Identification of almost invariant aggregates in reversible nearly uncoupled Markov chains

No abstract is available for this paper.

• Publication year

  2000

• Venue

  Linear Algebra and its Applications

• Publication date

  2000-08-15

• Fields of study

  Mathematics, Chemistry, Computer Science

• Identifiers
  DOI 10.1016/S0024-3795(00)00095-1
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• A Multigrid Method for the Complex Helmholtz Eigenvalue Problem

  1999cited by this paper
• Computational Molecular Dynamics: Challenges, Methods, Ideas

  1999cited by this paper
• From simulation data to conformational ensembles: Structure and dynamics‐based methods

  1999cited by this paper
• On the Approximation of Complicated Dynamical Behavior

  1999cited by this paper
• A Direct Approach to Conformational Dynamics Based on Hybrid Monte Carlo

  1999influential reference
• On the structure of stochastic matrices with a subdominant eigenvalue near 1

  1998cited by this paper
• Monte Carlo: Concepts, Algorithms, and Applications

  1997cited by this paper
• Computation of Essential Molecular Dynamics by Subdivision Techniques

  1996cited by this paper
• Introduction to Graph Theory

  1995cited by this paper
• Algorithms for Random Generation and Counting: A Markov Chain Approach

  1993cited by this paper
• Stochastic Complementation, Uncoupling Markov Chains, and the Theory of Nearly Reducible Systems

  1989cited by this paper
• On the Structure of Nearly Uncoupled Markov Chains

  1983influential reference
• CHAPTER 2 – NONNEGATIVE MATRICES

  1979cited by this paper
• Nonnegative Matrices in the Mathematical Sciences

  1979cited by this paper
• Molecular dynamics of liquid n-butane near its boiling point

  1975cited by this paper
• Markov Processes

  1968cited by this paper
• Perturbation theory for linear operators

  1966cited by this paper
• Konrad-zuse-zentrum F ¨ Ur Informationstechnik Berlin a Nonlinear Multigrid Eigenproblem Solver for the Complex Helmholtz Equation a Nonlinear Multigrid Eigenproblem Solver for the Complex Helmholtz Equation

  year unknowncited by this paper

• Dynamic insights into the structural evolution of ACE2-RBD interactions through molecular dynamics simulation, Markov state modeling, and large language model mutation prediction.

  2025cites this paper
• Universal structure in the relaxation of photoactive proteins.

  2025cites this paper
• Interactions between Inhibitors and 5-Lipoxygenase: Insights from Gaussian Accelerated Molecular Dynamics and Markov State Models

  2024cites this paper
• Quantifying Unbiased Conformational Ensembles from Biased Simulations Using ShapeGMM

  2024cites this paper
• Tutorial on how to build non-Markovian dynamic models from molecular dynamics simulations for studying protein conformational changes.

  2024cites this paper
• An encompassed representation of timescale hierarchies in first-order reaction network

  2024cites this paper
• Identifying Selectivity Filters in Protein Biosensor for Ligand Screening

  2023cites this paper
• Edge addition and the change in Kemeny's constant

  2023cites this paper
• Efficient Mobile Computation Offloading over a Finite-State Markovian Channel using Spectral State Aggregation

  2022cites this paper
• Driving and characterizing nucleation of urea and glycine polymorphs in water

  2022cites this paper
• Information-Theoretic Reduction of Markov Chains

  2022cites this paper
• Spectral analysis of weighted Laplacians arising in data clustering

  2021cites this paper
• Progress in deep Markov state modeling: Coarse graining and experimental data restraints.

  2021cites this paper
• A probabilistic algorithm for aggregating vastly undersampled large Markov chains

  2021cites this paper
• Independent Markov decomposition: Toward modeling kinetics of biomolecular complexes

  2021cites this paper
• Maximally predictive states: From partial observations to long timescales.

  2021cites this paper
• Unsupervised Learning Methods for Molecular Simulation Data

  2021cites this paper
• Markov State Models to Study the Functional Dynamics of Proteins in the Wake of Machine Learning

  2021cites this paper
• Spectral Properties of Effective Dynamics from Conditional Expectations

  2019cites this paper
• Deflation reveals dynamical structure in nondominant reaction coordinates

  2019cites this paper
• Leveraging Bayesian analysis to improve accuracy of approximate models

  2019cites this paper
• Amplifying state dissimilarity leads to robust and interpretable clustering of scientific data

  2018cites this paper
• Simultaneous coherent structure coloring facilitates interpretable clustering of scientific data by amplifying dissimilarity

  2018cites this paper
• Multiplicative ergodic theorems for transfer operators: towards the identification and analysis of coherent structures in non-autonomous dynamical systems

  2018cites this paper
• Markov chains under combinatorial constraints: analysis and synthesis

  2018cites this paper
• Spectral clustering for non-reversible Markov chains

  2018cites this paper
• Implications of PCCA+ in Molecular Simulation

  2018cites this paper
• Imaging Metastable States and Transitions in Proteins by Trajectory Map.

  2017cites this paper
• Coherent structures and transfer operators

  2017cites this paper
• Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes

  2016cites this paper
• Hidden Basis Recovery: Methods and Applications in Machine Learning

  2016cites this paper
• Elucidation of the Dynamics of Transcription Elongation by RNA Polymerase II using Kinetic Network Models.

  2016cites this paper
• Metastability and Markov State Models in Molecular Dynamics Modeling, Analysis

  2016cites this paper
• Markov State Models of gene regulatory networks

  2016influential citation
• First passage times and relaxation times of unfolded proteins and the funnel model of protein folding

  2016cites this paper
• Finding Dominant Structures of Nonreversible Markov Processes

  2016cites this paper
• The generating structure of spatial conformation dynamics

  2016cites this paper
• A novel Minkowski-distance-based consensus clustering algorithm

  2016cites this paper
• Optimal Kullback–Leibler approximation of Markov chains via nuclear norm regularisation

  2015cites this paper
• Component aggregation for PEPA models: An approach based on approximate strong equivalence

  2015cites this paper
• G-PCCA: Spectral Clustering for Non-reversible Markov Chains

  2015cites this paper
• Operator-theoretic identification of closed sub-systems of dynamical systems

  2015cites this paper
• PCCA+ and Its Application to Spatial Time Series Clustering

  2015influential citation
• Utilizing hitting times for finding metastable sets in non-reversible Markov chains

  2014influential citation
• ATLAS: A Geometric Approach to Learning High-Dimensional Stochastic Systems Near Manifolds

  2014cites this paper
• The Hidden Convexity of Spectral Clustering

  2014cites this paper
• Computing the Minimal Rebinding Effect Included in a Given Kinetics

  2014cites this paper
• An overview and practical guide to building Markov state models.

  2014cites this paper
• Almost-Invariant and Finite-Time Coherent Sets: Directionality, Duration, and Diffusion

  2014cites this paper
• Load balancing for Markov chains with a specified directed graph

  2014cites this paper
• Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification

  2013cites this paper
• A Computational Method to Extract Macroscopic Variables and Their Dynamics in Multiscale Systems

  2013cites this paper
• Normalized Cuts Are Approximately Inverse Exit Times

  2013influential citation
• Simple few-state models reveal hidden complexity in protein folding

  2012cites this paper
• Sequential Change Point Detection in Molecular Dynamics Trajectories

  2012cites this paper
• Information theory, model error, and predictive skill of stochastic models for complex nonlinear systems

  2012cites this paper
• Oja's algorithm for graph clustering, Markov spectral decomposition, and risk sensitive control

  2012cites this paper
• Compositional Approximate Markov Chain Aggregation for PEPA Models

  2012cites this paper
• Iterated Consensus Clustering : A Technique We Can All Agree On

  2012cites this paper
• Hierarchical kernel spectral clustering

  2012cites this paper
• Optimal Kullback-Leibler Aggregation via Spectral Theory of Markov Chains

  2011cites this paper
• Quantitative comparison of villin headpiece subdomain simulations and triplet–triplet energy transfer experiments

  2011cites this paper
• Simulating the T-jump triggered unfolding dynamics of Trpzip 2 peptide and its time resolved IR and 2 DIR signals using Markov State Model Approach

  2011cites this paper
• Conformational and functional analysis of molecular dynamics trajectories by Self-Organising Maps

  2011cites this paper
• Simulating the T-jump-triggered unfolding dynamics of trpzip2 peptide and its time-resolved IR and two-dimensional IR signals using the Markov state model approach.

  2011cites this paper
• A Combinatorial Approach to Nearly Uncoupled Markov Chains

  2011influential citation
• ON AN SVD-BASED ALGORITHM FOR IDENTIFYING META-STABLE STATES OF MARKOV CHAINS

  2011cites this paper
• Scalable Bayesian Reduced-Order Models for Simulating High-Dimensional Multiscale Dynamical Systems

  2011cites this paper
• On Metastable Conformational Analysis of Nonequilibrium Biomolecular Time Series

  2010cites this paper
• Optimal Fuzzy Aggregation of Networks

  2010cites this paper
• Observation uncertainty in reversible Markov chains.

  2010cites this paper
• On the Approximation Quality of Markov State Models

  2010cites this paper
• A Bayesian method for construction of Markov models to describe dynamics on various time-scales.

  2010influential citation
• Design of Beneficial Wave Dynamics for Engine Life and Operability Enhancement

  2010cites this paper
• Hidden Markov Models with time-continuous output behavior

  2009influential citation
• Transition Path Theory for Markov Jump Processes

  2009cites this paper
• Statistical Error Estimation and Grid-free Hierarchical Refinement in Conformation Dynamics

  2009influential citation
• Transition Path Sampling and Other Advanced Simulation Techniques for Rare Events

  2009cites this paper
• Exploring the Free Energy Landscape: From Dynamics to Networks and Back

  2009cites this paper
• Conformation Dynamics ∗

  2008cites this paper
• Diffusion Maps, Reduction Coordinates, and Low Dimensional Representation of Stochastic Systems

  2008cites this paper
• Mining social documents and networks

  2008influential citation
• Modelle für die Identifizierung der Konformationszustände von Proteinen und für die Berechnung ihrer Infrarotspektren

  2008influential citation
• Oja's algorithm for graph clustering and Markov spectral decomposition

  2008cites this paper
• Efficient uncertainty minimization for fuzzy spectral clustering.

  2007cites this paper
• Model reduction of nonreversible Markov chains

  2007cites this paper
• Identification of biomolecular conformations from incomplete torsion angle observations by hidden markov models

  2007cites this paper
• Errata on "Robust Perron Cluster Analysis in Conformation Dynamics"

  2006cites this paper
• Fluctuation Induced Almost Invariant Sets

  2006cites this paper
• Reduced Stochastic Models for Complex Molecular Systems

  2006cites this paper
• Mathematical and numerical analysis for molecular simulation: accomplishments and challenges

  2006cites this paper
• Topic evolution and social interactions: how authors effect research

  2006influential citation
• A comparative study of two stochastic mode reduction methods

  2005cites this paper
• Uncoupling-Coupling Techniques for Metastable Dynamical Systems

  2005influential citation
• A general model for clustering binary data

  2005cites this paper
• An Averaging Principle for Fast Degrees of Freedom Exhibiting Long-Term Correlations

  2004cites this paper
• A new criterion and method for amino acid classification.

  2004cites this paper
• Phase transitions and metastability in Markovian and molecular systems

  2004cites this paper
• Extracting Macroscopic Dynamics : Model Problems & Algorithms

  2003cites this paper
• Numerical Analysis in Modern Scientific Computing: An Introduction

  2003influential citation