Journal ArticleDOI
Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification
Susanna Röblitz,Marcus Weber +1 more
TLDR
It is demonstrated in this paper that PCCA+ always delivers an optimal fuzzy clustering for nearly uncoupled, not necessarily reversible, Markov chains with transition states.Abstract:
Given a row-stochastic matrix describing pairwise similarities between data objects, spectral clustering makes use of the eigenvectors of this matrix to perform dimensionality reduction for clustering in fewer dimensions. One example from this class of algorithms is the Robust Perron Cluster Analysis (PCCA+), which delivers a fuzzy clustering. Originally developed for clustering the state space of Markov chains, the method became popular as a versatile tool for general data classification problems. The robustness of PCCA+, however, cannot be explained by previous perturbation results, because the matrices in typical applications do not comply with the two main requirements: reversibility and nearly decomposability. We therefore demonstrate in this paper that PCCA+ always delivers an optimal fuzzy clustering for nearly uncoupled, not necessarily reversible, Markov chains with transition states.read more
Citations
More filters
Journal ArticleDOI
PyEMMA 2: A Software Package for Estimation, Validation, and Analysis of Markov Models.
Martin K. Scherer,Benjamin Trendelkamp-Schroer,Fabian Paul,Guillermo Pérez-Hernández,Moritz Hoffmann,Nuria Plattner,Christoph Wehmeyer,Jan-Hendrik Prinz,Frank Noé +8 more
TL;DR: The open-source Python package PyEMMA is presented, derived a systematic and accurate way to coarse-grain MSMs to few states and to illustrate the structures of the metastable states of the system.
Journal ArticleDOI
VAMPnets for deep learning of molecular kinetics.
TL;DR: A deep learning framework that automates construction of Markov state models from MD simulation data is introduced that performs equally or better than state-of-the-art Markov modeling methods and provides easily interpretable few-state kinetic models.
Journal ArticleDOI
Machine Learning for Molecular Simulation.
Frank Noé,Frank Noé,Alexandre Tkatchenko,Klaus-Robert Müller,Klaus-Robert Müller,Klaus-Robert Müller,Cecilia Clementi,Cecilia Clementi +7 more
TL;DR: Recent ML methods for molecular simulation are reviewed, with particular focus on (deep) neural networks for the prediction of quantum-mechanical energies and forces, on coarse-grained molecular dynamics, on the extraction of free energy surfaces and kinetics, and on generative network approaches to sample molecular equilibrium structures and compute thermodynamics.
Journal ArticleDOI
RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview.
Jiří Šponer,Giovanni Bussi,Miroslav Krepl,Miroslav Krepl,Pavel Banáš,Sandro Bottaro,Richard A. Cunha,Alejandro Gil-Ley,Giovanni Pinamonti,Simón Poblete,Petr Jurečka,Nils G. Walter,Michal Otyepka +12 more
TL;DR: An in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods are covered.
Journal ArticleDOI
Protein conformational plasticity and complex ligand-binding kinetics explored by atomistic simulations and Markov models
Nuria Plattner,Frank Noé +1 more
TL;DR: These wild-type simulations explore a space of conformations that can be individually stabilized by adding ligands or making suitable changes in protein sequence, and provide direct evidence of conformational plasticity in receptors.
References
More filters
Journal ArticleDOI
Markov models of molecular kinetics: Generation and validation
Jan-Hendrik Prinz,Hao Wu,Marco Sarich,Bettina G. Keller,Martin Senne,Martin Held,John D. Chodera,Christof Schütte,Frank Noé +8 more
TL;DR: An upper bound for the approximation error made by modeling molecular dynamics with a Markov chain is described and it is shown that this error can be made arbitrarily small with surprisingly little effort.
Journal ArticleDOI
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
TL;DR: In this article, a new method for the iterative computation of a few extremal eigenvalues of a symmetric matrix and their associated eigenvectors is proposed, based on an old and almost unknown method of Jacobi.
Journal ArticleDOI
On clusterings: Good, bad and spectral
TL;DR: A natural bicriteria measure for assessing the quality of a clustering that avoids the drawbacks of existing measures is motivated and a simple recursive heuristic is shown to have poly-logarithmic worst-case guarantees under the new measure.
Journal ArticleDOI
Merck molecular force field. IV. conformational energies and geometries for MMFF94
TL;DR: In this article, the authors describe the parameterization and performance of MMFF94 for conformational energies, rotational barriers, and equilibrium torsion angles from high-quality computational data.
Journal ArticleDOI
Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
TL;DR: A deflation procedure is introduced that is designed to improve the convergence of an implicitly restarted Arnoldi iteration for computing a few eigenvalues of a large matrix and implicitly deflates the converged approximations from the iteration.