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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Publication Restreint Efficient sampling of spreading processes on complex networks using a composition and rejection algorithm(Elsevier, 2019-02-19) Young, Jean-Gabriel; Hébert-Dufresne, Laurent; St-Onge, Guillaume; Dubé, Louis J.Efficient stochastic simulation algorithms are of paramount importance to the study of spreading phenomena on complex networks. Using insights and analytical results from network science, we discuss how the structure of contacts affects the efficiency of current algorithms. We show that algorithms believed to require O(log N) or even O(1) operations per update – where N is the number of nodes – display instead a polynomial scaling for networks that are either dense or sparse and heterogeneous. This significantly affects the required computation time for simulations on large networks. To circumvent the issue, we propose a node-based method combined with a composition and rejection algorithm, a sampling scheme that has an average-case complexity of O[log(log N)] per update for general networks. This systematic approach is first set-up for Markovian dynamics, but can also be adapted to a number of non-Markovian processes and can enhance considerably the study of a wide range of dynamics on networks.Publication Accès libre Structural 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.Publication Restreint On stochastic dynamics of hydrogenic ion transport through solids(North-Holland, 2000-09-07) Beuve, Michael; Dubé, Louis J.; Gervais, Benoît; Lamour, Emily; Rozet, Jean-Pierre; Vernhet, DominiqueWe investigate the problem of hydrogenic ion transport through solids. To this end, we consider a system made of a single electron in a given potential and driven by a stochastic force uniformly distributed in time [D.G. Arbò et al., Phys. Rev. A 60 (1999) 1091], and we derive the time evolution equation of the ensemble average density matrix. We show that the random phase approximation of this equation leads to the rate equation model used to describe ion transport [P. Nicolai et al., J. Phys. B 23 (1990) 3609; J.P. Rozet et al., J. Phys. B 22 (1988) 33]. With the help of the Wigner transform, we also demonstrate that both quantum and classical dynamics of an electron under a train of kicks obeys the same equation within the semiclassical approximation. We conclude that seemingly different approaches may be regarded as different approximations of the same quantum problem and we show with a numerical example where differences arise.Publication Restreint Spreading 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.Publication Accès libre On the universality of the stochastic block model(American Physical Society, 2018-09-24) Young, Jean-Gabriel; St-Onge, Guillaume; Dubé, Louis J.; Desrosiers, PatrickMesoscopic pattern extraction (MPE) is the problem of finding a partition of the nodes of a complex network that maximizes some objective function. Many well-known network inference problems fall in this category, including, for instance, community detection, core-periphery identification, and imperfect graph coloring. In this paper, we show that the most popular algorithms designed to solve MPE problems can in fact be understood as special cases of the maximum likelihood formulation of the stochastic block model (SBM) or one of its direct generalizations. These equivalence relations show that the SBM is nearly universal with respect to MPE problems.Publication Accès libre Propagation 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.