Exact two-terminal reliability of some directed networks

The calculation of network reliability in a probabilistic context has long been an issue of practical and academic importance. Conventional approaches (determination of bounds, sums of disjoint products algorithms, Monte Carlo evaluations, studies of the reliability polynomials, etc.) only provide approximations when the network's size increases, even when nodes do not fail and all edges have the same reliability p. We consider here a directed, generic graph of arbitrary size mimicking real-life long-haul communication networks, and give the exact, analytical solution for the two-terminal reliability. This solution involves a product of transfer matrices, in which individual reliabilities of edges and nodes are taken into account. The special case of identical edge and node reliabilities (p and rho, respectively) is addressed. We consider a case study based on a commonly-used configuration, and assess the influence of the edges being directed (or not) on various measures of network performance. While the two-terminal reliability, the failure frequency and the failure rate of the connection are quite similar, the locations of complex zeros of the two-terminal reliability polynomials exhibit strong differences, and various structure transitions at specific values of rho. The present work could be extended to provide a catalog of exactly solvable networks in terms of reliability, which could be useful as building blocks for new and improved bounds, as well as benchmarks, in the general case

Terminal-Set-Enhanced Community Detection in Social Networks

Community detection aims to reveal the community structure in a social network, which is one of the fundamental problems. In this paper we investigate the community detection problem based on the concept of terminal set. A terminal set is a group of users within which any two users belong to different communities. Although the community detection is hard in general, the terminal set can be very helpful in designing effective community detection algorithms. We first present a 2-approximation algorithm running in polynomial time for the original community detection problem. In the other issue, in order to better support real applications we further consider the case when extra restrictions are imposed on feasible partitions. For such customized community detection problems, we provide two randomized algorithms which are able to find the optimal partition with a high probability. Demonstrated by the experiments performed on benchmark networks the proposed algorithms are able to produce high-quality communities.Comment: INFOCOM 201

Communicating the sum of sources over a network

We consider the network communication scenario, over directed acyclic networks with unit capacity edges in which a number of sources $s_i$ each holding independent unit-entropy information $X_i$ wish to communicate the sum $\sum{X_i}$ to a set of terminals $t_j$. We show that in the case in which there are only two sources or only two terminals, communication is possible if and only if each source terminal pair $s_i/t_j$ is connected by at least a single path. For the more general communication problem in which there are three sources and three terminals, we prove that a single path connecting the source terminal pairs does not suffice to communicate $\sum{X_i}$. We then present an efficient encoding scheme which enables the communication of $\sum{X_i}$ for the three sources, three terminals case, given that each source terminal pair is connected by {\em two} edge disjoint paths.Comment: 12 pages, IEEE JSAC: Special Issue on In-network Computation:Exploring the Fundamental Limits (to appear

Personal area technologies for internetworked services

This article reviews wireless enabling technologies to support interworking of heterogeneous networks, and covers two relevant topics; personal area networks and multistandard terminals. The variability of the PAN channel is demonstrated, and the implications for air interface design are discussed. To ensure the effective operation in the shared spectrum, radio resource management and medium access control strategies for PANs are also discussed. It is recognized that the terminal cost has significant implications for user acceptance; therefore, by combining the functionality from different standards (cellular, wireless LAN, broadcast), the cost can be reduced. Technologies and architectures relevant for multistandard terminals are reviewed, including synchronization and linear RF processing. Finally, the potential for further simplifications within the framework of multicarrier CDMA is considered.This article reviews wireless enabling technologies to support interworking of heterogeneous networks, and covers two relevant topics; personal area networks and multistandard terminals. The variability of the PAN channel is demonstrated, and the implications for air interface design are discussed. To ensure effective operation in shared spectrum, radio resource management and medium access control strategies for PANs are also discussed. It is recognized that terminal cost has significant implications for user acceptance; therefore, by combining functionality from different standards (cellular, wireless LAN, broadcast), cost can be reduced. Technologies and architectures relevant for multistandard terminals are reviewed, including synchronization and linear RF processing. Finally, the potential for further simplifications within the framework of multicarrier CDMA is considered

Analysis by the Two-Fluids Model of the Dynamical Behavior of a Viscoelastic Fluid Probed by Dynamic Light Scattering

The dynamic properties of a model transient network have been studied by dynamic light scattering. The network is formed by microemulsion droplets linked by telechelic polymers (modified hydrophilic polymers with two grafted hydrophobic stickers). We compare the properties of two networks that are similar but for the residence time of the hydrophobic stickers in the droplets. The results are interpreted according to the so-called two-fluids model, which was initially developed for semidilute polymer solutions and which we extend here to any Maxwellian viscoelastic medium characterized by its elastic modulus and terminal time as measured by rheology. This model is found to describe consistently and quantitatively the experimental observations.Comment: novembre 200