POSTA 2012 - September 2nd-4th, 2012
The 4th International Symposium on Positive Systems
The plenary talks form a central part of the symposium and we are delighted to have managed to line up a distinguished group of speakers for the event this coming September. Abstracts for the plenary talks at POSTA 2012 are given below.
Professor Persi Diaconis, Stanford University
"Who Needs Positivity?"
Positivity is a basic aspect of all probability. Yet, one may ask, what aspects of basic theorems (e.g., the central limit theorem or Perron-Frobenius) remain without positivity. It turns out that lots remains, and some new things emerge. Another question: "Who cares?" It turns out that the study of convolutions of signed measures is important in statistical data smoothing algorithms, super kernels in stability analysis for standard schemes for running differential equations and elsewhere. There is still much to do and I hope that the POSTA community will join me in exploring the question. This is joint work with Laurent Saloff-Coste.
Professor Ludwig Elsner, University of Bielefeld
"Some applications of max-algebra and Perron-Frobenius"
To fit this topic in the title of this conference, we will speak here about nonnegative matrices and vectors with the usual multiplication and the addition replaced by the max operation. This is the so-called max-algebra. Clearly all results can be transformed into results about the max-plus algebra. The Perron-Frobenius theorem gives in this case the existence of the max eigenvalue and a max eigenvector of a nonnegative matrix. We will speak here about applications of these magnitudes in various fields. Many results are from joint work with Pauline van den Driessche
Professor Josef Hofbauer, University of Vienna.
"Evolutionary Game Dynamics"
I will give a survey about deterministic evolutionary dynamics for finite games, in particular, the replicator dynamics, the best response dynamics, and its smooth perturbations. For special classes of games, such as stable games, supermodular games, and partnership games, stability and convergence results are discussed.