2023
Wire Before You Walk
Asmara T, Bhaskar D, Adelstein I, Krishnaswamy S, Perlmutter M. Wire Before You Walk. 2023, 00: 714-716. DOI: 10.1109/ieeeconf59524.2023.10477089.Peer-Reviewed Original ResearchReduced-order modeling and analysis of dynamic cerebral autoregulation via diffusion maps
dos Santos K, Katsidoniotaki M, Miller E, Petersen N, Marshall R, Kougioumtzoglou I. Reduced-order modeling and analysis of dynamic cerebral autoregulation via diffusion maps. Physiological Measurement 2023, 44: 044001. PMID: 36963111, PMCID: PMC11271258, DOI: 10.1088/1361-6579/acc780.Peer-Reviewed Original ResearchConceptsDiffusion mapsState-space descriptionReduced-order modelingIntrinsic dynamicsTime derivativeLow-dimensional representationRandom walkMarkov matrixParsimonious modelingSignificant eigenvaluesEigenvalue ratioFurther dimension reductionEigenvalue analysisTransfer function analysisDimension reductionData-driven techniquesMain resultsDynamicsEigenvaluesFlow velocityModelingSuperior performanceMap techniqueGraphWalk
2020
Finding the Pattern: On-Line Extraction of Spatial Structure During Virtual Navigation
Graves KN, Antony JW, Turk-Browne NB. Finding the Pattern: On-Line Extraction of Spatial Structure During Virtual Navigation. Psychological Science 2020, 31: 1183-1190. PMID: 32853531, PMCID: PMC7542246, DOI: 10.1177/0956797620948828.Peer-Reviewed Original Research
2013
Distribution of directional change as a signature of complex dynamics
Burov S, Tabei S, Huynh T, Murrell M, Philipson L, Rice S, Gardel M, Scherer N, Dinner A. Distribution of directional change as a signature of complex dynamics. Proceedings Of The National Academy Of Sciences Of The United States Of America 2013, 110: 19689-19694. PMID: 24248363, PMCID: PMC3856831, DOI: 10.1073/pnas.1319473110.Peer-Reviewed Original ResearchConceptsMean square displacementRandom walkParticle tracking dataSelf-similar propertiesStochastic processOrder parameterComplex dynamicsStatistical featuresMore dimensionsSquare displacementSuccessive time intervalsWalkRelative angleCommon modelDynamicsColloidal systemsPossible scenariosTracking dataDistributionModelMotionTime intervalParameters
2008
Diffusion Maps - a Probabilistic Interpretation for Spectral Embedding and Clustering Algorithms
Nadler B, Lafon S, Coifman R, Kevrekidis I. Diffusion Maps - a Probabilistic Interpretation for Spectral Embedding and Clustering Algorithms. Lecture Notes In Computational Science And Engineering 2008, 58: 238-260. DOI: 10.1007/978-3-540-73750-6_10.Peer-Reviewed Original ResearchSpectral clusteringGraph LaplacianRandom walkSpectral embeddingMean exit timeNormalized graph LaplacianComplex high dimensional datasetsHigh-dimensional datasetsNon-linear dimensionality reductionMultiscale methodEmbedding algorithmClustering algorithmAdjacency matrixDimensional datasetsExit timeProbabilistic interpretationRelaxation timeDimensionality reductionMultiscale dataDiffusion mapsNecessary conditionEuclidean distanceProbabilistic analysisCharacteristic relaxation timeAlgorithm
2006
Diffusion maps, spectral clustering and reaction coordinates of dynamical systems
Nadler B, Lafon S, Coifman R, Kevrekidis I. Diffusion maps, spectral clustering and reaction coordinates of dynamical systems. Applied And Computational Harmonic Analysis 2006, 21: 113-127. DOI: 10.1016/j.acha.2005.07.004.Peer-Reviewed Original ResearchFokker-Planck operatorDynamical systemsDifferential operatorsHigh-dimensional stochastic systemsRandom walkProbability distributionDimensional stochastic systemsStochastic differential equationsCorresponding differential operatorComplex dynamical systemsTime evolutionLong-time asymptoticsLow-dimensional Euclidean spaceGeneral probability distributionNormalized graph LaplacianLaplace-Beltrami operatorDimensional Euclidean spaceDiffusion mapsLong-time evolutionSpectral clusteringStochastic systemsDifferential equationsHigh-dimensional dataSlow variablesLarge-scale simulations
2005
A Lower Bound on Convergence of a Distributed Network Consensus Algorithm
Cao M, Spielman D, Morse A. A Lower Bound on Convergence of a Distributed Network Consensus Algorithm. 2005, 2356-2361. DOI: 10.1109/cdc.2005.1582514.Peer-Reviewed Original Research
1993
Generalized Lévy-walk model for DNA nucleotide sequences
Buldyrev S, Goldberger A, Havlin S, Peng C, Simons M, Stanley H. Generalized Lévy-walk model for DNA nucleotide sequences. Physical Review E 1993, 47: 4514-4523. PMID: 9960527, DOI: 10.1103/physreve.47.4514.Peer-Reviewed Original Research
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