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Generating Signals with Multiscale Time Irreversibility: The Asymmetric Weierstrass Function.

Anton Burykin1, Madalena D Costa, Chung-Kang Peng

  • 1Emory Center for Critical Care (ECCC) and Department of Surgery, Emory University School of Medicine, Atlanta, GA.

Complexity
|July 21, 2012
PubMed
Summary

Researchers developed a new tool to generate model time series with tunable multiscale asymmetry. This asymmetric Weierstrass function W(A) aids in testing and refining measures of time series asymmetry.

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Area of Science:

  • Complex systems analysis
  • Time series analysis
  • Nonlinear dynamics

Background:

  • Time irreversibility is a key characteristic of natural processes.
  • Multiscale irreversibility, observed in healthy heart rate dynamics, presents complex time series asymmetry across various scales.
  • Existing methods for quantifying multiscale asymmetry lack a tunable model generator for validation.

Purpose of the Study:

  • To introduce a novel generator for model time series with adjustable multiscale asymmetry.
  • To provide a tool for testing and refining existing multiscale asymmetry indices.
  • To explore the relationship between multiscale asymmetry and other complexity measures.

Main Methods:

  • Construction of an asymmetric Weierstrass function W(A) using asymmetric sawtooth functions.
  • Generation of model time series with controllable multiscale asymmetry.
  • Analysis of the independence of multiscale asymmetry from fractal dimension and multiscale entropy.
  • Generalization of multiscale asymmetry to include time-dependent (local) measures.

Main Results:

  • The asymmetric Weierstrass function W(A) successfully generates time series with any desired level of multiscale asymmetry.
  • Multiscale asymmetry was found to be independent of fractal dimension and multiscale entropy.
  • Time-dependent (local) multiscale asymmetry was introduced and demonstrated.
  • The W(A) function allows independent tuning of fractality and multiscale time asymmetry.

Conclusions:

  • The W(A) function serves as a valuable tool for generating and analyzing time series with tunable multiscale asymmetry.
  • This generator facilitates the comparison and refinement of multiscale measures of time series asymmetry.
  • The findings contribute to a deeper understanding of complex fluctuations in natural processes.