We study a class of nonlocal partial differential equations presenting a tensor-mobility, in
space, obtained asymptotically from nonlocal dynamics on localising infinite graphs. Our …

Lipschitz learning is a graph-based semisupervised learning method where one extends
labels from a labeled to an unlabeled data set by solving the infinity Laplace equation on a …

In this paper we prove Gamma-convergence of a nonlocal perimeter of Minkowski type to a
local anisotropic perimeter. The nonlocal model describes the regularizing effect of …

Let $\mathcal {M}\subseteq\mathbb {R}^ d $ denote a low-dimensional manifold and let
$\mathcal {X}=\{x_1,\dots, x_n\} $ be a collection of points uniformly sampled from $\mathcal …

Ratio convergence rates for Euclidean first-passage percolation: Applications to the graph
infinity Laplacian Page 1 The Annals of Applied Probability 2024, Vol. 34, No. 4, 3870–3910 …

Laplace learning is a popular machine learning algorithm for finding missing labels from a
small number of labeled feature vectors using the geometry of a graph. More precisely …

In this paper we prove discrete to continuum convergence rates for Poisson Learning, a
graph-based semi-supervised learning algorithm that is based on solving the graph Poisson …

Motivated by applications in data science, we study partial differential equations on graphs.
By a classical fixed-point argument, we show existence and uniqueness of solutions to a …

Higher-order regularization problem formulations are popular frameworks used in machine
learning, inverse problems and image/signal processing. In this paper, we consider the …

We propose a monotone and consistent numerical scheme for the approximation of the
Dirichlet problem for the normalized infinity Laplacian, which could be related to the family of …