Waiting times for clumps of patterns and for structured motifs in random sequences
Identifieur interne : 009251 ( Main/Exploration ); précédent : 009250; suivant : 009252Waiting times for clumps of patterns and for structured motifs in random sequences
Auteurs : V. T. Stefanov [Australie] ; S. Robin [France] ; S. Schbath [France]Source :
- Discrete applied mathematics [ 0166-218X ] ; 2007.
Descripteurs français
- Pascal (Inist)
English descriptors
- KwdEn :
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.
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream PascalFrancis, to step Corpus: 003B39
- to stream PascalFrancis, to step Curation: 002549
- to stream PascalFrancis, to step Checkpoint: 003514
- to stream Main, to step Merge: 009C26
- to stream Main, to step Curation: 009251
Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" level="a">Waiting times for clumps of patterns and for structured motifs in random sequences</title><author><name sortKey="Stefanov, V T" sort="Stefanov, V T" uniqKey="Stefanov V" first="V. T." last="Stefanov">V. T. Stefanov</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>School of Mathematics and Statistics. The University of Western Australia</s1><s2>Crawley (Perth) 6009. WA</s2><s3>AUS</s3><sZ>1 aut.</sZ></inist:fA14><country>Australie</country><wicri:noRegion>School of Mathematics and Statistics. The University of Western Australia</wicri:noRegion></affiliation></author><author><name sortKey="Robin, S" sort="Robin, S" uniqKey="Robin S" first="S." last="Robin">S. Robin</name><affiliation wicri:level="1"><inist:fA14 i1="02"><s1>ENGREF/INA PG/INRA unit (if Applied Mathematics and Computer Sciences. 16, rue Claude Bernard</s1><s2>75005. Paris</s2><s3>FRA</s3><sZ>2 aut.</sZ></inist:fA14><country>France</country><wicri:noRegion>75005. Paris</wicri:noRegion><placeName><settlement type="city">Paris</settlement><region type="région" nuts="2">Île-de-France</region></placeName></affiliation></author><author><name sortKey="Schbath, S" sort="Schbath, S" uniqKey="Schbath S" first="S." last="Schbath">S. Schbath</name><affiliation wicri:level="1"><inist:fA14 i1="03"><s1>Unité Mathematique. Infiirmatique & Génome, Institut National de la Recherche Affronomique</s1><s2>78352 Jouy-en-Josas</s2><s3>FRA</s3><sZ>3 aut.</sZ></inist:fA14><country>France</country><wicri:noRegion>78352 Jouy-en-Josas</wicri:noRegion><wicri:noRegion>Institut National de la Recherche Affronomique</wicri:noRegion><wicri:noRegion>78352 Jouy-en-Josas</wicri:noRegion></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">INIST</idno><idno type="inist">07-0327533</idno><date when="2007">2007</date><idno type="stanalyst">PASCAL 07-0327533 INIST</idno><idno type="RBID">Pascal:07-0327533</idno><idno type="wicri:Area/PascalFrancis/Corpus">003B39</idno><idno type="wicri:Area/PascalFrancis/Curation">002549</idno><idno type="wicri:Area/PascalFrancis/Checkpoint">003514</idno><idno type="wicri:explorRef" wicri:stream="PascalFrancis" wicri:step="Checkpoint">003514</idno><idno type="wicri:doubleKey">0166-218X:2007:Stefanov V:waiting:times:for</idno><idno type="wicri:Area/Main/Merge">009C26</idno><idno type="wicri:Area/Main/Curation">009251</idno><idno type="wicri:Area/Main/Exploration">009251</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">Waiting times for clumps of patterns and for structured motifs in random sequences</title><author><name sortKey="Stefanov, V T" sort="Stefanov, V T" uniqKey="Stefanov V" first="V. T." last="Stefanov">V. T. Stefanov</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>School of Mathematics and Statistics. The University of Western Australia</s1><s2>Crawley (Perth) 6009. WA</s2><s3>AUS</s3><sZ>1 aut.</sZ></inist:fA14><country>Australie</country><wicri:noRegion>School of Mathematics and Statistics. The University of Western Australia</wicri:noRegion></affiliation></author><author><name sortKey="Robin, S" sort="Robin, S" uniqKey="Robin S" first="S." last="Robin">S. Robin</name><affiliation wicri:level="1"><inist:fA14 i1="02"><s1>ENGREF/INA PG/INRA unit (if Applied Mathematics and Computer Sciences. 16, rue Claude Bernard</s1><s2>75005. Paris</s2><s3>FRA</s3><sZ>2 aut.</sZ></inist:fA14><country>France</country><wicri:noRegion>75005. Paris</wicri:noRegion><placeName><settlement type="city">Paris</settlement><region type="région" nuts="2">Île-de-France</region></placeName></affiliation></author><author><name sortKey="Schbath, S" sort="Schbath, S" uniqKey="Schbath S" first="S." last="Schbath">S. Schbath</name><affiliation wicri:level="1"><inist:fA14 i1="03"><s1>Unité Mathematique. Infiirmatique & Génome, Institut National de la Recherche Affronomique</s1><s2>78352 Jouy-en-Josas</s2><s3>FRA</s3><sZ>3 aut.</sZ></inist:fA14><country>France</country><wicri:noRegion>78352 Jouy-en-Josas</wicri:noRegion><wicri:noRegion>Institut National de la Recherche Affronomique</wicri:noRegion><wicri:noRegion>78352 Jouy-en-Josas</wicri:noRegion></affiliation></author></analytic><series><title level="j" type="main">Discrete applied mathematics</title><title level="j" type="abbreviated">Discrete appl. math.</title><idno type="ISSN">0166-218X</idno><imprint><date when="2007">2007</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Discrete applied mathematics</title><title level="j" type="abbreviated">Discrete appl. math.</title><idno type="ISSN">0166-218X</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Clump</term><term>Computer theory</term><term>DNA sequence</term><term>Generating function</term><term>Genome</term><term>Pattern</term><term>Probability distribution</term><term>Random sequence</term><term>Structured motif</term><term>Waiting time</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Temps attente</term><term>Suite aléatoire</term><term>Loi probabilité</term><term>Fonction génératrice</term><term>Génome</term><term>Séquence DNA</term><term>Informatique théorique</term><term>Somme aléatoire</term><term>Dorme</term><term>Bloc</term><term>Motif structuré</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">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.</div></front></TEI><affiliations><list><country><li>Australie</li><li>France</li></country><region><li>Île-de-France</li></region><settlement><li>Paris</li></settlement></list><tree><country name="Australie"><noRegion><name sortKey="Stefanov, V T" sort="Stefanov, V T" uniqKey="Stefanov V" first="V. T." last="Stefanov">V. T. Stefanov</name></noRegion></country><country name="France"><region name="Île-de-France"><name sortKey="Robin, S" sort="Robin, S" uniqKey="Robin S" first="S." last="Robin">S. Robin</name></region><name sortKey="Schbath, S" sort="Schbath, S" uniqKey="Schbath S" first="S." last="Schbath">S. Schbath</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Asie/explor/AustralieFrV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 009251 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 009251 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Asie
|area= AustralieFrV1
|flux= Main
|étape= Exploration
|type= RBID
|clé= Pascal:07-0327533
|texte= Waiting times for clumps of patterns and for structured motifs in random sequences
}}
| This area was generated with Dilib version V0.6.33. |  |