Repository: Freie Universität Berlin, Math Department

Finding dominant structures of nonreversible Markov processes

Djurdjevac, N. and Weber, M. and Schütte, Ch. (2016) Finding dominant structures of nonreversible Markov processes. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 14 (4). pp. 1319-1340. ISSN 1540-3459

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Finding metastable sets as dominant structures of Markov processes has been shown to be especially useful in modeling interesting slow dynamics of various real world complex processes. Furthermore, coarse graining of such processes based on their dominant structures leads to better understanding and dimension reduction of observed systems. However, in many cases, e.g. for nonreversible Markov processes, dominant structures are often not formed by metastable sets but by important cycles or mixture of both. This paper aims at understanding and identifying these different types of dominant structures for reversible as well as nonreversible ergodic Markov processes. Our algorithmic approach generalizes spectral based methods for reversible process by using Schur decomposition techniques which can tackle also nonreversible cases. We illustrate the mathematical construction of our new approach by numerical experiments.

Item Type:Article
Subjects:Mathematical and Computer Sciences
Divisions:Department of Mathematics and Computer Science > Institute of Computer Science
Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group
ID Code:1749
Deposited By: BioComp Admin
Deposited On:30 Oct 2015 08:30
Last Modified:01 Nov 2016 15:13

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