ABSTRACT Image segmentation is a key computer vision technique used to divide images into semantically meaningful regions. However, noise and artifacts often introduce anomalies that degrade the accuracy of traditional segmentation algorithms. To address this, we propose an adaptive Petri net token flow (APNTF) method that models segmentation as a concurrent, data‐driven process using a formally defined Petri net. In this framework, each place represents an intensity bin, and transitions are generated based on a local entropy criterion, connecting neighboring bins only when additional texture refinement is needed. The process begins with an initial marking that assigns one token per pixel to its corresponding intensity value. Tokens then propagate through enabled transitions, yielding a context‐aware region‐growing mechanism. A region‐merging stage follows, combining bins with similar mean intensities to reduce over‐segmentation. The use of Petri nets ensures termination, reproducibility, and facilitates parallel execution. We evaluated the APNTF approach on a variety of images, including challenging medical images, using standard quantitative metrics. Experimental results show that the method improves segmentation accuracy and robustness in the presence of noise and artifacts. This approach provides a structured and adaptable solution for challenging image segmentation tasks involving complex visual data.

This paper addresses the problem of distributed estimation and motion control (DEMC) in multi-agent systems (MASs) with both linear and Lipschitz nonlinear dynamics. Unlike conventional DEMC methods designed for MASs under ideal conditions, this work investigates scenarios where all agents are vulnerable to various forms of attacks. The considered attacks comprise false-data injection (FDI) attacks and denial of service (DoS) attacks that affect the communication channels among agents to destabilize the MAS. Also, the unbounded actuator attacks which exist in practical environments to intentionally degrade the MAS performance is considered. To cope with these kinds of attacks, two novel resilient approaches are established aimed at estimating and following a mobile target under attacks. The proposed distributed attack-resilient control strategies are designed based on a dual-layer structure, guaranteeing effective DEMC with an ultimately bounded error. The results from two simulation examples are provided to validate the presented algorithms. Note to Practitioners—The motivation of this work is to deal with the DEMC problem for MASs under multiple attacks. In most of the existing DEMC schemes for MASs, having a healthy network and dynamics is a requirement. However, in practical environments, MASs as an important subclass of cyber-physical systems are subject to different types of attacks that affect the network and dynamics of MASs and may seriously jeopardize the performance of the DEMC algorithm, or even worse, lead to instability. Therefore, a resilient hierarchical DEMC algorithm is proposed for MASs which allows agents to estimate and follow a mobile target under multiple attacks. The proposed scheme is resilient to most existing cyber-attacks and is designed for MASs with both linear and nonlinear dynamics. It can be applied to various practical engineering systems such as autonomous vehicles, mobile robots, and intelligent transportation systems. The stability and convergence of the proposed algorithms are analyzed mathematically, and it is shown that the agents not only track the estimated target but also can cope with multiple attacks through simulation experiments.

Abstract This paper investigates the problem of resilient vector consensus for a group of dynamic agents against mobile malicious attacks. As real networks often operate under random environment and noises, we approach this problem by considering general random dynamic networks with weighted directed topologies. We propose three types of mobile attack models, which differ in the timing of moving of attackers and the capability of detecting such moving. By employing distributed discrete-time algorithms, the Lyapunov theory and martingale convergence theorem, resilient vector consensus is shown to be reached for all three models when the underlying network satisfies certain stochastic robustness conditions.

A fundamental organizing principle of real-world complex networked systems is modularity, where networks have interactions at different levels. In this paper we consider a modular graph G having modules with arbitrary intraconnections and random interconnections between activated vertices in different modules. The vertices in different modules are activated with probability r and linked by an interconnecting edge with probability p independently. We present results regarding the Cheeger constant, robustness, algebraic connectivity as well as the smallest eigenvalue for the Dirichlet Laplacian matrix of G with high probability. Our results suggest that r=(lnn)/n is a potential scaling for the recently observed external field-like phenomena of modular networks in statistical mechanics.

For a graph Gk on n vertices with a minimum degree of at least k→∞ as n→∞, let G(n,p) be a random subgraph of Gk taken by retaining each edge (i,j) independently with probability pij and p={pij}(i,j)∈Gk. We show that under certain conditions on the edge probabilities, the resulting random graph has a long path that covers almost all or all vertices with probability tending to 1 as n→∞.

We consider a multiplex random graph G(n,m,p) with m independent color layers over a common vertex set V of order n. In each layer, the edges are independent following the Erdős-Rényi model with edge probability p=c(ln⁡n+(k−1)ln⁡ln⁡n)/mn for some constant c>1. A rainbow path in this context means a path with all edges from distinct layers. For a graph G∈G(n,m,p), let rck(G) be its rainbow k-connectivity, namely the smallest required number of layers so that any pair of vertices in G can be connected by k internally vertex-disjoint rainbow paths. We show that with high probability, rck(G(n,m,p)) is concentrated on three consecutive numbers. These numbers are at distance Θ(ln⁡n/(ln⁡(ln⁡n+(k−1)ln⁡ln⁡n))2) to the diameter of the graph.

The ability of tracking is an important prerequisite for multiagent networks to perform collective activities. This article investigates the problem of containment for a weighted multiagent network with continuous-time agents under state constraints. The network is composed of uninformed and informed agents, where the latter receive external inputs. A new general class of distributed nonlinear controllers is designed for accomplishing both containment and consensus tracking, where the state of each agent is required to stay in its desired convex constraint set. We show that, by using matrix analysis, convex analysis, and Lyapunov theory, all agents eventually converge to the convex hull formed by the external inputs while they obey their constraints during the transience. No relationship is assumed between the convex hull and the intersection of all constraint sets. The consensus tracking problem with a single external input is also solved under this framework. As a generalization, we tackle the multiscaled constrained containment problem, where agents can specify their desired buffer zones by either zooming in or zooming out the convex hull. Numerical examples are provided to illustrate the theoretical results.

We investigate the problems of resilient cluster consensus in directed networks under three types of multiagent dynamics, namely, continuous-time multiagent systems, discrete-time multiagent systems, and switched multiagent systems composed of both continuous-time and discrete-time components. Resilient cluster censoring strategies are proposed to ensure cluster consensus against locally bounded Byzantine nodes in a purely distributed manner, where neither the number/identity of Byzantine nodes nor the division of clusters is assumed. We do not require complicated algebraic conditions or any balance conditions over intercluster structures, distinguishing the current work from previous results on cluster consensus problems besidesa fortiorithe attack-tolerant feature. Sufficient conditions are established in all the three scenarios based on the graph robustness. Furthermore, we solve the heterogenous cluster robustness problems and resilient scaled cluster consensus problems as extensions. The theoretical results are illustrated through numerical examples including the Santa Fe collaboration network.

This article proposes an opinion formation model featuring both a private and an expressed opinion for a given topic over dynamical networks. Each individual in the network has a private opinion, which is not known by others but evolves under local influence from the expressed opinions of its neighbors, and an expressed opinion, which varies under a peer pressure to conform to the local environment. We design the opinion sifting strategies which are purely distributed and provide resilience to a range of adversarial environment involving locally and globally bounded threats as well as malicious and Byzantine individuals. We establish the sufficient and necessary graph-theoretic criteria for normal individuals to attain opinion consensus in both directed-fixed and time-varying networks. Two classes of opinion clustering problems are introduced as an extension. By designing the resilient opinion separation algorithms, we develop necessary and sufficient criteria, which characterize the resilient opinion clustering in terms of the ratio of opinions as well as the difference of opinions. Numerical examples, including real-world jury deliberations, are presented to illustrate the effectiveness of the proposed approaches and test the correctness of our theoretical results.

Network measures derived from empirical observations are often poor estimators of the true structure of system as it is impossible to observe all components and all interactions in many real world complex systems. Here, we study attack robustness of complex networks with data missing caused by: 1) a uniform random sampling and 2) a nonuniform random sampling. By introducing the subgraph robustness problem, we develop analytically a framework to investigate robustness properties of the two types of subgraphs under random attacks, localized attacks, and targeted attacks. Interestingly, we find that the benchmark models, such as Erdos-Rényi graphs, random regular networks, and scale-free networks possess distinct characteristic subgraph robustness features. We show that the network robustness depends on several factors including network topology, attack mode, sampling method and the amount of data missing, generalizing some well-known robustness principles of complex networks. Our results offer insight into the structural effect of missing data in networks and highlight the significance of understanding different sampling processes and their consequences on attack robustness, which may be instrumental in designing robust systems.