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
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Journal ArticleDOI
Computing the minimal rebinding effect for non-reversible processes.
TL;DR: A minimal bound for the rebinding effect included in a given system is computed as the solution of an optimization problem, based on membership functions chosen as a linear combination of Schur vectors, this generalized approach includes reversible as well as non-reversible processes.
Journal ArticleDOI
Statistical analysis of tipping pathways in agent-based models
Luzie Helfmann,Luzie Helfmann,Luzie Helfmann,Jobst Heitzig,Péter Koltai,Jürgen Kurths,Jürgen Kurths,Christof Schütte,Christof Schütte +8 more
TL;DR: In this paper, the authors introduce a methodology for studying noise-induced tipping between relevant subsets of the agent state space representing characteristic configurations, and characterize the tipping behavior by means of transition path theory, which helps gaining a statistical understanding of the tipping paths such as their distribution, flux and rate.
Journal ArticleDOI
Unfolding dynamics of small peptides biased by constant mechanical forces
Fabian Knoch,Thomas Speck +1 more
TL;DR: It is shown how multi-ensemble Markov state models can be combined with constant-force equilibrium simulations to bridge the gap between simulation and experiments even for medium-sized biomolecules.
Critical role of backbone coordination in the mRNA recognition by RNA induced silencing complex.
TL;DR: Based on extensive all-atom molecular dynamics simulations, this paper constructed a quasi-Markov State Model (qMSM) to reveal the dynamics during recognition at position 6-7 in the seed region of human Argonaute 2 (hAgo2).
Journal ArticleDOI
Modeling of Multivalent Ligand-Receptor Binding Measured by kinITC
TL;DR: This paper describes how to solve the problem using kinITC and an invariant subspace projection and the algorithm is tested for multivalent systems with different valencies.
References
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Journal ArticleDOI
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