Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …

We review what is known, unknown, and expected about the mathematical properties of
Coulomb and Riesz gases. Those describe infinite configurations of points in R d interacting …

Spatial transcriptomic technologies and spatially annotated single-cell RNA sequencing
datasets provide unprecedented opportunities to dissect cell–cell communication (CCC) …

In this introductory chapter we first give a brief historical review of optimal transport, then we
recall some basic definitions and facts from measure theory and Riemannian geometry, and …

Encoding constraints into neural networks is attractive. This paper studies how to introduce
the popular positive linear satisfiability to neural networks. We propose the first differentiable …

With recent advances in multi-color super-resolution light microscopy, it is possible to
simultaneously visualize multiple subunits within biological structures at nanometer …

Finding node correspondence across networks, namely multi-network alignment, is an
essential prerequisite for joint learning on multiple networks. Despite great success in …

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 …

We study the complexity of approximating the multimarginal optimal transport (MOT)
distance, a generalization of the classical optimal transport distance, considered here …

The accuracy of modern machine learning algorithms deteriorates severely on adversarially
manipulated test data. Optimal adversarial risk quantifies the best error rate of any classifier …