In molecular science and other disciplines vast amounts of data building a times series can be produced but often not be interpreted due to its size. Markov state models (MSM) are coarse graining strategies allowing to describe the time series with less degrees of freedom, such that relevant features can be extracted. Often these methods reiy on the assumption, that the underlying time series is a reversible Markov chains, since this assumption allows for a projection of the data onto a low dimensional space.
This assumption is crucial and no always satisfied like eye tracking data or non equilibrated biological systems. Within this project we developed GenPCCA allowing a coarse grained description without the reversibility assumption on the
data.

Publications

2018
Spectral Clustering for Non-Reversible Markov Chains Computational and Applied Mathematics, 37(5), pp. 6376-6391, 2018 (preprint available as ) Konstantin Fackeldey, Alexander Sikorski, Marcus Weber BibTeX
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Markov State Models for NESS
2016
Finding dominant structures of nonreversible Markov processes Multiscale Modeling and Simulation, 14(4), pp. 1319-1340, 2016 (preprint available as ZIB-Report 15-40) Natasa Djurdjevac Conrad, Marcus Weber, Christof Schütte PDF (ZIB-Report)
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Markov State Models for NESS
The Monte Carlo Computation Error of Transition Probabilities Statistics & Probability Letters, Vol.118, pp. 163-170, 2016 (preprint available as ZIB-Report 16-37) Adam Nielsen PDF (ZIB-Report)
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Markov State Models for NESS
2015
Computing the nearest reversible Markov chain Numerical Linear Algebra with Applications, 22(3), pp. 483-499, 2015 (preprint available as ) Adam Nielsen, Marcus Weber BibTeX
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Markov State Models for NESS
G-PCCA: Spectral Clustering for Non-reversible Markov Chains ZIB-Report 15-35 Marcus Weber, Konstantin Fackeldey PDF
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Markov State Models for NESS
Markov State Models and Molecular Alchemy Molecular Physics, 113(1), pp. 69-78, 2015 (preprint available as ) Christof Schütte, Adam Nielsen, Marcus Weber BibTeX
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Markov State Models for NESS
PCCA+ and Its Application to Spatial Time Series Clustering Bachelor's thesis, Freie Universität Berlin, Marcus Weber (Advisor), 2015 Alexander Sikorski PDF
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Markov State Models for NESS
2014
Computing the Minimal Rebinding Effect Included in a Given Kinetics Multiscale Model. Simul., 12(1), pp. 318-334, 2014 (preprint available as ZIB-Report 13-12) Marcus Weber, Konstantin Fackeldey PDF (ZIB-Report)
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Markov State Models for NESS
2013
Adaptive spectral clustering with application to tripeptide conformation analysis The Journal of Chemical Physics, Vol.139, pp. 110-194, 2013 Fiete Haack, Konstantin Fackeldey, Susanna Röblitz, Olga Scharkoi, Marcus Weber, Burkhard Schmidt BibTeX
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Markov State Models for NESS
Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification Advances in Data Analysis and Classification, 7(2), pp. 147-179, 2013 Susanna Röblitz, Marcus Weber BibTeX
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Markov State Models for NESS
Singulärwertzerlegung mit Zufallsalgorithmen Bachelor's thesis, Freie Universität Berlin, Marcus Weber (Advisor), 2013 Jessica Schmiedel BibTeX
Markov State Models for NESS
2012
Laufzeitoptimierung der Robusten Perron Cluster Analyse (PCCA+) Master's thesis, Freie Universität Berlin, Susanna Röblitz, Marcus Weber (Advisors), 2012 Mascha Berg PDF
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Markov State Models for NESS
Quantifying the rebinding effect in multivalent chemical ligand-receptor systems J. Chem. Phys., 137(5), p. 054111, 2012 Marcus Weber, Alexander Bujotzek, Rainer Haag BibTeX
Markov State Models for NESS