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 give an algorithm that computes exact maximum flows and minimum-cost flows on
directed graphs with m edges and polynomially bounded integral demands, costs, and …

Many decision problems in science, engineering, and economics are affected by uncertain
parameters whose distribution is only indirectly observable through samples. The goal of …

While in principle exact, Kohn–Sham density functional theory—the workhorse of
computational chemistry—must rely on approximations for the exchange–correlation …

Optimal transport has recently been reintroduced to the machine learning community thanks
in part to novel efficient optimization procedures allowing for medium to large scale …

Computing optimal transport distances such as the earth mover's distance is a fundamental
problem in machine learning, statistics, and computer vision. Despite the recent introduction …

Cross-domain alignment between two sets of entities (eg, objects in an image, words in a
sentence) is fundamental to both computer vision and natural language processing. Existing …

Transport-based techniques for signal and data analysis have recently received increased
interest. Given their ability to provide accurate generative models for signal intensities and …

Multiplexed RNA sequencing in individual cells is transforming basic and clinical life
sciences,,–. Often, however, tissues must first be dissociated, and crucial information about …

Abstract Mean-Field Game (MFG) serves as a crucial mathematical framework in modeling
the collective behavior of individual agents interacting stochastically with a large population …