SC 98-03 Peter Deuflhard, Wilhelm Huisinga, Alexander Fischer, Christof Schütte: Identification of Almost Invariant Aggregates in Reversible
Nearly Uncoupled Markov Chains
Abstract: The topic of the present paper bas been motivated
by a recent computational approach to identify chemical conformations
and conformational changes within molecular systems.
After proper discretization, the conformations show up as almost invariant
aggregates in reversible nearly uncoupled Markov chains.
Most of the former work on this subject treated the direct problem:
given the aggregates, analyze the loose coupling in connection with
the computation of the stationary distribution (aggregation/disaggregation
techniques). In contrast to that the present paper focuses on the
inverse problem: given the system as a whole, identify the almost
invariant aggregates together with the associated transition probabilites.
A rather simple and robust algorithm is suggested and illustrated by its
application to the n-pentane molecule.
Keywords: essential molecular dynamics,
nearly reducible,
nearly completely decomposable,
nearly uncoupled Markov chain,
almost invariant aggregates,
transition probability
MSC: 15A18, 15A51, 60J10, 60J20, 65U05