TY - JOUR

T1 - Waiting times for clumps of patterns and for structured motifs in random sequences

AU - Stefanov, Valeri

AU - Robin, S.

AU - Schbath, S.

PY - 2007

Y1 - 2007

N2 - 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 ail application. we determine significant structured motifs in a data set of DNA regulatory sequences. (c) 2006 Elsevier B.V. All rights reserved.

AB - 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 ail application. we determine significant structured motifs in a data set of DNA regulatory sequences. (c) 2006 Elsevier B.V. All rights reserved.

U2 - 10.1016/j.dam.2005.07.016

DO - 10.1016/j.dam.2005.07.016

M3 - Article

VL - 155

SP - 868

EP - 880

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 6-7

ER -