Week 3: Optimal Mass Transport and Distributed Systems

Monday, June 9, 2014 - 7:00am - 9:00pm
Svetlozar (Zari) Rachev (State University of New York, Stony Brook (SUNY)), Allen Tannenbaum (State University of New York, Stony Brook (SUNY))
Allen Tannenbaum will be speaking on the theme of Optimal Mass Transport for Problems in Systems, Control, and Signal Processing. The lectures will be based on a number of published papers as well as lecture notes. He will lead participants through basic methods in the calculus of variations for the classical solution of the Monge-Kantorovich problem as well as the Monge-Ampere equation. He will then describe some newer, partial differential equation approaches. This will lead to a Riemannian structure on spaces of probability densities that allows one in turn to define a notion of curvature on rather general metric measure spaces. Applications to medical image processing, signal processing, control, and large networks will be provided.

Svetlozar Rachev will speak on the theme of Monge-Kantorovich Mass Transference Problem and Theory of Probability Metrics. The Monge-Kantorovich and the Kantorovich-Rubinstein problems are introduced and illustrated in a one-dimensional and multidimensional setting. These problems - more commonly referred to as the mass transportation and mass transshipment problems, respectively - are abstract formulations of optimization problems. Although the applications are important in areas such as job assignments, classification problems, and best allocation policy, our purpose will be their application to the Theory of Probability Metrics (TPM).