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Personne :
Laurence, Edward

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Laurence

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Edward

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Université Laval. Département de physique, de génie physique et d'optique

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ncf11897827

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Résultats de recherche

Voici les éléments 1 - 7 sur 7
  • PublicationAccès libre
    Complex networks as an emerging property of hierarchical preferential attachment
    (American Physical Society, 2015-12-09) Young, Jean-Gabriel; Hébert-Dufresne, Laurent; Allard, Antoine; Laurence, Edward; Dubé, Louis J.
    Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of complex systems can be modeled as an organization of many embedded levels (potentially infinite in number), all of them following the same universal growth principle known as preferential attachment. We give examples of such hierarchy in real systems, for instance, in the pyramid of production entities of the film industry. More importantly, we show how real complex networks can be interpreted as a projection of our model, from which their scale independence, their clustering, their hierarchy, their fractality, and their navigability naturally emerge. Our results suggest that complex networks, viewed as growing systems, can be quite simple, and that the apparent complexity of their structure is largely a reflection of their unobserved hierarchical nature.
  • PublicationAccès libre
    Finite-size analysis of the detectability limit of the stochastic block model
    (American Physical Society, 2017-06-19) Young, Jean-Gabriel; Hébert-Dufresne, Laurent; Laurence, Edward; Dubé, Louis J.; Desrosiers, Patrick
    It has been shown in recent years that the stochastic block model is sometimes undetectable in the sparse limit, i.e., that no algorithm can identify a partition correlated with the partition used to generate an instance, if the instance is sparse enough and infinitely large. In this contribution, we treat the finite case explicitly, using arguments drawn from information theory and statistics. We give a necessary condition for finite-size detectability in the general SBM. We then distinguish the concept of average detectability from the concept of instance-by-instance detectability and give explicit formulas for both definitions. Using these formulas, we prove that there exist large equivalence classes of parameters, where widely different network ensembles are equally detectable with respect to our definitions of detectability. In an extensive case study, we investigate the finite-size detectability of a simplified variant of the SBM, which encompasses a number of important models as special cases. These models include the symmetric SBM, the planted coloring model, and more exotic SBMs not previously studied. We conclude with three appendices, where we study the interplay of noise and detectability, establish a connection between our information-theoretic approach and random matrix theory, and provide proofs of some of the more technical results.
  • PublicationAccès libre
    Spectral dimension reduction of complex dynamical networks
    (American Physical Society, 2019-03-04) Laurence, Edward; Dubé, Louis J.; Doyon, Nicolas; Desrosiers, Patrick
    Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve (nodes’ dynamics). Despite substantial progress, little is known about why some subtle changes in the network structure, at the so-called critical points, can provoke drastic shifts in its dynamics. We tackle this challenging problem by introducing a method that reduces any network to a simplified low-dimensional version. It can then be used to describe the collective dynamics of the original system. This dimension reduction method relies on spectral graph theory and, more specifically, on the dominant eigenvalues and eigenvectors of the network adjacency matrix. Contrary to previous approaches, our method is able to predict the multiple activation of modular networks as well as the critical points of random networks with arbitrary degree distributions. Our results are of both fundamental and practical interest, as they offer a novel framework to relate the structure of networks to their dynamics and to study the resilience of complex systems.
  • PublicationAccès 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, Charles
    We 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.
  • PublicationAccès 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, Charles
    We 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.
  • PublicationAccès libre
    Exact analytical solution of irreversible binary dynamics on networks
    (American Physical Society, 2018-03-02) Young, Jean-Gabriel; Laurence, Edward; Melnik, Sergey; Dubé, Louis J.
    In binary cascade dynamics, the nodes of a graph are in one of two possible states (inactive, active), andnodes in the inactive state make an irreversible transition to the active state, as soon as their precursors satisfya predetermined condition. We introduce a set of recursive equations to compute the probability of reachingany final state, given an initial state, and a specification of the transition probability function of each node.Because the naive recursive approach for solving these equations takes factorial time in the number of nodes, wealso introduce an accelerated algorithm, built around a breath-first search procedure. This algorithm solves theequations as efficiently as possible in exponential time.
  • PublicationRestreint
    Deep learning of contagion dynamics on complex networks
    (Nature Publishing Group, 2021-08-05) Murphy, Charles; Laurence, Edward; Allard, Antoine
    Forecasting the evolution of contagion dynamics is still an open problem to which mechanistic models only offer a partial answer. To remain mathematically or computationally tractable, these models must rely on simplifying assumptions, thereby limiting the quantitative accuracy of their predictions and the complexity of the dynamics they can model. Here, we propose a complementary approach based on deep learning where effective local mechanisms governing a dynamic on a network are learned from time series data. Our graph neural network architecture makes very few assumptions about the dynamics, and we demonstrate its accuracy using different contagion dynamics of increasing complexity. By allowing simulations on arbitrary network structures, our approach makes it possible to explore the properties of the learned dynamics beyond the training data. Finally, we illustrate the applicability of our approach using real data of the COVID-19 outbreak in Spain. Our results demonstrate how deep learning offers a new and complementary perspective to build effective models of contagion dynamics on networks.