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.
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 |