Detection of almost invariant sets, graphs and molecular conformations

Michael Dellnitz, Professor of Applied Mathematics, University of Paderborn, Germany

For a dynamical system an almost invariant set is a region in phase space for which there is a small probability that trajectories entering such a subset will leave that subset in a short time. Thus, these subsets define macroscopic structures preserved by the dynamical process and these structures correspond to conformations in the context of molecular dynamics. Almost invariant sets can be identified in two steps: first the dynamical behavior is approximated by a Markov chain; second the detection of almost invariant sets is done by finding minimal cuts in the associated graph. In this talk we will discuss different techniques for solving this optimization problem. One basic ingredient is to use the Perron cluster analysis in combination with graph theoretic algorithms for finding minimal cuts. This is joint work with Gary Froyland (BHPBilliton Minerals Discovery Technologies, Melbourne, Australia) and Robert Preis (Sandia National Laboratories, Albuquerque).