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Personne :
Desrosiers, Patrick

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Desrosiers

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Patrick

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

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ncf11852206

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  • 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
    Threefold way to the dimension reduction of dynamics on networks : an application to synchronization
    (American Physical Society, 2020-11-11) Thibeault, Vincent; St-Onge, Guillaume; Dubé, Louis J.; Desrosiers, Patrick
    Several complex systems can be modeled as large networks in which the state of the nodes continuously evolves through interactions among neighboring nodes, forming a high-dimensional nonlinear dynamical system. One of the main challenges of Network science consists in predicting the impact of network topology and dynamics on the evolution of the states and, especially, on the emergence of collective phenomena, such as synchronization. We address this problem by proposing a Dynamics Approximate Reduction Technique (DART) that maps high-dimensional (complete) dynamics unto low-dimensional (reduced) dynamics while preserving the most salient features, both topological and dynamical, of the original system. DART generalizes recent approaches for dimension reduction by allowing the treatment of complex-valued dynamical variables, heterogeneities in the intrinsic properties of the nodes as well as modular networks with strongly interacting communities. Most importantly, we identify three major reduction procedures whose relative accuracy depends on whether the evolution of the states is mainly determined by the intrinsic dynamics, the degree sequence, or the adjacency matrix. We use phase synchronization of oscillator networks as a benchmark for our threefold method. We successfully predict the synchronization curves for three phase dynamics (Winfree, Kuramoto, theta) on the stochastic block model. Moreover, we obtain the bifurcations of the Kuramoto-Sakaguchi model on the mean stochastic block model with asymmetric blocks and we show numerically the existence of periphery chimera state on the two-star graph. This allows us to highlight the critical role played by the asymmetry of community sizes on the existence of chimera states. Finally, we systematically recover well-known analytical results on explosive synchronization by using DART for the Kuramoto-Sakaguchi model on the star graph. Our work provides a unifying framework for studying a vast class of dynamical systems on networks.
  • PublicationAccès libre
    Effects of global change on bird and beetle populations in boreal forest landscape : an assemblage dissimilarity analysis
    (Wiley-Blackwell Publishing Ltd., 2023-04-26) Labadie, Guillemette; Bouderbala, Ilhem; Béland, Jean-Michel; Boulanger, Yan; Hébert, Christian; Desrosiers, Patrick; Allard, Antoine; Fortin, Daniel
    Aim Despite an increasing number of studies highlighting the impacts of climate change on boreal species, the main factors that will drive changes in species assemblages remain ambiguous. We study how species community composition would change following anthropogenic and natural disturbances. We determine the main drivers of assemblage dissimilarity for bird and beetle communities. Location Côte-Nord, Québec, Canada. Methods We quantify two climate-induced pathways based on direct and indirect effects on species occurrence under different forest harvest management scenarios. The direct climate effects illustrate the impact of climate variables while the indirect effects are reflected through habitat-based climate change. We develop empirical models to predict the distribution of 127 and 108 species under climate-habitat and habitat-only models, respectively, over the next century. We analyse the regional and the latitudinal species assemblage dissimilarity by decomposing it into balanced variation in species occupancy and occurrence and occupancy and occurrence gradient. Results Both pathways increased dissimilarity in species assemblage. At the regional scale, both effects have an impact on decreasing the number of winning species. Yet, responses are much larger in magnitude under mixed climate effects. Regional assemblage dissimilarity reached 0.77 and 0.69 under mixed effects versus 0.09 and 0.10 under indirect effects for beetles and birds, respectively, between RCP8.5 and baseline climate scenarios when considering forest harvesting. Latitudinally, assemblage dissimilarity increased following the climate conditions pattern. Main conclusions The two pathways are complementary and alter biodiversity, mainly caused by species turnover. Yet, responses are much larger in magnitude under mixed climate effects. Therefore, inclusion of climatic variables considers aspects other than just those related to forest landscapes, such as life cycles of animal species. Moreover, we expect differences in occupancy between the two studied taxa. This could indicate the potential range of change in boreal species concerning novel environmental conditions.
  • PublicationAccès libre
    Counting hidden neural networks
    (Université de Waterloo (Canada), 2016-05-10) Young, Richard A.; Hardy, Simon; Doyon, Nicolas; Desrosiers, Patrick
    We apply combinatorial tools, including P´olya’s theorem, to enumerate all possible networks for which (1) the network contains distinguishable input and output nodes as well as partially distinguishable intermediate nodes; (2) all connections are directed and for each pair of nodes, there are at most two connections, that is, at most one connection per direction; (3) input nodes send connections but don’t receive any, while output nodes receive connections but don’t send any; (4) every intermediate node receives a path from an input node and sends a path to at least one output node; and (5) input nodes don’t send direct connections to output nodes. We first obtain the generating function for the number of such networks, and then use it to obtain precise estimates for the number of networks. Finally, we develop a computer algorithm that allows us to generate these networks. This work could become useful in the field of neuroscience, in which the problem of deciphering the structure of hidden networks is of the utmost importance, since there are several instances in which the activity of input and output neurons can be directly measured, while no direct access to the intermediate network is possible. Our results can also be used to count the number of finite automata in which each cell plays a relevant role.
  • PublicationAccès libre
    Dimension matters when modeling network communities in hyperbolic spaces
    (Oxford : National Academy of Sciences, 2023-04-18) Désy, Béatrice; Desrosiers, Patrick; Allard, Antoine
    Over the last decade, random hyperbolic graphs have proved successful in providing geometric explanations for many key properties of real-world networks, including strong clustering, high navigability, and heterogeneous degree distributions. These properties are ubiquitous in systems as varied as the internet, transportation, brain or epidemic networks, which are thus unified under the hyperbolic network interpretation on a surface of constant negative curvature. Although a few studies have shown that hyperbolic models can generate community structures, another salient feature observed in real networks, we argue that the current models are overlooking the choice of the latent space dimensionality that is required to adequately represent clustered networked data. We show that there is an important qualitative difference between the lowest-dimensional model and its higher-dimensional counterparts with respect to how similarity between nodes restricts connection probabilities. Since more dimensions also increase the number of nearest neighbors for angular clusters representing communities, considering only one more dimension allows us to generate more realistic and diverse community structures.
  • PublicationAccès libre
    Long-term effect of forest harvesting on boreal species assemblages under climate change
    (Public Library of Science, 2023-03-15) Bouderbala, Ilhem; Labadie, Guillemette; Béland, Jean-Michel; Tremblay, Junior A.; Boulanger, Yan; Hébert, Christian; Desrosiers, Patrick; Allard, Antoine; Fortin, Daniel
    Logging is the main human disturbance impacting biodiversity in forest ecosystems. However, the impact of forest harvesting on biodiversity is modulated by abiotic conditions through complex relationships that remain poorly documented. Therefore, the interplay between forest management and climate change can no longer be ignored. Our aim was to study the expected long-term variations in the assemblage of bird and beetle communities following modifications in forest management under different climate change scenarios. We developed species distribution models to predict the occurrence of 88 species of birds and beetles in eastern Canadian boreal forests over the next century. We simulated three climate scenarios (baseline, RCP4.5 and RCP8.5) under which we varied the level of harvesting. We also analyzed the regional assemblage dissimilarity by decomposing it into balanced variations in species occupancy and occupancy gradient. We predict that forest harvesting will alter the diversity by increasing assemblage dissimilarity under all the studied climate scenarios, mainly due to species turnover. Species turnover intensity was greater for ground-dwelling beetles, probably because they have lower dispersal capacity than flying beetles or birds. A good dispersal capacity allows species to travel more easily between ecosystems across the landscape when they search for suitable habitats after a disturbance. Regionally, an overall increase in the probability of occupancy is projected for bird species, whereas a decrease is predicted for beetles, a variation that could reflect differences in ecological traits between taxa. Our results further predict a decrease in the number of species that increase their occupancy after harvest under the most severe climatic scenario for both taxa. We anticipate that under severe climate change, increasing forest disturbance will be detrimental to beetles associated with old forests but also with young forests after disturbances.
  • PublicationAccès 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, Patrick
    Mesoscopic 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.
  • PublicationAccès libre
    Dimension reduction of dynamics on modular and heterogeneous directed networks
    (Oxford University Press, 2023-05-02) Vegué, Marina; Thibeault, Vincent; Desrosiers, Patrick; Allard, Antoine
    Dimension reduction is a common strategy to study nonlinear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of the key dynamical features of the original system. Finding such a reduced representation for complex systems is, however, a difficult task. We address this problem for dynamics on weighted directed networks, with special emphasis on modular and heterogeneous networks. We propose a two-step dimension-reduction method that takes into account the properties of the adjacency matrix. First, units are partitioned into groups of similar connectivity profiles. Each group is associated to an observable that is a weighted average of the nodes' activities within the group. Second, we derive a set of equations that must be fulfilled for these observables to properly represent the original system's behavior, together with a method for approximately solving them. The result is a reduced adjacency matrix and an approximate system of ODEs for the observables' evolution. We show that the reduced system can be used to predict some characteristic features of the complete dynamics for different types of connectivity structures, both synthetic and derived from real data, including neuronal, ecological, and social networks. Our formalism opens a way to a systematic comparison of the effect of various structural properties on the overall network dynamics. It can thus help to identify the main structural driving forces guiding the evolution of dynamical processes on networks.
  • PublicationAccès libre
    Sensory afferents use different coding strategies for heat and cold
    (Cell Press, 2018-05-15) Bélanger, Erik; De Koninck, Yves; Côté, Sylvain L.; Wang, Feng; Côté, Daniel; Prescott, Steven A.; Desrosiers, Patrick
    Primary afferents transduce environmental stimuli into electrical activity that is transmitted centrally to be decoded into corresponding sensations. However, it remains unknown how afferent populations encode different somatosensory inputs. To address this, we performed two-photon Ca2+ imaging from thousands of dorsal root ganglion (DRG) neurons in anesthetized mice while applying mechanical and thermal stimuli to hind paws. We found that approximately half of all neurons are polymodal and that heat and cold are encoded very differently. As temperature increases, more heating-sensitive neurons are activated, and most individual neurons respond more strongly, consistent with graded coding at population and single-neuron levels, respectively. In contrast, most cooling-sensitive neurons respond in an ungraded fashion, inconsistent with graded coding and suggesting combinatorial coding, based on which neurons are co-activated. Although individual neurons may respond to multiple stimuli, our results show that different stimuli activate distinct combinations of diversely tuned neurons, enabling rich population-level coding.