Estimação em classes de processos estocásticos com decaimento hiperbólico da função de autocorrelação

Neste trabalho analisamos processos estocásticos com decaimento polinomial (também chamado hiperbólico) da função de autocorrelação. Nosso estudo tem enfoque nas classes dos Processos ARFIMA e dos Processos obtidos à partir de iterações da transformação de Manneville-Pomeau. Os objetivos principais são comparar diversos métodos de estimação para o parâmetro fracionário do processo ARFIMA, nas situações de estacionariedade e não estacionariedade e, além disso, obter resultados similares para o parâmetro do processo de Manneville-Pomeau. Entre os diversos métodos de estimação para os parâmetros destes dois processos destacamos aquele baseado na teoria de wavelets por ser aquele que teve o melhor desempenho.

Complicações pós-operatórias em cirurgia torácica relacionadas aos índices e testes preditores de risco cirúrgico pré-operatórios

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dimensões fractais para certos sistemas dinâmicos discretos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Executive functions of children born very preterm--deficit or delay?

This cross-sectional study examined the performance of children born very preterm and/or at very low birth weight (VPT/VLBW) and same-aged term-born controls in three core executive functions: inhibition, working memory, and shifting. Children were divided into two age groups according to the median (young, 8.00-9.86 years; old, 9.87-12.99 years). The aims of the study were to investigate whether (a) VPT/VLBW children of both age groups performed poorer than controls (deficit hypothesis) or caught up with increasing age (delay hypothesis) and (b) whether VPT/VLBW children displayed a similar pattern of performance increase in executive functions with advancing age compared with the controls. Fifty-six VPT/VLBW children born in the cohort of 1998-2003 and 41 healthy-term-born controls were recruited. All children completed tests of inhibition (Color-Word Interference Task, Delis-Kaplan Executive Function System (D-KEFS)), working memory (Digit Span Backwards, HAWIK-IV), and shifting (Trail Making Test, Number-Letter Sequencing, D-KEFS). Results revealed that young VPT/VLBW children performed significantly poorer than the young controls in inhibition, working memory, and shifting, whereas old VPT/VLBW children performed similar to the old controls across all three executive functions. Furthermore, the frequencies of impairment in inhibition, working memory and shifting were higher in the young VPT/VLBW group compared with the young control group, whereas frequencies of impairment were equal in the old groups. In both VPT/VLBW children and controls, the highest increase in executive performance across the ages of 8 to 12 years was observed in shifting, followed by working memory, and inhibition.

Medidas autosemejantes en el plano, momentos y matrices de Hessenberg

La tesis MEDIDAS AUTOSEMEJANTES EN EL PLANO, MOMENTOS Y MATRICES DE HESSENBERG se enmarca entre las áreas de la teoría geométrica de la medida, la teoría de polinomios ortogonales y la teoría de operadores. La memoria aborda el estudio de medidas con soporte acotado en el plano complejo vistas con la óptica de las matrices infinitas de momentos y de Hessenberg asociadas a estas medidas que en la teoría de los polinomios ortogonales las representan. En particular se centra en el estudio de las medidas autosemejantes que son las medidas de equilibrio definidas por un sistema de funciones iteradas (SFI). Los conjuntos autosemejantes son conjuntos que tienen la propiedad geométrica de descomponerse en unión de piezas semejantes al conjunto total. Estas piezas pueden solaparse o no, cuando el solapamiento es pequeño la teoría de Hutchinson [Hut81] funciona bien, pero cuando no existen restricciones falla. El problema del solapamiento consiste en controlar la medida de este solapamiento. Un ejemplo de la complejidad de este problema se plantea con las convoluciones infinitas de distribuciones de Bernoulli, que han resultado ser un ejemplo de medidas autosemejantes en el caso real. En 1935 Jessen y A. Wintner [JW35] ya se planteaba este problema, lejos de ser sencillo ha sido estudiado durante más de setenta y cinco años y siguen sin resolverse las principales cuestiones planteadas ya por A. Garsia [Gar62] en 1962. El interés que ha despertado este problema así como la complejidad del mismo está demostrado por las numerosas publicaciones que abordan cuestiones relacionadas con este problema ver por ejemplo [JW35], [Erd39], [PS96], [Ma00], [Ma96], [Sol98], [Mat95], [PS96], [Sim05],[JKS07] [JKS11]. En el primer capítulo comenzamos introduciendo con detalle las medidas autosemejante en el plano complejo y los sistemas de funciones iteradas, así como los conceptos de la teoría de la medida necesarios para describirlos. A continuación se introducen las herramientas necesarias de teoría de polinomios ortogonales, matrices infinitas y operadores que se van a usar. En el segundo y tercer capítulo trasladamos las propiedades geométricas de las medidas autosemejantes a las matrices de momentos y de Hessenberg, respectivamente. A partir de estos resultados se describen algoritmos para calcular estas matrices a partir del SFI correspondiente. Concretamente, se obtienen fórmulas explícitas y algoritmos de aproximación para los momentos y matrices de momentos de medidas fractales, a partir de un teorema del punto fijo para las matrices. Además utilizando técnicas de la teoría de operadores, se han extendido al plano complejo los resultados que G. Mantica [Ma00, Ma96] obtenía en el caso real. Este resultado es la base para definir un algoritmo estable de aproximación de la matriz de Hessenberg asociada a una medida fractal u obtener secciones finitas exactas de matrices Hessenberg asociadas a una suma de medidas. En el último capítulo, se consideran medidas, μ, más generales y se estudia el comportamiento asintótico de los autovalores de una matriz hermitiana de momentos y su impacto en las propiedades de la medida asociada. En el resultado central se demuestra que si los polinomios asociados son densos en L2(μ) entonces necesariamente el autovalor mínimo de las secciones finitas de la matriz de momentos de la medida tiende a cero. ABSTRACT The Thesis work “Self-similar Measures on the Plane, Moments and Hessenberg Matrices” is framed among the geometric measure theory, orthogonal polynomials and operator theory. The work studies measures with compact support on the complex plane from the point of view of the associated infinite moments and Hessenberg matrices representing them in the theory of orthogonal polynomials. More precisely, it concentrates on the study of the self-similar measures that are equilibrium measures in a iterated functions system. Self-similar sets have the geometric property of being decomposable in a union of similar pieces to the complete set. These pieces can overlap. If the overlapping is small, Hutchinson’s theory [Hut81] works well, however, when it has no restrictions, the theory does not hold. The overlapping problem consists in controlling the measure of the overlap. The complexity of this problem is exemplified in the infinite convolutions of Bernoulli’s distributions, that are an example of self-similar measures in the real case. As early as 1935 [JW35], Jessen and Wintner posed this problem, that far from being simple, has been studied during more than 75 years. The main cuestiones posed by Garsia in 1962 [Gar62] remain unsolved. The interest in this problem, together with its complexity, is demonstrated by the number of publications that over the years have dealt with it. See, for example, [JW35], [Erd39], [PS96], [Ma00], [Ma96], [Sol98], [Mat95], [PS96], [Sim05], [JKS07] [JKS11]. In the first chapter, we will start with a detailed introduction to the self-similar measurements in the complex plane and to the iterated functions systems, also including the concepts of measure theory needed to describe them. Next, we introduce the necessary tools from orthogonal polynomials, infinite matrices and operators. In the second and third chapter we will translate the geometric properties of selfsimilar measures to the moments and Hessenberg matrices. From these results, we will describe algorithms to calculate these matrices from the corresponding iterated functions systems. To be precise, we obtain explicit formulas and approximation algorithms for the moments and moment matrices of fractal measures from a new fixed point theorem for matrices. Moreover, using techniques from operator theory, we extend to the complex plane the real case results obtained by Mantica [Ma00, Ma96]. This result is the base to define a stable algorithm that approximates the Hessenberg matrix associated to a fractal measure and obtains exact finite sections of Hessenberg matrices associated to a sum of measurements. In the last chapter, we consider more general measures, μ, and study the asymptotic behaviour of the eigenvalues of a hermitian matrix of moments, together with its impact on the properties of the associated measure. In the main result we demonstrate that, if the associated polynomials are dense in L2(μ), then necessarily follows that the minimum eigenvalue of the finite sections of the moments matrix goes to zero.

Compressão fractal de imagens

Neste trabalho será apresentado um método recente de compressão de imagens baseado na teoria dos Sistemas de Funções Iteradas (SFI), designado por Compressão Fractal. Descrever-se-á um modelo contínuo para a compressão fractal sobre o espaço métrico completo Lp, onde será definido um operador de transformação fractal contractivo associado a um SFI local com aplicações. Antes disso, será introduzida a teoria dos SFIs no espaço de Hausdorff ou espaço fractal, a teoria dos SFIs Locais - uma generalização dos SFIs - e dos SFIs no espaço Lp. Fornecida a fundamentação teórica para o método será apresentado detalhadamente o algoritmo de compressão fractal. Serão também descritas algumas estratégias de particionamento necessárias para encontrar o SFI com aplicações, assim como, algumas estratégias para tentar colmatar o maior entrave da compressão fractal: a complexidade de codificação. Esta dissertação assumirá essencialmente um carácter mais teórico e descritivo do método de compressão fractal, e de algumas técnicas, já implementadas, para melhorar a sua eficácia.

Visual function and the ageing visual system

The population is ageing. Globally, the number of older adults (aged 60 years or over) is expected to more than double, from 841 million people in 2013 to more than 2 billion in 2050.1 In light of the increasing size of the older adult population, there is a pressing need to better identify the nature of, and mechanisms underlying, age-related vision impairment and the functional impact it has on the performance of everyday activities in older adults. The content of this feature issue reflects the diversity of research currently being undertaken on the topic of the ageing visual system and the important visual challenges that this presents for our ageing patient population. The scope is broad and includes topics relating to three main related themes: 1) The treatment of age-related ocular disorders and diseases and their consequences, including presbyopia and AMD; 2) The impact of age-related visual changes on everyday activities in older people, including mobility, driving and falls, and; 3) The interaction of age-related visual impairments and other age-related impairments including hearing and cognitive changes.

Comparison of ocular modulation transfer function determined by a ray-tracing aberrometer and a double-pass system in early cataract patients

BACKGROUND: The evaluation of retinal image quality in cataract eyes has gained importance and the clinical modulation transfer functions (MTF) can obtained by aberrometer and double pass (DP) system. This study aimed to compare MTF derived from a ray tracing aberrometer and a DP system in early cataractous and normal eyes. METHODS: There were 128 subjects with 61 control eyes and 67 eyes with early cataract defined according to the Lens Opacities Classification System III. A laser ray-tracing wavefront aberrometer (iTrace) and a double pass (DP) system (OQAS) assessed ocular MTF for 6.0 mm pupil diameters following dilation. Areas under the MTF (AUMTF) and their correlations were analyzed. Stepwise multiple regression analysis assessed factors affecting the differences between iTrace- and OQAS-derived AUMTF for the early cataract group. RESULTS: For both early cataract and control groups, iTrace-derived MTFs were higher than OQAS-derived MTFs across a range of spatial frequencies (P < 0.01). No significant difference between the two groups occurred for iTrace-derived AUMTF, but the early cataract group had significantly smaller OQAS-derived AUMTF than did the control group (P < 0.01). AUMTF determined from both the techniques demonstrated significant correlations with nuclear opacities, higher-order aberrations (HOAs), visual acuity, and contrast sensitivity functions, while the OQAS-derived AUMTF also demonstrated significant correlations with age and cortical opacity grade. The factors significantly affecting the difference between iTrace and OQAS AUMTF were root-mean-squared HOAs (standardized beta coefficient = -0.63, P < 0.01) and age (standardized beta coefficient = 0.26, P < 0.01). CONCLUSIONS: MTFs determined from a iTrace and a DP system (OQAS) differ significantly in early cataractous and normal subjects. Correlations with visual performance were higher for the DP system. OQAS-derived MTF may be useful as an indicator of visual performance in early cataract eyes.