@misc{WeberWalterKubeetal.2006, author = {Weber, Marcus and Walter, Lionel and Kube, Susanna and Deuflhard, Peter}, title = {Stable computation of probability densities for metastable dynamical systems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9331}, number = {06-39}, year = {2006}, abstract = {Whenever the invariant stationary density of metastable dynamical systems decomposes into almost invariant partial densities, its computation as eigenvector of some transition probability matrix is an ill-conditioned problem. In order to avoid this computational difficulty, we suggest to apply an aggregation/disaggregation method which only addresses wellconditioned sub-problems and thus results in a stable algorithm. In contrast to existing methods, the aggregation step is done via a sampling algorithm which covers only small patches of the sampling space. Finally, the theoretical analysis is illustrated by two biomolecular examples.}, language = {en} } @misc{WeberKubeRiemeretal.2006, author = {Weber, Marcus and Kube, Susanna and Riemer, Alexander and Bujotzek, Alexander}, title = {Efficient Sampling of the Stationary Distribution of Metastable Dynamical Systems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9467}, number = {07-03}, year = {2006}, abstract = {In this article we aim at an efficient sampling of the stationary distribution of dynamical systems in the presence of metastabilities. In the past decade many sophisticated algorithms have been inven ted in this field. We do not want to simply add a further one. We address the problem that one has applied a sampling algorithm for a dynamical system many times. This leads to different samplings which more or less represent the stationary distribution partially very well, but which are still far away from ergodicity or from the global stationary distribution. We will show how these samplings can be joined together in order to get one global sampling of the stationary distribution.}, language = {en} } @misc{KubeWeber2005, author = {Kube, Susanna and Weber, Marcus}, title = {Identification of Metastabilities in Monomolecular Conformation Kinetics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8956}, number = {06-01}, year = {2005}, abstract = {The identification of metastable conformations of molecules plays an important role in computational drug design. One main difficulty is the fact that the underlying dynamic processes take place in high dimensional spaces. Although the restriction of degrees of freedom to a few dihedral angles significantly reduces the complexity of the problem, the existing algorithms are time-consuming. They are based on the approximation of transition probabilities by an extensive sampling of states according to the Boltzmann distribution. We present a method which can identify metastable conformations without sampling the complete distribution. Our algorithm is based on local transition rates and uses only pointwise information about the potential energy surface. In order to apply the cluster algorithm PCCA+, we compute a few eigenvectors of the rate matrix by the Jacobi-Davidson method. Interpolation techniques are applied to approximate the thermodynamical weights of the clusters. The concluding example illustrates our approach for epigallocatechine, a molecule which can be described by seven dihedral angles.}, language = {en} } @article{KubeWeber2007, author = {Kube, Susanna and Weber, Marcus}, title = {A Coarse Graining Method for the Identification of Transition rates between Molecular Conformations}, volume = {126}, journal = {Journal of Chemical Physics}, number = {2}, doi = {10.1063/1.2404953}, year = {2007}, language = {en} } @inproceedings{WeberKube2005, author = {Weber, Marcus and Kube, Susanna}, title = {Robust Perron Cluster Analysis for Various Applications in Computational Life Science}, booktitle = {Computational Life Sciences}, pages = {57 -- 66}, year = {2005}, language = {en} } @inproceedings{KubeWeber2008, author = {Kube, Susanna and Weber, Marcus}, title = {Computation of equilibrium densities in metastable dynamical systems by domain decomposition}, volume = {1048}, booktitle = {Numerical Analysis and Applied Mathematics, International Conference on Numerical Analysis and Applied Mathematics 2008}, publisher = {AIP Conference Proceedings}, pages = {339 -- 342}, year = {2008}, language = {en} } @inproceedings{KubeWeber2008, author = {Kube, Susanna and Weber, Marcus}, title = {Preserving the Markov Property of Reduced Reversible Markov Chains}, volume = {1048}, booktitle = {Numerical Analysis and Applied Mathematics, International Conference on Numerical Analysis and Applied Mathematics 2008}, pages = {593 -- 596}, year = {2008}, language = {en} } @article{WeberKubeWalteretal.2007, author = {Weber, Marcus and Kube, Susanna and Walter, Lionel and Deuflhard, Peter}, title = {Stable Computation of Probability Densities of Metastable Dynamical Systems}, volume = {6}, journal = {SIAM J. Multiscale Model. Simul.}, number = {2}, pages = {396 -- 416}, year = {2007}, language = {en} } @article{KubeLasserWeber2008, author = {Kube, Susanna and Lasser, Caroline and Weber, Marcus}, title = {Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics}, volume = {228}, journal = {Journal of Computational Physics}, number = {6}, doi = {10.1016/j.jcp.2008.11.016}, pages = {1947 -- 1962}, year = {2008}, language = {en} } @misc{KubeWeber2005, author = {Kube, Susanna and Weber, Marcus}, title = {Conformation Kinetics as a Reduced Model for Transition Pathways}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8763}, number = {05-43}, year = {2005}, abstract = {The complexity of molecular kinetics can be reduced significantly by a restriction to metastable conformations which are almost invariant sets of molecular dynamical systems. With the Robust Perron Cl uster Analysis PCCA+, developed by Weber and Deuflhard, we have a tool available which can be used to identify these conformations from a transition probability matrix. This method can also be applied to the corresponding transition rate matrix which provides important information concerning transition pathways of single molecules. In the present paper, we explain the relationship between these tw o concepts and the extraction of conformation kinetics from transition rates. Moreover, we show how transition rates can be approximated and conclude with numerical examples.}, language = {en} }