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 …

In 1931--1932, Erwin Schrödinger studied a hot gas Gedankenexperiment (an instance of
large deviations of the empirical distribution). Schrödinger's problem represents an early …

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 …

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

Complex disordered matter is of central importance to a wide range of disciplines, from
bacterial colonies and embryonic tissues in biology to foams and granular media in …

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 …

Graph kernels are widely used for measuring the similarity between graphs. Many existing
graph kernels, which focus on local patterns within graphs rather than their global …

We study the nonlinear Fokker-Planck equation on graphs, which is the gradient flow in the
space of probability measures supported on the nodes with respect to the discrete …

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 …