1-D random landscapes and non-random data series

T. M. A. Fink; K. Willbrand; F. C. S. Brown

doi:10.1209/0295-5075/79/38006

All issues

Volume 79 / No 3 (August 2007)

EPL, 79 3 (2007) 38006

Abstract

Issue		EPL Volume 79, Number 3, August 2007


Article Number		38006
Number of page(s)		5
Section		Interdisciplinary Physics and Related Areas of Science and Technology
DOI		https://doi.org/10.1209/0295-5075/79/38006
Published online		17 July 2007

EPL, 79 (2007) 38006

1-D random landscapes and non-random data series

T. M. A. Fink¹^,2, K. Willbrand³ and F. C. S. Brown⁴

¹ 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

Received: 4 May 2007
Accepted: 11 June 2007

Abstract

We study the simplest random landscape, the curve formed by joining consecutive data points $f_{1},\ldots,f_{N+1}$ with line segments, where the f_i are i.i.d. random numbers and $f_{i}\ne f_{j}$ . We label each segment increasing (+) or decreasing (-) and call this string of +'s and -'s the up-down signature $\sigma$ . We calculate the probability $P(\sigma (f))$ for a random curve and use it to bound the algorithmic information content of f. We show that f can be compressed by $k = \log_2 {1/P(\sigma)} - N$ 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

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