• Title, Summary, Keyword: pointwise dimension

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METRIC THEOREM AND HAUSDORFF DIMENSION ON RECURRENCE RATE OF LAURENT SERIES

  • Hu, Xue-Hai;Li, Bing;Xu, Jian
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.1
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    • pp.157-171
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    • 2014
  • We show that the recurrence rates of Laurent series about continued fractions almost surely coincide with their pointwise dimensions of the Haar measure. Moreover, let $E_{{\alpha},{\beta}}$ be the set of points with lower and upper recurrence rates ${\alpha},{\beta}$, ($0{\leq}{\alpha}{\leq}{\beta}{\leq}{\infty}$), we prove that all the sets $E_{{\alpha},{\beta}}$, are of full Hausdorff dimension. Then the recurrence sets $E_{{\alpha},{\beta}}$ have constant multifractal spectra.

A Study on the Quantitative Regularity Measures That Are Suitable for Biological Signal Analysis - Standard Data and 24 Hour R-R interval Analysis

  • Nam, Y.H.;Lee, J.M.;Han, J.M.;Park, K.S.
    • Proceedings of the KOSOMBE Conference
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    • v.1998 no.11
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    • pp.197-198
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    • 1998
  • We tested the capability of Pointwise Correlation Dimension(PD2), Approximate Entropy (ApEn) and LZ complexity, as alternative measures of a biological signal. For this purpose, we analyzed standard data and a healthy child's 24-hour heart rate variability. Our conclusion is as follows. First, PD2, ApEn and LZ complexity can be used for discerning chaotic attractor, white noise, and periodic signal. Second, these measures show different characteristics on day and night. Third, these measures can be used for detecting time-varying characteristics of biological signals.

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