Search Results (69)

We analyze long-range dependence (LRD) for word time series, understood as a slower than exponential decay of the two-point Shannon mutual information. We achieve this by examining the decay of the cosine correlation, a proxy object defined in terms of the cosine similarity between word2vec embeddings of two words, computed by an analogy to the Pearson correlation. By the Pinsker inequality, the squared cosine correlation between two random vectors lower bounds the mutual information between them. Using the Standardized Project Gutenberg Corpus, we find that the cosine correlation between word2vec embeddings exhibits a readily visible stretched exponential decay for lags roughly up to 1000 words, thus corroborating the presence of LRD. By contrast, for the Human vs. LLM Text Corpus entailing texts generated by large language models, there is no systematic signal of LRD. Our findings may support the need for novel memory-rich architectures in large language models that exceed not only hidden Markov models but also Transformers. Full article

This paper addresses fault estimation in discrete-time semi-Markov jump neural networks (s-MJNNs) under the Round-Robin protocol and proposes an innovative extended state observer-based approach. Unlike studies considering only constant transition rates, this work investigates s-MJNNs with time-varying transition probabilities, which more closely reflect practical situations. By incorporating actuator and sensor faults as augmented state variables, an extended state observer is proposed to estimate system states and faults simultaneously. To alleviate network congestion and optimize communication resources, the Round-Robin protocol is adopted to schedule data transmission efficiently. By constructing a Lyapunov–Krasovskii functional and applying the discrete Wirtinger inequality, sufficient conditions are derived to ensure the mean square exponential stability and dissipative performance of the system. The observer gain parameters are computed using the linear matrix inequality (LMI) method. Numerical simulations validate the effectiveness and performance of the proposed fault estimation method. Full article

This paper is dedicated to dealing with the design issue of a non-fragile state estimator for a type of nonlinear complex network subject to random couplings and random multiple time delays under binary encoding schemes (BESs). The BESs are put into use in the transmission of data from the sensor to the remote estimator. The phenomenon of bit errors is considered in the process of signal transmission, whose description utilizes a Bernoulli-distributed random sequence. The random couplings are represented by using the Kronecker delta function as well as a Markov chain. This paper aims to conduct a non-fragile state estimation such that, in the presence of some variations/perturbations in the gain parameter of the estimator, the estimation error dynamics will reach exponential ultimate boundedness in mean square and the ultimate bound will be minimized. Utilizing both stochastic analysis and matrix inequality processing, a sufficient condition is provided to guarantee that the constructed estimator satisfies the expected estimation performance, and the estimator gains are acquired by tackling an optimization issue constrained by some linear matrix inequalities. Eventually, two simulation examples are conducted, whose results verify that the approach to the design of a non-fragile estimator in this paper is effective. Full article

This paper studies the composite anti-disturbance static output feedback control problem of networked nonlinear Markov jump systems with general transition probabilities subject to multiple disturbances and deception attacks. The transition probabilities cover the known, uncertain with known bounds, and unknown cases. The unmatched disturbance and deception attacks are attenuated by the static output controller, while the matched disturbance is observed and compensated by the disturbance observer. Then, a composite anti-disturbance static output controller, including a linear part and a nonlinear part, is constructed to satisfy the stochastic $H_{\infty }$ stability. By using the Finsler lemma, sufficient conditions formed as symmetric linear matrix inequalities are derived to design the gains of disturbance observer and the output feedback controller. Finally, some simulations are given to illustrate the feasibility of the developed strategy. Full article

Despite numerous clinical attempts to treat tumors, malignant tumors remain a significant threat to human health due to associated side effects. Consequently, researchers are dedicated to studying the dynamical evolution of tumors in order to provide guidance for therapeutic treatment. This paper presents a stochastic tumor–immune model to discover the role of the regime switching in microenvironments and analyze tumor evolution under comprehensive pulse effects. By selecting an appropriate Lyapunov function and applying Itô’s formula, the ergodicity theory of Markov chains, and inequality analysis methods, we undertake a systematic investigation of a tumor’s behavior, focusing on its extinction, its persistence, and the existence of a stationary distribution. Our detailed analysis uncovers a profound impact of environmental regime switching on the dynamics of tumor cells. Specifically, we find that when the system is subjected to a high-intensity white noise environment over an extended duration, the growth of tumor cells is markedly suppressed. This critical finding reveals the indispensable role of white noise intensity and exposure duration in the long-term evolution of tumors. The tumor cells exhibit a transition from persistence to extinction when the environmental regime switches between two states. Furthermore, the growth factor of the tumor has an essential influence on the steady-state distribution of the tumor evolution. The theoretical foundations in this paper can provide some practical insights to develop more effective tumor treatment strategies, ultimately contributing to advancements in cancer research and care. Full article

Effectively controlling the carbon emissions intensity of the transportation sector (TSCEI) is essential to promote the sustainable development of the transportation industry in China. This study, which builds upon trend analysis, the Dagum Gini coefficient, and spatial autocorrelation analysis to reveal the spatiotemporal differentiation of TSCEI, employs both traditional and spatial Markov chain to analyze the dynamic evolution of TSCEI and forecast its future development trend. Furthermore, econometric models are constructed to examine the convergence characteristics of TSCEI. The empirical results reveal the following key findings: (1) TSCEI in China has significantly declined, exhibiting a spatial distribution pattern of “higher in the north, lower in the south; higher in the west, lower in the east”. (2) Inter-regional differences are the main contributors to overall TSCEI disparities, with provincial TSCEI exhibiting positive spatial autocorrelation, primarily characterized by high–high and low–low agglomeration. (3) TSCEI tends to gradually shift from high- to low-intensity states over time, with an equilibrium probability of 90.98% for transferring to lower intensity state. Provincial TSCEI shows significant spatial spillover effects, influenced by neighboring provinces’ states. (4) TSCEI demonstrates convergence characteristics at national and regional levels, including $\sigma$ convergence, absolute and conditional $\beta$ convergence, with the transportation energy structure and technological progress playing a particularly prominent role in facilitating the convergence of TSCEI towards lower values. The policy implications of promoting TSCEI convergence and reducing spatial inequality are discussed. Full article

This study presents an approach to enhancing the robustness of $H_{\infty }$ control in It$\widehat{o}$-type stochastic Markov jump systems, addressing uncertainties in parameters, time-varying delays, and nonlinear perturbations. In this study, the nonlinearities are not exactly known, so an adaptive control strategy is employed. Firstly, an adaptive state observer of full dimension is constructed along with the derivation of error dynamics. Subsequently, different from traditional methods, two linear sliding surfaces are designed, respectively, for the state observer system and error dynamics, resulting in two sliding mode dynamics. Secondly, by employing the linear matrix inequality (LMI) method, sufficient conditions are established to ensure mean-square exponential stability of the closed-loop systems, including observer sliding mode dynamics and error sliding mode dynamics, along with an $H_{\infty }$ attenuation performance index $\gamma$. Thirdly, adaptive sliding mode controllers are proposed, ensuring the finite-time arrival and maintenance of the established sliding surfaces. Finally, the efficacy of the derived outcomes is illustrated utilizing the Tunnel Diode circuit model as a demonstrative case study. In this example, the system’s state responses, sliding surface functions, control input, and estimated parameters are simulated under different operating modes and external disturbances. The results demonstrate that the proposed adaptive sliding mode control strategy ensures faster and better convergence compared to error dynamics without control. Full article

The fault-tolerant time-varying formation (TVF) trajectory tracking control problem is investigated in this paper for uncertain multi-agent systems (MASs) with external disturbances subject to time delays under semi-Markov switching topologies. Firstly, based on the characteristics of actuator faults, a failure distribution model is established, which can better describe the occurrence of the failures in practice. Secondly, switching the network topologies is assumed to follow a semi-Markov stochastic process that depends on the sojourn time. Subsequently, a novel distributed state-feedback control protocol with time-varying delays is proposed to ensure that the MASs can maintain a desired formation configuration. To reduce the impact of disturbances imposed on the system, the $H_{\infty }$ performance index is introduced to enhance the robustness of the controller. Furthermore, by constructing an advanced Lyapunov–Krasovskii (LK) functional and utilizing the reciprocally convex combination theory, the TVF control problem can be transformed into an asymptotic stability issue, achieving the purpose of decoupling and reducing conservatism. Furthermore, sufficient conditions for system stability are obtained through linear matrix inequalities (LMIs). Eventually, the availability and superiority of the theoretical results are validated by three simulation examples. Full article

Comprehensive land prices for expropriation zones can effectively alleviate many conflicts in China’s land expropriation practices. This contributes to achieving sustainable development goals such as “SDG-10: Reduced Inequalities” and “ SDG-11: Sustainable Cities and Communities”. The reasonable delineation of expropriation zones and scientific calculation of zone prices have become crucial. This study used the Cangzhou urban area in Hebei Province, China, as a case study. By integrating the CA–Markov model, multiple linear regression model, coupling coordination degree model, relative development degree model, and GIS spatial analysis techniques, the study deeply analyzed the spatiotemporal coupling relationship between land use and comprehensive land prices for expropriation zones from 2009 to 2021. Furthermore, it simulated and forecasted the changes in land use, expropriation zones, and zone prices in 2027. The study yielded the following conclusions: (1) The changes in land use reflected land economic value, land resource condition and land location condition shifts, which formed an interactive feedback mechanism with the comprehensive land price for land expropriation zones. (2) Land use impacted zone distribution through the spatial distribution characteristics of construction land, with recent development zones in the central urban area primarily extending east and southeast due to planning and policies related to land use for construction. (3) The coupling coordination and relative developmental degree between land use degree and zone price gradually develop in a good direction. A linear relationship is observed among land economic value, land resource condition, and land location condition concerning the zone price. Based on this, the predicted adjustment ranges for zone prices from high to low in 2027 will be 2.6400 to 2.7210, 2.1900 to 2.2537, and 1.8300 to 1.9306 million CNY/hectare. This study provides a new method for studying comprehensive land prices for expropriation zones, supporting decision making. Full article

This paper studies the output feedback $H\infty$ control problem of event-triggered Markov-type networked control systems. Firstly, a new Lyapunov–Krasovskii functional is constructed, which contains an event-triggered scheme, Markovian jump system, and quantified information. Secondly, the upper bound of the weak infinitesimal generation operator of the Lyapunov–Krasovskii function is estimated by combining Wirtinger’s-based integral inequality and reciprocally convex inequality. Finally, based on the Lyapunov stability theory, the closed-loop stability criterion of event-triggered Markov-type networked control systems and the design method of the output feedback $H\infty$ controller for the disturbance attenuation level $\gamma$ are given in the terms of linear matrix inequalities. The effectiveness and superiority of the proposed method are verified using three numerical examples. Full article

The primary objective of this paper is to address the challenge of designing finite-time fault-tolerant control mechanisms for nonlinear flexible spacecraft systems, which are particularly vulnerable to randomized actuator faults. Diverging from traditional methodologies, our research harnesses the capabilities of the Takagi–Sugeno (T–S) fuzzy framework. A unique feature of our model is the representation of actuator failures as stochastic signals following a Markov process, thereby offering a robust solution for addressing timeliness concerns. In this paper, we introduce a generalized reciprocally convex inequality that includes adjustable parameters, broadening the scope of previous results by accommodating them as special cases. Through the amalgamation of this enhanced inequality and flexible independent parameters, we propose an innovative controller design strategy. This approach establishes a stability standard that guarantees mean-square $H_{\infty }$ performance. In order to validate the efficacy of the suggested strategy, we present a numerical illustration involving a nonlinear spacecraft system, showcasing the practical advantages and feasibility of our proposed technique. Full article

This paper is concerned with exponential synchronization for a class of coupled neural networks with hybrid delays and stochastic distributed delayed impulses. First of all, based on the average impulsive interval method, total probability formula and ergodic theory, several novel impulsive Halanay differential inequalities are established. Two types of stochastic impulses, i.e., stochastic distributed delayed impulses with dependent property and Markov property have been taken into account, respectively. Secondly, some criteria on exponential synchronization in the mean square of a class of coupled neural networks with stochastic distributed delayed impulses are acquired by combining the proposed lemmas and graph theory. The validity of the theoretical results is demonstrated by several numerical simulation examples. Full article

Inequalities serve as fundamental tools for analyzing various important concepts in stochastic differential problems. In this study, we present results on the existence, uniqueness, and averaging principle for fractional neutral stochastic differential equations. We utilize Jensen, Burkholder–Davis–Gundy, Grönwall–Bellman, Hölder, and Chebyshev–Markov inequalities. We generalize results in two ways: first, by extending the existing result for $\mathrm{p}=2$ to results in the ${\mathbb{L}}^{\mathrm{p}}$ space; second, by incorporating the Caputo–Katugampola fractional derivatives, we extend the results established with Caputo fractional derivatives. Additionally, we provide examples to enhance the understanding of the theoretical results we establish. Full article

Perturbation bounds are powerful tools for investigating the phenomenon of insensitivity to perturbations, also referred to as stability, for stochastic and deterministic systems. This perspective article presents a focused account of some of the main concepts and results in inequality-based perturbation theory for finite state-space, time-homogeneous, continuous-time Markov chains. The diversity of perturbation bounds and the logical relationships between them highlight the essential stability properties and factors for this class of stochastic processes. We discuss the linear time dependence of general perturbation bounds for Markov chains, as well as time-independent (i.e., time-uniform) perturbation bounds for chains whose stationary distribution is unique. Moreover, we prove some new results characterizing the absolute and relative tightness of time-uniform perturbation bounds. Specifically, we show that, in some of them, an equality is achieved. Furthermore, we analytically compare two types of time-uniform bounds known from the literature. Possibilities for generalizing Markov-chain stability results, as well as connections with stability analysis for other systems and processes, are also discussed. Full article

This paper aims to address the exponential stability and stabilization problems for a class of delayed nonlinear Markov jump systems under randomly occurring Denial-of-Service (DoS) attacks and packet loss. Firstly, the stochastic characteristics of DoS attacks and packet loss are depicted by the attack success rate and packet loss rate. Secondly, a Period Observation Window (POW) method and a hybrid-input strategy are proposed to compensate for the impact of DoS attack and packet loss on the system. Thirdly, A Dynamic Event-triggered Mechanism (DETM) is introduced to save more network resources and ensure the security and reliability of the systems. Then, by constructing a general common Lyapunov functional and combining it with the DETM and other inequality analysis techniques, the less conservative stability and stabilization criteria for the underlying systems are derived. In the end, the effectiveness of our result is verified through two examples. Full article