Personne : St-Onge, Guillaume
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St-Onge
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Guillaume
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Département de physique, de génie physique et d'optique, Faculté des sciences et de génie, Université Laval
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ncf11909369
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Publication Accès libre Geometric evolution of complex networks with degree correlations(American Physical Society, 2018-03-19) Allard, Antoine; St-Onge, Guillaume; Laurence, Edward; Dubé, Louis J.; Murphy, CharlesWe present a general class of geometric network growth mechanisms by homogeneous attachment in which the links created at a given time t are distributed homogeneously between a new node and the existing nodes selected uniformly. This is achieved by creating links between nodes uniformly distributed in a homogeneous metric space according to a Fermi-Dirac connection probability with inverse temperature β and general time-dependent chemical potential μ(t). The chemical potential limits the spatial extent of newly created links. Using a hidden variable framework, we obtain an analytical expression for the degree sequence and show that μ(t) can be fixed to yield any given degree distributions, including a scale-free degree distribution. Additionally, we find that depending on the order in which nodes appear in the network—its history—the degree-degree correlations can be tuned to be assortative or disassortative. The effect of the geometry on the structure is investigated through the average clustering coefficient ⟨c⟩. In the thermodynamic limit, we identify a phase transition between a random regime where ⟨c⟩→ 0 when β<βc and a geometric regime where ⟨c⟩ > 0 when β>βc.Publication Accès libre Phase transition of the susceptible-infected-susceptible dynamics on time-varying configuration model networks(American Physical Society, 2018-02-12) Young, Jean-Gabriel; St-Onge, Guillaume; Laurence, Edward; Dubé, Louis J.; Murphy, CharlesWe present a degree-based theoretical framework to study the susceptible-infected-susceptible (SIS) dynamics on time-varying (rewired) configuration model networks. Using this framework on a given degree distribution, we provide a detailed analysis of the stationary state using the rewiring rate to explore the whole range of the time variation of the structure relative to that of the SIS process. This analysis is suitable for the characterization of the phase transition and leads to three main contributions: (1) We obtain a self-consistent expression for the absorbing-state threshold, able to capture both collective and hub activation. (2) We recover the predictions of a number of existing approaches as limiting cases of our analysis, providing thereby a unifying point of view for the SIS dynamics on random networks. (3) We obtain bounds for the critical exponents of a number of quantities in the stationary state. This allows us to reinterpret the concept of hub-dominated phase transition. Within our framework, it appears as a heterogeneous critical phenomenon: observables for different degree classes have a different scaling with the infection rate. This phenomenon is followed by the successive activation of the degree classes beyond the epidemic threshold.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 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.