no code implementations • 15 Feb 2023 • Imane Akjouj, Walid Hachem, Mylène Maïda, Jamal Najim
Ecosystems with a large number of species are often modelled as Lotka-Volterra dynamical systems built around a large random interaction matrix.
no code implementations • 12 Dec 2022 • Imane Akjouj, Matthieu Barbier, Maxime Clenet, Walid Hachem, Mylène Maïda, François Massol, Jamal Najim, Viet Chi Tran
Ecosystems represent archetypal complex dynamical systems, often modelled by coupled differential equations of the form $$ \frac{d x_i}{d t} = x_i \varphi_i(x_1,\cdots, x_N)\ , $$ where $N$ represents the number of species and $x_i$, the abundance of species $i$.
no code implementations • 4 Aug 2021 • Pascal Bianchi, Walid Hachem, Sholom Schechtman
Consequently, generically in the class of definable weakly convex functions, the SGD converges to a local minimizer.
no code implementations • 23 Jan 2019 • Pascal Bianchi, Walid Hachem, Adil Salim
The proposed algorithm is proven to converge to a saddle point of the Lagrangian function.
no code implementations • 3 Apr 2018 • Adil Salim, Pascal Bianchi, Walid Hachem
The Douglas Rachford algorithm is an algorithm that converges to a minimizer of a sum of two convex functions.
no code implementations • 19 Dec 2017 • Adil Salim, Pascal Bianchi, Walid Hachem
When applying the proximal gradient algorithm to solve this problem, there exist quite affordable methods to implement the proximity operator (backward step) in the special case where the graph is a simple path without loops.