Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains

The topic of the present paper has 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 probabilities. A rather simple and robust algorithm is suggested and illustrated by its application to the n-pentane molecule