@misc{Haack, author = {Haack, Fiete}, title = {Properties of Reduced Reversible Markov Chains}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10941}, number = {08-42}, abstract = {The enormous time lag between fast atomic motion and complex pro- tein folding events makes it almost impossible to compute molecular dy- namics on a high resolution. A common way to tackle this problem is to model the system dynamics as a Markov process. Yet for large molec- ular systems the resulting Markov chains can hardly be handled due to the curse of dimensionality. Coarse graining methods can be used to re- duce the dimension of a Markov chain, but it is still unclear how far the coarse grained Markov chain resembles the original system. In order to answer this question, two different coarse-graining methods were analysed and compared: a classical set-based reduction method and an alternative subspace-based approach, which is based on membership vectors instead of sets. On the basis of a small toy system, it could be shown, that in con- trast to the subset-based approach, the subspace-based reduction method preserves the Markov property as well as the essential dynamics of the original system.}, language = {en} } @misc{BestHege, author = {Best, Christoph and Hege, Hans-Christian}, title = {Visualizing conformations in molecular dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3859}, number = {SC-98-42}, abstract = {The Monte Carlo simulation of the dynamics of complex molecules produces trajectories with a large number of different configurations to sample configuration space. It is expected that these configurations can be classified into a small number of conformations representing essential changes in the shape of the molecule. We present a method to visualize these conformations by point sets in the plane based on a geometrical distance measure between individual configurations. It turns out that different conformations appear as well-separated point sets. The method is further improved by performing a cluster analysis of the data set. The point-cluster representation is used to control a three-dimensional molecule viewer application to show individual configurations and conformational changes. The extraction of essential coordinates and visualization of molecular shape is discussed.}, language = {en} }