It is increasingly common to encounter data in the form of cross-sectional population
measurements over time, particularly in biomedical settings. Recent attempts to model …

With the advent of high-throughput single-cell measurement technologies, the daunting
prospect of charting Waddington's landscape is coming within reach. This holds tremendous …

It is a crucial challenge to reconstruct population dynamics using unlabeled samples from
distributions at coarse time intervals. Recent approaches such as flow-based models or …

We devise a theoretical framework and a numerical method to infer trajectories of a
stochastic process from samples of its temporal marginals. This problem arises in the …

The dynamical formulation of the optimal transport can be extended through various choices
of the underlying geometry ($\textit {kinetic energy} $), and the regularization of density …

Optimal transportation, modelling and numerical simulation Optimal transportation, modelling
and numerical simulation Abstract We present an overviewof the basic theory, modern optimal …

We extend the recently introduced genetic column generation algorithm for high-
dimensional multimarginal optimal transport from symmetric to general problems. We use …

We propose a new method for smoothly interpolating probability measures using the
geometry of optimal transport. To that end, we reduce this problem to the classical Euclidean …

We consider the problems of tracking an ensemble of indistinguishable agents with linear
dynamics based only on output measurements. In this setting, the dynamics of the agents …

Our account begins in 1931/1932, when one of the fathers of quantum theory, Erwin
Schrodinger, proposed a Gedankenexperiment to comprehend the propagation of a cloud of …