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Frank Suits - One of the best experts on this subject based on the ideXlab platform.
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describing protein folding kinetics by molecular dynamics simulations 1 theory
Journal of Physical Chemistry B, 2004Co-Authors: William C. Swope, Jed W. Pitera, Frank SuitsAbstract:A rigorous formalism for the extraction of state-to-state transition functions from a Boltzmann-weighted ensemble of microcanonical molecular dynamics simulations has been developed as a way to study the kinetics of protein folding in the context of a Markov chain. Analysis of these transition functions for signatures of Markovian behavior is described. The method has been applied to an example problem that is based on an underlying Markov process. The example problem shows that when an instance of the process is analyzed under the assumption that the underlying states have been aggregated into Macrostates, a procedure known as lumping, the resulting chain appears to have been produced by a non-Markovian process when viewed at high temporal resolution. However, when viewed on longer time scales, and for appropriately lumped Macrostates, Markovian behavior can be recovered. The potential for extracting the long time scale behavior of the folding process from a large number of short, independent molecular dynamics simulations is also explored.
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Describing Protein Folding Kinetics by Molecular Dynamics Simulations. 1. Theory †
The Journal of Physical Chemistry B, 2004Co-Authors: William C. Swope, Jed W. Pitera, Frank SuitsAbstract:A rigorous formalism for the extraction of state-to-state transition functions from a Boltzmann-weighted ensemble of microcanonical molecular dynamics simulations has been developed as a way to study the kinetics of protein folding in the context of a Markov chain. Analysis of these transition functions for signatures of Markovian behavior is described. The method has been applied to an example problem that is based on an underlying Markov process. The example problem shows that when an instance of the process is analyzed under the assumption that the underlying states have been aggregated into Macrostates, a procedure known as lumping, the resulting chain appears to have been produced by a non-Markovian process when viewed at high temporal resolution. However, when viewed on longer time scales, and for appropriately lumped Macrostates, Markovian behavior can be recovered. The potential for extracting the long time scale behavior of the folding process from a large number of short, independent molecular dynamics simulations is also explored. A rigorous formalism for the extraction of state-to-state transition functions from a Boltzmann-weighted ensemble of microcanonical molecular dynamics simulations has been developed as a way to study the kinetics of protein folding in the context of a Markov chain. Analysis of these transition functions for signatures of Markovian behavior is described. The method has been applied to an example problem that is based on an underlying Markov process. The example problem shows that when an instance of the process is analyzed under the assumption that the underlying states have been aggregated into Macrostates, a procedure known as lumping, the resulting chain appears to have been produced by a non-Markovian process when viewed at high temporal resolution. However, when viewed on longer time scales, and for appropriately lumped Macrostates, Markovian behavior can be recovered. The potential for extracting the long time scale behavior of the folding process from a large number of short, independent molecular dynamics simulations is also explored.
William C. Swope - One of the best experts on this subject based on the ideXlab platform.
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describing protein folding kinetics by molecular dynamics simulations 1 theory
Journal of Physical Chemistry B, 2004Co-Authors: William C. Swope, Jed W. Pitera, Frank SuitsAbstract:A rigorous formalism for the extraction of state-to-state transition functions from a Boltzmann-weighted ensemble of microcanonical molecular dynamics simulations has been developed as a way to study the kinetics of protein folding in the context of a Markov chain. Analysis of these transition functions for signatures of Markovian behavior is described. The method has been applied to an example problem that is based on an underlying Markov process. The example problem shows that when an instance of the process is analyzed under the assumption that the underlying states have been aggregated into Macrostates, a procedure known as lumping, the resulting chain appears to have been produced by a non-Markovian process when viewed at high temporal resolution. However, when viewed on longer time scales, and for appropriately lumped Macrostates, Markovian behavior can be recovered. The potential for extracting the long time scale behavior of the folding process from a large number of short, independent molecular dynamics simulations is also explored.
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Describing Protein Folding Kinetics by Molecular Dynamics Simulations. 1. Theory †
The Journal of Physical Chemistry B, 2004Co-Authors: William C. Swope, Jed W. Pitera, Frank SuitsAbstract:A rigorous formalism for the extraction of state-to-state transition functions from a Boltzmann-weighted ensemble of microcanonical molecular dynamics simulations has been developed as a way to study the kinetics of protein folding in the context of a Markov chain. Analysis of these transition functions for signatures of Markovian behavior is described. The method has been applied to an example problem that is based on an underlying Markov process. The example problem shows that when an instance of the process is analyzed under the assumption that the underlying states have been aggregated into Macrostates, a procedure known as lumping, the resulting chain appears to have been produced by a non-Markovian process when viewed at high temporal resolution. However, when viewed on longer time scales, and for appropriately lumped Macrostates, Markovian behavior can be recovered. The potential for extracting the long time scale behavior of the folding process from a large number of short, independent molecular dynamics simulations is also explored. A rigorous formalism for the extraction of state-to-state transition functions from a Boltzmann-weighted ensemble of microcanonical molecular dynamics simulations has been developed as a way to study the kinetics of protein folding in the context of a Markov chain. Analysis of these transition functions for signatures of Markovian behavior is described. The method has been applied to an example problem that is based on an underlying Markov process. The example problem shows that when an instance of the process is analyzed under the assumption that the underlying states have been aggregated into Macrostates, a procedure known as lumping, the resulting chain appears to have been produced by a non-Markovian process when viewed at high temporal resolution. However, when viewed on longer time scales, and for appropriately lumped Macrostates, Markovian behavior can be recovered. The potential for extracting the long time scale behavior of the folding process from a large number of short, independent molecular dynamics simulations is also explored.
Jed W. Pitera - One of the best experts on this subject based on the ideXlab platform.
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describing protein folding kinetics by molecular dynamics simulations 1 theory
Journal of Physical Chemistry B, 2004Co-Authors: William C. Swope, Jed W. Pitera, Frank SuitsAbstract:A rigorous formalism for the extraction of state-to-state transition functions from a Boltzmann-weighted ensemble of microcanonical molecular dynamics simulations has been developed as a way to study the kinetics of protein folding in the context of a Markov chain. Analysis of these transition functions for signatures of Markovian behavior is described. The method has been applied to an example problem that is based on an underlying Markov process. The example problem shows that when an instance of the process is analyzed under the assumption that the underlying states have been aggregated into Macrostates, a procedure known as lumping, the resulting chain appears to have been produced by a non-Markovian process when viewed at high temporal resolution. However, when viewed on longer time scales, and for appropriately lumped Macrostates, Markovian behavior can be recovered. The potential for extracting the long time scale behavior of the folding process from a large number of short, independent molecular dynamics simulations is also explored.
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Describing Protein Folding Kinetics by Molecular Dynamics Simulations. 1. Theory †
The Journal of Physical Chemistry B, 2004Co-Authors: William C. Swope, Jed W. Pitera, Frank SuitsAbstract:A rigorous formalism for the extraction of state-to-state transition functions from a Boltzmann-weighted ensemble of microcanonical molecular dynamics simulations has been developed as a way to study the kinetics of protein folding in the context of a Markov chain. Analysis of these transition functions for signatures of Markovian behavior is described. The method has been applied to an example problem that is based on an underlying Markov process. The example problem shows that when an instance of the process is analyzed under the assumption that the underlying states have been aggregated into Macrostates, a procedure known as lumping, the resulting chain appears to have been produced by a non-Markovian process when viewed at high temporal resolution. However, when viewed on longer time scales, and for appropriately lumped Macrostates, Markovian behavior can be recovered. The potential for extracting the long time scale behavior of the folding process from a large number of short, independent molecular dynamics simulations is also explored. A rigorous formalism for the extraction of state-to-state transition functions from a Boltzmann-weighted ensemble of microcanonical molecular dynamics simulations has been developed as a way to study the kinetics of protein folding in the context of a Markov chain. Analysis of these transition functions for signatures of Markovian behavior is described. The method has been applied to an example problem that is based on an underlying Markov process. The example problem shows that when an instance of the process is analyzed under the assumption that the underlying states have been aggregated into Macrostates, a procedure known as lumping, the resulting chain appears to have been produced by a non-Markovian process when viewed at high temporal resolution. However, when viewed on longer time scales, and for appropriately lumped Macrostates, Markovian behavior can be recovered. The potential for extracting the long time scale behavior of the folding process from a large number of short, independent molecular dynamics simulations is also explored.
Daniel Korenblum - One of the best experts on this subject based on the ideXlab platform.
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Macrostate mixture models for probabilistic multiscale nonparametric kernelized spectral clustering
arXiv: Machine Learning, 2015Co-Authors: Daniel KorenblumAbstract:Automating the discovery of meaningful structures in large complex datasets is an important problem in many application areas including machine learning, source separation, and dimensionality reduction. Mixture models are one category of methods for discovering structure using convex sums of probability distributions to represent structures or clusters in data. Spectral clustering is another category of methods where eigenspaces of Laplacian matrices are used prior to or as part of the clustering process. Macrostate theory defines nonparametric mixture models directly from Laplacian eigensystems, providing a connection between nonhierarchical spectral clustering and nonparametric mixture modeling. Unlike other spectral clustering methods, Macrostates are self-contained and predict both the appropriate number of mixture components and the cluster assignment distributions directly from Laplacian eigensystems. Macrostates reduce the number of input parameters and steps required compared to other spectral clustering methods and avoid issues of explicit density estimation in higher dimensional input data spaces. Previous formulations used customized algorithms to compute Macrostate clustering solutions, limiting their practical accessibility. The new formulation presented here depends only on standardized linear programming solvers and is very easily parallelized, improving the practicality and performance compared to previous formulations. Numerical examples compare the performance of other finite mixture modeling and spectral clustering methods to Macrostate clustering.
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Macrostate mixture models for multiscale spectral clustering and nonparametric source separation
arXiv: Machine Learning, 2015Co-Authors: Daniel KorenblumAbstract:Mixture modeling, cluster analysis, and graph partitioning methods are widely used in a variety of scientific and engineering disciplines. Accurately estimating the number of mixture components/clusters/partitions and their distributions is an active area of research. Macrostate theory describes the metastable states of physical systems and has an equivalent form to that of mixture models. Reformulating the original physical definition of Macrostates in terms of mixture modeling problems encourages their use in data science and statistics applications outside of physics. Macrostate mixture models combine representation and inference into a single algorithm and also predict the appropriate number of mixture components directly from the spectrum of a data-dependent operator, unlike most other spectral clustering methods. Numerical examples on nonphysical mixture problems demonstrate the effectiveness and compare the advantages and disadvantages of this approach to other methods.
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Macrostate data clustering
Physical Review E, 2003Co-Authors: Daniel Korenblum, David ShallowayAbstract:We develop an effective nonhierarchical data clustering method using an analogy to the dynamic coarse graining of a stochastic system. Analyzing the eigensystem of an interitem transition matrix identifies fuzzy clusters corresponding to the metastable macroscopic states (Macrostates) of a diffusive system. A ``minimum uncertainty criterion'' determines the linear transformation from eigenvectors to cluster-defining window functions. Eigenspectrum gap and cluster certainty conditions identify the proper number of clusters. The physically motivated fuzzy representation and associated uncertainty analysis distinguishes Macrostate clustering from spectral partitioning methods. Macrostate data clustering solves a variety of test cases that challenge other methods.
Bruce Turkington - One of the best experts on this subject based on the ideXlab platform.
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An introduction to the thermodynamic and Macrostate levels of nonequivalent ensembles
Physica A: Statistical Mechanics and its Applications, 2020Co-Authors: Hugo Touchette, Richard S. Ellis, Bruce TurkingtonAbstract:This short paper presents a nontechnical introduction to the problem of nonequivalent microcanonical and canonical ensembles. Both the thermodynamic and the Macrostate levels of definition of nonequivalent ensembles are introduced. The many relationships that exist between these two levels are also explained in simple physical terms.Comment: Revtex4, 5 pages, 1 figur
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The Large Deviation Principle for Coarse-Grained Processes
arXiv: Mathematical Physics, 2011Co-Authors: Richard S. Ellis, Kyle Haven, Bruce TurkingtonAbstract:The large deviation principle is proved for a class of L 2 -valued processes that arise from the coarse-graining of a random field. Coarse-grained processes of this kind form the basis of the analysis of local mean-field models in statistical mechanics by exploiting the long-range nature of the interaction function defining such models. In particular, the large deviation principle is used in a companion paper [8] to derive the variational principles that characterize equilibrium Macrostates in statistical models of two-dimensional and quasi-geostrophic turbulence. Such Macrostates correspond to large-scale, long-lived flow structures, the description of which is the goal of the statistical equilibrium theory of turbulence. The large deviation bounds for the coarse-grained process under consideration are shown to hold with respect to the strong L 2 topology, while the associated rate function is proved to have compact level sets with respect to the weak topology. This compactness property is nevertheless sufficient to establish the existence of equilibrium Macrostates for both the microcanonical and canonical ensembles.
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The Generalized Canonical Ensemble and Its Universal Equivalence with the Microcanonical Ensemble
Journal of Statistical Physics, 2005Co-Authors: Marius Costeniuc, Richard S. Ellis, Hugo Touchette, Bruce TurkingtonAbstract:Shortened abstract: Microcanonical equilibrium Macrostates are characterized as the solutions of a constrained minimization problem, while canonical equilibrium Macrostates are characterized as the solutions of a related, unconstrained minimization problem. In Ellis, Haven, and Turkington (J. Stat. Phys. 101, 999, 2000) the problem of ensemble equivalence was completely solved at two separate, but related levels: the level of equilibrium Macrostates, which focuses on relationships between the corresponding sets of equilibrium Macrostates, and the thermodynamic level, which focuses on when the microcanonical entropy $s$ can be expressed as the Legendre-Fenchel transform of the canonical free energy. The present paper extends the results of Ellis et al. significantly by addressing the following motivational question. Given that the microcanonical ensemble can be nonequivalent with the canonical ensemble, is it possible to replace the canonical ensemble with a generalized canonical ensemble that is equivalent with the microcanonical ensemble? The generalized canonical ensemble that we consider is obtained from the standard canonical ensemble by adding an exponential factor involving a continuous function $g$ of the Hamiltonian. As in the paper by Ellis et al., we analyze the equivalence of the two ensembles at both the level of equilibrium Macrostates and the thermodynamic level. A neat but not quite precise statement of the main result in the present paper is that the microcanonical and generalized canonical ensembles are equivalent at the level of equilibrium Macrostates if and only if they are equivalent at the thermodynamic level, which is the case if and only if the generalized microcanonical entropy $s-g$ is concave.Comment: 30 pages, revtex
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an introduction to the thermodynamic and Macrostate levels of nonequivalent ensembles
Physica A-statistical Mechanics and Its Applications, 2004Co-Authors: Hugo Touchette, Richard S. Ellis, Bruce TurkingtonAbstract:This short paper presents a nontechnical introduction to the problem of nonequivalent microcanonical and canonical ensembles. Both the thermodynamic and the Macrostate levels of definition of nonequivalent ensembles are introduced. The many relationships that exist between these two levels are also explained in simple physical terms.
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Large Deviation Principles and Complete Equivalence and Nonequivalence Results for Pure and Mixed Ensembles
arXiv: Probability, 2000Co-Authors: Richard S. Ellis, Kyle Haven, Bruce TurkingtonAbstract:We consider a general class of statistical mechanical models of coherent structures in turbulence, which includes models of two-dimensional fluid motion, quasi-geostrophic flows, and dispersive waves. First, large deviation principles are proved for the canonical ensemble and the microcanonical ensemble. For each ensemble the set of equilibrium Macrostates is defined as the set on which the corresponding rate function attains its minimum of 0. We then present complete equivalence and nonequivalence results at the level of equilibrium Macrostates for the two ensembles.
