2023
Robust Estimation of Position-Dependent Anisotropic Diffusivity Tensors from Molecular Dynamics Trajectories
Domingues T, Coifman R, Haji-Akbari A. Robust Estimation of Position-Dependent Anisotropic Diffusivity Tensors from Molecular Dynamics Trajectories. The Journal Of Physical Chemistry B 2023, 127: 8644-8659. PMID: 37757480, DOI: 10.1021/acs.jpcb.3c03581.Peer-Reviewed Original ResearchMechanical observablesDiffusivity tensorEfficient correction schemeAnisotropic diffusivity tensorStochastic counterpartSame qualitative featuresStochastic trajectoriesVan Hove correlation functionRobust estimationCovariance estimatorMolecular simulation communityCorrelation functionsDiffusivity profilesRotational symmetryLennard-Jones fluidEstimatorQualitative featuresDiffusion mapsSpatial profileObservablesTensorCorrection schemeTransport propertiesProperty functionsPrevious paperRobust Estimation of Position-Dependent Anisotropic Diffusivity Tensors from Stochastic Trajectories
Domingues T, Coifman R, Haji-Akbari A. Robust Estimation of Position-Dependent Anisotropic Diffusivity Tensors from Stochastic Trajectories. The Journal Of Physical Chemistry B 2023, 127: 5273-5287. PMID: 37261948, DOI: 10.1021/acs.jpcb.3c00670.Peer-Reviewed Original ResearchTime discretizationStochastic trajectoriesMechanical observablesDiffusivity tensorAnisotropic diffusivity tensorPointwise estimatesRigorous generalizationRobust estimationCovariance estimatorDifferent functional formsLocal covarianceKernel-based approachEstimatorFunctional estimatesDiscretizationFunctional formOrthogonal functionsBulk systemKernel functionConfined systemSuch methodsObservablesTensorTransport propertiesCovariance-based estimator
2010
Coarse Collective Dynamics of Animal Groups
Frewen T, Couzin I, Kolpas A, Moehlis J, Coifman R, Kevrekidis I. Coarse Collective Dynamics of Animal Groups. Lecture Notes In Computational Science And Engineering 2010, 75: 299-309. DOI: 10.1007/978-3-642-14941-2_16.Peer-Reviewed Original ResearchCollective dynamicsExtraction of informationDimensionality reduction approachCoarse observablesAppropriate observablesGood observablesParsimonious usageBroad classSuch observablesComplex systemsObservablesCoherent behaviorCollective systemComputational modelIndividual-based modelMacroscopic levelDynamicsSimulation protocolModelComputer-assisted analysisSystemApproachUsageGroup dynamicsInformation
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
2007
Variable-free exploration of stochastic models: A gene regulatory network example
Erban R, Frewen TA, Wang X, Elston TC, Coifman R, Nadler B, Kevrekidis IG. Variable-free exploration of stochastic models: A gene regulatory network example. The Journal Of Chemical Physics 2007, 126: 155103. PMID: 17461667, DOI: 10.1063/1.2718529.Peer-Reviewed Original ResearchConceptsStochastic modelEquation-free approachLow-dimensional descriptionLong-time behaviorNetwork exampleAppropriate observablesStochastic simulationGood observablesGene regulatory networksObservablesComplex systemsDiffusion mapsSimulation dataPhysical variablesPrevious paperLong-term dynamicsAppropriate valuesDynamicsEigenvectorsLaplacianComputationRegulatory networksGraphModelRestriction procedures