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 -