1. Detection of Patterns Within Randomness
- Author
-
Markus Christen, Ruedi Stoop, University of Zurich, Thiel, Marco, Kurths, Jürgen, Romano, M Carman, Moura, Alessandro, Károlyi, György, and Stoop, Ruedi
- Subjects
2206 Computational Mechanics ,Noise (signal processing) ,610 Medicine & health ,1702 Artificial Intelligence ,Plot (graphics) ,170 Ethics ,1712 Software ,Dimension (vector space) ,10222 Institute of Biomedical Ethics and History of Medicine ,Embedding ,Linear independence ,10001 Center for Ethics ,Algorithm ,Randomness ,Jitter ,Integer (computer science) - Abstract
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.
- Published
- 2010