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Hierarchical Uncoupling-Coupling of Metastable Conformations

  • Alexander Fischer
  • Christof Schütte
  • Peter Deuflhard
  • Frank Cordes
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 24)

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 met as t ability hierarchical annealing hybrid Monte Carlo n-pentane molecule ratio of normalizing constants reweighting uncoupling-coupling 

Mathematical Subject Classification

60J22 65C05 65C40 82B80 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Alexander Fischer
    • 1
  • Christof Schütte
    • 1
  • Peter Deuflhard
    • 1
    • 2
  • Frank Cordes
    • 2
  1. 1.Institut für Mathematik IIFreie Universität BerlinBerlinGermany
  2. 2.Konrad-Zuse-ZentrumBerlinGermany

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