Orthology and paralogy distinguish whether a pair of genes originated by a speciation or a gene duplication event, whereas xenology refers to horizontal gene transfer. These concepts play a key role in phylogenomics and species tree inference is one of its prevalent tasks. Commonly, species tree inference is performed using sequence-based phylogenetic methods which heavily rely on the initial data sets to be solely composed of 1:1 orthologs. Such approaches are strongly restricted to a small set of genes that provide information about the species tree. In this work, it is shown that the restriction to 1:1 orthologs is not necessary to reconstruct a reliable hypothesis on the evolutionary history of species. Besides orthology, knowledge on all three major driving forces of gene evolution can be considered: speciation, gene duplication, and horizontal gene transfer. The corresponding concepts of orthology, paralogy, and xenology imply binary relations on pairs of genes. These relations, in turn, convey meaningful phylogenetic information and allow the inference of plausible phylogenetic species trees. To this end, it is shown that orthology, paralogy, and xenology have to fulfill certain mathematical properties. In particular, they have to be representable as a tree – the so-called gene tree. This work investigates the theoretical concepts of tree representable sets of binary relations to unfold the underlying mathematical structure. Various novel characterizations for those relations are given and the close connection between tree representable sets of binary relations and cographs, symbolic ultrametrics, and so-called unp 2-structures is revealed. Based on the novel characterizations, polynomial-time recognition algorithms for tree representable sets of relations are presented. In the case, a set of relations is tree representable, the corresponding tree representation can be found in polynomial time as well. Moreover, for the NP-complete problems of editing a given set of relations to its closest tree representable set, exact algorithms are developed by means of formulations as integer linear program. Finally, all algorithms have been implemented in the software ParaPhylo, a species tree inference method based on orthology and paralogy data. It is demonstrated on simulated data sets, as well as real-life data sets, that non-trivial phylogenies can indeed be reconstructed from tree-free orthology estimates alone.

This thesis defines and designs succinct indexes for several abstract data types (ADTs). The concept is to design auxiliary data structures that ideally occupy asymptotically less space than the information-theoretic lower bound on the space required to encode the given data, and support an extended set of operations using the basic operators defined in the ADT. As opposed to succinct (integrated data/index) encodings, the main advantage of succinct indexes is that we make assumptions only on the ADT through which the main data is accessed, rather than the way in which the data is encoded. This allows more freedom in the encoding of the main data. In this thesis, we present succinct indexes for various data types, namely strings, binary relations, multi-labeled trees and multi-labeled graphs, as well as succinct text indexes. For strings, binary relations and multi-labeled trees, when the operators in the ADTs are supported in constant time, our results are comparable to previous results, while allowing more flexibility in the encoding of the given data. Using our techniques, we improve several previous results. We design succinct representations for strings and binary relations that are more compact than previous results, while supporting access/rank/select operations efficiently. Our high-order entropy compressed text index provides more efficient support for searches than previous results that occupy essentially the same amount of space. Our succinct representation for labeled trees supports more operations than previous results do. We also design the first succinct representations of labeled graphs. To design succinct indexes, we also have some preliminary results on succinct data structure design. We present a theorem that characterizes a permutation as a suffix array, based on which we design succinct text indexes. We design a succinct representation of ordinal trees that supports all the navigational operations supported by various succinct tree representations. In addition, this representation also supports two other encodings schemes of ordinal trees as abstract data types. Finally, we design succinct representations of planar triangulations and planar graphs which support the rank/select of edges in counter clockwise order in addition to other operations supported in previous work, and a succinct representation of k-page graph which supports more efficient navigation than previous results for large values of k.

This thesis defines and designs succinct indexes for several abstract data types (ADTs). The concept is to design auxiliary data structures that ideally occupy asymptotically less space than the information-theoretic lower bound on the space required to encode the given data, and support an extended set of operations using the basic operators defined in the ADT. As opposed to succinct (integrated data/index) encodings, the main advantage of succinct indexes is that we make assumptions only on the ADT through which the main data is accessed, rather than the way in which the data is encoded. This allows more freedom in the encoding of the main data. In this thesis, we present succinct indexes for various data types, namely strings, binary relations, multi-labeled trees and multi-labeled graphs, as well as succinct text indexes. For strings, binary relations and multi-labeled trees, when the operators in the ADTs are supported in constant time, our results are comparable to previous results, while allowing more flexibility in the encoding of the given data. Using our techniques, we improve several previous results. We design succinct representations for strings and binary relations that are more compact than previous results, while supporting access/rank/select operations efficiently. Our high-order entropy compressed text index provides more efficient support for searches than previous results that occupy essentially the same amount of space. Our succinct representation for labeled trees supports more operations than previous results do. We also design the first succinct representations of labeled graphs. To design succinct indexes, we also have some preliminary results on succinct data structure design. We present a theorem that characterizes a permutation as a suffix array, based on which we design succinct text indexes. We design a succinct representation of ordinal trees that supports all the navigational operations supported by various succinct tree representations. In addition, this representation also supports two other encodings schemes of ordinal trees as abstract data types. Finally, we design succinct representations of planar triangulations and planar graphs which support the rank/select of edges in counter clockwise order in addition to other operations supported in previous work, and a succinct representation of k-page graph which supports more efficient navigation than previous results for large values of k.

The diploma thesis presents a collection of solved problems in binary relations. Students are familiarized with various applications of binary relations on high school mathematics and geometry. The work focuses on graphical representation of binary relations and their use in solving equations, inequalities and their sys- tems. It is a teaching text designated for a mathematics seminar at high school. In addition to exercises, it also includes an introduction of new concepts which are supplemented by relevant definitions and illustrative examples. 1

La quantité d'information disponible dans le domaine biomédical ne cesse d'augmenter. Pour que cette information soit facilement utilisable par les experts d'un domaine, il est nécessaire de l'extraire et de la structurer. Pour avoir des données structurées, il convient de détecter les relations existantes entre les entités dans les textes. Nos recherches se sont focalisées sur la question de l'extraction de relations complexes représentant des résultats expérimentaux, et sur la détection et la catégorisation de relations binaires entre des entités biomédicales. Nous nous sommes intéressée aux résultats expérimentaux présentés dans les articles scientifiques. Nous appelons résultat expérimental, un résultat quantitatif obtenu suite à une expérience et mis en relation avec les informations permettant de décrire cette expérience. Ces résultats sont importants pour les experts en biologie, par exemple pour faire de la modélisation. Dans le domaine de la physiologie rénale, une base de données a été créée pour centraliser ces résultats d'expérimentation, mais l'alimentation de la base est manuelle et de ce fait longue. Nous proposons une solution pour extraire automatiquement des articles scientifiques les connaissances pertinentes pour la base de données, c'est-à-dire des résultats expérimentaux que nous représentons par une relation n-aire. La méthode procède en deux étapes : extraction automatique des documents et proposition de celles-ci pour validation ou modification par l'expert via une interface. Nous avons également proposé une méthode à base d'apprentissage automatique pour l'extraction et la classification de relations binaires en domaine de spécialité. Nous nous sommes intéressée aux caractéristiques et variétés d'expressions des relations, et à la prise en compte de ces caractéristiques dans un système à base d'apprentissage. Nous avons étudié la prise en compte de la structure syntaxique de la phrase et la simplification de phrases dirigée pour la tâche d'extraction de relations. Nous avons en particulier développé une méthode de simplification à base d'apprentissage automatique, qui utilise en cascade plusieurs classifieurs. / The amount of available scientific literature is constantly growing. If the experts of a domain want to easily access this information, it must be extracted and structured. To obtain structured data, both entities and relations of the texts must be detected. Our research is about the problem of complex relation extraction which represent experimental results, and detection and classification of binary relations between biomedical entities. We are interested in experimental results presented in scientific papers. An experimental result is a quantitative result obtained by an experimentation and linked with information that describes this experimentation. These results are important for biology experts, for example for doing modelization. In the domain of renal physiology, a database was created to centralize these experimental results, but the base is manually populated, therefore the population takes a long time. We propose a solution to automatically extract relevant knowledge for the database from the scientific papers, that is experimental results which are represented by a n-ary relation. The method proceeds in two steps: automatic extraction from documents and proposal of information extracted for approval or modification by the experts via an interface. We also proposed a method based on machine learning for extraction and classification of binary relations in specialized domains. We focused on the variations of the expression of relations, and how to represent them in a machine learning system. We studied the way to take into account syntactic structure of the sentence and the sentence simplification guided by the task of relation extraction. In particular, we developed a simplification method based on machine learning, which uses a series of classifiers.

La thèse se situe dans le domaine de l'analyse latticielle de données dans la situation, très générale, ou des objets de nature diverse sont décrits par des variables de types divers ; on fait simplement l'hypothèse (réaliste) selon laquelle chaque variable prend ses valeurs dans un treillis. Les problèmes de traitement de telles données (extraction de connaissance) reviennent souvent à chercher à obtenir des familles de Moore de type particulier, par exemple arborescent, et donc à imposer des contraintes structurelles. Dans ce cadre, nous étudions d'abord les familles de Moore particulières que sont les hiérarchies, dont nous caractérisons la base canonique d'implications. Pour ce faire, nous introduisons un nouveau type de relations binaires sur les parties d'un ensemble, appelées (\em relations d'emboitement). Nous les mettons en correspondance bi-univoque avec les familles de Moore quelconques, établissons leur lien avec l'une des relations flèche, et revenons sur leurs propriétés dans le cas hiérarchique, ou elles sont d'abord apparues. Dans une seconde partie, nous nous intéressons à la correspondance de Galois associée à un tableau binaire (auquel les données du type indiqué ci-dessus peuvent toujours être ramenées). Nous examinons alors les contraintes à imposer à un tableau binaire pour que les fermés obtenus appartiennent à des familles de Moore prescrites, ou de type voulu. On obtient alors des relations binaires dites (\em bifermées). Etant donnés deux espaces de fermeture $(E, \varphi)$ et $(E', \varphi')$, une relation est bifermée si toute ligne de sa représentation matricielle correspond à un fermé par $\varphi$, et toute colonne à un fermé par $\varphi'$. Nous établissons l'isomorphisme entre l'ensemble des relations bifermées et celui des correspondances de Galois entre les deux treillis de fermés induits par $\varphi$ et $\varphi'$. Dans le cas fini, on en déduit des algorithmes efficaces pour l'ajustement d'une correspondance de Galois à une application quelconque entre deux treillis, ou pour le calcul du supremum de deux polarités. Dans une troisième partie, nous appliquons les résultats précédents à l'étude de l'introduction de contraintes classificatoires sur un tableau de données. Nous revenons sur divers usages des correspondances de Galois (ou des couples application résiduée / résiduelle) dans les modèles et les méthodes de la classification. Ceux-ci sont revisités dans l'optique d'une présentation unifiée fondée sur les bifermées, et, en prenant en compte les résultats de la première partie, des voies sont tracées pour la définition de nouvelles méthodes. Ces parties sont précédées d'une synthèse sur les treillis et les correspondances de Galois.

La thèse est consacrée à des problématiques d’algorithmique et de complexité sur deux sujets. Le premier sujet s’intéresse à la composition comportementale des services web. Ce problème a été réduit à la simulation d’un automate par le produit fermé d’un ensemble d’automates. La thèse étudie dans sa première partie la complexité de ce problème en considérant deux paramètres : le nombre des instances considéré de chaque service et la présence des états hybrides : état à la fois intermédiaire et final dans un automate. Le second sujet porte sur les systèmes de fermeture et s’intéresse au calcul de l’extension maximale d’un système de fermeture ainsi qu’à l’énumération des clefs candidates d’une base implicative. On donne un algorithme incrémental polynomial qui génère l’extension maximale d’un treillis codé par une relation binaire. Puis, la notion de key-ideal est définie, en prouvant que leur énumération est équivalente à l’énumération des clefs candidates. Ensuite, on donne un algorithme qui permet de générer les key-ideal minimaux en temps incrémental polynomial et les key-ideal non minimaux en délai polynomial. / This thesis investigates complexity and computational issues in two parts. The first concerns an issue related to web services composition problem: Deciding whether the behaviour of a web service can be composed out of an existing repository of web services. This question has been reduced to simulating a finite automata to the product closure of an automata set. We study the complexity of this problem considering two parameters; the number of considered instances in the composition and the presence of the so-called hybrid states (states that are both intermediate and final). The second part concerns closure systems and two related issues; Maximal extension of a closure system : we give an incremental polynomial algorithm that computes a lattice's maximal extension when the input is a binary relation. Candidate keys enumeration : we introduce the notion of key-ideal sets and prove that their enumeration is equivalent to candidate keys enumeration. We then give an efficient algorithm that generates all non-minimal key-ideal sets in a polynomial delay and all minimal ones in incremental polynomial time.