@misc{GalliatDeuflhardRoitzschetal., author = {Galliat, Tobias and Deuflhard, Peter and Roitzsch, Rainer and Cordes, Frank}, title = {Automatic Identification of Metastable Conformations via Self-Organized Neural Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6197}, number = {00-51}, abstract = {As has been shown recently, the identification of metastable chemical conformations leads to a Perron cluster eigenvalue problem for a reversible Markov operator. Naive discretization of this operator would suffer from combinatorial explosion. As a first remedy, a pre-identification of essential degrees of freedom out of the set of torsion angles had been applied up to now. The present paper suggests a different approach based on neural networks: its idea is to discretize the Markov operator via self-organizing (box) maps. The thus obtained box discretization then serves as a prerequisite for the subsequent Perron cluster analysis. Moreover, this approach also permits exploitation of additional structure within embedded simulations. As it turns out, the new method is fully automatic and efficient also in the treatment of biomolecules. This is exemplified by numerical results.}, language = {en} } @misc{WeberGalliat, author = {Weber, Marcus and Galliat, Tobias}, title = {Characterization of Transition States in Conformational Dynamics using Fuzzy Sets}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6791}, number = {02-12}, abstract = {Recently, a novel approach for the analysis of molecular dynamics on the basis of a transfer operator has been introduced. Therein conformations are considered to be disjoint metastable clusters within position space of a molecule. These clusters are defined by almost invariant characteristic functions that can be computed via {\em Perron Cluster} analysis. The present paper suggests to replace crisp clusters with {\em fuzzy} clusters, i.e. to replace characteristic functions with membership functions. This allows a more sufficient characterization of transiton states between different confor conformations and therefore leads to a better understanding of molecular dynamics. Fur thermore, an indicator for the uniqueness of metastable fuzzy clusters and a fast algorithm for the computation of these clusters are described. Numerical examples are included.}, language = {en} }