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Contribution Details

Type Book Chapter
Scope Discipline-based scholarship
Title Detection of Patterns Within Randomness
Organization Unit
  • Ruedi Stoop
  • Markus Christen
  • Marco Thiel
  • Jürgen Kurths
  • M Carman Romano
  • Alessandro Moura
  • György Károlyi
Item Subtype Original Work
Refereed No
Status Published in final form
  • English
Booktitle Nonlinear Dynamics and Chaos. Advances and Perspectives
ISBN 978-3-6420-4628-5
Place of Publication Berlin
Publisher Springer
Page Range 271 - 290
Date 2010
Abstract Text The identification of jittered regular signals (="patterns#) embedded in a noisy background is an important and difficult task, particularly in the neurosciences. Traditional methods generally fail to capture such signals. Staircase-like structures in the log–log correlation plot, however, are reliable indicators of such signal components.We provide a number of applications of this method and derive an analytic relationship between the length of the pattern n and the maximal number of steps s(n,m) that are observable at a chosen embedding dimension m. For integer linearly independent patterns and small jitter and noise, the length of the embedded pattern can be calculated from the number of steps. The method is demonstrated to have a huge potential for experimental applications.
Digital Object Identifier 10.1007/978-3-642-04629-2_12
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