An edit distance between quotiented trees

International audienceIn this paper we propose a dynamic programming algorithm to compare two quotiented trees using a constrained edit distance. A quotiented tree is a tree defined with an additional equivalent relation on vertices and such that the quotient graph is also a tree. The core of the method relies on an adaptation of an algorithm recently proposed by Zhang for comparing unordered rooted trees. This method is currently being used in plant architecture modelling to quantify different types of variability between plants represented by quotiented trees

Local Similarity Between Quotiented Ordered Trees

International audienceIn this paper we propose a dynamic programming algorithm to evaluate local similarity between ordered quotiented trees using a constrained edit scoring scheme. A quotiented tree is a tree defined with an additional equivalent relation on vertices and such that the quotient graph is also a tree. The core of the method relies on two adaptations of an algorithm proposed by Zhang et al. [K. Zhang, D. Shasha, Simple fast algorithms for the editing distance between trees and related problems (1989) 1245-1262] for comparing ordered rooted trees. After some preliminary definitions and the description of this tree edit algorithm, we propose extensions to globally and locally compare two quotiented trees. This last method allows to find the region in each tree with the highest similarity. Algorithms are currently being used in genomic analysis to evaluate variability between RNA secondary structures

A multiple layer model to compare RNA secondary structures

International audienceWe formally introduce a new data structure, called MiGaL for ``Multiple Graph Layers'', that is composed of various graphs linked together by relations of abstraction/refinement. The new structure is useful for representing information that can be described at different levels of abstraction, each level corresponding to a graph. We then propose an algorithm for comparing two MiGaLs. The algorithm performs a step-by-step comparison starting with the most ``abstract'' level. The result of the comparison at a given step is communicated to the next step using a special colouring scheme. MiGaLs represent a very natural model for comparing RNA secondary structures that may be seen at different levels of detail, going from the sequence of nucleotides, single or paired with another to participate in a helix, to the network of multiple loops that is believed to represent the most conserved part of RNAs having similar function. We therefore show how to use MiGaLs to very efficiently compare two RNAs of any size at different levels of detail

A statistical modeling framework for analyzing tree-indexed data: Application to plant development on microscopic and macroscopic scales

We address statistical models for tree-indexed data.In Virtual Plants team, the host team for this thesis, applications of interest focus on plant development and its modulation by environmental and genetic factors.We thus focus on plant developmental applications both at a microscopic level with the study of the cell lineage in the biological tissue responsible for the plant growth, and at a macroscopic level with the mechanism of branch production.Far fewer models are available for tree-indexed data than for path-indexed data.This thesis therefore aims to propose a statistical modeling framework for studying patterns in tree-indexed data.To this end, two different classes of statistical models, Markov and change-point models, are investigatedNous nous intéressons à des modèles statistiques pour données indexées par des arborescences. Dans le contexte de l'équipe Virtual Plants, les applications portent sur le développement de la plante et sa modulation par des facteurs génétiques et environnementaux. Les modèles statistiques pour données indexées par des arborescences sont beaucoup moins développés que ceux pour séquences ou séries temporelles. Cette thèse vise à proposer un cadre de modélisation statistique pour l'identification de patterns dans des données indexées par des arborescences. Deux classes de modèles statistiques, les modèles de Markov et leur extension aux modèles de Markov cachés et les modèles de détection de ruptures multiples, sont étudiés. Nous proposons notamment de nouvelles méthodes dinférence de la structure dindépendance conditionnelle entre nuds parent et enfants dans les modèles de Markov reposant sur des algorithmes de sélection de graphes dans des modèles graphiques probabilistes. Les modèles étudiés sont appliqués dune part à des arborescences de lignage cellulaire à léchelle microscopique et dautre part à des systèmes ramifiés à léchelle macroscopique