. Numerical experiments are provided to illustrate the theoretical results.

In this paper, an adaptive backstepping event-triggered control approach is developed for a class of fractional-order nonstrict-feedback nonlinear systems subject to dynamical full-state constraints and external perturbations. Firstly, a fuzzy echo state network (FESN) is employed to identify each parameter uncertainty, and the problem of algebraic loop is circumvented. Secondly, in virtue of barrier Lyapunov functions, each of the whole states can be constrained in a specific compact set. Moreover, global sliding mode technique is incorporated into the designed event-triggered control (ETC) mechanism, which guarantees the global sliding motion of error variables towards the origin without additional reaching process, and the communication load caused by persistent sampling can be drastically attenuated. Finally, the validity of the presented controller is testified via two simulation examples. The comparison of performance indicators is discussed among the traditional fuzzy ETC (FLS-ETC), the presented fuzzy sliding mode ETC (FLS-SM-ETC) and the presented FESN-based sliding mode ETC (FESN-SM-ETC), where the integral of absolute errors using FLS-ETC (resp. FLS-SM-ETC, FESN-SM-ETC) is $1.4207$ (resp. $1.2668$, $1.1609$), and the settling time is $4.5000$ (resp. $1.5950$, $1.5550$) seconds. The above numerical results unveil that the tracking accuracy and convergence rate of the suggested scheme are superior than the ones of conventional fuzzy-based algorithms.

This paper studies zeroth-order optimization for distributed finite-sum problems with strongly convex objective functions. To address the high computational and sampling costs of accurate gradient estimation in high-dimensional settings, we design a 2-point variance-reduced gradient estimator based on coordinate-wise gradient estimation. The proposed estimator preserves the low sampling cost of conventional 2-point methods while achieving unbiased estimation equivalent to that of the more expensive $2d$-point gradient estimator. By incorporating this estimator within a gradient tracking framework, we establish a linear convergence rate of $\mathcal{O}(Md^2\kappa^2\ln(1/\epsilon))$ for smooth and strongly convex functions, where $d$ is the problem dimension, $\kappa$ is the condition number, and $M$ is the maximum number of local component functions across all agents. Numerical experiments, benchmarking our method against distributed algorithms using a standard 2-point estimator, demonstrate its superior convergence performance.

Linear regression is fundamentally a problem of estimating the joint covariance structure between predictors and responses. From this perspective, we propose a factor least squares (FLS) method that incorporates factor analysis into linear regression by estimating a low-rank-plus-diagonal covariance matrix and substituting it into the population least squares coefficient. The resulting estimator regularizes regression through covariance estimation rather than coefficient shrinkage and produces non-sparse solutions that complement sparsity-based methods. We establish consistency and asymptotic normality of the FLS estimator in a high-dimensional regime where both the sample size and predictor dimension diverge, and propose a cross-validation procedure for selecting the number of factors. Simulation studies and real data applications demonstrate that FLS performs competitively across a range of models and is particularly effective when the joint covariance exhibits approximate factor structure.

In this paper, we present a method for lifting a homogeneous polynomial of $n$ variables and degree $d$ to a permutation-symmetric tensor in $\otimes^d \mathbb{R}^n$. This tensor can be viewed as a multivariate, grouped, and multilinear function with $n \times d$ variables. We also introduce a mapping that transforms the vertices of a polyhedron in $\mathbb{R}^n$ into a finite point set in $\mathbb{R}^{n \times d}$. By calculating the values of the constructed tensors at these finite points, along with the barycenter partition technique, we establish a method for proving the positive definiteness of the given homogeneous polynomials on the polyhedron.

Quantifying the strength of correlation between two random variables X and Y is a basic problem in statistics. In this paper, we revisit Hoeffding’s D correlation coeffcient. Based on it, we propose a novel correlation coeffcient measure and obtain its three desirable properties: (1) It is equal to 0 if and only if X and Y are independent; (2) It is equal to 1 if and only if a monotonic functional relationship exists between X and Y; (3) Both the observed and theoretic values belong to [0, 1]. Furthermore, we derive its asymptotic distribution under both independence and dependence conditions. Extensive numerical simulations and a real-data application are conducted to verify the practical applicability of the proposed measure.

This paper addresses the containment control problem of multi-agent systems under directed binary-valued communication. A novel algorithm that alternates between control and estimation is proposed. By analyzing the explicit closed-form solution for the containment error, we examine the asymptotic convergence properties of the algorithm and provide sufficient conditions for achieving containment control in the mean-square sense. The final positions of the followers are also derived in the same sense. Numerical simulations are conducted to validate the algorithm’s effectiveness.

In this paper, the authors focus on the Polynomial univariate representation (PUR) of zero-dimensional polynomial ideal I⊂k[x₁, x₂; ···， x_n]. For a zero-dimensional polynomial ideal I of breadth at most one, authors introduce fast linear algebra techniques to improve the existing algorithm. For a zero-dimensional polynomial ideal I of breadth κ (1 < κ ≤ n), the authors propose a computational process to transform I into an ideal of breadth at most one, ensuring that both ideals have the same zeros. The authors present a new algorithm to compute PUR of zero-dimensional polynomial ideals by linear algebra. Complexity analyses of all proposed methods and experimental examples are provided.

Topology optimization offers lightweight and high-performance solutions for structural design. With the rapid advancement of neural networks, topology optimization methods leveraging neural architectures have gained increasing attention. Among these methods, positional encoding is crucial for enabling neural networks to capture high-frequency geometry features, making its integration into neural network-based optimization methods a promising direction for exploration. This paper focuses on positional encoding by introducing a spline-based positional encoding into the neural topology optimization framework, in which spatial coordinates are transformed using spline basis functions before being input into the neural network. The performance of different classic spline basis functions is comprehensively evaluated, including the Bézier spline, B-spline, and NURBS spline. Experimental results demonstrate that positional encoding based on quadratic B-spline basis functions yields the highest structural stiffness. To further validate the effectiveness of the proposed method, a comparative analysis is performed against Fourier and super-Gaussian positional encoding schemes. The results show that spline-based encoding outperforms both alternatives in terms of structural compliance in most cases. Moreover, the resulting topologies exhibit smooth boundaries, free from oscillations and superfluous geometric details.

This paper presents a stochastic chemostat model driven by three independent Brownian motions. In addition to the direct disturbances caused by environmental noise on microorganisms and substrates (such as fluctuations in mortality rates and dilution rates), the feature of this paper is the introduction of randomness in the absorption or metabolic process of microorganisms for substrates, which reflects the interaction between substrates and microorganisms being modulated by common environmental noise and also describes the two-way stochastic coupling of substrate consumption and microbial growth. We focus on the dynamics of the system and successfully define the threshold λ that determines the existence and extinction of the population: when λ is positive, microorganisms will persist existence, and we prove the existence of unique stationary distribution of the system by constructing an auxiliary function; when λ is negative, microorganisms tend to extinction, and the substrate concentration distribution weakly converges to the probability measure π₁^*. Numerical simulation results are in complete agreement with theoretical analysis, and we illustrate how the intensity of noise affects the threshold λ through specific examples. We also verify the uniqueness of the stationary distribution by using kernel density estimation.

This paper presents a time-efficient trajectory planning method for robots moving along predefined geometric paths under velocity, acceleration and jerk constraints. Building on a discrete-time formulation, we propose a bidirectional rapid search framework that combines backward reachability with forward greedy propagation. Key to our approach is a hierarchical directed search that transforms nonlinear and nonconvex dynamic limits into tractable interval constraints via extremum comparisons, avoiding switching-point detection and singularity handling. Extensive simulations and real-world experiments demonstrate computational savings compared with baseline methods, while maintaining feasible, smooth motion profiles.

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.