This chapter describes techniques for the numerical resolution of optimal transport
problems. We will consider several discretizations of these problems, and we will put a …

Network science is the field dedicated to the investigation and analysis of complex systems
via their representations as networks. We normally model such networks as graphs: sets of …

We propose a technique for interpolating between probability distributions on discrete
surfaces, based on the theory of optimal transport. Unlike previous attempts that use linear …

Optimal transportation provides a means of lifting distances between points on a geometric
domain to distances between signals over the domain, expressed as probability …

Many tools from discrete differential geometry (DDG) were inspired by practical
considerations in areas like computer graphics and vision. Disciplines like these require fine …

We describe a problem in complex networks we call the Node Vector Distance (NVD)
problem, and we survey algorithms currently able to address it. Complex networks are a …

We consider dynamical transport metrics for probability measures on discretizations of a
bounded convex domain in \mathbbR^d. These metrics are natural discrete counterparts to …

We consider the problem of minimizing the entropy of a law with respect to the law of a
reference branching Brownian motion under density constraints at an initial and final time …

Finding meaningful ways to measure the statistical dependency between random variables
$\xi $ and $\zeta $ is a timeless statistical endeavor. In recent years, several novel concepts …

The dynamical formulation of optimal transport, also known as Benamou–Brenier
formulation or computational fluid dynamics formulation, amounts to writing the optimal …