On Reversible Markov Chains and Maximization of Directed Information

Thursday, March 11, 2010
ENS 637

Time reversibility plays an important role in disciplinesconcerning dynamical systems, e.g. in physics, statistical mechanics,stochastic processes, and biology. However, its use inproviding information-theoretic fundamental limits appears tobe somewhat limited. Recent developments at the intersectionof information theory and control have demonstrated howdirected information characterizes fundamentallimitations of stochastic systems with dynamics.In this talk, we connect time reversibility of Markov chainsto maximization of directed information for a classof stochastic dynamical systems. With this framework, wecharacterize the capacity of a class channels with (infinite) memoryand provide optimality "matching " conditions for sequential sequentialestimation of a random process over a communication channel withfeedback. Examples include communication over queuing timing channelsas well as Blackwell 's trapdoor (chemical) channel, along withsequential estimation within the context of decentralized control.



Fellow Appointment

Todd P. Coleman received the B.S. degrees in electrical engineering(summa cum laude), as well as computer engineering (summa cum laude)from the University of Michigan, Ann Arbor, in 2000, along with the M.S.and Ph.D. degrees in electrical engineering from the MassachusettsInstitute of Technology (MIT), Cambridge, in 2002, and 2005. During the2005-2006 academic year, he was a postdoctoral scholar at MIT andMassachusetts General Hospital in computational neuroscience. Since thefall of 2006, he has been on the faculty in the ECE Department andNeuroscience Program at UIUC.

His research interests include information theory, operations research,and computational neuroscience. Dr. Coleman, a National ScienceFoundation Graduate Research Fellowship recipient, was awarded theUniversity of Michigan College of Engineering's Hugh Rumler Senior ClassPrize in 1999 and was awarded the MIT EECS Department's Morris J. LevinAward for Best Masterworks Oral Thesis Presentation in 2002. In Fall2008, he was a co-recipient of the University of Illinois College of Engineering's Grainger Award in Emerging Technologies for development ofa novel, practical timing-based technology. Beginning Fall 2009, Colemanhas served as a co-Principal Investigator on an NSF IGERTinterdisciplinary training grant for graduate students, titled "Neuro-engineering: A Unified Educational Program for SystemsEngineering and Neuroscience ". Coleman also has been serving on the DARPA ISAT study group for a 3-year term, beginning Fall 2009. Recently he has been selected for a Fellow appointment with the University o fIllinois Center for Advanced Study (CAS) for the 2010-2011 academicyear, pending approval of the Board of Trustees.