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
Glycerol transport through the aquaglyceroporin GlpF: bridging dynamics and kinetics with atomic simulation.
TL;DR: In this paper, the authors presented a new strategy to extract non-equilibrium kinetic information from equilibrium molecular dynamics simulation, which can provide great insight into the substrate transport mechanism of GlpF and membrane channels alike.
Posted ContentDOI
Dinucleotides as simple models of the base stacking-unstacking component of DNA 'breathing' mechanisms
Eric R. Beyerle,Mohammadhasan Dinpajooh,Huiying Ji,Peter H. von Hippel,Andrew H. Marcus,Marina Guenza +5 more
TL;DR: The analyses show that the CD spectrum of dApdA is defined by two distinct chiral conformations that correspond, respectively, to a Watson-Crick form and a hybrid form with one base in a Hoogsteen configuration, and find also that ionic structure and water orientation around d ApdA play important roles in controlling its breathing fluctuations.
Introduction to Markov state modeling with the PyEMMA software — v1.0
TL;DR: This tutorial provides an introduction to the construction of Markov models of molec- ular kinetics from molecular dynamics trajectory data with the PyEMMA software using tutorial notebooks and short exercises to self check the learning progress.
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Advances in Molecular Simulation
Matteo Aldeghi,Philip C. Biggin +1 more
TL;DR: The combination of significant developments in all three of these key areas means that molecular simulation of biomolecules is not only a mature research field in its own right, but also a valuable, if not an essential component for medicinal chemistry research.
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Dynamics Rationalize Proteolytic Susceptibility of the Major Birch Pollen Allergen Bet v 1
TL;DR: Estimating the thermodynamics and kinetics of local unfolding around an initial cleavage site, it is found that the Bet v 1 variant with the highest cleavage rate also shows the highest probability for local unfolding, which strengthens the link between the conformational dynamics of allergen proteins and their stability during endolysosomal degradation.
References
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Book
Perturbation theory for linear operators
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Normalized cuts and image segmentation
Jianbo Shi,Jitendra Malik +1 more
TL;DR: This work treats image segmentation as a graph partitioning problem and proposes a novel global criterion, the normalized cut, for segmenting the graph, which measures both the total dissimilarity between the different groups as well as the total similarity within the groups.
Journal ArticleDOI
A tutorial on spectral clustering
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Proceedings Article
On Spectral Clustering: Analysis and an algorithm
TL;DR: A simple spectral clustering algorithm that can be implemented using a few lines of Matlab is presented, and tools from matrix perturbation theory are used to analyze the algorithm, and give conditions under which it can be expected to do well.
Journal ArticleDOI
Laplacian Eigenmaps for dimensionality reduction and data representation
Mikhail Belkin,Partha Niyogi +1 more
TL;DR: In this article, the authors proposed a geometrically motivated algorithm for representing high-dimensional data, based on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold and the connections to the heat equation.