Seminar by Manoj Gopalkrishnan
Chemical reaction networks: a generalization of Markov chains
Manoj Gopalkrishnan
TIFR
Date: Wednesday, June 27th, 2012
Time: 4PM
Venue: CS101.Abstract:
Chemical reaction networks appear not just in the study of chemistry, but also in distributed systems as Petri nets, in computer science as quadratic dynamical systems, and in algebraic statistics as toric statistical models. I hope to argue that chemical reaction networks are objects of intrinsic mathematical interest, and that their study may be of value to systems engineers.
A chemical reaction network is a Markov chain embedded in a lattice of the positive integers. The time evolution is nonlinear, and allows all sorts of wild behavior including multiple equilibria, periodic orbits, chaotic motion, etc. However, under fairly mild assumptions, several properties of Markov chains like detailed balance, relative entropy, etc. can be generalized for this larger class, while some other properties remain open problems. For example, an analog of the Perron-Frobenius theorem for detailed-balanced chemical reaction networks, which is called the Global Attractor Conjecture in the chemical reaction community, has been open since 1972.
My talk will be at a tutorial level, intended to introduce the audience to the basic results and open problems in the area. The presentation will be mostly self-contained, except for an occasional appeal to Information Theory.