Results 1  10
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317
Performance Modeling of Epidemic Routing
 In Proceedings of IFIP Networking
, 2006
"... Abstract. In this paper, we develop a rigorous, unified framework based on Ordinary Differential Equations (ODEs) to study epidemic routing and its variations. These ODEs can be derived as limits of Markovian models under a natural scaling as the number of nodes increases. While an analytical study ..."
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Cited by 164 (11 self)
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Abstract. In this paper, we develop a rigorous, unified framework based on Ordinary Differential Equations (ODEs) to study epidemic routing and its variations. These ODEs can be derived as limits of Markovian models under a natural scaling as the number of nodes increases. While an analytical study of Markovian models is quite complex and numerical solution impractical for large networks, the corresponding ODE models yield closedform expressions for several performance metrics of interest, and a numerical solution complexity that does not increase with the number of nodes. Using this ODE approach, we investigate how resources such as buffer space and power can be traded for faster delivery, illustrating the differences among the various epidemic schemes considered. Finally we consider the effect of buffer management by complementing the forwarding models with Markovian and fluid buffer models.
Evolutionary games on graphs
, 2007
"... Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to ..."
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Cited by 93 (0 self)
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Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in nonequilibrium statistical physics. This review gives a tutorialtype overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by nonmeanfieldtype social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner’s Dilemma, the Rock–Scissors–Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
A generalized model of social and biological contagion
 JOURNAL OF THEORETICAL BIOLOGY
, 2005
"... We present a model of contagion that unifies and generalizes existing models of the spread of social influences and microorganismal infections. Our model incorporates individual memory of exposure to a contagious entity (e.g. a rumor or disease), variable magnitudes of exposure (dose sizes), and het ..."
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Cited by 47 (3 self)
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We present a model of contagion that unifies and generalizes existing models of the spread of social influences and microorganismal infections. Our model incorporates individual memory of exposure to a contagious entity (e.g. a rumor or disease), variable magnitudes of exposure (dose sizes), and heterogeneity in the susceptibility of individuals. Through analysis and simulation, we examine in detail the case where individuals may recover from an infection and then immediately become susceptible again (analogous to the socalled SIS model). We identify three basic classes of contagion models which we call epidemic threshold, vanishing critical mass, and critical mass classes, where each class of models corresponds to different strategies for prevention or facilitation. We find that the conditions for a particular contagion model to belong to one of the these three classes depend only on memory length and the probabilities of being infected by one and two exposures, respectively. These parameters are in principle measurable for real contagious influences or entities, thus yielding empirical implications for our model. We also study the case where individuals attain permanent immunity once recovered, finding that epidemics inevitably die out but may be surprisingly persistent when individuals possess memory.
Dynamical models of tuberculosis and their applications
 Mathematical Biosciences and Engineering
"... Abstract. The reemergence of tuberculosis (TB) from the 1980s to the early 1990s instigated extensive researches on the mechanisms behind the transmission dynamics of TB epidemics. This article provides a detailed review of the work on the dynamics and control of TB. The earliest mathematical model ..."
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Cited by 24 (3 self)
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Abstract. The reemergence of tuberculosis (TB) from the 1980s to the early 1990s instigated extensive researches on the mechanisms behind the transmission dynamics of TB epidemics. This article provides a detailed review of the work on the dynamics and control of TB. The earliest mathematical models describing the TB dynamics appeared in the 1960s and focused on the prediction and control strategies using simulation approaches. Most recently developed models not only pay attention to simulations but also take care of dynamical analysis using modern knowledge of dynamical systems. Questions addressed by these models mainly concentrate on TB control strategies, optimal vaccination policies, approaches toward the elimination of TB in the U.S.A., TB coinfection with HIV/AIDS, drugresistant TB, responses of the immune system, impacts of demography, the role of public transportation systems, and the impact of contact patterns. Model formulations involve a variety of mathematical areas, such as ODEs (Ordinary Differential Equations) (both autonomous and nonautonomous systems), PDEs (Partial Differential Equations), system
Time series analysis via mechanistic models. In review; prepublished at arxiv.org/abs/0802.0021
, 2008
"... The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consi ..."
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Cited by 21 (8 self)
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The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consideration of implicit dynamic models, meaning statistical models for stochastic dynamical systems which are specified by a simulation algorithm to generate sample paths. Inference procedures that operate on implicit models are said to have the plugandplay property. Our work builds on recently developed plugandplay inference methodology for partially observed Markov models. We introduce a class of implicitly specified Markov chains with stochastic transition rates, and we demonstrate its applicability to open problems in statistical inference for biological systems. As one example, these models are shown to give a fresh perspective on measles transmission dynamics. As a second example, we present a mechanistic analysis of cholera incidence data, involving interaction between two competing strains of the pathogen Vibrio cholerae. 1. Introduction. A
From processes to ODEs by Chemistry
 in TCS 2008, Fifth IFIP International Conference on Theoretical Computer Science
, 2004
"... We investigate the collective behavior of processes in terms of differential equations, using chemistry as a stepping stone. Chemical reactions can be converted to ordinary differential equations, and also to processes in a stochastic process algebra. Conversely, certain stochastic processes (in Che ..."
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Cited by 20 (0 self)
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We investigate the collective behavior of processes in terms of differential equations, using chemistry as a stepping stone. Chemical reactions can be converted to ordinary differential equations, and also to processes in a stochastic process algebra. Conversely, certain stochastic processes (in Chemical Parametric Form, or CPF) can be converted to chemical reactions. CPF is a subset of πcalculus, but is already more powerful that what is strictly needed to represent chemistry: it supports also parameterization and compositional reuse of models. The mapping of CPF to chemistry thus induces a parametric and compositional mapping of CPF to differential equations; the indirect mapping through chemistry is easier to define and understand than a direct mapping. As an example, we derive a quantitative interleaving law from the differential equations. 1
Human immunodeficiency virus drug therapy and virus
, 1997
"... Analysis of the shortterm dynamics of human immunodeficiency virus (HIV) type 1 infection in response to drug therapy has elucidated crucial kinetic properties of viral dynamics in vivo (D. D. Ho et al., Nature 373:123–126, 1995; A. S. Perelson et al., Science 271:1582–1586, 1996; X. Wei et al., Na ..."
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Cited by 19 (0 self)
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Analysis of the shortterm dynamics of human immunodeficiency virus (HIV) type 1 infection in response to drug therapy has elucidated crucial kinetic properties of viral dynamics in vivo (D. D. Ho et al., Nature 373:123–126, 1995; A. S. Perelson et al., Science 271:1582–1586, 1996; X. Wei et al., Nature 373:117–122, 1995). Here we investigated longterm changes in virus load in patients treated with a combination of lamivudine and zidovudine to identify principal factors responsible for the observed 10 to 100fold sustained suppression of virus load in vivo. Interestingly, most standard accounts of virus dynamics cannot explain a large sustained reduction without shifting the virus very close to extinction. The effect can be explained by taking into consideration either (i) the immune response against HIV, (ii) the killing of uninfected CD4 cells, or (iii) the differential efficacies of the drugs in different cell populations. Longterm treatment of human immunodeficiency virus type 1 (HIV1)infected patients with a combination of lamivudine and zidovudine results in a 10 to 100fold reduction of virus load and a 25 % increase in CD4 cell count, which is usually sustained for at least 1 year (5) (Fig. 1). Patients receiving this therapy show a rapid decline in virus load over several orders
Economics of Antibiotics Resistance: A Theory of Optimal Use
 Journal of Environmental Economics and Management
, 2001
"... portion of this paper may be reproduced without permission of the authors. Discussion papers are research materials circulated by their authors for purposes of information and discussion. They have not necessarily undergone formal peer review or editorial treatment. ii ..."
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Cited by 17 (3 self)
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portion of this paper may be reproduced without permission of the authors. Discussion papers are research materials circulated by their authors for purposes of information and discussion. They have not necessarily undergone formal peer review or editorial treatment. ii
Stochastic and deterministic models for agricultural production networks
 Math. Biosci. Eng
"... An approach to modeling the impact of disturbances in an agricultural production network is presented. A stochastic model and its approximate deterministic model for averages over sample paths of the stochastic system are developed. Simulations, sensitivity and generalized sensitivity analyses are g ..."
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Cited by 16 (12 self)
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An approach to modeling the impact of disturbances in an agricultural production network is presented. A stochastic model and its approximate deterministic model for averages over sample paths of the stochastic system are developed. Simulations, sensitivity and generalized sensitivity analyses are given. Finally, it is shown how diseases may be introduced into the network and corresponding simulations are discussed.
X.Li, PeertoPeer in Metric Space and Semantic Space
 IEEE Transactions on Knowledge and Data Engineering
, 2007
"... Abstract—This paper first proposes three improved gossip mechanisms by mapping links into metric space and dynamically adapting the number of selected neighbors to disseminate messages. Experiments and comparisons show that these mechanisms can improve the performance of gossip in peertopeer (P2P) ..."
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Cited by 15 (9 self)
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Abstract—This paper first proposes three improved gossip mechanisms by mapping links into metric space and dynamically adapting the number of selected neighbors to disseminate messages. Experiments and comparisons show that these mechanisms can improve the performance of gossip in peertopeer (P2P) networks. This is the effect of mapping a network into a metric space that differentiates nodes and links according to linking characteristics and controlling local information flow with knowing such differences. A further study about query routing on P2P semantic link network shows that mapping a network into a semantic space can also improve the performance. An intrinsic rule is found by experimental comparisons and analysis: The performance of a P2P network can be improved by designing an appropriate mapping from the network into metric space or semantic space. A general framework for networking with metric space and semantic space is suggested.