## A Subspace Approach to Molecular Markov State Models via a New Infinitesimal Generator

Please always quote using this URN: urn:nbn:de:0297-zib-14025

- Supercomputers can simulate complex molecular systems. However, there is a very large gap between the fastest oscillations of covalent bonds of a molecule and the time-scale of the dominant processes. In order to extract the dominant time-scales and to identify the dominant processes, a clustering of information is needed. This thesis shows that only the subspace-based Robust Perron Cluster Analysis (PCCA+) can solve this problem correctly by the construction of a Markov State Model. PCCA+ allows for time-extrapolation in molecular kinetics. This thesis shows the difference between molecular dynamics and molecular kinetics. Only in the molecular kinetics framework a definition of transition rates is possible. In this context, the existence of an infinitesimal generator of the dynamical processes is discussed. If the existence is assumed, the Theorem of Gauß can be applied in order to compute transition rates efficiently. Molecular dynamics, however, is not able to provide a suitable statistical basis for the determination of the transition pattern.

Author: | Marcus Weber |
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Document Type: | Habilitation |

Tag: | Conformation Dynamics; Markov State Models; Molecular Kinetics; Transition Rates |

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 / 60J25 Continuous-time Markov processes on general state spaces |

62-XX STATISTICS / 62Hxx Multivariate analysis [See also 60Exx] / 62H30 Classification and discrimination; cluster analysis [See also 68T10] | |

82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Bxx Equilibrium statistical mechanics / 82B30 Statistical thermodynamics [See also 80-XX] | |

Granting Institution: | Freie Universität Berlin |

Date of final exam: | 2011/07/13 |

Publishing Institution: | Zuse Institute Berlin (ZIB) |

Date of first Publication: | 2011/09/15 |

Licence (German): | Creative Commons - Namensnennung-Keine kommerzielle Nutzung-Weitergabe unter gleichen Bedingungen |