Waiting times for clumps of patterns and for structured motifs in random sequences |
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| Institution: | 1. School of Mathematics and Statistics, The University of Western Australia, Crawley (Perth) 6009, W.A., Australia;2. ENGREF / INA PG / INRA unit of Applied Mathematics and Computer Sciences, 16, rue Claude Bernard, 75005, Paris, France;3. Unité Mathématique, Informatique & Génome, Institut National de la Recherche Agronomique, 78352 Jouy-en-Josas, France;1. Department of Computer Science and Center for Computational Molecular Biology, Brown University, 115 Waterman St, Box 1910, Providence, RI 02912, USA;2. Department of Computer Science and Engineering, University of California San Diego, APM 3132, 9500 Gilman Drive Dept. 0114, La Jolla, CA 92093-0114, USA;3. School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel |
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| Abstract: | This paper provides exact probability results for waiting times associated with occurrences of two types of motifs in a random sequence. First, we provide an explicit expression for the probability generating function of the interarrival time between two clumps of a pattern. It allows, in particular, to measure the quality of the Poisson approximation which is currently used for evaluation of the distribution of the number of clumps of a pattern. Second, we provide explicit expressions for the probability generating functions of both the waiting time until the first occurrence, and the interarrival time between consecutive occurrences, of a structured motif. Distributional results for structured motifs are of interest in genome analysis because such motifs are promoter candidates. As an application, we determine significant structured motifs in a data set of DNA regulatory sequences. |
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