Almost invariant sets are regions in phase space
for which there is a small probability that
trajectories entering such a subset will leave
that subset in a short period of time. Thus, these subsets
define
macroscopic structures preserved by the
dynamical process which 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 graph theoretic approaches
for solving this optimization problem. Particular
attention is paid to the use of the congestion and
spectral properties of the underlying graph. This is joint
work with Gary Froyland (BHP Billiton, Australia)
and Robert Preis (University of Paderborn, Germany).
