Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains

Please always quote using this URN: urn:nbn:de:0297-zib-3469
  • The topic of the present paper bas been motivated by a recent computational approach to identify chemical conformations and conformational changes within molecular systems. After proper discretization, the conformations show up as almost invariant aggregates in reversible nearly uncoupled Markov chains. Most of the former work on this subject treated the direct problem: given the aggregates, analyze the loose coupling in connection with the computation of the stationary distribution (aggregation/disaggregation techniques). In contrast to that the present paper focuses on the inverse problem: given the system as a whole, identify the almost invariant aggregates together with the associated transition probabilites. A rather simple and robust algorithm is suggested and illustrated by its application to the n-pentane molecule.

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Metadaten
Author:Peter Deuflhard, Wilhelm Huisinga, Alexander Fischer, Christof Schütte
Document Type:ZIB-Report
Tag:almost invariant aggregates; essential molecular dynamics; nearly completely decomposable; nearly reducible; nearly uncoupled Markov chain; trans
MSC-Classification:15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A18 Eigenvalues, singular values, and eigenvectors
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 / 60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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 / 60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]
Date of first Publication:1998/01/21
Series (Serial Number):ZIB-Report (SC-98-03)
Published in:Appeared in: Lin. Alg. Appl. 315 (2000) 39-59