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
SN - 0166-218X
VL - 155
SP - 868
EP - 880
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
IS - 6-7
ER -