Personne : Dubé, Louis J.
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Dubé
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Louis J.
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Université Laval. Département de physique, de génie physique et d'optique
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ncf11850600
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- PublicationRestreintBond percolation on a class of correlated and clustered random graphs(IOP Pub., 2012-08-15) Hébert-Dufresne, Laurent; Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Marceau, Vincent.We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the configuration model where nodes of different types are connected via different types of hyperedges, edges that can link more than two nodes. We argue that the multitype approach coupled with the use of clustered hyperedges can reproduce a wide spectrum of complex patterns, and thus enhances our capability to model real complex networks. As an illustration of this claim, we use our formalism to highlight unusual behaviours of the size and composition of the components (small and giant) in a synthetic, albeit realistic, social network.
- PublicationAccès libreHeterogeneous bond percolation on multitype networks with an application to epidemic dynamics(Published by the American Physical Society through the American Institute of Physics, 2009-03-26) Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Pourbohloul, BabakConsiderable attention has been paid, in recent years, to the use of networks in modeling complex real-world systems. Among the many dynamical processes involving networks, propagation processes—in which the final state can be obtained by studying the underlying network percolation properties—have raised formidable interest. In this paper, we present a bond percolation model of multitype networks with an arbitrary joint degree distribution that allows heterogeneity in the edge occupation probability. As previously demonstrated, the multitype approach allows many nontrivial mixing patterns such as assortativity and clustering between nodes. We derive a number of useful statistical properties of multitype networks as well as a general phase transition criterion. We also demonstrate that a number of previous models based on probability generating functions are special cases of the proposed formalism. We further show that the multitype approach, by naturally allowing heterogeneity in the bond occupation probability, overcomes some of the correlation issues encountered by previous models. We illustrate this point in the context of contact network epidemiology.
- PublicationRestreintExact solution of bond percolation on small arbitrary graphs(Éditions de physique, 2012-03-02) Hébert-Dufresne, Laurent; Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Marceau, Vincent.We introduce a set of iterative equations that exactly solves the size distribution of components on small arbitrary graphs after the random removal of edges. We also demonstrate how these equations can be used to predict the distribution of the node partitions (i.e., the constrained distribution of the size of each component) in undirected graphs. Besides opening the way to the theoretical prediction of percolation on arbitrary graphs of large but finite size, we show how our results find application in graph theory, epidemiology, percolation and fragmentation theory.
- PublicationAccès libreStructural preferential aAttachment : network organization beyond the link(American Physical Society, 2011-10-06) Hébert-Dufresne, Laurent; Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Marceau, Vincent.We introduce a mechanism which models the emergence of the universal properties of complex networks, such as scale independence, modularity and self-similarity, and unifies them under a scale-free organization beyond the link. This brings a new perspective on network organization where communities, instead of links, are the fundamental building blocks of complex systems. We show how our simple model can reproduce social and information networks by predicting their community structure and more importantly, how their nodes or communities are interconnected, often in a self-similar manner.
- PublicationAccès libreDes ponts d'Euler à la grippe aviaire(Institut des sciences mathématiques, 2009-02-22) Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.
- PublicationRestreintSpreading dynamics on complex networks : a general stochastic approach(Springer Nature, 2013-12-24) Hébert-Dufresne, Laurent; Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Marceau, Vincent.Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible and susceptible-infectious-removed dynamics (e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions.
- PublicationAccès libreModeling the dynamical interaction between epidemics on overlay networks(American Physical Society, 2011-08-05) Hébert-Dufresne, Laurent; Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Marceau, Vincent.Epidemics seldom occur as isolated phenomena. Typically, two or more viral agents spread within the same host population and may interact dynamically with each other. We present a general model where two viral agents interact via an immunity mechanism as they propagate simultaneously on two networks connecting the same set of nodes. By exploiting a correspondence between the propagation dynamics and a dynamical process performing progressive network generation, we develop an analytical approach that accurately captures the dynamical interaction between epidemics on overlay networks. The formalism allows for overlay networks with arbitrary joint degree distribution and overlap. To illustrate the versatility of our approach, we consider a hypothetical delayed intervention scenario in which an immunizing agent is disseminated in a host population to hinder the propagation of an undesirable agent (e.g., the spread of preventive information in the context of an emerging infectious disease).
- PublicationAccès librePropagation on networks : an exact alternative perspective(American Physical Society, 2012-03-16) Hébert-Dufresne, Laurent; Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Marceau, Vincent.By generating the specifics of a network structure only when needed (on-the-fly), we derive a simple stochastic process that exactly models the time evolution of susceptible-infectious dynamics on finite-size networks. The small number of dynamical variables of this birth-deathMarkov process greatly simplifies analytical calculations. We show how a dual analytical description, treating large scale epidemics with a Gaussian approximation and small outbreaks with a branching process, provides an accurate approximation of the distribution even for rather small networks. The approach also offers important computational advantages and generalizes to a vast class of systems.
- PublicationAccès libreStructural preferential attachment : stochastic process for the growth of scale-free, modular, and self-similar systems(American Physical Society, 2012-02-13) Hébert-Dufresne, Laurent; Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Marceau, Vincent.Many complex systems have been shown to share universal properties of organization, such as scale independence, modularity, and self-similarity. We borrow tools from statistical physics in order to study structural preferential attachment (SPA), a recently proposed growth principle for the emergence of the aforementioned properties. We study the corresponding stochastic process in terms of its time evolution, its asymptotic behavior, and the scaling properties of its statistical steady state. Moreover, approximations are introduced to facilitate the modeling of real systems, mainly complex networks, using SPA. Finally, we investigate a particular behavior observed in the stochastic process, the peloton dynamics, and show how it predicts some features of real growing systems using prose samples as an example.
- PublicationAccès librePropagation dynamics on networks featuring complex topologies(American Physical Society through the American Institute of Physics, 2010-09-27) Hébert-Dufresne, Laurent; Allard, Antoine; Noël, Pierre-André; Dubé, Louis J.; Marceau, Vincent.Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently couple the dynamics of the network elements (such as nodes, vertices, individuals, etc.) on the one hand and their recurrent topological patterns (such as subgraphs, groups, etc.) on the other hand. In a susceptible-infectious-susceptible (SIS) model of epidemic spread on social networks with community structure, this approach yields a set of ordinary differential equations for the time evolution of the system, as well as analytical solutions for the epidemic threshold and equilibria. The results obtained are in good agreement with numerical simulations and reproduce the behavior of random networks in the appropriate limits which highlights the influence of topology on the processes. Finally, it is demonstrated that our model predicts higher epidemic thresholds for clustered structures than for equivalent random topologies in the case of networks with zero degree correlation.