2013
Nonlinear intrinsic variables and state reconstruction in multiscale simulations
Dsilva CJ, Talmon R, Rabin N, Coifman RR, Kevrekidis IG. Nonlinear intrinsic variables and state reconstruction in multiscale simulations. The Journal Of Chemical Physics 2013, 139: 184109. PMID: 24320256, DOI: 10.1063/1.4828457.Peer-Reviewed Original ResearchHigh-dimensional simulation dataLow-dimensional descriptionSimulation dataEnzyme reaction networksSlow time scaleStochastic simulationMeasurement noisePartial observationsPhysical phenomenaMultiscale simulationsReaction networksIntrinsic variablesSimulation ensemblesAlanine dipeptideSimulationsState reconstructionEnsembleProcess variabilityTime scalesAtomistic simulationsVariablesNoiseApproachSimple features
2009
Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps
Singer A, Erban R, Kevrekidis IG, Coifman RR. Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps. Proceedings Of The National Academy Of Sciences Of The United States Of America 2009, 106: 16090-16095. PMID: 19706457, PMCID: PMC2752552, DOI: 10.1073/pnas.0905547106.Peer-Reviewed Original ResearchConceptsStochastic dynamical systemsModel reduction approachHigh dimensional dynamic dataDynamical systemsNonlinear independent component analysisLocal principal component analysisSlow variablesMarkov matrixGood observablesDiffusion mapsNetwork simulationAnisotropic diffusionReduction approachData analysis techniqueAnalysis techniquesEigenvectorsDynamic dataObservablesIndependent component analysisComponent analysisSimulationsMatrix
1997
Adapted Waveform Analysis for ATDIR.
Coifman R, Rokhlin V. Adapted Waveform Analysis for ATDIR. 1997 DOI: 10.21236/ada326111.Peer-Reviewed Original Research