2017
Reconstruction of normal forms by learning informed observation geometries from data
Yair O, Talmon R, Coifman RR, Kevrekidis IG. Reconstruction of normal forms by learning informed observation geometries from data. Proceedings Of The National Academy Of Sciences Of The United States Of America 2017, 114: e7865-e7874. PMID: 28831006, PMCID: PMC5617245, DOI: 10.1073/pnas.1620045114.Peer-Reviewed Original ResearchNormal formNonlinear differential equationsDynamical systems theoryAppropriate normal formFundamental physical quantitiesDifferential equationsDynamical regimesState variablesPhysical quantitiesPhysical lawsSystems theoryGeometry learningEmpirical observationsObservation geometryHeart of scienceDynamicsPrior knowledgeEquationsRealizationLawParametersGeometryTheoryExplicit referenceForm
2015
Manifold Learning for Latent Variable Inference in Dynamical Systems
Talmon R, Mallat S, Zaveri H, Coifman R. Manifold Learning for Latent Variable Inference in Dynamical Systems. IEEE Transactions On Signal Processing 2015, 63: 3843-3856. DOI: 10.1109/tsp.2015.2432731.Peer-Reviewed Original ResearchDynamical systemsLatent variable inferenceOutput signal measurementsNonlinear observerEigenvector problemLaplace operatorSignal geometryIntrinsic distanceSignal measurementsAccurate recoveryIntrinsic variablesLatent variablesObserverInferenceMeasurement deviceManifoldOperatorsVariablesGeometryIntracranial electroencephalography signalsKernelDynamicsPropertiesProblemSolution
2013
Empirical intrinsic geometry for nonlinear modeling and time series filtering
Talmon R, Coifman RR. Empirical intrinsic geometry for nonlinear modeling and time series filtering. Proceedings Of The National Academy Of Sciences Of The United States Of America 2013, 110: 12535-12540. PMID: 23847205, PMCID: PMC3732962, DOI: 10.1073/pnas.1307298110.Peer-Reviewed Original ResearchIntrinsic geometryNon-Gaussian tracking problemsHigh-dimensional time seriesNonlinear filtering frameworkTime series filteringInformation geometryStochastic settingParametric manifoldTracking problemStatistical modelBayesian approachNonlinear modelingEmpirical distributionFiltering frameworkEmpirical dynamicsInstrumental modalitiesInferred modelGeometryTime seriesTime series analysisDifferent observationsReal signalsSeries analysisDynamicsAnalysis tools
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
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