Consensus and Products of Random Stochastic Matrices: Exact Rate for Convergence in Probability

Distributed consensus and other linear systems with system stochastic matrices $W_k$ emerge in various settings, like opinion formation in social networks, rendezvous of robots, and distributed inference in sensor networks. The matrices $W_k$ are often random, due to, e.g., random packet dropouts in wireless sensor networks. Key in analyzing the performance of such systems is studying convergence of matrix products $W_kW_{k-1}... W_1$. In this paper, we find the exact exponential rate $I$ for the convergence in probability of the product of such matrices when time $k$ grows large, under the assumption that the $W_k$'s are symmetric and independent identically distributed in time. Further, for commonly used random models like with gossip and link failure, we show that the rate $I$ is found by solving a min-cut problem and, hence, easily computable. Finally, we apply our results to optimally allocate the sensors' transmission power in consensus+innovations distributed detection

Hearing the clusters in a graph: A distributed algorithm

We propose a novel distributed algorithm to cluster graphs. The algorithm recovers the solution obtained from spectral clustering without the need for expensive eigenvalue/vector computations. We prove that, by propagating waves through the graph, a local fast Fourier transform yields the local component of every eigenvector of the Laplacian matrix, thus providing clustering information. For large graphs, the proposed algorithm is orders of magnitude faster than random walk based approaches. We prove the equivalence of the proposed algorithm to spectral clustering and derive convergence rates. We demonstrate the benefit of using this decentralized clustering algorithm for community detection in social graphs, accelerating distributed estimation in sensor networks and efficient computation of distributed multi-agent search strategies

Hierarchical Design Based Intrusion Detection System For Wireless Ad hoc Network

In recent years, wireless ad hoc sensor network becomes popular both in civil and military jobs. However, security is one of the significant challenges for sensor network because of their deployment in open and unprotected environment. As cryptographic mechanism is not enough to protect sensor network from external attacks, intrusion detection system needs to be introduced. Though intrusion prevention mechanism is one of the major and efficient methods against attacks, but there might be some attacks for which prevention method is not known. Besides preventing the system from some known attacks, intrusion detection system gather necessary information related to attack technique and help in the development of intrusion prevention system. In addition to reviewing the present attacks available in wireless sensor network this paper examines the current efforts to intrusion detection system against wireless sensor network. In this paper we propose a hierarchical architectural design based intrusion detection system that fits the current demands and restrictions of wireless ad hoc sensor network. In this proposed intrusion detection system architecture we followed clustering mechanism to build a four level hierarchical network which enhances network scalability to large geographical area and use both anomaly and misuse detection techniques for intrusion detection. We introduce policy based detection mechanism as well as intrusion response together with GSM cell concept for intrusion detection architecture.Comment: 16 pages, International Journal of Network Security & Its Applications (IJNSA), Vol.2, No.3, July 2010. arXiv admin note: text overlap with arXiv:1111.1933 by other author

VLSI implementation of an energy-aware wake-up detector for an acoustic surveillance sensor network

We present a low-power VLSI wake-up detector for a sensor network that uses acoustic signals to localize ground-base vehicles. The detection criterion is the degree of low-frequency periodicity in the acoustic signal, and the periodicity is computed from the "bumpiness" of the autocorrelation of a one-bit version of the signal. We then describe a CMOS ASIC that implements the periodicity estimation algorithm. The ASIC is functional and its core consumes 835 nanowatts. It was integrated into an acoustic enclosure and deployed in field tests with synthesized sounds and ground-based vehicles.Fil: Goldberg, David H.. Johns Hopkins University; Estados UnidosFil: Andreou, Andreas. Johns Hopkins University; Estados UnidosFil: Julian, Pedro Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; ArgentinaFil: Pouliquen, Philippe O.. Johns Hopkins University; Estados UnidosFil: Riddle, Laurence. Signal Systems Corporation; Estados UnidosFil: Rosasco, Rich. Signal Systems Corporation; Estados Unido

Dynamic change-point detection using similarity networks

From a sequence of similarity networks, with edges representing certain similarity measures between nodes, we are interested in detecting a change-point which changes the statistical property of the networks. After the change, a subset of anomalous nodes which compares dissimilarly with the normal nodes. We study a simple sequential change detection procedure based on node-wise average similarity measures, and study its theoretical property. Simulation and real-data examples demonstrate such a simply stopping procedure has reasonably good performance. We further discuss the faulty sensor isolation (estimating anomalous nodes) using community detection.Comment: appeared in Asilomar Conference 201