93 citations · 766 across the 42 of their papers we have counts for
6 papers · 1 filter
The determining role of covariances in large networks of stochastic neurons
Vincent Painchaud, Patrick Desrosiers, Nicolas Doyon
Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both…
Dimension matters when modeling network communities in hyperbolic spaces
Béatrice Désy, Patrick Desrosiers, Antoine Allard
Over the last decade, random hyperbolic graphs have proved successful in providing geometric explanations for many key properties of real-world networks, including strong clusterin…
The low-rank hypothesis of complex systems
Vincent Thibeault, Antoine Allard, Patrick Desrosiers
Complex systems are high-dimensional nonlinear dynamical systems with intricate interactions among their constituents. To make interpretable predictions about their large-scale beh…
Dimension reduction of dynamics on modular and heterogeneous directed networks
Marina Vegué, Vincent Thibeault, Patrick Desrosiers +1
Dimension reduction is a common strategy to study non-linear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose ti…
Duality between predictability and reconstructability in complex systems
Charles Murphy, Vincent Thibeault, Antoine Allard +1
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing th…
Beyond Wilson-Cowan dynamics: oscillations and chaos without inhibition
Vincent Painchaud, Nicolas Doyon, Patrick Desrosiers
Fifty years ago, Wilson and Cowan developed a mathematical model to describe the activity of neural populations. In this seminal work, they divided the cells in three groups: activ…