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Estimatingthedistributionofdynamicinvariants:illustratedwithanapplicationtohumanphoto-plethysmographictimeseries
MichaelSmall
DepartmentofElectronicandInformationEngineering
HongKongPolytechnicUniversity,HungHom,Kowloon,HongKong
Email:ensmall@polyu.edu.hk;
CorrespondingauthorAbstract
Dynamicinvariantsareoftenestimatedfromexperimentaltimeserieswiththeaimofdi erentiatingbetweendi erentphysicalstatesintheunderlyingsystem.Themostpopularschemesforestimatingdynamicinvariantsarecapableofestimatingcon denceintervals,however,suchcon denceintervalsdonotre ectvariabilityintheunderlyingdynamics.Weproposeasurrogatebasedmethodtoestimatetheexpecteddistributionofvaluesunderthenullhypothesisthattheunderlyingdeterministicdynamicsarestationary.Wedemonstratetheapplicationofthismethodbyconsideringfourrecordingsofhumanpulsewaveformsindi eringphysiologicalstatesandshowthatcorrelationdimensionandentropyareinsu cienttodi erentiatebetweenthesestates.Incontrast,algorithmiccomplexitycanclearlydi erentiatebetweenallfourrhythms.
1Background
Variousdynamicinvariantsareoftenestimatedfromtimeseriesinawidevarietyofscienti cdisciplines.Ithaslongbeenknownthattheseestimates(andinparticularcorrelationdimensionestimates)alonearenotsu cienttodi erentiatebetweenchaosandnoise.Mostnotably,themethodofsurrogatedata[1]was
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Estimating the distribution of dynamic invariants: illustrated with an application to human photo-plethysmographic time series Michael Small Department of ...
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