Preprint No.
A-01-08
Alexander Fischer, Christoph Schütte, Peter Deuflhard, Frank Cordes
Hierarchical Coupling-Uncoupling of Metastable
Conformations
Abstract:
Uncoupling-coupling Monte Carlo (UCMC) combines uncoupling
techniques for finite Markov chains with Markov chain Monte Carlo
methodology. UCMC aims at avoiding the typical metastable or
trapping behavior of Monte Carlo techniques. From the viewpoint of
Monte Carlo, a slowly converging long-time Markov chain is replaced
by a limited number of rapidly mixing short-time ones. Therefore,
the state space of the chain has to be hierarchically decomposed
into its metastable conformations. This is done by means of
combining the technique of conformation analysis as recently
introduced by the authors, and appropriate annealing strategies. We
present a detailed examination of the uncoupling-coupling procedure
which uncovers its theoretical background, and illustrates the
hierarchical algorithmic approach. Furthermore, application of the
UCMC algorithm to the $n$-pentane molecule allows us to discuss the
effect of its crucial steps in a typical molecular scenario.
Keywords:
almost invariant sets, bridge sampling,
metastability, hierarchical annealing, hybrid Monte Carlo,
$n$-pentane molecule, ratio of normalizing constants, reweighting,
uncoupling-coupling
Mathematics Subject Classification
(MSC2000):
60J22, 65C05, 65C40, 82B80
Language: ENG
Available: Pr-A-01-08.ps
Pr-A-01-08.ps.gz
Contact: Alexander Fischer, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (alexander.fischer@math.fu-berlin.de)
[Home Page] - [Up] - [Search] - [Help] - Created: 20010417 -