Yilun Shang

Bio: Yilun Shang is an academic researcher from Northumbria University. The author has contributed to research in topics: Mathematics & Computer science. The author has an hindex of 29, co-authored 103 publications receiving 1975 citations. Previous affiliations of Yilun Shang include Tongji University & University of Texas at San Antonio.

Finite-time consensus for multi-agent systems with fixed topologies

Abstract: In this article, we study finite-time state consensus problems for continuous multi-agent systems with nonlinear protocols. Building on the theory of finite-time Lyapunov stability, we propose sufficient criteria which guarantee the system to reach a consensus in finite time, provided that the underlying directed network contains a spanning tree. Novel finite-time consensus protocols are introduced as examples for applying the criteria. Simulations are also presented to illustrate our theoretical results.

Influence of the number of topologically interacting neighbors on swarm dynamics

Abstract: Recent empirical and theoretical works on collective behaviors based on a topological interaction are beginning to offer some explanations as for the physical reasons behind the selection of a particular number of nearest neighbors locally affecting each individual's dynamics. Recently, flocking starlings have been shown to topologically interact with a very specific number of neighbors, between six to eight, while metric-free interactions were found to govern human crowd dynamics. Here, we use network- and graph-theoretic approaches combined with a dynamical model of locally interacting self-propelled particles to study how the consensus reaching process and its dynamics are influenced by the number k of topological neighbors. Specifically, we prove exactly that, in the absence of noise, consensus is always attained with a speed to consensus strictly increasing with k. The analysis of both speed and time to consensus reveals that, irrespective of the swarm size, a value of k ~ 10 speeds up the rate of convergence to consensus to levels close to the one of the optimal all-to-all interaction signaling. Furthermore, this effect is found to be more pronounced in the presence of environmental noise.

Subgraph Robustness of Complex Networks Under Attacks

Abstract: 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 Erdős-Renyi 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.

Group consensus of multi-agent systems in directed networks with noises and time delays

Abstract: In this paper, group consensus problems in fixed directed networks of dynamic agents are investigated. Group consensus means that the agents in each group share a consistent value while there is no agreement between any two groups. Based on algebraic graph theory, sufficient conditions guaranteeing group consensus under the proposed control protocol in the presence of random noises and communication delays are derived. The analysis uses a stability result of Mao for stochastic differential delay equations, which ensures the consensus can be achieved almost surely and exponentially fast. Numerical examples are provided to demonstrate the availability of the obtained results as well as the effect of time delay/noise intensity.

Random graphs

Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

The Web of Human Sexual Contacts

Abstract: Many ``real-world'' networks are clearly defined while most ``social'' networks are to some extent subjective. Indeed, the accuracy of empirically-determined social networks is a question of some concern because individuals may have distinct perceptions of what constitutes a social link. One unambiguous type of connection is sexual contact. Here we analyze data on the sexual behavior of a random sample of individuals, and find that the cumulative distributions of the number of sexual partners during the twelve months prior to the survey decays as a power law with similar exponents $\alpha \approx 2.4$ for females and males. The scale-free nature of the web of human sexual contacts suggests that strategic interventions aimed at preventing the spread of sexually-transmitted diseases may be the most efficient approach.

An Introduction to the Theory of Graph Spectra: Spectral techniques

Abstract: Preface 1. Introduction 2. Graph operations and modifications 3. Spectrum and structure 4. Characterizations by spectra 5. Structure and one eigenvalue 6. Spectral techniques 7. Laplacians 8. Additional topics 9. Applications Appendix Bibliography Index of symbols Index.