Rate-of-decay of probability of isolation in dense sensor networks with bounding constraints
13 Jun 2010-pp 1898-1902
TL;DR: The work establishes the asymptotic rate of decay for the probability of node isolation in bounded wireless sensor networks, in the high density regime, and reveals the role of the most isolated neighborhoods of the bounding region in exponentially increasing the average probability of isolation.
Abstract: The work establishes the asymptotic rate of decay for the probability of node isolation in bounded wireless sensor networks, in the high density regime. In this regime, the exposition reveals the role of the most isolated neighborhoods of the bounding region in exponentially increasing the average probability of isolation. The problem is treated for a large family of random spatial distributions of nodes, random shapes of node coverage areas, and random topography of the network's bounding region. Different examples are presented to insightfully describe the detrimental effect of boundedness in network isolation. Finally we address different aspects relating to extremely isolating bounding regions, and densities that vary exponentially in time.
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27 Mar 1998
TL;DR: The LDP for Abstract Empirical Measures and applications-The Finite Dimensional Case and Applications of Empirically Measures LDP are presented.
Abstract: LDP for Finite Dimensional Spaces.- Applications-The Finite Dimensional Case.- General Principles.- Sample Path Large Deviations.- The LDP for Abstract Empirical Measures.- Applications of Empirical Measures LDP.
5,578 citations
TL;DR: An introduction to the theory of point processes can be found in this article, where the authors introduce the concept of point process and point process theory and introduce point processes as a theory for point processes.
Abstract: An introduction to the theory of point processes , An introduction to the theory of point processes , کتابخانه دیجیتال جندی شاپور اهواز
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TL;DR: This paper shows that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks.
Abstract: The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are nonuniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.
3,138 citations
TL;DR: A variety of methods are described that allow the mixing network, or an approximation to the network, to be ascertained and how the two fields of network theory and epidemiological modelling can deliver an improved understanding of disease dynamics and better public health through effective disease control are suggested.
Abstract: Networks and the epidemiology of directly transmitted infectious diseases are fundamentally linked. The foundations of epidemiology and early epidemiological models were based on population wide random-mixing, but in practice each individual has a finite set of contacts to whom they can pass infection; the ensemble of all such contacts forms a ‘mixing network’. Knowledge of the structure of the network allows models to compute the epidemic dynamics at the population scale from the individual-level behaviour of infections. Therefore, characteristics of mixing networks—and how these deviate from the random-mixing norm—have become important applied concerns that may enhance the understanding and prediction of epidemic patterns and intervention measures. Here, we review the basis of epidemiological theory (based on random-mixing models) and network theory (based on work from the social sciences and graph theory). We then describe a variety of methods that allow the mixing network, or an approximation to the network, to be ascertained. It is often the case that time and resources limit our ability to accurately find all connections within a network, and hence a generic understanding of the relationship between network structure and disease dynamics is needed. Therefore, we review some of the variety of idealized network types and approximation techniques that have been utilized to elucidate this link. Finally, we look to the future to suggest how the two fields of network theory and epidemiological modelling can deliver an improved understanding of disease dynamics and better public health through effective disease control.
1,737 citations
"Rate-of-decay of probability of iso..." refers background in this paper
...[2], [3]), where the network’s propagation characteristics are a function of the isolation/connectivity properties, as well as a function of the bounding region representing natural or constructed alterations of the network topology....
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01 Jan 1999
TL;DR: It is shown that if n nodes are placed in a disc of unit area in !
Abstract: In wireless data networks each transmitter’s power needs to be high enough to reach the intended receivers, while generating minimum interference on other receivers sharing the same channel. In particular, if the nodes in the network are assumed to cooperate in routing each others’ packets, as is the case in ad hoc wireless networks, each node should transmit with just enough power to guarantee connectivity in the network. Towards this end, we derive the critical power a node in the network needs to transmit in order to ensure that the network is connected with probability one as the number of nodes in the network goes to infinity. It is shown that if n nodes are placed in a disc of unit area in ℜ2 and each node transmits at a power level so as to cover an area of πr 2 = (log n + c(n))/n, then the resulting network is asymptotically connected with probability one if and only if c(n) → +∞.
1,282 citations