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      Entropy Analysis of Short-Term Heartbeat Interval Time Series during Regular Walking

      , , , ,
      Entropy
      MDPI AG

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          Physiological time-series analysis using approximate entropy and sample entropy.

          Entropy, as it relates to dynamical systems, is the rate of information production. Methods for estimation of the entropy of a system represented by a time series are not, however, well suited to analysis of the short and noisy data sets encountered in cardiovascular and other biological studies. Pincus introduced approximate entropy (ApEn), a set of measures of system complexity closely related to entropy, which is easily applied to clinical cardiovascular and other time series. ApEn statistics, however, lead to inconsistent results. We have developed a new and related complexity measure, sample entropy (SampEn), and have compared ApEn and SampEn by using them to analyze sets of random numbers with known probabilistic character. We have also evaluated cross-ApEn and cross-SampEn, which use cardiovascular data sets to measure the similarity of two distinct time series. SampEn agreed with theory much more closely than ApEn over a broad range of conditions. The improved accuracy of SampEn statistics should make them useful in the study of experimental clinical cardiovascular and other biological time series.
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            Permutation Entropy: A Natural Complexity Measure for Time Series

            We introduce complexity parameters for time series based on comparison of neighboring values. The definition directly applies to arbitrary real-world data. For some well-known chaotic dynamical systems it is shown that our complexity behaves similar to Lyapunov exponents, and is particularly useful in the presence of dynamical or observational noise. The advantages of our method are its simplicity, extremely fast calculation, robustness, and invariance with respect to nonlinear monotonous transformations.
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              New Effect Size Rules of Thumb

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                Author and article information

                Contributors
                Journal
                ENTRFG
                Entropy
                Entropy
                MDPI AG
                1099-4300
                October 2017
                October 24 2017
                : 19
                : 10
                : 568
                Article
                10.3390/e19100568
                c29e9176-01d7-4075-ac0e-55ee243c88bf
                © 2017

                https://creativecommons.org/licenses/by/4.0/

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