Abstract of the Talk
The distribution of signals such as spike trains is naturally modeled through stochastic processes where the probability of future states depend on the pattern of past spikes. Mathematically, this corresponds to distributions *conditioned on the past*. From a signal-theoretic point of view, however, one could wonder whether a more efficient description could be obtained through the simultaneous conditioning of past *and* future. Furthermore, such a formalism could be appropriate when discussing string without a particular “time” order, such as the distribution of DNA nucleotides, or even issues related to anticipation and prediction in neuroscience. On the mathematical level this double conditioning would correspond to a Gibbsian description analogous to the one adopted in statistical mechanics. In this talk I will introduce and contrast both approaches ---process and Gibbsian based--- reviewing existing results on scope and limitations of them.
Biography
Master in Physics from the University of Buenos Aires and PhD in Mathematics from Virginia Tech. His work focuses on rigorous statistical mechanics and the theory of stochastic processes. He has hold positions in Rutgers University, University of Texas at Austin, Zurich Polytechnic Institute, Lausanne Polytechnic Institute, Princeton University (as part of a Guggenheim fellowship), Argentinian Research Agency (Conicet) and University of Sao Paulo. He has hold professorships at the Universities of Rouen (France) and of Utrecht (The Netherlands). He is currently a long-term visiting professorship at NYUSH.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai