Unbalanced Multi-marginal Optimal Transport

Curvature of Hypergraphs via Multi-Marginal Optimal Transport

We introduce a novel definition of curvature for hypergraphs, a natural generalization of graphs, by introducing a multimarginal optimal transport problem for a naturally defined random walk on the hypergraph. This curvature, termed coarse scalar curvature, generalizes a recent definition of Ricci curvature for Markov chains on metric spaces by Ollivier [Journal of Functional Analysis 256 (2009...

Decoupling of DeGiorgi-type systems via multi-marginal optimal transport∗

We exhibit a surprising relationship between elliptic gradient systems of PDEs, multi-marginal MongeKantorovich optimal transport problem, and multivariable Hardy-Littlewood inequalities. We show that the notion of an orientable elliptic system, conjectured in [6] to imply that (in low dimensions) solutions with certain monotonicity properties are essentially 1-dimensional, is equivalent to the...

Eulerian models and algorithms for unbalanced optimal transport

Tomographic Reconstruction from a Few Views: A Multi-Marginal Optimal Transport Approach

In this article, we focus on tomographic reconstruction. The problem is to determine the shape of the interior interface using a tomographic approach while very few X-ray radiographs are performed. We use a multi-marginal optimal transport approach. Preliminary numerical results are presented.

Multi-Robot Marginal-SLAM

This paper has two goals. First, it expands the presentation of the marginal particle filter for SLAM proposed recently in [Martinez-Cantin et al., 2006]. In particular, it presents detailed pseudo-code to enable practitioners to implement the algorithm easily. Second, it proposes an extension to the multirobot setting. In the marginal representation, the robots share a common map and their loc...