Complex 3D digital objects are used in many domains such as animation films, scientific visualization, medical imaging and computer vision. These objects are usually represented by triangular meshes with many triangles. The simplification of those objects in order to keep them as close as possible to the original has received a lot of attention in the recent years. In this context, we propose a simplification algorithm which is focused on the accuracy of the simplifications. The mesh simplification uses edges collapses with vertex relocation by minimizing an error metric. Accuracy is obtained with the two error metrics we use: the Accurate Measure of Quadratic Error (AMQE) and the Symmetric Measure of Quadratic Error (SMQE). AMQE is computed as the weighted sum of squared distances between the simplified mesh and the original one. Accuracy of the measure of the geometric deviation introduced in the mesh by an edge collapse is given by the distances between surfaces. The distances are computed in between sample points of the simplified mesh and the faces of the original one. SMQE is similar to the AMQE method but computed in the both, direct and reverse directions, i.e. simplified to original and original to simplified meshes. The SMQE approach is computationnaly more expensive than the AMQE but the advantage of computing the AMQE in a reverse fashion results in the preservation of boundaries, sharp features and isolated regions of the mesh. For both measures we obtain better results than methods proposed in the literature.

Large-scale data management systems rely more and more on cloud storage, where the need for efficient search capabilities clashes with the need for data confidentiality. Encryption and efficient accessibility are naturally at odds, as for instance strong encryption necessitates that ciphertexts reveal nothing about underlying data. Searchable encryption is an active field in cryptography studying encryption schemes that provide varying levels of efficiency, functionality, and security, and efficient searchable encryption focuses on schemes enabling sub-linear (in the size of the database) search time. I present the first cryptographic study of efficient searchable symmetric encryption schemes supporting two types of search queries, range queries and error-tolerant queries. The natural solution to accommodate efficient range queries on ciphertexts is to use order-preserving encryption (OPE). I propose a security definition for OPE schemes, construct the first OPE scheme with provable security, and further analyze security by characterizing one-wayness of the scheme. Efficient error-tolerant queries are enabled by efficient fuzzy-searchable encryption (EFSE). For EFSE, I introduce relevant primitives, an optimal security definition and a (somewhat space-inefficient, but in a sense efficient as possible) scheme achieving it, and more efficient schemes that achieve a weaker, but practical, security notion. In all cases, I introduce new appropriate security definitions, construct novel schemes, and prove those schemes secure under standard assumptions. The goal of this line of research is to provide constructions and provable security analysis that should help practitioners decide whether OPE or FSE provides a suitable efficiency-security-functionality tradeoff for a given application.

Reziumė Disertacijoje nagrinėjamos atsitiktinių keitinių problemos yra priskirtinos tikimybinei kombinatorikai. Gauti rezultatai aprašo visiškai adityviųjų funkcijų, apibrėžtų simetrinėje grupėje, reikšmių asimptotinius skirstinius Evenso tikimybinio mato atžvilgiu, kai grupės eilė neaprėžtai didėja. Išvestos adityviųjų funkcijų laipsninių ir faktorialinių momentų formulės. Funkcijų, išreiškiančių atsitiktinio keitinio ciklų su bet kokiais apribojimais skaičius, atveju rastos būtinos ir pakankamos ribinių tikimybinių dėsnių egzistavimo sąlygos. Išsamiai išnagrinėtas konvergavimas į Puasono, quasi-Puasono, Bernulio, binominio ir kitus skirstinius, sukoncentruotus sveikųjų neneigiamų skaičių aibėje. Rezultatai apibendrinti sveikareikšmių visiškai adityviųjų funkcijų klasėje. Darbe įrodytas bendras silpnasis didžiųjų skaičių dėsnis, rastos būtinos ir pakankamos adityviųjų funkcijų sekų pasiskirstymo funkcijų konvergavimo į išsigimusį nuliniame taške dėsnį egzistavimo sąlygos. Sprendžiamos problemos yra susietos su tikimybiniais vektorių, turinčių sveikąsias neneigiamas koordinates, uždaviniais. Adicinėje tokių vektorių pusgrupėje išnagrinėti multiplikatyviųjų funkcijų vidurkiai tikimybinio mato, vadinamo Evanso atrankos formule, atžvilgiu. Gauti tikslūs viršutinieji ir apatinieji įverčiai. Iš jų išplaukia svarbios atsitiktinių keitinių tikimybių savybės. Disertacijoje plėtojami faktorialinių momentų ir kiti kombinatoriniai bei tikimybiniai metodai. / In the thesis the examining problems of random permutations are attributed to the probabilistic combinatorics. Obtained results describe asymptotical distributions of completely additive functions values defined on a symmetric group with respect to Ewens probability measure, if the group order unbounded increases. Power and factorial moments formulae of additive functions are derived. There are established necessary and sufficient conditions under which the distributions of a number of cycles with restricted lengths obey the limit probability laws. The convergence to the Poisson, quasi-Poisson, Bernoulli, binomial and other distributions, defined on the positive whole - number set are exhaustively investigated. The results are generalized on the class of whole - number completely additive functions. The general weak law of large numbers is proved in the thesis, necessary and sufficient existence conditions, under which the distributions of the sequences of additive functions converge to the degenerate at the point zero limit law are established. Examining problems are related to the probability tasks of the vectors, which have whole - numbered nonnegative coordinates. The mean values of multiplicative functions defined on those vectors’ additive semigroup with respect to the Ewens measure, called Ewens Sampling Formula, and investigated. Lower and upper sharp estimates are obtained. From the latter results follow important probabilities’ properties of random... [to full text]

Technologies such as direct broad cast satellite system (DBSS), Geosynchronous Earth Orbit (GEO) and Low Earth Orbit (LEO) satellite communications , global positioning system (GPS), high accuracy airborne navigation system and a large variety of radar systems demand for high level of antenna performance. Similar is the requirement for upcoming land based wireless systems such as cellular and indoor communication systems that is needed some more specific and additional features added to the antenna to compensate for the deficiencies encountered in system's performance. Though metallic antennas are capable enough to fulfil all the operational requirements, however at very high frequencies and under hostile temperature conditions they are constrained to face certain limitations. To avoid these constraints the performance of Dielectric Resonator Antennas (DRAs) is evaluated and their new applications are proposed. In the thesis, two types of antenna applications are sought :-First is for tracking and satellite applications that needs a larger aperture coverage in elevation plane. This coverage is realized with a good CP purity by proposing two ports dual linearly polarized DRA working at X-band. The DRA is excited by two orthogonal H-shaped aperture slots yielding two orthogonal polarizations in the broadside direction. A common impedance bandwidth of 5.9% and input port isolation of -35 dB are obtained. The broadside radiation patterns are found to be highly symmetric and stable with cross polarization levels -15dB or better over the entire matching frequency band. The maximum measured gain is found to be 2.5dBi at 8.4 GHz.- The 2nd type of antenna is a dual pattern diversity antenna to be used in the Body Area Network (BAN) context. This antenna combines a slot loop and DRA yielding broadside and end-fire radiation patterns respectively. Based upon the feeding techniques, the DG antenna is further divided into two categories one with planar feeds and the other with non-planar feeds (slot loop excited by planar CPW but DRA excited by vertical monopole) .Both types are successfully designed and measured upon body when configured into different propagation scenarios. The non-planar feeds antenna allows wider common impedance bandwidths than the planar feeds (4.95% vs 1.5%).In both cases, a maximum value of DG=9.5dB was achieved when diversity performance tests were carried out in rich fading environments. This value is close to the one (10 dB) theoretically reached in a pure Rayleigh environment and was obtained with efficiencies of 70% and 85% for the slot loop and the DRA respectively. Therefore, we conclude that these antennas could be used on the shoulders or the chest of professional clothes (firemen, policemen, soldier) where full planar integration is not a key issue but where the communication must be efficient in harsh environments and for various gestures, positions and scenarios

The strength of efficient metal-free catalysis will be examined in this thesis. Efforts towards more sustainable processes will be demonstrated through implementation of strategies that meet several of the 12 principles of Green Chemistry.In the first part, a stereoselective total synthesis of multiple alkaloids from the Corynantheine and Ipecac families together with their non-natural analogues will be disclosed. A highly efficient, common synthetic strategy is applied leading to high overall yields starting from easily available starting material. Overall operational simplicity and sustainability have been the main focus. Time-consuming and waste-generating isolations and purifications of intermediates have been minimized, as well as the introduction of protection-group chemistry. Moreover, the first example of the total synthesis of Hydroxydihydrocorynantheol together with its non-natural epimer has been accomplished in multi-gram scale without protection groups and without a single isolation or purification step in high overall yield and diastereoselectivity.In the second part, carbocations will be presented as highly effective and versatile non-metal Lewis acid catalysts. Lewis acidity-tuning of carbocations will be introduced and applied in several reactions to suppress competing reactions. Finally, the broad scope of carbocation catalyzed transformations will be exposed.At large, evident progress has been made towards more sustainable chemistry. / <p>QC 20140425</p>

By using the Kaluza-Klein reduction, the derivation of the maximal supergravities from the D=11 supergravity theory, as well as the Abelian Yang-Mills supergravities from the D=10 type I supergravity theory are discussed. After a thorough review of the symmetric spaces the symmetric space sigma model is studied in detail. The first-order formulation of both the pure and the matter coupled symmetric space sigma model is presented in a general formalism. The dualisation of the non-gravitational Bosonic sectors of the D=11, IIB and the maximal supergravities are also reviewed in a concise but a self-contained formulation. As an example of the dualisation of the matter coupled supergravities, the doubled formalism is constructed for the D=8 Salam-Sezgin supergravity.

The supersymmetric solutions of PT-/non-PT symmetric and Hermitian/non-Hermitian forms of quantum systems are obtained by solving the Schr&Auml / odinger equation with the deformed Morse, Hulth&para / en, P&Auml / oschl-Teller, Hyperbolic Kratzer-like, Screened Coulomb, and Exponential-Cosine Screened Coulomb (ECSC) potentials. The Hamiltonian hi- erarchy method is used to get the real energy eigenvalues and corresponding wave functions.

This thesis deals with different aspects of string and /p/-brane theories. One of the motivations for string theory is to unify the forces in nature and produce a quantum theory of gravity. /p/-branes and related objects arise in string theory and are related to a non-perturbative definition of the theory. The results of this thesis might help in understanding string theory better. The first part of the thesis introduces and discusses relevant topics for the second part of the thesis which consists of five papers. In the three first papers we develop and treat a perturbative approach to relativistic /p/-branes around stretched geometries. The unperturbed theory is described by a string- or particle-like theory. The theory is solved, within perturbation theory, by constructing successive canonical transformations which map the theory to the unperturbed one order by order. The result is used to define a quantum theory which requires for consistency d = 25 + p dimensions for the bosonic /p/-branes and d = 11 for the supermembrane. This is one of the first quantum results for extended objects beyond string theory and is a confirmation of the expectation of an eleven-dimensional quantum membrane. The two last papers deal with a gauged WZNW-approach to strings moving on non-trivial space-times. The groups used in the formulation of these models are connected to Hermitian symmetric spaces of non-compact type. We have found that the GKO-construction does not yield a unitary spectrum. We will show that there exists, however, a different approach, the BRST approach, which gives unitarity under certain conditions. This is the first example of a difference between the GKO- and BRST construction. This is one of the first proofs of unitarity of a string theory in a non-trivial non-compact space-time. Furthermore, new critical string theories in dimensions less then 26 or 10 is found for the bosonic and supersymmetric string, respectively.

Malgré son indéniable succès pour décrire les systèmes physiques à l'équilibre thermodynamique (grâce à la distribution de Boltzmann, reflétant la maximisation de l'entropie, et permettant la construction systématique de potentiels thermodynamiques), la physique statistique n'offre pas de cadre général pour étudier les phénomènes hors d'équilibre, i.e dans lesquels on observe un courant moyen non nul d'une grandeur physique (énergie, charge, particules...).L'objectif de la thèse est de décrire de tels systèmes à l'aide de modèles très simples mais qui retranscrivent néanmoins les principales caractéristiques physiques de ceux-ci. Ces modèles sont constitués de particules se déplacant de manière aléatoire sur un réseau unidimensionnel connecté à des réservoirs et soumises à un principe d'exclusion. L'enjeu est de calculer exactement l'état stationnaire du modèle, notamment le courant de particules, ses fluctuations et plus particulièrement sa fonction de grande déviation (qui pourrait jouer le rôle d'un potentiel thermodynamique hors d'équilibre).Une première partie de la thèse vise à construire des modèles dits intégrables, dans lesquels il est possible de mener à bien des calculs exacts de quantités physiques. De nouveaux modèles hors d'équilibre sont proposés grâce à la résolution dans des cas particuliers de l'équation de Yang-Baxter et de l'équation de réflexion. De nouvelles structures algébriques permettant la construction de ces solutions par une procédure de Baxtérisation sont introduites.Une deuxième partie de la thèse consiste à calculer exactement l'état stationnaire de tels modèles en utilisant l'ansatz matriciel. Les liens entre cette technique et l'intégrabilité du modèle ont été mis en lumière au travers de deux relations clef: la relation de Zamolodchikov-Faddeev et la relation de Ghoshal-Zamolodchikov. L'intégrabilité a aussi été exploitée au travers des equations de Knizhnik-Zamolodchikov quantiques, afin de calculer les fluctuations du courant, mettant en lumière des connexions avec la théorie despolynômes symétriques (polynômes de Koornwinder en particulier).Enfin une dernière partie de la thèse porte sur la limite hydrodynamique des modèles étudiés, i.e lorsque la maille du réseau tend vers zero et que le nombre de constituants du système tend vers l'infini. Les résultats exacts obtenus sur les modèles à taille finie ont permis de vérifier les prédictions de la théorie des fluctuations macroscopiques (concernant les fluctuations du courant et du profil de densité dans l'état stationnaire) et de l'étendre à des modèles comprenant plusieurs espèces de particules. / Although statistical physics has been very successful to describe physical systems at thermal equilibrium (thanks to the Boltzmann distribution, which reflects the maximization of the entropy, and allows one to construct in a systematic way thermodynamic potentials), it remains elusive to provide an efficient framework to study phenomena that are out-of-equilibrium, i.e displaying non vanishing current of physical quantities (energy, charge, particles...).The goal of the thesis is to describe such systems with very simple models which retain nevertheless their main physical features. The models consist in particles evolving randomly on a one dimensional lattice connected to reservoirs and subject to hard-core repulsion. The challenge lies in computing exactly the stationary state of the model, especially the particle current, its fluctuations and more precisely its large deviation function (which is expected to play the role of an out-of-equilibrium thermodynamic potential).In the first part of the thesis we construct models, called integrable, in which we can perform exact computations of physical quantities. We introduce several new out-of-equilibrium models that are obtained by solving, in specific cases, the Yang-Baxter equation and the reflection equation. We provide new algebraic structures which allow us to construct the solutions through a Baxterisation procedure.In the second part of the thesis we compute exactly the stationary state of these models using a matrix ansatz. We shed light on the connection between this technique and the integrability of the model by pointing out two key relations: the Zamolodchikov-Faddeev relation and the Ghoshal-Zamolodchikov relation. The integrability is also exploited, through the quantum Knizhnik-Zamolodchikov equations, to compute the fluctuations of the particles current, unrevealing connections with the theory of symmetric polynomials (the Koornwinder polynomials in particular).Finally the last part of the thesis deals with the hydrodynamic limit of the models, i.e when the lattice spacing tends to $0$ and the number of particles tends to infinity. The exact results obtained for a finite size system allow us to check the validity of the predictions of the macroscopic fluctuations theory (concerning the fluctuations of the current and the density profile in the stationary state) and to extend the theory to systems with several species of particles.

In this thesis we classify singular vectors in scalar parabolic Verma modules for those pairs (sl(n, C), p) of complex Lie algebras where the homogeneous space SL(n, C)/P is the Grassmannian of k-planes in Cn . We calculate cohomology of nilpotent radicals with values in certain unitarizable highest weight modules. According to [BH09] these modules have BGG resolutions with weights determined by this cohomology. Such resolutions induce complexes of invariant differential operators on sections of associated bundles over Hermitian symmetric spaces. We describe formal completions of unitarizable highest weight modules that one can use to modify method from [CD01] that constructs sequences of differential operators over any 1-graded (aka almost Hermitian) geometry. We suggest uniform description of octonionic planes that could serve as a basis for better understanding of the exceptional Hermitian symmetric space for group E6.