This is a residential house in Brno. The supporting structure is reinforced concrete. The building has one basement and six floors. Vertical load-bearing structures are made up of reinforced concrete columns and walls. Horizontal load-bearing structures are formed by slabs (bearing in both directions). The staircase is concrete slab. Foundation is on piles. Infill vertical structures are brick. In the fifth floor pool is located.

Die Quantilsregression untersucht die Quantilfunktion QY |X (τ ), sodass ∀τ ∈ (0, 1), FY |X [QY |X (τ )] = τ erfu ̈llt ist, wobei FY |X die bedingte Verteilungsfunktion von Y gegeben X ist. Die Quantilsregression ermo ̈glicht eine genauere Betrachtung der bedingten Verteilung u ̈ber die bedingten Momente hinaus. Diese Technik ist in vielerlei Hinsicht nu ̈tzlich: beispielsweise fu ̈r das Risikomaß Value-at-Risk (VaR), welches nach dem Basler Akkord (2011) von allen Banken angegeben werden muss, fu ̈r ”Quantil treatment-effects” und die ”bedingte stochastische Dominanz (CSD)”, welches wirtschaftliche Konzepte zur Messung der Effektivit ̈at einer Regierungspoli- tik oder einer medizinischen Behandlung sind. Die Entwicklung eines Verfahrens zur Quantilsregression stellt jedoch eine gro ̈ßere Herausforderung dar, als die Regression zur Mitte. Allgemeine Regressionsprobleme und M-Scha ̈tzer erfordern einen versierten Umgang und es muss sich mit nicht- glatten Verlustfunktionen besch ̈aftigt werden. Kapitel 2 behandelt den Einsatz der Quantilsregression im empirischen Risikomanagement w ̈ahrend einer Finanzkrise. Kapitel 3 und 4 befassen sich mit dem Problem der h ̈oheren Dimensionalit ̈at und nichtparametrischen Techniken der Quantilsregression. / Quantile regression studies the conditional quantile function QY|X(τ) on X at level τ which satisfies FY |X QY |X (τ ) = τ , where FY |X is the conditional CDF of Y given X, ∀τ ∈ (0,1). Quantile regression allows for a closer inspection of the conditional distribution beyond the conditional moments. This technique is par- ticularly useful in, for example, the Value-at-Risk (VaR) which the Basel accords (2011) require all banks to report, or the ”quantile treatment effect” and ”condi- tional stochastic dominance (CSD)” which are economic concepts in measuring the effectiveness of a government policy or a medical treatment. Given its value of applicability, to develop the technique of quantile regression is, however, more challenging than mean regression. It is necessary to be adept with general regression problems and M-estimators; additionally one needs to deal with non-smooth loss functions. In this dissertation, chapter 2 is devoted to empirical risk management during financial crises using quantile regression. Chapter 3 and 4 address the issue of high-dimensionality and the nonparametric technique of quantile regression.

Structural adhesives are widely used with great success, and yet occasional failures can occur, often resulting from improper bonding procedures or joint design, overload or other detrimental service situations, or in response to a variety of environmental challenges. In these situations, cracks can start within the adhesive layer or debonds can initiate near an interface. The paths taken by propagating cracks can affect the resistance to failure and the subsequent service lives of the bonded structures. The behavior of propagating cracks in adhesive joints remains of interest, including when some critical environments, complicated loading modes, or uncertainties in material/interfacial properties are involved. From a mechanics perspective, areas of current interest include understanding the growth of damage and cracks, loading rate dependency of crack propagation, and the effect of mixed mode fracture loading scenarios on crack path selection. This dissertation involves analytical, numerical, and experimental evaluations of crack propagation in several adhesive joint configurations. The main objective is an investigation of crack path selection in adhesively bonded joints, focusing on in-plane fracture behavior (mode I, mode II, and their combination) of bonded joints with uniform bonding, and those with locally weakened interfaces. When removing cured components from molds, interfacial debonds can sometimes initiate and propagate along both mold surfaces, resulting in the molded product partially bridging between the two molds and potentially being damaged or torn. Debonds from both adherends can sometimes occur in weak adhesive bonds as well, potentially altering the apparent fracture behavior. To avoid or control these multiple interfacial debonding, more understanding of these processes is required. An analytical model of 2D parallel bridging was developed and the interactions of interfacial debonds were investigated using Euler-Bernoulli beam theory. The numerical solutions to the analytical results described the propagation processes with multiple debonds, and demonstrated some common phenomena in several different joints corresponding to double cantilever beam configurations. The analytical approach and results obtained could prove useful in extensions to understanding and controlling debonding in such situations and optimization of loading scenarios. Numerical capabilities for predicting crack propagation, confirmed by experimental results, were initially evaluated for crack behavior in monolithic materials, which is also of interest in engineering design. Several test cases were devised for modified forms of monolithic compact tension specimens (CT) were developed. An asymmetric variant of the CT configuration, in which the initial crack was shifted to two thirds of the total height, was tested experimentally and numerically simulated in ABAQUS®, with good agreement. Similar studies of elongated CT specimens with different specimen lengths also revealed good agreement, using the same material properties and cohesive zone model (CZM) parameters. The critical specimen length when the crack propagation pattern abruptly switches was experimentally measured and accurately predicted, building confidence in the subsequent studies where the numerical method was applied to bonded joints. In adhesively bonded joints, crack propagation and joint failure can potentially result from or involve interactions of a growing crack with a partially weakened interface, so numerical simulations were initiated to investigate such scenarios using ABAQUS®. Two different cohesive zone models (CZMs) are applied in these simulations: cohesive elements for strong and weak interfaces, and the extended finite element method (XFEM) for cracks propagating within the adhesive layer. When the main crack approaches a locally weakened interface, interfacial damage can occur, allowing for additional interfacial compliance and inducing shear stresses within the adhesive layer that direct the growing crack toward the weak interface. The maximum traction of the interfacial CZM appears to be the controlling parameter. Fracture energy of the weakened interface is shown to be of secondary importance, though can affect the results when particularly small (e.g. 1% that of the bulk adhesive). The length of the weakened interface also has some influence on the crack path. Under globally mixed mode loadings, the competition between the loading and the weakened interface affects the shear stress distribution and thus changes the crack path. Mixed mode loading in the opposite direction of the weakened interface is able to drive the crack away from the weakened interface, suggesting potential means to avoid failure within these regions or to design joints that fail in a particular manner. In addition to the analytical and numerical studies of crack path selection in adhesively bonded joints, experimental investigations are also performed. A dual actuator load frame (DALF) is used to test beam-like bonded joints in various mode mixity angles. Constant mode mixity angle tracking, as well as other versatile loading functions, are developed in LabVIEW® for use with a new controller system. The DALF is calibrated to minimize errors when calculating the compliance of beam-like bonded joints. After the corrections, the resulting fracture energies ( ) values are considered to be more accurate in representing the energy released in the crack propagation processes. Double cantilever beam (DCB) bonded joints consisting of 6061-T6 aluminum adherends bonded with commercial epoxy adhesives (J-B Weld, or LORD 320/322) are tested on the DALF. Profiles of the values for different constant mode mixity angles, as well as for continuously increasing mode mixity angle, are plotted to illustrate the behavior of the crack in these bonded joints. Finally, crack path selection in DCB specimens with one of the bonding surfaces weakened was studied experimentally, and rate-dependency of the crack path selection was found. Several contamination schemes are attempted, involving of graphite flakes, silicone tapes, or silane treatments on the aluminum oxide interfaces. In all these cases, tests involving more rapid crack propagation resulted in interfacial failures at the weakened areas, while slower tests showed cohesive failure throughout. One possible explanation of this phenomenon is presented using the rate-dependency of the yield stress (commonly considered to be corresponding to the maximum traction) of the epoxy adhesives. These experimental observations may have some potential applications tailoring adhesive joint configurations and interface variability to achieve or avoid particular failure modes. / Ph. D.

Dans cette thèse, nous étudions les effets d'un environnement stochastique et de l'utilisation d'une stratégie d'opting-out sur l'évolution de la coopération dans les jeux évolutionnaires. La thèse contient 8 articles, dont 6 sont déjà publiés dans des revues avec comité de lecture. Outre l'introduction, la thèse est divisée en deux parties, la partie 1 composée de 5 articles et la partie 2 de 3 articles. La partie 1 étudie l'impact de gains randomisés dans les jeux évolutionnaires. L'article 1 introduit les concepts de stabilité pour les jeux avec matrice de paiement aléatoire 2x2 dans des populations infinies avec des générations discrètes sans chevauchement dans un environnement stochastique. On y donne les conditions pour qu'un équilibre, sur la frontière ou à l'intérieur du simplexe des fréquences des stratégies, soit stochastiquement localement stable ou instable. L'article 2 étend les résultats de l'article 1 au cas où la valeur sélective est une fonction exponentielle du gain attendu suite à des interactions aléatoires par paires et montre que, de manière inattendue, le bruit aléatoire environnemental peut rompre un cycle périodique et favoriser la stabilité d'un équilibre intérieur. L'article 3 discute des effets de la sélection faible. Alors que les conditions de stabilité dans un environnement aléatoire reviennent aux conditions du cas déterministe lorsque l'intensité de la sélection diminue, les fluctuations aléatoires des gains peuvent accélérer la vitesse de convergence vers un équilibre stable sous une sélection plus faible. L'article 4 applique la théorie de la stabilité évolutive stochastique à un jeu randomisé de dilemme du prisonnier. On y montre que l'augmentation de la variance des gains de défection est propice à l'évolution de la coopération. L'article 5 étudie les jeux matriciels randomisés dans des populations finies et donne les conditions pour que la sélection favorise l'évolution de la coopération dans le contexte du jeu randomisé de dilemme du prisonnier. La partie 2 considère un jeu répété de dilemme du prisonnier dans le cas où un comportement d'opting-out est adopté par chaque joueur dans les interactions par paires. L'article 6 étudie la dynamique évolutive de la coopération et de la défection dans ce contexte et montre une possible coexistence à long terme, en supposant une population infinie et un équilibre rapide (en fait, instantané) dans les fréquences des paires. L'article 7 rapporte des résultats expérimentaux avec 264 étudiants universitaires utilisant la stratégie d'opting-out qui soutiennent la prédiction théorique d'une coexistence à long terme de coopération et de défection. L'article 8 étend l'analyse du modèle avec la stratégie d'opting-out au cas d'une population finie et fournit une preuve rigoureuse des deux échelles de temps pour les fréquences de coopération et de défection d'une part et les fréquences de paires de stratégies d'autre part. / In this thesis, we study the effects of a stochastic environment and the use of an opting-out strategy on the evolution of cooperation in evolutionary games. The thesis contains 8 articles, among which 6 are already published in peer-reviewed journals. Apart from the introduction, the thesis is divided into two parts, Part 1 made with 5 articles and Part 2 with 3 articles. Part 1 studies randomized payoffs in evolutionary games. Article 1 introduces stability concepts for 2x2 matrix games in infinite populations undergoing discrete, non-overlapping generations in a stochastic environment and gives conditions for an equilibrium, either on the boundary or in the interior of the simplex of all strategy frequencies, to be stochastically locally stable or unstable. Article 2 extends the results of Article 1 to the case where fitness is an exponential function of expected payoff in random pairwise interactions and shows that, unexpectedly, environmental random noise can break a periodic cycle and promote stability of an interior equilibrium. Article 3 discusses the effects of weak selection. While stability conditions in a random environment return to conditions in the deterministic case as selection intensity diminishes, random fluctuations in payoffs can accelerate the speed of convergence toward a stable equilibrium under weaker selection. Article 4 applies stochastic evolutionary stability theory to a randomized Prisoner's dilemma game and shows that increasing the variance in payoffs for defection is conducive to the evolution of cooperation. Article 5 studies randomized matrix games in finite populations and gives conditions for selection to favor the evolution of cooperation in the context of a randomized Prisoner's dilemma. Part 2 considers a repeated Prisoner's dilemma game with an opting-out behavior adopted by every player in pairwise interactions. Article 6 studies the evolutionary dynamics of cooperation and defection in this context and shows possible long-term coexistence, assuming an infinite population and fast (actually, instantaneous) equilibrium in the pair frequencies. Article 7 reports experimental results with 264 university students using the opting-out strategy that support the theoretical prediction of a long-term coexistence of cooperation and defection. Article 8 extends the analysis of the model with the opting-out strategy to the case of a finite population and provides a rigorous proof of the two-time scales for the frequencies of cooperation and defection on one hand and the frequencies of strategy pairs on the other.

Background Primary radiochemotherapy with photons is the standard treatment for locally advanced-stage non-small cell lung cancer (NSCLC) patients. Acute radiation-induced side effects such as oesophagitis and radiation pneumonitis limit patients’ quality of life, and the latter can be potentially life-threatening. Due to its distinct physical characteristics, proton therapy enables better sparing of normal tissues, which is supposed to translate into a reduction of radiation-induced side effects. Methods/design This is a single-centre, prospective, randomised controlled, phase II clinical trial to compare photon to proton radiotherapy up to 66 Gy (RBE) with concomitant standard chemotherapy in patients with locally advanced-stage NSCLC. Patients will be allocated in a 1:1 ratio to photon or proton therapy, and treatment will be delivered slightly accelerated with six fractions of 2 Gy (RBE) per week. Discussion The overall aim of the study is to show a decrease of early and intermediate radiation-induced toxicity using proton therapy. For the primary endpoint of the study we postulate a decrease of radiation-induced side effects (oesophagitis and pneumonitis grade II or higher) from 39 to 12%. Secondary endpoints are locoregional and distant failure, overall survival and late side effects. Trial registration Registered at ClinicalTrials.gov with Identifier NCT02731001 on 1 April 2016.

Dans le cadre de cette thèse, nous nous sommes intéressés d'abord au mécanisme de résonance locale en développant différents modèles théoriques pour l'étude de nouveaux cristaux phononiques à résonance locale (CPRL) en plaque dont l'élément principal et l'élastomère (silicone rubber). Le mode opératoire de ce mécanisme a été étudié et les ouvertures des bandes interdites ont été interprétées théoriquement ainsi que les phénomènes physiques mis en jeu. La mise en évidence expérimentale de la bande interdite a été réalisée par la fabrication et la caractérisation de structures CPRL et une parfaite concordance a été constatée entre les résultats théoriques et expérimentaux. Une étude des phénomènes de guidage a permis par ailleurs de montrer la possibilité du confinement et de la transmission d'un seul mode élastique au niveau d'un CPRL. Dans un second temps, nous avons montré que les propriétés d'un CPRL peuvent être reproduites dans le régime hypersonique. En effet, par le biais de la mise en place d'un nouveau modèle théorique et en proposant un nouveau CPRL à ondes de surface à base de films de diamant, nous avons pu montrer que ce type de cristal peut faire l'objet d'applications potentielles à des fins de guidage et de démultiplexage et ainsi initier la conception de nouveaux dispositifs miniaturisés à ondes de surface destinés aux systèmes de télécommunications (>GHz). / In this PhD work, we focused our interest on the theoretical and experimental study of locally resonant phononic crystals (LRPC) operating in sonic and hypersonic regimes. We first developed numerical models to understand the dispersion behaviour of elastic waves in those plate-type LRPC in which the silicone rubber plays a key role. We showed that with such structure, we can understand clearly how the local resonance (LR) mechanism operates to give rise to opening of low frequency BG two orders of magnitude that the one allowed by Bragg diffusion. The physics behind such structures was also figured out by means of theoretical models. An experimental study was then undertaken by manufacturing a new LRPC plate which has been characterized in terms of elastic behaviour and BG investigation. A perfect concordance was demonstrated between the theoretical an experimental results by evidencing a 2kHz BG opening using a 6mm diameter rubber stub and 1cm periodicity. In addition, waveguiding phenomena was investigated in those structures and showed the possibility of guiding of only one defect mode unlike conventional PCs in which many defects modes are generated. A second part of this study was dealt with LR mechanism in hypersonic regime. Using a new numerical and theoretical approach, we were able to show the BG opening and waveguiding for surface acoustic waves (SAW) in a LRPC composed of metallic stubs arranged on a diamond semi-infinite substrate. The added value of LR in such frequency regime remains in its ability to select only one guided mode due to the longer involved wavelengths. Such structures can then be suitable for filtering and demultiplexing applications.

Soit p un nombre premier. Les résultats de cette thèse s'inscrivent dans le cadre du programme de Langlands p-adique. Lorsque V est une représentation p-adique de dimension 2 du groupe Gal(\bar{Qp}/Qp), on sait lui associer une représentation p-adique continue B(V) de GL₂(Qp). Si F est une extension finie non triviale de Qp, la question d'associer des représentations p-adiques de GL₂(F) aux représentations p-adiques de dimension 2 de Gal(\bar{Qp}/F) dans l'esprit d'une correspondance locale à la Langlands s'annonce beaucoup plus délicate. Dans ce texte, nous considérons des espaces de Banach p-adiques, munis d'une action linéaire continue de GL₂(F), qui sont des complétions unitaires universelles de certaines représentations localement Qp-analytiques de GL₂(F). Celles-ci sont susceptibles de jouer un rôle important dans une éventuelle correspondance de Langlands locale p-adique pour GL₂(F). Le résultat principal de cette thèse est démontré dans le Chapitre 3 et généralise des résultats antérieurs de Berger et Breuil. Il consiste en une description explicite de ces complétés unitaires universels à l'aide des fonctions continues sur F d'un certain type. Pour ce faire, nous introduisons dans le Chapitre 2 des espaces de Banach de fonctions de classe C^r, où r est un nombre rationnel positif, et leurs espaces duaux de distributions d'ordre r. Nous construisons une base de Banach et nous donnons un critère de prolongement des formes linéaires définies sur un espace de fonctions localement Qp-polynomiales en distributions d'ordre r. Ce faisant, nous généralisons des résultats classiques dus à Amice-Vélu et Vishik. Dans le Chapitre 4, nous exhibons des cas de non nullité pour les complétions unitaires universelles considérées par construction explicite de réseaux invariants. Cela donne de nouveaux cas de la conjecture proposée par Breuil et Schneider sur l'équivalence entre l'existence de normes invariantes sur certaines représentations localement algébriques de GL_d(F) et l'existence de certaines représentations de de Rham de Gal(\bar{Qp}/F). / Let p be a prime. The subject of this thesis is the p-adic Langlands correspondence. If V is a p-adic representation of dimension 2 of the group Gal(\bar{Qp}/Qp), it is known how to associate to it a continuous p-adic representation B(V) of GL₂(Qp). If F is a non-trivial finite extension of Qp, the issue of associating p-adic representations of GL₂(F) to p-adic representations of dimension 2 of Gal(\bar{Qp}/F) in the spirit of a local Langlands correspondence appears much more delicate. In this text we consider a class of p-adic Banach spaces, endowed with a continuous linear action of GL₂(F), which are obtained as universal unitary completions of certain locally Qp-analytic representations of GL₂(F). Such representations are likely to play an important role in a future local p-adic Langlands correspondence for GL₂(F). The main result of this thesis is proved in Chapter 3 and generalizes some previous results of Berger and Breuil. It consists in an explicit description of these universal unitary completions by means of a certain class of continuous functions on F. In order to do this, we introduce in Chapter 2 a class of Banach spaces of functions of class C^r, where r is a positive rational number, as well as their dual spaces of distributions of order r. We build a Banach base and we give a criterion for telling when a linear form defined on a space of locally Qp-polynomial functions extends to a distribution of order r. As a consequence, we generalize some classical results due to Amice-Vélu and Vishik. In Chapter 4 we exhibit cases of non-nullity for these universal unitary completions, by an explicit construction of invariant lattices. This also provides new instances of the Breuil-Schneider conjecture about the equivalence between the existence of invariant norms on certain locally algebraic representations of GL_d(F) and the existence of certain De Rham representations of Gal(\bar{Qp}/F).

Dans le Chapitre 1 nous étudions les groupes localement compacts lacunaires hyperboliques. Nous caractérisons les groupes ayant un cône asymptotique qui est un arbre réel et dont l'action naturelle est focale. Nous étudions également la structure des groupes lacunaires hyperboliques, et montrons que dans le cas unimodulaire les sous-groupes ne satisfont pas de loi. Nous appliquons au Chapitre 2 les résultats précédents pour résoudre le problème de l'existence de points de coupure dans un cône asymptotique dans le cas des groupes de Lie connexes. Dans le Chapitre 3 nous montrons que le groupe de Neretin est compactement présenté et donnons une borne supérieure sur sa fonction de Dehn. Nous étudions également les propriétés métriques du groupe de Neretin, et prouvons que certains sous-groupes remarquables sont quasi-isométriquement plongés. Nous étudions dans le Chapitre 4 une famille de groupes agissant sur un arbre, et dont l'action locale est prescrite par un groupe de permutations. Nous montrons entre autres que ces groupes ont la propriété (PW), et exhibons des groupes simples au sein de cette famille. Dans le Chapitre 5 nous introduisons l'éventail des relations d'un groupe de type fini, qui est l'ensemble des longueurs des relations non engendrées par des relations plus courtes. Nous établissons un lien entre la simple connexité d'un cône asymptotique et l'éventail des relations du groupe, et donnons une grande classe de groupes dont l'éventail des relations est aussi grand que possible. / In Chapter 1 we investigate the class of locally compact lacunary hyperbolic groups. We characterize locally compact groups having one asymptotic cone that is a real tree and whose natural isometric action is focal. We also study the structure of lacunary hyperbolic groups, and prove that in the unimodular case subgroups cannot satisfy a law. We apply the previous results in Chapter 2 to solve the problem of the existence of cut-points in asymptotic cones for connected Lie groups. In Chapter 3 we prove that Neretin's group is compactly presented and give an upper bound on its Dehn function. We also study metric properties of Neretin's group, and prove that some remarkable subgroups are quasi-isometrically embedded. In Chapter 4 we study a family of groups acting on a tree, and whose local action is prescribed by some permutation group. We prove among other things that these groups have property (PW), and exhibit some simple groups in this family. In Chapter 5 we introduce the relation range of a finitely generated group, which is the set of lengths of relations that are not generated by relations of smaller length. We establish a link between simple connectedness of asymptotic cones and the relation range of the group, and give a large class of groups having a relation range as large as possible.

Le phénomène du religieux joue un rôle important en Europe. Le droit ecclésiastique stipule les rapports juridiques entre l’Etat et les Eglises et les Religions. L’article 9 CEDH et son développement jurisprudentiel créent les conditions d’existence d’un droit ecclésiastique européen de facto. En outre, la Déclaration 11 annexée au Traité d’Amsterdam, la Charte des Droits fondamentaux de l’Union et le Traité de Lisbonne forment les fondements d’un droit ecclésiastique de l’Union, dans la perspective d’une convergence plus avancée. La contribution de l’Eglise Orthodoxe à la construction européenne est considérée indispensable par le biais des Représentations des Eglises Orthodoxes localement établies au sein de l’Union Européenne, ainsi que de sa tradition ecclésiale. / The religious phenomenon plays an important role in Europe. The ecclesiastical law regulates the relationship between the State and the Churches/Religions. The article 9 of the ECHR and its jurisprudential development create conditions for the existence of a de facto European ecclesiastical law. In addition, the Declaration 11 annexed to the Amsterdam Treaty, the Charter of Fundamental Rights of the European Union and the Lisbon Treaty are the foundations of an Ecclesiastical law of the Union from the perspective of a more advanced convergence. The contribution of the Orthodox Church to the European construction is considered indispensable through representations of the locally established Orthodox Churches, within the European Union and its ecclesiastical tradition. / Το θρησκευτικό φαινόμενο παίζει ένα σημαντικό ρόλο στην Ευρώπη. Το εκκλησιαστικό δίκαιο ρυθμίζει τις σχέσεις Εκκλησιών και Θρησκειών με το κράτος. Το άρθρο 9 ΕΣΔΑ και η νομολογιακή του ανάπτυξη δημιουργούν τις δομές ύπαρξης ενός ευρωπαϊκού εκκλησιαστικού δικαίου de facto. Από την άλλη, η Δήλωση 11 της Συνθήκης του Άμστερνταμ, ο Χάρτης Θεμελιωδών δικαιωμάτων και η Συνθήκη της Λισσαβόνας διαμορφώνουν τα θεμέλια ενός Εκκλησιαστικού δικαίου της Ένωσης, υπό τη προοπτική μίας πιο προχωρημένης σύγκλησης. Η συνεισφορά της Ορθόδοξης Εκκλησίας στην οικοδομή της Ευρώπης θεωρείται απαραίτητη μέσω των αντιπροσωπειών των κατά τόπους Ορθόδοξων Εκκλησιών στην Ευρωπαϊκή Ένωση αλλά και μέσω της εκκλησιαστική της παράδοση.

La thèse se concentre sur une recherche méthodologique sur l'optimisation structurelle catégorielle au moyen d'un apprentissage multiple. Dans cette thèse, les variables catégorielles non ordinales sont traitées comme des variables discrètes multidimensionnelles. Afin de réduire la dimensionnalité, les nombreuses techniques d'apprentissage sont introduites pour trouver la dimensionnalité intrinsèque et mapper l'espace de conception d'origine sur un espace d'ordre réduit. Les mécanismes des techniques d'apprentissage à la fois linéaires et non linéaires sont d'abord étudiés. Ensuite, des exemples numériques sont testés pour comparer les performances de nombreuses techniques d’apprentissage. Sur la base de la représentation d'ordre réduit obtenue par Isomap, les opérateurs de mutation et de croisement évolutifs basés sur les graphes sont proposés pour traiter des problèmes d'optimisation structurelle catégoriels, notamment la conception du dôme, du cadre rigide de six étages et des structures en forme de dame. Ensuite, la méthode de recherche continue consistant à déplacer des asymptotes est exécutée et fournit une solution compétitive, mais inadmissible, en quelques rares itérations. Ensuite, lors de la deuxième étape, une stratégie de recherche discrète est proposée pour rechercher de meilleures solutions basées sur la recherche de voisins. Afin de traiter le cas dans lequel les instances de conception catégorielles sont réparties sur plusieurs variétés, nous proposons une méthode d'apprentissage des variétés k-variétés basée sur l'analyse en composantes principales pondérées. / The thesis concentrates on a methodological research on categorical structural optimizationby means of manifold learning. The main difficulty of handling the categorical optimization problems lies in the description of the categorical variables: they are presented in a category and do not have any orders. Thus the treatment of the design space is a key issue. In this thesis, the non-ordinal categorical variables are treated as multi-dimensional discrete variables, thus the dimensionality of corresponding design space becomes high. In order to reduce the dimensionality, the manifold learning techniques are introduced to find the intrinsic dimensionality and map the original design space to a reduced-order space. The mechanisms of both linear and non-linear manifold learning techniques are firstly studied. Then numerical examples are tested to compare the performance of manifold learning techniques mentioned above. It is found that the PCA and MDS can only deal with linear or globally approximately linear cases. Isomap preserves the geodesic distances for non-linear manifold however, its time consuming is the most. LLE preserves the neighbour weights and can yield good results in a short time. KPCA works like a non-linear classifier and we proves why it cannot preserve distances or angles in some cases. Based on the reduced-order representation obtained by Isomap, the graph-based evolutionary crossover and mutation operators are proposed to deal with categorical structural optimization problems, including the design of dome, six-story rigid frame and dame-like structures. The results show that the proposed graph-based evolutionary approach constructed on the reduced-order space performs more efficiently than traditional methods including simplex approach or evolutionary approach without reduced-order space. In chapter 5, the LLE is applied to reduce the data dimensionality and a polynomial interpolation helps to construct the responding surface from lower dimensional representation to original data. Then the continuous search method of moving asymptotes is executed and yields a competitively good but inadmissible solution within only a few of iteration numbers. Then in the second stage, a discrete search strategy is proposed to find out better solutions based on a neighbour search. The ten-bar truss and dome structural design problems are tested to show the validity of the method. In the end, this method is compared to the Simulated Annealing algorithm and Covariance Matrix Adaptation Evolutionary Strategy, showing its better optimization efficiency. In chapter 6, in order to deal with the case in which the categorical design instances are distributed on several manifolds, we propose a k-manifolds learning method based on the Weighted Principal Component Analysis. And the obtained manifolds are integrated in the lower dimensional design space. Then the method introduced in chapter 4 is applied to solve the ten-bar truss, the dome and the dame-like structural design problems.