Ein fragment-basierter Ansatz zur Berechnung von vertikalen Anregungsenergien in periodischen Systemen wurde entwickelt. Das Ziel war eine wellenfunktions-basierte Hierarchie von lokalen post-Hartree-Fock Methoden, welche über das weitverbreitete Ein-Elektronen Bild der Bandlücke hinausgehen und eine Möglichkeit zur systematischen Verbesserung der Ergebnisse liefern. Darüber hinaus sollte durch die Verwendung von lokalen Orbitalen eine nahtlose Einbettung des Fragments ermöglicht und eine effektive Methode für die Untersuchung von Defekten in periodischen Systemen geschaffen werden. Als erster Schritt wird das fragment-basierte Configuration Interaction Singles (CIS) Model vorgestellt. Im Anschluss erfolgt der Wechsel zum fragment-basierten lokalen algebraic-diagrammatic construction Modells zweiter Ordnung (DF-LADC(2)). Beide Methoden wurden für ein neutrales Farbzentrum in Magnesiumoxid (MgO) getestet. Dabei wurden Fragmente mit bis zu 57 Atomen verwendet. Eine Konvergenz mit der Fragmentgröße, der Größe der Superzellen und des K-mesh konnte erreicht werden. Dennoch wurde eine erste Anregungsenergie von 5.9 eV erhalten, was 0.9 eV über dem veröffentlichten experimentellen Wert liegt. Mit hoher Wahrscheinlichkeit rührt die Abweichung vom Basissatzvollständigkeitsfehler her. ”Finite-Cluster”-Berechnungen bestätigen entsprechende Basissatzfehler. Interessanterweise stimmt die erste Anregungsenergie für ein Oberflächenfarbzentrum in MgO mit einigen experimentellen Werten überein. Allerdings decken die experimentellen Werte für diese Systeme einen weiten Bereich ab (1.15 - 4.2 eV). / An embedded-fragment approach for calculation of vertical excitation energies in periodic systems has been developed. The aim is a wave-function-based hierarchy of local post-Hartree-Fock models, which goes beyond the very common one-electron picture of the band gap and offers a way for systematic improvability of the results. The use of local occupied and virtual orbitals allows for a seamless embedding model for the fragment and becomes especially effective in studying defects in solids. As a first step in the hierarchy an embedded-fragment Configuration Interaction Singles (CIS) model is presented. The second step is an embedded-fragment local algebraic diagrammatic construction scheme of second order (DF-LADC(2)). Both methods are tested for an neutral color center in bulk and surface magnesium oxide (MgO). Different fragments with up to 57 atoms were studied. A convergence with fragment size, super-cell size and k-mesh has been achieved. However a first excitation energy of 5.9 eV is obtained for the bulk MgO, which is 0.9 eV above the reported experimental value. The deviation most likely originates from the basis set incompleteness error, which, according to finite cluster studies, can be sizable. Interestingly for a surface color center in MgO the observed first excitation energy of 4.1 eV agrees with some of the experimental values (4.2 eV). However for the surface color centers in MgO the scatter of the experimental results is very large (1.15 eV - 4.2 eV).

Diese Dissertation präsentiert neue Techniken der Integration für verschiedene Probleme der Finanzmathematik und einige Anwendungen in der Wahrscheinlichkeitstheorie. Zu Beginn entwickeln wir zwei Zugänge zur robusten stochastischen Integration. Der erste, ähnlich der Ito’schen Integration, basiert auf einer Topologie, erzeugt durch ein äußeres Maß, gegeben durch einen minimalen Superreplikationspreis. Der zweite gründet auf der Integrationtheorie für rauhe Pfade. Wir zeigen, dass das entsprechende Integral als Grenzwert von nicht antizipierenden Riemannsummen existiert und dass sich jedem "typischen Preispfad" ein rauher Pfad im Ito’schen Sinne zuordnen lässt. Für eindimensionale "typische Preispfade" wird sogar gezeigt, dass sie Hölder-stetige Lokalzeiten besitzen. Zudem erhalten wir Verallgemeinerungen von Föllmer’s pfadweiser Ito-Formel. Die Integrationstheorie für rauhe Pfade kann mit dem Konzept der kontrollierten Pfade und einer Topologie, welche die Information der Levy-Fläche enthält, entwickelt werden. Deshalb untersuchen wir hinreichende Bedingungen an die Kontrollstruktur für die Existenz der Levy-Fläche. Dies führt uns zur Untersuchung von Föllmer’s Ito-Formel aus der Sicht kontrollierter Pfade. Para-kontrollierte Distributionen, kürzlich von Gubinelli, Imkeller und Perkowski eingeführt, erweitern die Theorie rauher Pfade auf den Bereich von mehr-dimensionale Parameter. Wir verallgemeinern diesen Ansatz von Hölder’schen auf Besov-Räume, um rauhe Differentialgleichungen zu lösen, und wenden die Ergebnisse auf stochastische Differentialgleichungen an. Zum Schluß betrachten wir stark gekoppelte Systeme von stochastischen Vorwärts-Rückwärts-Differentialgleichungen (FBSDEs) und erweitern die Theorie der Existenz, Eindeutigkeit und Regularität der sogenannten Entkopplungsfelder auf Markovsche FBSDEs mit lokal Lipschitz-stetigen Koeffizienten. Als Anwendung wird das Skorokhodsche Einbettungsproblem für Gaußsche Prozesse mit nichtlinearem Drift gelöst. / In this thesis new robust integration techniques, which are suitable for various problems from stochastic analysis and mathematical finance, as well as some applications are presented. We begin with two different approaches to stochastic integration in robust financial mathematics. The first one is inspired by Ito’s integration and based on a certain topology induced by an outer measure corresponding to a minimal superhedging price. The second approach relies on the controlled rough path integral. We prove that this integral is the limit of non-anticipating Riemann sums and that every "typical price path" has an associated Ito rough path. For one-dimensional "typical price paths" it is further shown that they possess Hölder continuous local times. Additionally, we provide various generalizations of Föllmer’s pathwise Ito formula. Recalling that rough path theory can be developed using the concept of controlled paths and with a topology including the information of Levy’s area, sufficient conditions for the pathwise existence of Levy’s area are provided in terms of being controlled. This leads us to study Föllmer’s pathwise Ito formulas from the perspective of controlled paths. A multi-parameter extension to rough path theory is the paracontrolled distribution approach, recently introduced by Gubinelli, Imkeller and Perkowski. We generalize their approach from Hölder spaces to Besov spaces to solve rough differential equations. As an application we deal with stochastic differential equations driven by random functions. Finally, considering strongly coupled systems of forward and backward stochastic differential equations (FBSDEs), we extend the existence, uniqueness and regularity theory of so-called decoupling fields to Markovian FBSDEs with locally Lipschitz continuous coefficients. These results allow to solve the Skorokhod embedding problem for a class of Gaussian processes with non-linear drift.

Interactions are formed and shaped differently from culture to culture. This thesis focuses on this phenomenon and in the first part deals with (from a theoretical view) the question, how the interplay between language-use and culture can be described. A cross-disciplinary approach within the scope of cross-cultural communication research is developed as is a semiotic concept, based on mainly linguistic, interactional and anthropological theories and methods. In order to describe different culture-specific interactional styles the semiotic field called embedding culture is outlined as an important resource for participants organizing talk-in-interactions. In the second part of this book the relevance of this approach is applied and tested. With the aid of various video recordings of ‘lunch-talks’ among colleagues at a restaurant in Sweden and Germany, this specific type of action and their cultural patterns are analyzed in order to describe cultural-specific styles in face-to-face-interaction. The methodological problem of recorded interaction is pointed out and the role of the camera highlighted. As the analyzed data is mainly based on interactions between men also gender-aspects are discussed. Furthermore, the scenario, time aspects and the customs and rituals of interactions at table are taken into account as relevant features of the embedding culture, all going into a culture-specific style of interaction. The results of the empirical study are, finally, correlated with other, not interaction-based analyses in the field of cross-cultural communication, and the specific national-cultural dimensions are critically discussed. / Interaktioner utformas och gestaltas olika från kultur till kultur. Avhandlingen fokuserar på denna aspekt och behandlar först ur ett teoretiskt perspektiv hur detta fenomen kan beskrivas. Med en tvärvetenskaplig ansats inom ramen av den s.k. interkulturella kommunikationsforskningen (cross-cultural communication) kombineras kulturanalytiska med lingvistiska och samtalsanalytiska teorier och metoder. Ett semiotiskt koncept utarbetas med hjälp av vilka olika kulturspecifika interaktionsstilar kan beskrivas. Det semiotiska fältet som koncipierats kallas för Einbettungskultur (’inbäddningskulturen’). I den andra delen används och prövas detta koncept. Med hjälp av ett flertal videoinspelade lunchsamtal i Sverige och Tyskland analyseras konkreta exempel på kommunikativ praxis och deras kulturella mönster i jämförbara interaktionssituationer. Det beskrivs hur den kulturspecifika interaktionsstilen vid lunchen bland svenska arbetskollegor kan skilja sig från det tyskspråkiga sättet att gestalta samma interaktionstyp. Inspelningssituationen problematiseras och kamerans roll i interaktionen diskuteras. Eftersom analyserna huvudsakligen baseras på samtal mellan män tas genusperspektivet upp. Vid sidan av själva samtalen analyseras även scenariot, tidsaspekten och ritualiseringen av interaktionen vid bordet som tre aspekter av inbäddningskulturen som tillsammans bidrar till en kulturspecifik interaktionsstil. Resultaten av den kulturella analysen som tar sin utgångspunkt i en konkret och jämförbar interaktionssituation i olika kulturer relateras avslutningsvis till andra, icke-interaktionsbaserade analyser inom den interkulturella kommunikationsforskningen och nationalkulturella beskrivningar problematiseras.

This Master Thesis deals with the drawing algorithms of graphs known from the mathematical theory. These algorithms deals with an appropriate distribution of the graph vertices in order to obtain the most clear and readable graphs for human readers. The main objective of this work was also to implement the drawing algorithm in the application that would allow to edit the graph. This work deals also with graphs representation in computers.

<p dir="ltr">We now live in a world where we can reach people directly through social media, without relying on traditional media such as television and radio. The landscape of social media is highly distributed, as users generate and consume a variety of content. On the other hand, social media platforms collect vast amounts of data and create very specific profiles of different users through targeted advertising. Various interest groups, politicians, advertisers, and stakeholders utilize these platforms to target potential users to advance their interests by adapting their messaging.  A significant challenge lies in understanding this messaging and how it changes depending on the targeted user groups. Another challenge arises when we do not know who the users are and what their motivations are for engaging with content. The initial phase of our research focuses on comprehensively understanding users and their underlying motivations, whether practitioner-based or promotional. Gaining this understanding is crucial in reshaping our perspective on the content disseminated by these users. Step beyond that, assuming the identification of the involved parties, this study aims to characterize the messaging and explore how it adapts based on various targeted demographic groups. This thesis addresses these challenges by developing computational approaches and frameworks for (1) characterizing user types and their motivations, (2) analyzing the messaging based on topics relevant to the users and their responses to it, and (3) delving into the deeper understanding of the themes and arguments involved in the messaging.</p>

Multiobjective Stochastic Linear Programming is a relevant topic. As a matter of fact, many real life problems ranging from portfolio selection to water resource management may be cast into this framework. There are severe limitations in objectivity in this field due to the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice does not hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this thesis, we resort to the bounded rationality and chance-constrained principles to define satisficing solutions for Multiobjective Stochastic Linear Programming problems. These solutions are then characterized for the cases of normal, exponential, chi-squared and gamma distributions. Ways for singling out such solutions are discussed and numerical examples provided for the sake of illustration. Extension to the case of fuzzy random coefficients is also carried out. / Decision Sciences

Nowadays, the near-horizon regions of black holes have enjoyed great attention thanks to their role in the popular AdS/CFT correspondence and their specific geometry suitable for formulations of uniqueness theorems in higher dimensions. A strictly general-relativistic point of view reveals also many interesting phenomena taking place near black-hole horizons. Our aim was to investigate how horizon multiplicity affects near-horizon geometry, geodesical distance, radial motion of photons and massive, charged particles, and also the possibility of collision processes leading to unbound collision energies near the horizon. We chose the Reissner-Nordström-de Sitter metric, which, on the one hand, is simple thanks to being static and spherically symmetric but which, on the other hand, is rich enough to enable the existence of up to a doubly degenerate ultra-extreme horizon. After discussing the physical feasibility of the near-horizon limit, we applied it to single, double, and triple horizons, their near-horizon geometries, and local collision processes. We found continuous coordinate systems covering all types of horizons and analytic solutions for motion of radial photons and special or critical, massive, charged particles in their vicinity. We addressed particle collisions in the immediate vicinity of horizons...

Les principaux objets étudiés dans cette thèse sont les équations décrivant le morphisme de groupe sur une variété abélienne, plongée dans un espace projectif, et leurs applications en cryptographie. Notons g sa dimension et k son corps de définition. Ce mémoire est composé de deux parties. La première porte sur l'étude des courbes d'Edwards, un modèle pour les courbes elliptiques possédant un sous-groupe de points k-rationnels cyclique d'ordre 4, connues en cryptographie pour l'efficacité de leur loi d'addition et la possibilité qu'elle soit définie pour toute paire de points k-rationnels (loi d'addition k-complète). Nous en donnons une interprétation géométrique et en déduisons des formules explicites pour le calcul du couplage de Tate réduit sur courbes d'Edwards tordues, dont l'efficacité rivalise avec les modèles elliptiques couramment utilisés. Cette partie se conclut par la génération, spécifique au calcul de couplages, de courbes d'Edwards dont les tailles correspondent aux standards cryptographiques actuellement en vigueur. Dans la seconde partie nous nous intéressons à la notion de complétude introduite ci-dessus. Cette propriété est cryptographiquement importante car elle permet d'éviter des attaques physiques, comme les attaques par canaux cachés, sur des cryptosystèmes basés sur les courbes elliptiques ou hyperelliptiques. Un précédent travail de Lange et Ruppert, basé sur la cohomologie des fibrés en droite, permet une approche théorique des lois d'addition. Nous présentons trois résultats importants : tout d'abord nous généralisons un résultat de Bosma et Lenstra en démontrant que le morphisme de groupe ne peut être décrit par strictement moins de g+1 lois d'addition sur la clôture algébrique de k. Ensuite nous démontrons que si le groupe de Galois absolu de k est infini, alors toute variété abélienne peut être plongée dans un espace projectif de manière à ce qu'il existe une loi d'addition k-complète. De plus, l'utilisation des variétés abéliennes nous limitant à celles de dimension un ou deux, nous démontrons qu'une telle loi existe pour leur plongement projectif usuel. Finalement, nous développons un algorithme, basé sur la théorie des fonctions thêta, calculant celle-ci dans P^15 sur la jacobienne d'une courbe de genre deux donnée par sa forme de Rosenhain. Il est désormais intégré au package AVIsogenies de Magma. / The main objects we study in this PhD thesis are the equations describing the group morphism on an abelian variety, embedded in a projective space, and their applications in cryptograhy. We denote by g its dimension and k its field of definition. This thesis is built in two parts. The first one is concerned by the study of Edwards curves, a model for elliptic curves having a cyclic subgroup of k-rational points of order 4, known in cryptography for the efficiency of their addition law and the fact that it can be defined for any couple of k-rational points (k-complete addition law). We give the corresponding geometric interpretation and deduce explicit formulae to calculate the reduced Tate pairing on twisted Edwards curves, whose efficiency compete with currently used elliptic models. The part ends with the generation, specific to pairing computation, of Edwards curves with today's cryptographic standard sizes. In the second part, we are interested in the notion of completeness introduced above. This property is cryptographically significant, indeed it permits to avoid physical attacks as side channel attacks, on elliptic -- or hyperelliptic -- curves cryptosystems. A preceeding work of Lange and Ruppert, based on cohomology of line bundles, brings a theoretic approach of addition laws. We present three important results: first of all we generalize a result of Bosma and Lenstra by proving that the group morphism can not be described by less than g+1 addition laws on the algebraic closure of k. Next, we prove that if the absolute Galois group of k is infinite, then any abelian variety can be projectively embedded together with a k-complete addition law. Moreover, a cryptographic use of abelian varieties restricting us to the dimension one and two cases, we prove that such a law exists for their classical projective embedding. Finally, we develop an algorithm, based on the theory of theta functions, computing this addition law in P^15 on the Jacobian of a genus two curve given in Rosenhain form. It is now included in AVIsogenies, a Magma package.

La tendance à la numérisation de nombreux secteurs industriels tels que l’automobile, l’agriculture, les transports, la gestion urbaine, etc. révèle la nécessité de nouveaux usages des services de communication point-à-multipoint, tels que la fourniture massive de mises à jour logicielles et livraison fiable de messages d’alerte à la population, etc. D’un autre côté, la mise en logiciel des réseaux de nouvelle génération, avec notamment l’adoption croissante des réseaux définis par logiciel (SDN), apporte au réseau la flexibilité et les capacités de programmation permettant de prendre en charge des services de distribution point-à-multipoint de manière rentable. Cette thèse contribue au problème général de la fourniture de services de communication point-à-multipoint avec des exigences de qualité de service (QoS) dans un réseau SDN multi-domaines. Il considère également que certains des domaines sont des réseaux multi-sauts sans-fil. Tout d’abord, une technique d’agrégation de topologie de domaine basée sur une arborescence de Steiner, combinée à un algorithme heuristique d’allocation de ressources, sont proposés pour prendre en charge des services point-à-multipoint couvrant plusieurs domaines. Ensuite, un service de découverte de topologie générique est proposé pour les réseaux multi-sauts sans-fil basés sur le SDN afin de permettre au contrôleur SDN de créer et de gérer une vue complète du réseau avec divers attributs de nœud et de liaison sans-fil. Le contrôleur peut alors exposer des vues personnalisées aux applications de contrôle du réseau, telles que, par exemple, l’application en charge de la fourniture de services point-à-multipoint sur un réseau multi-sauts sans-fil basé sur le paradigme SDN. Un algorithme basé sur la programmation linéaire en nombres entiers et un algorithme génétique sont également proposés pour l’allocation de liens virtuels point-à-multipoint sur un réseau sans-fil multi-radio, multi-canaux et multi-sauts basé sur SDN. Enfin, pour traiter le cas des services dynamiques point-à-multipoint, nous proposons un schéma de réallocation de ressources qui répond aux exigences changeantes tout en réduisant les interuptions de service. / The movement towards the digitalization of many industry sectors such as automotive, agriculture, transportation, city management, etc. is revealing the need for novel usages of point-to-multipoint network delivery services, such as massive delivery of software updates to objects, secure and reliable delivery of alert messages to population, etc. On another side, the softwarization of next generation networks, with amongst, the increasing adoption of Software Defined Networks (SDN) is bringing to the network the flexibility and programming capabilities that enable the support of point-to-multipoint delivery services in an efficient and cost-effective way. This PhD work contributes to the general problem of providing point-tomultipoint delivery services with Quality of Service (QoS) requirements in a multidomain SDN network. It also considers that some of the domains are wireless multi hop networks. First, a Steiner tree based network domain topology aggregation combined with a resource allocation heuristic algorithm is proposed to support point-to-multipoint delivery services that span multiple domains. Then, a generic topology discovery service is proposed for SDN based wireless multi-hop networks to let the SDN controller build and maintain a comprehensive view of the network with various node and wireless link attributes. From there, customized views can be exposed by the controller to network control applications, as, for instance, the application in charge of provisioning point-to-multipoint services on a SDN based wireless multi-hop network. An Integer linear programming based algorithm and a genetic algorithm are also proposed for the embedding of point-to-multipoint services on a SDN based multi-radio, multi-channel and multi-hop wireless network. Last, to address the case of dynamic point-to-multipoint services, we propose a resource reallocation scheme that meets the changing requirements while reducing service disruption.

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.