Volume 79, Number 3, August 2007
|Number of page(s)||5|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||17 July 2007|
1-D random landscapes and non-random data series
Systems Biology and CNRS UMR 144, Institut Curie Paris 75005, France
2 Theory of Condensed Matter, Cavendish Laboratory - Cambridge CB3 0HE, UK
3 Laboratoire de Physique Statistique, Ecole Normale Supérieure - 75005 Paris, France
4 Departement de Mathematique, Ecole Normale Supérieure - 75005 Paris, France
Accepted: 11 June 2007
We study the simplest random landscape, the curve formed by joining consecutive data points with line segments, where the fi are i.i.d. random numbers and . We label each segment increasing (+) or decreasing (-) and call this string of +'s and -'s the up-down signature . We calculate the probability for a random curve and use it to bound the algorithmic information content of f. We show that f can be compressed by bits, where k is a universal currency for comparing the amount of pattern in different curves. By applying our results to microarray time series data, we blindly identify regulatory genes.
PACS: 89.70.+c – Information theory and communication theory / 87.14.Gg – DNA, RNA / 89.75.-k – Complex systems
© Europhysics Letters Association, 2007
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