“Density flows and applications”
Dr. Tryphon Georgiou, UC Irvine
Wednesday, February 8, 2017 2:00 - 3:00PM EEB 248
Abstract: We will discuss the relation between Optimal Mass Transport (OMT) and the Schroedinger's Bridge Problem (SBP). OMT was formulated by Gaspar Monge in 1781, recast as a linear program by L. Kantorovich in the 1940's, and reformulated as a density-flow problem by Benamou and Brenier in the 1990's–it has since been the cornerstone of several developments in physics, econometrics, probability theory, and many other fields. On the other hand, the SBP was introduced by Erwin Schroedinger in 1931 in an attempt to explain Quantum Mechanics in a classical manner. OMT and SBP can be seen as the problems to control the Liouville and Fokker-Planck equations, respectively. We will highlight the connection between the two, present a numerical scheme for their solution based on a fixed-point iteration (Sinkhorn-like), and highlight the relevance of the two in the control of particle ensembles, thermodynamic systems, flows of power spectra, morphing of images, and the transport of resources over networks. Finally we will discuss Quantum Mechanical density flows and show that the Lindblad equation of open quantum systems represents in a similar manner a ``non-commutative'' density flow. The talk is based on joint works with Yongxin Chen (MSKCC), Michele Pavon (University of Padova), and Allen Tannenbaum (Stony Brook).
Bio: Tryphon T. Georgiou received the Diploma in Mechanical and Electrical Engineering from the National Technical University of Athens, Greece, in 1979, and the Ph.D. degree from the University of Florida, Gainesville, in 1983. He served on the faculty of Florida Atlantic University (1983-86), Iowa State University (1986-89) and the University of Minnesota (1989-2016). At Minnesota he was the Hermes-Luh Chair in Electrical Engineering (2002-2016) and the co-director (together with Gary Balas) of the Control Science and Dynamical Systems Center (1990-2016). He is currently a UCI Chancellor's Professor in Mechanical and Aerospace Engineering at the University of California, Irvine. He has served on the Board of Governors of the Control Systems Society of the IEEE (2002-2005), and as a member on several Editorial Boards (IEEE Trans. on Automatic Control, IEEE Trans. on Signal Processing, IMA Journal of Mathematical Control and Information, SIAM Journal on Control and Optimization, Systems and Control Letters). He has been a co-recipient of the George S. Axelby Outstanding Paper award of the IEEE Control Systems Society three times, for the years 1992, 1999, and 2003. He is a Fellow of the Institute of Electrical and Electronic Engineers (IEEE), a Fellow of the International Federation of Automatic Control (IFAC), and a Foreign Member of the Royal Swedish Academy of Engineering Sciences (IVA).