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Properties of Reduced Reversible Markov Chains

Please always quote using this URN: urn:nbn:de:0297-zib-10941
  • The enormous time lag between fast atomic motion and complex pro- tein folding events makes it almost impossible to compute molecular dy- namics on a high resolution. A common way to tackle this problem is to model the system dynamics as a Markov process. Yet for large molec- ular systems the resulting Markov chains can hardly be handled due to the curse of dimensionality. Coarse graining methods can be used to re- duce the dimension of a Markov chain, but it is still unclear how far the coarse grained Markov chain resembles the original system. In order to answer this question, two different coarse-graining methods were analysed and compared: a classical set-based reduction method and an alternative subspace-based approach, which is based on membership vectors instead of sets. On the basis of a small toy system, it could be shown, that in con- trast to the subset-based approach, the subspace-based reduction method preserves the Markov property as well as the essential dynamics of the original system.

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Metadaten
Author:Fiete Haack
Document Type:ZIB-Report
Tag:Conformation dynamics; Markov Chain; PCCA+
MSC-Classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J22 Computational methods in Markov chains [See also 65C40]
62-XX STATISTICS / 62-07 Data analysis
65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C40 Computational Markov chains
Advisor:Marcus Weber
Date of first Publication:2008/10/24
Series (Serial Number):ZIB-Report (08-42)
ISSN:1438-0064
ZIB-Reportnumber:08-42
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