Please join us for the next CSE Seminar in the conference room, 2 MetroTech, 10th floor, 10.099.
Speaker: Dr. Yongxin Chen, Memorial Sloan Kettering Cancer Center
The study of densities and density flows is a rich area both theoretically and practically. Densities may describe the collective response of dynamical systems as well as the distribution of resources, image intensities, and power, and thus are key in a wide range of applications. I will present several recent developments in the subject. More specifically, I will cover two interrelated basic topics i) control of collective dynamics, ii) matrix-valued optimal mass transport. In both, the central task is to estimate, compare and control distributions. The first topic, concerns the steering of a particle system from an initial distribution to a final one over a specified finite time-window with minimum-energy control. It turns out that this is closely related to Optimal Mass Transport (OMT) and to a problem in probability theory with deep physical roots known as the Schrodinger bridge problem (SBP). Recognizing that both OMT and SBP, are in essence control problems allows the development of a substantially broader theory. Our second topic is a far reaching generalization of OMT to the novel setting of matrix-valued densities. Our original motivation aimed at developing tools for multivariate time series modeling and matrix-valued power spectral analysis. However, the emergent theory turned out to have immediate applications in diffusion tensor imaging (DTI) where ``images'' are now tensor fields representing orientation and shape of brain white-matter tracts. Thus, the framework I have developed and will present allows us to compare, interpolate and fuse DTI images in a rigorous manner and, thereby, may lead to high resolution advances that in turn promise improved in vivo imaging of important brain structures.
Yongxin Chen received his BSc in Mechanical Engineering from Shanghai Jiao Tong University, China, in 2011. He obtained his Ph.D. in Mechanical Engineering from University of Minnesota in 2016 under the supervision of Tryphon Georgiou, with a Ph.D. minor in Mathematics. He is now a postdoctoral researcher in the Department of Medical Physics at Memorial Sloan Kettering cancer center. He is interested in the application of mathematics in engineering, physics, economics and biology. His current research focuses on control theory, stochastic processes and optimal mass transport theory.