In this paper, we survey the primary research on the theory and applications of
distributionally robust optimization (DRO). We start with reviewing the modeling power and …

Heuristically, a discrete-time stochastic process has the Markov property if the past and
future are independent given the present. In this introductory chapter, we give the formal …

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 …

Learning to predict multi-label outputs is challenging, but in many problems there is a
natural metric on the outputs that can be used to improve predictions. In this paper we …

Why a new book on optimal transport? Were the two books by Fields Medalist Cédric Villani
not enough? And what about the Bible of Gradient Flows, the book by Luigi Ambrosio …

This book gives an exposition of the principal concepts and results related to second order
elliptic and parabolic equations for measures, the main examples of which are Fokker …

Now back in print by the AMS, this is a significantly revised edition of a book originally
published in 1987 by Academic Press. This book gives the reader an introduction to the …

We present a bouquet of continuity bounds for quantum entropies, falling broadly into two
classes: first, a tight analysis of the Alicki–Fannes continuity bounds for the conditional von …

We present a fascinating model that has lately caught attention among physicists working in
complexity related fields. Though it originated from mathematics and later from economics …

Free-hand sketches are highly illustrative, and have been widely used by humans to depict
objects or stories from ancient times to the present. The recent prevalence of touchscreen …