We develop a theoretical analysis of generalization performances of regularized least-squares on reproducing kernel Hilbert spaces for supervised learning. We show that the concept of effective dimension of an integral operator plays a central role in the definition of a criterion for the choice of the regularization parameter as a function of the number of samples. In fact, a minimax analysis is performed which shows asymptotic optimality of the above-mentioned criterion.

Orientador: Manoel Ferreira Borges Neto / Banca: Gilberto Aparecido Pratavieira / Banca: José Márcio Machado / Resumo: Em considerando-se dois subsistemas A e B com espaço de estados HA e HB e com o espaço do sistema total ( A+B ) associado ao produto tensorial HA ? HB, alguns vetores desse sistema total podem ser decompostos em um produto tensorial de dois vetores descrevendo o estado do sistema A e B. Quando essa decomposição não é possível, diz-se que os subsistemas estão emaranhados. Uma medida de emaranhamento utilizada é a entropia de von Neumann de um dos subsistemas. Neste trabalho utiliza-se a entropia de Tsallis, uma generalização da entropia de von Neumann, como medida de emaranhamento.Faz-se uma comparação entre essas duas entropias como medida do emaranhamento entre campos emergentes de um divisor de feixes óticos. / Abstract: Let A and B be two subsystems with space of states HA and HB respectively, being the space of the total system (A + B) associated to the tensorial product HA ? HB; some vectors of the total system may be decomposed in a tensorial product of two vectors describing the state of system A and B . When this decomposition is not possible, we say that the subsystems are entangled. An usual measure of entanglement used in each one of the subsystems is called von Neumann entropy. In this work we use Tsallis' entropy, a generalization of the von Neumann's measure to entanglement. We compare the two entropies as a measure of the entanglement between emerging fields of an optical beam splitter. / Mestre

Made available in DSpace on 2014-06-11T19:26:56Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-02-27Bitstream added on 2014-06-13T18:55:33Z : No. of bitstreams: 1 felix_hm_me_sjrp.pdf: 466258 bytes, checksum: 32a3a8d16827478e36816f3317716601 (MD5) / O estudo da obtenção de fórmulas assintóticas para polinômios ortogonais clássicos foi amplamente desenvolvido por Szegö. Recentemente, a necessidade de obtenção de assintóticas para polinômios, ortogonais com respeito a funções peso variadas, foi renovada devido a novos estudos na teoria de matrizes randômicas. Nestes estudos, uma das principais ferramentas utilizadas é a teoria dos problemas de Riemann-Hilbert, caracterizada pelo método de máxima descida de autoria de Deft e Zhou. Essas novas técnicas também aprimoraram os resultados obtidos por Szegö e outros autores predecessores. O objetivo do presente trabalho é esclarecer a conexão entre as teorias de polinômios ortogonais e problemas de Riemann-Hilbert, demonstrando os passos que devem ser seguidos a fim de se obter assintóticas que valham em qualquer subconjunto compacto do plano complexo. Como aplicação, escolhemos os polinômios ortogonais em [¡1; 1] com respeito a uma função peso modificada de Jacobi. / The study of obtaining asymptotics for Classical Orthogonal Polynomials was vas- tly developed by Szegö. Recently, the need for obtaining asymptotics for polynomials, orthogonal with respect to varied weight functions, was renewed due to new researches in the theory of Random Matrices. In these studies, one of the most important tools used lies in the theory of Riemann-Hilbert problems, enforced by the steepest descent method of Deft and Zhou. These new techniques also have improved the results obtained by Szegö and other previous authors. The main purpose of this work is to explain the connection between the theories of Orthogonal Polynomials and Riemann-Hilbert problems, showing the steps to be followed on the way of finding asymptotics which hold true for any compact subsets of the complex plane. As an application, we choose the polynomials orthogonal on [¡1; 1] with respect to a modified Jacobi weight.

Made available in DSpace on 2014-06-11T19:27:08Z (GMT). No. of bitstreams: 0 Previous issue date: 2005-12-16Bitstream added on 2014-06-13T20:08:14Z : No. of bitstreams: 1 godoy_r_me_sjrp.pdf: 1009803 bytes, checksum: 156b74c6b6bc9b086abf40743673384e (MD5) / Em considerando-se dois subsistemas A e B com espaço de estados HA e HB e com o espaço do sistema total ( A+B ) associado ao produto tensorial HA ? HB, alguns vetores desse sistema total podem ser decompostos em um produto tensorial de dois vetores descrevendo o estado do sistema A e B. Quando essa decomposição não é possível, diz-se que os subsistemas estão emaranhados. Uma medida de emaranhamento utilizada é a entropia de von Neumann de um dos subsistemas. Neste trabalho utiliza-se a entropia de Tsallis, uma generalização da entropia de von Neumann, como medida de emaranhamento.Faz-se uma comparação entre essas duas entropias como medida do emaranhamento entre campos emergentes de um divisor de feixes óticos. / Let A and B be two subsystems with space of states HA and HB respectively, being the space of the total system (A + B) associated to the tensorial product HA ? HB; some vectors of the total system may be decomposed in a tensorial product of two vectors describing the state of system A and B . When this decomposition is not possible, we say that the subsystems are entangled. An usual measure of entanglement used in each one of the subsystems is called von Neumann entropy. In this work we use Tsallis' entropy, a generalization of the von Neumann's measure to entanglement. We compare the two entropies as a measure of the entanglement between emerging fields of an optical beam splitter.

Made available in DSpace on 2014-06-11T19:27:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-11-30Bitstream added on 2014-06-13T19:47:34Z : No. of bitstreams: 1 machado_lb_me_rcla.pdf: 1035969 bytes, checksum: aa3cdd04f049c7a6251e1a19935af959 (MD5) / O presente trabalho, intitulado Análise Funcional e Aplicações, tem por objetivo realizar um estudo sobre espaços de funções, principalmente, os espaços de dimensão infinita. Em particular, apresentar resultados sobre a teoria de funcionais lineares e espaço dual, conceitos de ortogonalidade e teoremas fundamentais em Análise Funcional como, por exemplo, o Teorema da Representação de Riesz e os Teoremas de Hahn- Banach / This work, entitled Functional Analysis and Applications, has by objective to carry an study on function spaces, mainly, spaces of infinite dimension. In particular, to present results on the theory of linear functionals and dual space, concepts of orthogonality and fundamental theorems in Functional Analysis as, for example, the Riesz Representation Theorem and the Hahn-Banach Theorems

abstract: In this thesis, I investigate the C*-algebras and related constructions that arise from combinatorial structures such as directed graphs and their generalizations. I give a complete characterization of the C*-correspondences associated to directed graphs as well as results about obstructions to a similar characterization of these objects for generalizations of directed graphs. Viewing the higher-dimensional analogues of directed graphs through the lens of product systems, I give a rigorous proof that topological k-graphs are essentially product systems over N^k of topological graphs. I introduce a "compactly aligned" condition for such product systems of graphs and show that this coincides with the similarly-named conditions for topological k-graphs and for the associated product systems over N^k of C*-correspondences. Finally I consider the constructions arising from topological dynamical systems consisting of a locally compact Hausdorff space and k commuting local homeomorphisms. I show that in this case, the associated topological k-graph correspondence is isomorphic to the product system over N^k of C*-correspondences arising from a related Exel-Larsen system. Moreover, I show that the topological k-graph C*-algebra has a crossed product structure in the sense of Larsen. / Dissertation/Thesis / Ph.D. Mathematics 2011

Orientador: Marta Cilene Gadotti / Banca: Adilson José Vieira Brandão / Banca: Wladimir Seixas / Resumo: Neste trabalho, abordaremos os principais conceitos e propriedades sobre espaço de Banach e espaço de Hilbert com o objetivo de oferecer o conteúdo necessário para discutirmos algumas aplicações desses conceitos. Mostraremos a existência e unicidade de solução de Equações Diferenciais Ordinárias de Primeira Ordem, existência e unicidade de solução de certas Equações Integrais e existência e unicidade de melhor aproximação em espaços normados e de Hilbert / Abstract: In this work, we will discuss the main concepts and properties on Banach space and Hilbert space in order to offer the necessary content to discuss some applications of these concepts. We will show the existence and uniqueness of the solution of First Order Ordinary Differential Equations, existence and uniqueness of solution of certain Integral Equations and existence and uniqueness of better approximation in normed and Hilbert spaces / Mestre

From the beginning of the study of spaces in functional analysis, bases have been an indispensable tool for operating with vectors and functions over a concrete space. Bases can be organized by types, depending on their properties. This thesis is intended to give an overview of some bases and their relations. We study Hamel basis, Schauder basis and Orthonormal basis; we give some properties and compare them in different spaces, explaining the results. For example, an infinite dimensional Hilbert space will never have a basis which is a Schauder basis and a Hamel basis at the same time, but if this space is separable it has an orthonormal basis, which is also a Schauder basis. The project deals mainly with Banach spaces, but we also talk about the case when the space is a pre Hilbert space.

This thesis presents the investigations conducted in the use of ultrasonic technology to measure two-phase flow in both horizontal and vertical pipe flows which is important for the petroleum industry. However, there are still key challenges to measure parameters of the multiphase flow accurately. Four methods of ultrasonic technologies were explored. The Hilbert-Huang transform (HHT) was first applied to the ultrasound signals of air-water flow on horizontal flow for measurement of the parameters of the two- phase slug flow. The use of the HHT technique is sensitive enough to detect the hydrodynamics of the slug flow. The results of the experiments are compared with correlations in the literature and are in good agreement. Next, experimental data of air-water two-phase flow under slug, elongated bubble, stratified-wavy and stratified flow regimes were used to develop an objective flow regime classification of two-phase flow using the ultrasonic Doppler sensor and artificial neural network (ANN). The classifications using the power spectral density (PSD) and discrete wavelet transform (DWT) features have accuracies of 87% and 95.6% respectively. This is considerably more promising as it uses non-invasive and non-radioactive sensors. Moreover, ultrasonic pulse wave transducers with centre frequencies of 1MHz and 7.5MHz were used to measure two-phase flow both in horizontal and vertical flow pipes. The liquid level measurement was compared with the conductivity probes technique and agreed qualitatively. However, in the vertical with a gas volume fraction (GVF) higher than 20%, the ultrasound signals were attenuated. Furthermore, gas-liquid and oil-water two-phase flow rates in a vertical upward flow were measured using a combination of an ultrasound Doppler sensor and gamma densitometer. The results showed that the flow gas and liquid flow rates measured are within ±10% for low void fraction tests, water-cut measurements are within ±10%, densities within ±5%, and void fractions within ±10%. These findings are good results for a relatively fast flowing multiphase flow.

O monitoramento de vibração de máquinas rotativas é de grande interesse da indústria, uma vez que se tem a possibilidade de detectar, com certa antecedência, problemas relacionados à condição de funcionamento do equipamento, possibilitando reparos, ajustes ou consertos e, assim, minimizando custos no caso de falhas graves ou paradas inesperadas. Neste trabalho é feita a adequação de uma bancada de testes para estudo de técnicas de detecção de falhas em rolamentos de esferas por análise de vibração. O objetivo é o de localizar falhas em rolamentos utilizando o monitoramento dos sinais das vibrações (aceleração) no mancal que suporta o rolamento de teste e o posterior processamento com o auxílio de alguma técnica de detecção. Neste trabalho a técnica do envelope foi escolhida. A bancada, assim desenvolvida, permite a retirada e colocação dos rolamentos em estudo de maneira simples e rápida, permitindo a execução de diversos testes com rapidez. A investigação da detecção de falhas em rolamentos é feita comparando-se rolamentos em condições normais com rolamentos que têm um defeito induzido. Inicialmente é apresentada a descrição das origens e formas de propagação das falhas em elementos de rolamentos e também as formas como estas falhas são induzidas em locais específicos de cada rolamento. Uma breve revisão sobre métodos de detecção de falhas no domínio do tempo e da frequência é feita. Ênfase é dada ao método do envelope que faz uso da transformada de Hilbert (Hilbert Transform) conjuntamente com a transformada Rápida de Fourier (Fast Fourier Transform). Em seguida, descreve-se como foram geradas as falhas e separados os grupos de teste, também é descrito como os ensaios foram executados com os danos induzidos em local pré-determinado no rolamento. Os resultados obtidos possibilitaram identificar as origens das falhas induzidas tanto na pista externa quanto na interna dos rolamentos analisando os sinais de vibração do mancal onde está montado o rolamento em teste com o pós-processamento dos mesmos com a técnica investigada. Os testes simulam as condições extremas encontradas em sistemas rotativos de equipamentos industriais através da imposição de cargas verticais ao rolamento. Este estudo de detecção das falhas em rolamentos propiciou uma melhor compreensão e análise do processo de falha nestes componentes. / The vibration monitoring of rotating machines is of great interest to industries since it has the ability to detect, in advance, problems related to the operational condition of the equipment, enabling fixing, adjustments or repair, and thus, minimizing the cost in case of faults or unexpected downtime. In this work, the study of the adequacy of a test bench for detecting faults in ball bearings by vibration analysis techniques is developed. It aims at locating faults in ball bearings using vibration monitoring signals (acceleration) in the journal bearings that support this elements and further processing with the aid of some detection technique. In this work the envelope technique was chosen. The developed test bench thus allows the removal and placement of the bearings in a simple and fast way allowing running quickly several tests. The investigation of detecting faults in ball bearings is made by comparing the bearings under normal conditions with bearings which have an induced defect. First of all is presented a description of the origins and forms of propagation of faults in bearing elements and also the ways in which these failures are induced in specific locations of each bearing. A brief review of methods for detecting faults in the time and frequency domain is made. Emphasis is given to the Envelope Method which uses the Hilbert Transform with the Fast Fourier Transform. Then it is described how the tests were accomplished with the induced damage in predetermined sites in the bearing. The results obtained allowed to identify the origins of the induced bearing failures in both outer and inner races just by reading the vibration signals and post-processing them with the investigated technique. The tests take care to simulate conditions close to those found in actual rotatory systems of industrial equipment by imposing vertical loads to the bearing. This study in detecting flaws in balls bearings provided a better understanding of the analysis failure process in these components.