# Détection de courts segments inversés dans les génomes - méthodes et applications

Abstract : Inversion of short segments (less than 1000 bases) is suspected to be a major mechanism of genome's evolution. Two methods to detect ab initio these segments are presented. The sequence is modelized by a Markov chain $X^+$. Therefore the inverted complementary sequence is modelized by a Markov chain denoted $X^-$. The first chapter didactically presents the Markov models used in genomic sequence analysis. A generalization to order greater than 1 of a result on the speed of convergence of a Markov chain to its stationnary distribution is also established. The second chapter deals with the theory of local score $H_(n)=\max_(1\leq i \leq j \leq n)(Y_i+...+Y_j)$, for a sequence $(Y_1,...,Y_n) \in \R^n$. The asymptotic joint distribution of the $r$ greatest values of the local score is established using the extreme value theory. Finally a multiple test approach is derived to determine $r$. The third chapter propose a statistic of detection based on a likelihood ratio (model $X^+$ vs $X^-$) when the length of the inverted segment is known. A scan-approach'' is then applied. A known approximation of the distribution of the maximum of this type of statistic is then used for obtaining a p-value. In the forth chapter, the method of the local score is applied to deal with segments of unknown length and calculate the corresponding p-value. The fifth chapter presents the application of these methods to viral genomes. A software which implemented both methods is also presented.
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https://tel.archives-ouvertes.fr/tel-00010628
Contributor : David Robelin <>
Submitted on : Friday, October 14, 2005 - 12:05:47 PM
Last modification on : Tuesday, March 17, 2020 - 2:58:07 AM
Long-term archiving on: : Friday, April 2, 2010 - 10:40:04 PM

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• HAL Id : tel-00010628, version 1

### Citation

David Robelin. Détection de courts segments inversés dans les génomes - méthodes et applications. Sciences du Vivant [q-bio]. Université Paris Sud - Paris XI, 2005. Français. ⟨tel-00010628⟩

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