Zobrazeno 1 - 10
of 962
pro vyhledávání: '"Arnaudon, A"'
Given a family of rotationally symmetric compact manifolds indexed by the dimension and a weight function, the goal of this paper is to investigate the cut-off phenomenon for the Brownian motions on this family. We provide a class of compact manifold
Externí odkaz:
http://arxiv.org/abs/2409.19997
Inspired by Y. Ollivier's coarse Ricci curvature, we introduce a novel concept of coarse extrinsic curvature on Riemannian submanifolds. This is defined through Wasserstein distances between test probability measures supported in the tubular neighbou
Externí odkaz:
http://arxiv.org/abs/2407.08031
We propose a new simple construction of a coupling at a fixed time of two sub-Riemannian Brownian motions on the Heisenberg group and on the free step 2 Carnot groups. The construction is based on a Legendre expansion of the standard Brownian motion
Externí odkaz:
http://arxiv.org/abs/2407.04321
Publikováno v:
Geometric Science of Information 2017, 2017, Paris, France
This paper is concerned with the computation of an optimal matching between two manifold-valued curves. Curves are seen as elements of an infinite-dimensional manifold and compared using a Riemannian metric that is invariant under the action of the r
Externí odkaz:
http://arxiv.org/abs/2401.04743
Autor:
Nurisso, Marco, Arnaudon, Alexis, Lucas, Maxime, Peach, Robert L., Expert, Paul, Vaccarino, Francesco, Petri, Giovanni
Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified framework to describe different variants of these models, categorized into
Externí odkaz:
http://arxiv.org/abs/2305.17977
Autor:
Gosztolai, Adam, Peach, Robert L., Arnaudon, Alexis, Barahona, Mauricio, Vandergheynst, Pierre
The dynamics of neuron populations commonly evolve on low-dimensional manifolds. Thus, we need methods that learn the dynamical processes over neural manifolds to infer interpretable and consistent latent representations. We introduce a representatio
Externí odkaz:
http://arxiv.org/abs/2304.03376
We investigate renormalized curvature flow (RCF) and stochastic renormalized curvature flow (SRCF) for convex sets in the plane.RCF is the gradient descent flow for logarithm of $\sigma/\lambda^2$ where $\sigma$ is the perimeter and $\lambda$ is the
Externí odkaz:
http://arxiv.org/abs/2303.07921
Autor:
Arnaudon, Alexis, Schindler, Dominik J., Peach, Robert L., Gosztolai, Adam, Hodges, Maxwell, Schaub, Michael T., Barahona, Mauricio
We present PyGenStability, a general-use Python software package that provides a suite of analysis and visualisation tools for unsupervised multiscale community detection in graphs. PyGenStability finds optimized partitions of a graph at different le
Externí odkaz:
http://arxiv.org/abs/2303.05385
We show that the generalized Ricci tensor of a weighted complete Riemannian manifold can be retrieved asymptotically from a scaled metric derivative of Wasserstein 1-distances between normalized weighted local volume measures. As an application, we d
Externí odkaz:
http://arxiv.org/abs/2303.04228
The stability analysis of possibly time varying positive semigroups on non necessarily compact state spaces, including Neumann and Dirichlet boundary conditions is a notoriously difficult subject. These crucial questions arise in a variety of areas o
Externí odkaz:
http://arxiv.org/abs/2301.03484