Neste trabalho, inicialmente, apresentamos uma classe de núcleos positivos definidos, os núcleos de Mercer. As funções nesta classe se enquadram na representação de núcleos dada pelo conhecido Teorema de Mercer. Exploramos algumas de suas propriedades convenientes para o contexto do trabalho e construímos seu espaço nativo. Em seguida, tratamos dos núcleos em multiescalas, um caso particular dos núcleos de Mercer. Após estabelecer algumas propriedades interessantes destes núcleos, analisamos o operador integral gerado por um núcleo em multiescalas, no contexto \'L POT.2\' , considerando os seguintes aspectos: limitação, compacidade e positividade do operador, especificidades da imagem do operador e informações sobre seus autovalores e autofunções. Analisamos ainda algumas propriedades do operador integral envolvendo o espaço nativo do núcleo em multiescalas / We study Mercer like kernels, a very special class of positive definite kernels possessing the description given by many results labeled as Mercer\'s Theorem. We explore some of their properties which are needed in the development of this work and construct their native space. In the second half of the work, we consider Mercer kernels defined by a multi-scale procedure. After establishing some of its properties, we analyze integral operators generated by multi-scale kernels, in the \'L POT.2\' context, centering on the following aspects: boundedness, compactness, positiveness, eigenvalues and eigen- functions. We also consider additional properties of the operator, mainly those involving the native space of the multi-scale kernel

Este estudo investiga o uso variado da realização do artigo definido em DPs possessivos, no paradigma das três pessoas do discurso, em vídeos e cartas que representam o português paulista dos séculos XX e XXI. Tal fenômeno tem atraído a atenção dos estudiosos, a partir da tradição filológica e normativa, chegando aos estudos linguísticos correntes, uma vez que se verifica o intrigante fato de que o português europeu (PE) e o português brasileiro (PB) se distanciaram no seu percurso histórico em um aspecto crucial: enquanto no PE a presença do artigo diante do possessivo é praticamente categórica, no PB a variação ainda parece ser possível, ora produzindo DP possessivos com artigo (o meu livro está em cima da mesa), ora sem (meu livro está em cima da mesa). Entre os objetivos da pesquisa destacam-se a descrição do fenômeno no português paulista, a apresentação de uma proposta de análise para caracterizar o estatuto variável na realização do artigo em contextos possessivos, bem como o mapeamento dos fatores linguísticos e extralinguísticos que possam estar condicionando a variação. Para tanto, apoiamo-nos numa perspectiva teórica que engloba pressupostos gerativistas, tais como desenvolvidos na Teoria dos Princípios e Parâmetros (CHOMSKY, 1981, 1986), incluindo alguns refinamentos do Programa Minimalista (CHOMSKY, 1995, 1998, 2000, 2001), além de pressupostos da Sociolinguística Variacionista, tais como desenvolvidos em Weinreich, Labov e Herzog (1968) e Labov (1972, 1994). Os resultados da análise quantitativa mostraram um aumento significativo no preenchimento do artigo definido no DP possessivo e mudança nos fatores condicionantes para a variação apontados por pesquisas anteriores. A abordagem teórica está ainda ancorada nos estudos recentes sobre a estrutura sintática do DP possessivo (FLORIPI, 2008; GALO, 2015; BRITO e LOPES, 2016). Finalmente, esta pesquisa buscou caracterizar com mais rigor o estatuto semântico do artigo definido no contexto dos DPs possessivos, com base nas particularidades do licenciamento dos Nomes Nus no PB (CYRINO e ESPINAL, 2016; FERREIRA e CORREIA 2016). A hipótese que assumimos foi a de que, o artigo definido nos DPs possessivos, tanto realizado lexicalmente, como nulo fonologicamente, licencia uma leitura que expressa uma relação possessiva, diferente da leitura denotada pelo artigo definido em DPs definidos. Portanto não se trata de um definido expletivo (CASTRO, 2006). / This thesis investigates the varied use of the definite article in possessives DPs, in the paradigm of the 1st, 2nd and 3rd persons, in videos and letters that represent the Paulistian Brazilian Portuguese from the 20th and 21st centuries. Such phenomenon has attracted experts attention, from the philological and normative tradition to current linguistic studies, since an intriguing fact is verified: European Portuguese (PE) and Brazilian Portuguese (PB) have distanced themselves in their historical course in a crucial aspect: In PE the use of the definite article in possessive noun phrases is nearly mandatory, while in PB this use of the article is variable. Amongst the goals of this research, the following stand out: to describe this phenomenon in Paulistian Brazilian Portuguese, present a proposal of analysis to characterize the variation status in the presence of the article in possessives contexts, as well as mapping the linguistic and extralinguistic factors that may be conditioning the variation. To achieve them, we adopt an approach based on Principles and Parameters Model (CHOMSKY, 1981, 1986), including some refinements of the Minimalist Program (CHOMSKY, 1995, 1998, 2000, 2001), as well as a Quantitative Sociolinguistics approach (WEINREICH, LABOV and HERZOG, 1968; LABOV, 1972, 1994). The results of the quantitative analysis showed a significant increase in the usage of the definite article in the possessive DP and change of conditioning factors for the variation pointed out by previous researches. The theoretical approach is also anchored in recent studies on the syntactic structure of possessive DP (FLORIPI, 2008; GALO, 2015; BRITTO e LOPES, 2016). Finally, this research attempted to thoroughly characterize the semantic status of the definite article in the context of the possessive DPs, based on the peculiarities of the Bare Nouns licensing in PB (CYRINO e ESPINAL, 2016; FERREIRA e CORREIA, 2016). We assumed the hypothesis that the definite article in the possessive DPs, lexically realized or phonologically null, allows a reading that expresses a possessive relation, different from the reading denoted by the definite article in definite DPs. Therefore, it is not an expletive definite article (CASTRO, 2006).

Neste trabalho analisamos a positividade definida estrita de núcleos contínuos sobre um espaço compacto 2-homogêneo. R. Gangolli (1967) apresentou uma caracterização completa para os núcleos que são contínuos, isotrópicos e positivos definidos sobre um espaço compacto 2-homogêneo Md: a parte isotrópica do núcleo é uma série de Fourier uniformemente convergente, com coeficientes não negativos, em relação a certos polinômios de Jacobi atrelados a Md. Uma das contribuições de nosso trabalho é uma caracterização para a positividade definida estrita de tais núcleos, complementando a caracterização apresentada por Chen et al. (2003) no caso em que Md é uma esfera unitária de dimensão maior ou igual a 2. Outra contribuição do trabalho é uma extensão do resultado de Gangolli para núcleos sobre produtos cartesianos de espaços compactos 2-homogêneos, e a consequente caracterização para núcleos estritamente positivos definidos neste mesmo contexto. Por fim, a última contribuição do trabalho envolve a análise do grau de diferenciabilidade da parte isotrópica de um núcleo contínuo, isotrópico e positivo definido sobre Md e a aplicabilidade de tal análise em resultados envolvendo a positividade definida estrita. / In this work we analyze the strict positive definiteness of continuous kernels on compact two-point homogeneous spaces Md. R. Gangolli (1967) presented a complete characterization for continuous, isotropic and positive definite kernels on Md: the isotropic part of the kernel is a uniformly convergent Fourier series of certain Jacobi polynomials associated to Md, with nonnegative coefficients. One of the contributions of our work is a characterization for the strict positive definiteness of such kernels, completing that one presented by Chen et al. (2003) in the case Md is the unit sphere of dimension at least 2. Another contribuition of this work is an extension of Gangolli\'s result for kernels on a product of compact two-point homogeneous spaces, and the subsequent characterization of strict positive definiteness in this same context. Finally, the last contribution in this work involves the analysis of the differentiability of the isotropic part of a continuous, isotropic and positive definite kernel on Md and the applicability of such analysis in results involving the strict positive definiteness.

Apresentamos uma caracterização das funções positivas definidas em esferas complexas, generalizando assim, um resultado de Schoenberg ([41]). Como no caso real, uma classe importante dessas funções é aquela composta pelas funções estritamente positivas definidas de uma certa ordem; estas podem ser utilizadas para resolver certos problemas de interpolação de dados arbitrários associados a pontos distintos distribuídos nas esferas. Com esse objetivo, obtivemos algumas condições necessárias e suficientes (separadamente) para que funções positivas definidas sejam estritamente positivas definidas. Os resultados apresentados fornecem uma caracterização final elementar para funções estritamente positivas definidas de todas as ordens em quase todas as esferas complexas. Funções estritamente positivas definidas de ordem 2 são caracterizadas em todas as esferas complexas. Analisamos também a relação entre funções estritamente positivas definidas em esferas complexas e funções estritamente positivas definidas em esferas reais. / We characterize positive definite functions on complex spheres, generalizing a famous result due to I. J. Schoenberg ([41]). As in the real case, we study the so-called strictly positive definite functions. They can be used to perform interpolation of scattered data on those spheres. We present (separated) necessary and sufficient conditions for a positive definite function to be strictly positive definite of a certain order. These conditions produce a final characterization for those positive definite functions which are strictly positive definite of all orders, on almost all spheres. Strictly positive definite functions of order 2 are identified. Finally, we study a connection between strictly positive definite functions on real spheres and strictly positive definite functions on complex spheres.

Este estudo investiga o uso variado da realização do artigo definido em DPs possessivos, no paradigma das três pessoas do discurso, em vídeos e cartas que representam o português paulista dos séculos XX e XXI. Tal fenômeno tem atraído a atenção dos estudiosos, a partir da tradição filológica e normativa, chegando aos estudos linguísticos correntes, uma vez que se verifica o intrigante fato de que o português europeu (PE) e o português brasileiro (PB) se distanciaram no seu percurso histórico em um aspecto crucial: enquanto no PE a presença do artigo diante do possessivo é praticamente categórica, no PB a variação ainda parece ser possível, ora produzindo DP possessivos com artigo (o meu livro está em cima da mesa), ora sem (meu livro está em cima da mesa). Entre os objetivos da pesquisa destacam-se a descrição do fenômeno no português paulista, a apresentação de uma proposta de análise para caracterizar o estatuto variável na realização do artigo em contextos possessivos, bem como o mapeamento dos fatores linguísticos e extralinguísticos que possam estar condicionando a variação. Para tanto, apoiamo-nos numa perspectiva teórica que engloba pressupostos gerativistas, tais como desenvolvidos na Teoria dos Princípios e Parâmetros (CHOMSKY, 1981, 1986), incluindo alguns refinamentos do Programa Minimalista (CHOMSKY, 1995, 1998, 2000, 2001), além de pressupostos da Sociolinguística Variacionista, tais como desenvolvidos em Weinreich, Labov e Herzog (1968) e Labov (1972, 1994). Os resultados da análise quantitativa mostraram um aumento significativo no preenchimento do artigo definido no DP possessivo e mudança nos fatores condicionantes para a variação apontados por pesquisas anteriores. A abordagem teórica está ainda ancorada nos estudos recentes sobre a estrutura sintática do DP possessivo (FLORIPI, 2008; GALO, 2015; BRITO e LOPES, 2016). Finalmente, esta pesquisa buscou caracterizar com mais rigor o estatuto semântico do artigo definido no contexto dos DPs possessivos, com base nas particularidades do licenciamento dos Nomes Nus no PB (CYRINO e ESPINAL, 2016; FERREIRA e CORREIA 2016). A hipótese que assumimos foi a de que, o artigo definido nos DPs possessivos, tanto realizado lexicalmente, como nulo fonologicamente, licencia uma leitura que expressa uma relação possessiva, diferente da leitura denotada pelo artigo definido em DPs definidos. Portanto não se trata de um definido expletivo (CASTRO, 2006). / This thesis investigates the varied use of the definite article in possessives DPs, in the paradigm of the 1st, 2nd and 3rd persons, in videos and letters that represent the Paulistian Brazilian Portuguese from the 20th and 21st centuries. Such phenomenon has attracted experts attention, from the philological and normative tradition to current linguistic studies, since an intriguing fact is verified: European Portuguese (PE) and Brazilian Portuguese (PB) have distanced themselves in their historical course in a crucial aspect: In PE the use of the definite article in possessive noun phrases is nearly mandatory, while in PB this use of the article is variable. Amongst the goals of this research, the following stand out: to describe this phenomenon in Paulistian Brazilian Portuguese, present a proposal of analysis to characterize the variation status in the presence of the article in possessives contexts, as well as mapping the linguistic and extralinguistic factors that may be conditioning the variation. To achieve them, we adopt an approach based on Principles and Parameters Model (CHOMSKY, 1981, 1986), including some refinements of the Minimalist Program (CHOMSKY, 1995, 1998, 2000, 2001), as well as a Quantitative Sociolinguistics approach (WEINREICH, LABOV and HERZOG, 1968; LABOV, 1972, 1994). The results of the quantitative analysis showed a significant increase in the usage of the definite article in the possessive DP and change of conditioning factors for the variation pointed out by previous researches. The theoretical approach is also anchored in recent studies on the syntactic structure of possessive DP (FLORIPI, 2008; GALO, 2015; BRITTO e LOPES, 2016). Finally, this research attempted to thoroughly characterize the semantic status of the definite article in the context of the possessive DPs, based on the peculiarities of the Bare Nouns licensing in PB (CYRINO e ESPINAL, 2016; FERREIRA e CORREIA, 2016). We assumed the hypothesis that the definite article in the possessive DPs, lexically realized or phonologically null, allows a reading that expresses a possessive relation, different from the reading denoted by the definite article in definite DPs. Therefore, it is not an expletive definite article (CASTRO, 2006).

Neste trabalho analisamos o papel das funções layout de um núcleo positivo definido K sobre um espaço topológico de Hausdor E com relação a duas propriedades específicas: a universalidade de K e a ortogonalidade no espaço de Hilbert de reprodução de K a partir de suportes disjuntos. As funções layout sempre existem mas podem não ser únicas. De uma maneira geral, a função layout e uma aplicação que transfere, convenientemente, informações do espaço E para um espaço com produto interno de dimensão alta, onde métodos lineares podem ser usados. Tanto a universalidade quanto a ortogonalidade pressupõem a continuidade do núcleo. O primeiro conceito exige que para cada compacto não vazio X de E, o conjunto de \"seções\" {K(., y) : y \'PERTENCE\' X} seja total no espaço de todas as funções contínuas com domínio X, munido da topologia da convergência uniforme. Um dos resultados principais do trabalho caracteriza a universalidade de um núcleo K através de uma propriedade de universalidade semelhante da função layout. A ortogonalidade a partir de suportes disjuntos almeja então a ortogonalidade de quaisquer duas funções do espaço de Hilbert de reprodução de K quando seus suportes não se intersectam / We analyze the role of feature maps of a positive denite kernel K acting on a Hausdorff topological space E in two specific properties: the universality of K and the orthogonality in the reproducing kernel Hilbert space of K from disjoint supports. Feature maps always exist but may not be unique. A feature map may be interpreted as a kernel based procedure that maps the data from the original input space E into a potentially higher dimensional \"feature space\" in which linear methods may then be used. Both properties, universality and orthogonality from disjoint supports, make sense under continuity of the kernel. Universality of K is equivalent to the fundamentality of {K(. ; y) : y \'IT BELONGS\' X} in the space of all continuous functions on X, with the topology of uniform convergence, for all nonempty compact subsets X of E. One of the main results in this work is a characterization of the universality of K from a similar concept for the feature map. Orthogonality from disjoint supports seeks the orthogonality of any two functions in the reproducing kernel Hilbert space of K when the functions have disjoint supports

In the last decade, there has been an explosive growth in different applications of wireless technology, due to users' increasing expectations for multi-media services. With the current trend, the present systems will not be able to handle the required data traffic. Lattice codes have attracted considerable attention in recent years, because they provide high data rate constellations. In this thesis, the applications of implementing lattice codes in different communication systems are investigated. The thesis is divided into two major parts. Focus of the first part is on constellation shaping and the problem of lattice labeling. The second part is devoted to the lattice decoding problem. In constellation shaping technique, conventional constellations are replaced by lattice codes that satisfy some geometrical properties. However, a simple algorithm, called lattice labeling, is required to map the input data to the lattice code points. In the first part of this thesis, the application of lattice codes for constellation shaping in Orthogonal Frequency Division Multiplexing (OFDM) and Multi-Input Multi-Output (MIMO) broadcast systems are considered. In an OFDM system a lattice code with low Peak to Average Power Ratio (PAPR) is desired. Here, a new lattice code with considerable PAPR reduction for OFDM systems is proposed. Due to the recursive structure of this lattice code, a simple lattice labeling method based on Smith normal decomposition of an integer matrix is obtained. A selective mapping method in conjunction with the proposed lattice code is also presented to further reduce the PAPR. MIMO broadcast systems are also considered in the thesis. In a multiple antenna broadcast system, the lattice labeling algorithm should be such that different users can decode their data independently. Moreover, the implemented lattice code should result in a low average transmit energy. Here, a selective mapping technique provides such a lattice code. Lattice decoding is the focus of the second part of the thesis, which concerns the operation of finding the closest point of the lattice code to any point in N-dimensional real space. In digital communication applications, this problem is known as the integer least-square problem, which can be seen in many areas, e.g. the detection of symbols transmitted over the multiple antenna wireless channel, the multiuser detection problem in Code Division Multiple Access (CDMA) systems, and the simultaneous detection of multiple users in a Digital Subscriber Line (DSL) system affected by crosstalk. Here, an efficient lattice decoding algorithm based on using Semi-Definite Programming (SDP) is introduced. The proposed algorithm is capable of handling any form of lattice constellation for an arbitrary labeling of points. In the proposed methods, the distance minimization problem is expressed in terms of a binary quadratic minimization problem, which is solved by introducing several matrix and vector lifting SDP relaxation models. The new SDP models provide a wealth of trade-off between the complexity and the performance of the decoding problem.

In the last decade, there has been an explosive growth in different applications of wireless technology, due to users' increasing expectations for multi-media services. With the current trend, the present systems will not be able to handle the required data traffic. Lattice codes have attracted considerable attention in recent years, because they provide high data rate constellations. In this thesis, the applications of implementing lattice codes in different communication systems are investigated. The thesis is divided into two major parts. Focus of the first part is on constellation shaping and the problem of lattice labeling. The second part is devoted to the lattice decoding problem. In constellation shaping technique, conventional constellations are replaced by lattice codes that satisfy some geometrical properties. However, a simple algorithm, called lattice labeling, is required to map the input data to the lattice code points. In the first part of this thesis, the application of lattice codes for constellation shaping in Orthogonal Frequency Division Multiplexing (OFDM) and Multi-Input Multi-Output (MIMO) broadcast systems are considered. In an OFDM system a lattice code with low Peak to Average Power Ratio (PAPR) is desired. Here, a new lattice code with considerable PAPR reduction for OFDM systems is proposed. Due to the recursive structure of this lattice code, a simple lattice labeling method based on Smith normal decomposition of an integer matrix is obtained. A selective mapping method in conjunction with the proposed lattice code is also presented to further reduce the PAPR. MIMO broadcast systems are also considered in the thesis. In a multiple antenna broadcast system, the lattice labeling algorithm should be such that different users can decode their data independently. Moreover, the implemented lattice code should result in a low average transmit energy. Here, a selective mapping technique provides such a lattice code. Lattice decoding is the focus of the second part of the thesis, which concerns the operation of finding the closest point of the lattice code to any point in N-dimensional real space. In digital communication applications, this problem is known as the integer least-square problem, which can be seen in many areas, e.g. the detection of symbols transmitted over the multiple antenna wireless channel, the multiuser detection problem in Code Division Multiple Access (CDMA) systems, and the simultaneous detection of multiple users in a Digital Subscriber Line (DSL) system affected by crosstalk. Here, an efficient lattice decoding algorithm based on using Semi-Definite Programming (SDP) is introduced. The proposed algorithm is capable of handling any form of lattice constellation for an arbitrary labeling of points. In the proposed methods, the distance minimization problem is expressed in terms of a binary quadratic minimization problem, which is solved by introducing several matrix and vector lifting SDP relaxation models. The new SDP models provide a wealth of trade-off between the complexity and the performance of the decoding problem.

Graph partitioning is a fundamental optimization problem that has been intensively studied. Many graph partitioning formulations are important as building blocks for divide-and-conquer algorithms on graphs as well as to many applications such as VLSI layout, packet routing in distributed networks, clustering and image segmentation. Unfortunately such problems are notorious for the huge gap between known best known approximation algorithms and hardness of approximation results. In this thesis, we study approximation algorithms for graph partitioning problems using a strong hierarchy of relaxations based on semi-definite programming, called Lasserre Hierachy. Our main contribution in this thesis is a propagation based rounding framework for solutions arising from such relaxations. We present a novel connection between the quality of solutions it outputs and column based matrix reconstruction problem. As part of our work, we derive optimal bounds on the number of columns necessary together with efficient randomized and deterministic algorithms to find such columns. Using this framework, we derive approximation schemes for many graph partitioning problems with running times dependent on how fast the graph spectrum grows. Our final contribution is a fast SDP solver for this rounding framework: Even though SDP relaxation has nO(r) many variables, we achieve running times of the form 2O(r) poly(n) by only partially solving the relevant part of relaxation. In order to achieve this, we present a new ellipsoid algorithm that returns certificate of infeasibility.

En el trabajo la semántica y pragmática de formas contraídas y no-contraídas en Alemán serán discutidas. Formas contraídas son preposiciones con sufijos flexionales, obligatorias en contextos en las que el contenido descriptivo del sintagma nominal es cierto de un individual o evento (expresiones que excluyen alternativas, referentes deducibles, Situative Unika, infinitivos nominalizados, referentes no específicos). Muchos autores consideran que las formas tienen artículos definidos que fusionan con una preposición. En contrario, propongo un análisis en términos de incorporación semántica en que una preposición tiene rasgos de caso, número y género. Interpretaciones únicas provienen del número singular y del contexto. Interpretaciones no específicas provienen de la semántica y el hecho de que el argumento nominal tiene menos rango que el argumento eventivo. / The semantics and pragmatics of contracted and non-contracted forms found in German will be discussed. Contracted form are prepositions with inflectional endings, and obligatory in contexts in which the descriptive content of the noun fits only one individual or event ("alternative-excluding" expressions, inferable referents, Situative Unika, nominalized infinitives, non-specific referents). Most accounts assume that contracted forms have underlying definite articles which have amalgamated with a preposition. In contrast, I propose to analyse these forms as semantically incorporating prepositions, which are inflected for (singular) number, gender, and case, and combine with noun phrases. Uniqueness effects are derived from singular number and from contextual entailments. Non-specific readings can directly be accounted for since the semantics predicts narrow scope of the nominal argument with respect to the event argument.