O objetivo deste artigo é avaliar previsões da inflação brasileira a partir do método não-paramétrico de Análise Espectral Singular (SSA). O exercício de previsão utiliza o esquema de janelas rolantes. Diferentes estratégias de combinação de previsões e procedimentos de seleção de variáveis para métodos multivariados foram contempladas. Para robustez, cinco horizontes de previsão foram utilizados. A avaliação das previsões considera diversos procedimentos e medidas estatísticas para oferecer conclusões confiáveis, incluindo razões de erro quadrático médio de previsão, teste de igualdade condicional de habilidade preditiva, diferenças de erro quadrático médio de previsão cumulativas e Model Confidence Set. Os resultados mostram que o SSA supera consistentemente os métodos competidores. Quase todas as previsões SSA superam os competidores em termos de erro quadrático médio de previsão, e em vários casos, com significância estatística. A análise da porção fora da amostra indica superioridade em performance relativa do SSA, especialmente no período de choque nos preços de energia elétrica. Adicionalmente, métodos SSA sempre foram incluídos no conjunto superior do Model Confidence Set. A falta de estudos relacionados com previsão da inflação brasileira e a relativa escassez de análises de previsões via métodos não-paramétricos ressaltam a relevância deste artigo. Não existem pesquisas na literatura de previsão de inflação brasileira aplicando SSA. Uma das estratégias de combinação de previsões aplicadas neste artigo não é comumente encontrada na literatura, na medida em que envolve combinações de diferentes especificações para cada método de previsão. Adicionalmente, restrições de parâmetros foram impostas nas previsões SSA, uma prática não reportada na literatura. / The purpose of this paper is to evaluate Brazilian inflation forecasts produced by the nonparametric method Singular Spectrum Analysis (SSA). This forecasting exercise employs rolling windows scheme. Different strategies of forecast combinations and variable selection procedures for multivariate methods were contemplated. For robustness, five forecast horizons were used. The forecast evaluation considers several statistical measures and procedures to offer reliable conclusions, including mean squared forecast error ratios, tests of equal conditional predictive ability, cumulative square forecast error difference and Model Confidence Set. The results show that SSA consistently outperforms the competitive methods. Almost all SSA forecasts outperforms the competitors in the mean squared forecast error sense, and several with statistical significance. Analysis of the out-of-sample portion indicates relative superior performance of SSA, especially over the period of electricity shock of prices. SSA methods were always included in the superior set of Model Confidence Set procedures. The lack of studies related to Brazilian inflation forecasting and the relative scarcity of nonparametric methods of forecasting analysis highlights the relevance of this paper. There is no research in Brazilian inflation literature applying SSA. One of the forecast combination strategies applied in this paper is not commonly found in the literature, as it involves combinations of different specifications for each forecast method. Additionally, parameter restrictions on SSA forecasts were imposed, a practice which is not reported in the literature.

The non-linear Hartree-Fock (HF) equations are usually solved via the iterative self-consistent field method. However, there is no a priori guarantee of convergence, especially in systems with strong electron correlation where symmetry breaking occurs. This work focuses on closed- shell systems in the HF approximation and the (in)stability of the found solutions, and proposes new deterministic methods for the localization of both symmetry-adapted and broken symmetry solutions. We employ a perturbative method and show how one can always obtain a symmetry-adapted solution of the HF equations. We also determine the radius of convergence, related to the existence of at least one bound state, of the perturbative series. Next, we rederive the matrix of stability and adapt it to spin and orbital symmetry. Calculation of higher energy variations follows, first in terms of spin-orbitals and then orbitals. Motivated by the investigation of the structure of a broken-symmetry solution, we propose a new deterministic method for the localization of a broken-symmetry solution. The general expressions are verified by reformulating the stability conditions for simple cases. The proposed methods are successfully applied to helium-, beryllium- and neon-like systems.

O objetivo deste artigo é avaliar previsões da inflação brasileira a partir do método não-paramétrico de Análise Espectral Singular (SSA). O exercício de previsão utiliza o esquema de janelas rolantes. Diferentes estratégias de combinação de previsões e procedimentos de seleção de variáveis para métodos multivariados foram contempladas. Para robustez, cinco horizontes de previsão foram utilizados. A avaliação das previsões considera diversos procedimentos e medidas estatísticas para oferecer conclusões confiáveis, incluindo razões de erro quadrático médio de previsão, teste de igualdade condicional de habilidade preditiva, diferenças de erro quadrático médio de previsão cumulativas e Model Confidence Set. Os resultados mostram que o SSA supera consistentemente os métodos competidores. Quase todas as previsões SSA superam os competidores em termos de erro quadrático médio de previsão, e em vários casos, com significância estatística. A análise da porção fora da amostra indica superioridade em performance relativa do SSA, especialmente no período de choque nos preços de energia elétrica. Adicionalmente, métodos SSA sempre foram incluídos no conjunto superior do Model Confidence Set. A falta de estudos relacionados com previsão da inflação brasileira e a relativa escassez de análises de previsões via métodos não-paramétricos ressaltam a relevância deste artigo. Não existem pesquisas na literatura de previsão de inflação brasileira aplicando SSA. Uma das estratégias de combinação de previsões aplicadas neste artigo não é comumente encontrada na literatura, na medida em que envolve combinações de diferentes especificações para cada método de previsão. Adicionalmente, restrições de parâmetros foram impostas nas previsões SSA, uma prática não reportada na literatura. / The purpose of this paper is to evaluate Brazilian inflation forecasts produced by the nonparametric method Singular Spectrum Analysis (SSA). This forecasting exercise employs rolling windows scheme. Different strategies of forecast combinations and variable selection procedures for multivariate methods were contemplated. For robustness, five forecast horizons were used. The forecast evaluation considers several statistical measures and procedures to offer reliable conclusions, including mean squared forecast error ratios, tests of equal conditional predictive ability, cumulative square forecast error difference and Model Confidence Set. The results show that SSA consistently outperforms the competitive methods. Almost all SSA forecasts outperforms the competitors in the mean squared forecast error sense, and several with statistical significance. Analysis of the out-of-sample portion indicates relative superior performance of SSA, especially over the period of electricity shock of prices. SSA methods were always included in the superior set of Model Confidence Set procedures. The lack of studies related to Brazilian inflation forecasting and the relative scarcity of nonparametric methods of forecasting analysis highlights the relevance of this paper. There is no research in Brazilian inflation literature applying SSA. One of the forecast combination strategies applied in this paper is not commonly found in the literature, as it involves combinations of different specifications for each forecast method. Additionally, parameter restrictions on SSA forecasts were imposed, a practice which is not reported in the literature.

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Made available in DSpace on 2014-06-12T18:27:29Z (GMT). No. of bitstreams: 2 arquivo1000_1.pdf: 571217 bytes, checksum: 93a758c7adac1d3cf14e47e2bb42147d (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2010 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / Nasrollah Nejad, Abbas; Simis, Aron. The Aluffi algebra of an ideal. 2010. Tese (Doutorado). Programa de Pós-Graduação em Matemática, Universidade Federal de Pernambuco, Recife, 2010.

Magister Scientiae - MSc / This thesis is concerned with singularly perturbed two-parameter problems. We study a tted nite difference method as applied on two different meshes namely a piecewise mesh (of Shishkin type) and a graded mesh (of Bakhvalov type) as well as a tted operator nite di erence method. We notice that results on Bakhvalov mesh are better than those on Shishkin mesh. However, piecewise uniform meshes provide a simpler platform for analysis and computations. Fitted operator methods are even simpler in these regards due to the ease of operating on uniform meshes. Richardson extrapolation is applied on one of the tted mesh nite di erence method (those based on Shishkin mesh) as well as on the tted operator nite di erence method in order to improve the accuracy and/or the order of convergence. This is our main contribution to this eld and in fact we have achieved very good results after extrapolation on the tted operator finitete difference method. Extensive numerical computations are carried out on to confirm the theoretical results. / South Africa

>Magister Scientiae - MSc / With the development of technology seen in the last few decades, numerous solvers have been developed to provide adequate solutions to the problems that model different aspects of science and engineering. Quite often, these solvers are tailor-made for specific classes of problems. Therefore, more of such must be developed to accompany the growing need for mathematical models that help in the understanding of the contemporary world. This thesis treats two point boundary value singularly perturbed problems. The solution to this type of problem undergoes steep changes in narrow regions (called boundary or internal layer regions) thus rendering the classical numerical procedures inappropriate. To this end, robust numerical methods such as finite difference methods, in particular fitted mesh and fitted operator methods have extensively been used. While the former consists of transforming the continuous problem into a discrete one on a non-uniform mesh, the latter involves a special discretisation of the problem on a uniform mesh and are known to be more accurate. Both classes of methods are suitably designed to accommodate the rapid change(s) in the solution. Quite often, finite difference methods on piece-wise uniform meshes (of Shishkin-type) are adopted. However, methods based on such non-uniform meshes, though layer-resolving, are not easily extendable to higher dimensions. This work aims at investigating the possibility of capitalising on the advantages of both fitted mesh and fitted operator methods. Theoretical results are confirmed by extensive numerical simulations.

Estruturas de dados volumétricas são de extrema utilidade em várias aplicações, e em particular na área de Visualização Científica. Essas estruturas são úteis em duas etapas do processo de visualização. A primeira é na representação de dados, isto é, de informações associadas aos valores, medidos ou simulados, os quais se deseja visualizar. A outra fase que necessita de uma estrutura de dados é a fase de exploração, ou seja, o modelo criado é usado tanto para exploração interativa quanto para a realização de simulações sobre o mesmo, por exemplo, numa cirurgia virtual. Está em desenvolvimento no ICMC, uma estrutura de dados volumétrica, chamada Singular Half-Face, que tem como característica a modelagem explícita das singularidades presentes no modelo, além de outros elementos topológicos. Este trabalho de mestrado visa testar a viabilidade da estrutura num contexto de visualização em fluxo de dados, incorporando-a à biblioteca gráfica de visualização Visualization ToolKit (VTK), que possui definição extremamente pobre da topologia dos objetos que representa. Adicionando essa nova classe e realizando sobre ela técnicas convencionais de visualização e exploração de dados, é estudada sua capacidade de apoiar todas as fases do processo de visualização. / Volumetric data structures are of extreme utility in various applications, and particularly in the area of Scientific Visualization. These structures are useful in two stages of the visualization process. The first one is in data representation, that is, in the organization of information associated with the values, measured or simulated, to be visualized. The other phase of the visualization data flow that needs a data structure is the exploration phase. It would be useful to have a model designed to be used both for interactive exploration and for simulation in a number of application, for example, in virtual surgery. A volumetric data structure, named Singular Half-Face (SHF) is being developed at the ICMC, that has as its main characteristic the explicit modeling of singularities present in the model, besides other essential topological elements. This dissertation aims at testing the viability of this structure in a context of visualization in data flow, by incorporating it in the Visualization ToolKit (VTK) class library, whose data structures are extremely poor in definition of the topology of the objects that they represent. By adding SHF to this library and carrying out conventional visualization and data exploration on it, we wish to study its support to all the phases of the visualization process.

Cette thèse vise à développer des outils d'analyse harmonique non-commutative. Elle porte plus précisément sur les inégalités de Khintchine non-commutatives et les intégrales singulières à valeurs opérateur. La première partie est dédiée à des questions d'interpolation des espaces Lp classiques. On généralise et on énonce de nouvelles caractérisations des espaces interpolés entre espaces Lp. Dans une seconde partie, on démontre une forme des inégalités de Khintchine non-commutatives valides dans tous les espaces interpolés entre espace Lp. Celle-ci permet d’unifier les cas p < 2 et p > 2 ainsi que de traiter les espaces Lp faibles, même pour p = 1 ou 2. En s'appuyant sur la première partie, on caractérise les espaces dans lesquels les formules usuelles pour les inégalités de Khintchine sont valides. Dans une dernière partie, on donne une preuve simplifiée de l'inégalité de type (1,1) faible pour les intégrales singulières non-commutatives, un résultat précédemment obtenu par Parcet. Cette simplification nous permet de retrouver rapidement deux autres résultats connus : la pseudolocalisation Lp et l’inégalité de type faible pour les intégrales singulières non-commutatives dont le noyau est à valeurs dans un espace de Hilbert. / The purpose of this thesis is to develop tools of noncommutative harmonic analysis. More precisely, it deals with noncommutative Khintchine inequalities and operator-valued singular integrals. The first part is dedicated to questions of interpolation between classical Lp-spaces. We generalize and state new characterisations of interpolation spaces between Lp-spaces. In a second part, we introduce a form of the noncommutative Khintchine inequalities which holds in every interpolation space between two Lp-spaces. It enables us to unify the cases p < 2 and p > 2 and to deal with weak Lp-spaces even when p = 1 or 2. By relying on the first part, we characterize spaces in which the usual formulas for Khintchine inequalities hold. In a last part, we give a simplified proof of the weak boundedness of noncommutative singular integrals, a result previously obtained by Parcet. This simplification allows us to recover quickly two results: the Lp pseudolocalisation and the weak type inequality for noncommutative singular integrals associated to Hilbert-valued kernels.

As shown by Zagier, singular moduli can be represented by the coefficients of a certain half integer weight modular form. Congruences for singular moduli modulo arbitrary primes have been proved by Ahlgren and Ono, Edixhoven, and Jenkins. Computation suggests that stronger congruences hold for small primes $p \in \{2, 3, 5, 7, 11\}$. Boylan proved stronger congruences hold in the case where $p=2$. We conjecture congruences for singular moduli modulo powers of $p \in \{3, 5, 7, 11\}$. In particular, we study the case where $p=3$ and reduce the conjecture to a congruence for a simpler modular form.