2014
Diffusion maps for changing data
Coifman R, Hirn M. Diffusion maps for changing data. Applied And Computational Harmonic Analysis 2014, 36: 79-107. DOI: 10.1016/j.acha.2013.03.001.Peer-Reviewed Original ResearchParameter spaceDiffusion mapsHigh-dimensional dataLow-dimensional spaceApproximation theoremGraph LaplacianIntrinsic geometryDimensional spaceSet of parametersNonlinear mappingDimensional dataGlobal behaviorEmbedding changesSpaceTypes of dataTheoremPowerful toolLaplacianGraphGeometryTermsEmbeddingDistanceParameters
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