Made available in DSpace on 2017-07-21T20:43:48Z (GMT). No. of bitstreams: 1 Charles Betuel Mansende Mvumbi.pdf: 3357827 bytes, checksum: 822a91a949448c4769ce680ef684f74d (MD5) Previous issue date: 2016-01-29 / The ceramic porcelains are produced from natural raw materials (silica, feldspar and kaolin). In some applications other materials are added to increase the mechanical and dielectric strength. They are used in the manufacture of several products. Therefore, they are very studied and have been developed for long time. In this work, porcelains with different compositions were characterized and submitted to fragmentation by mechanical disruption in a ballistic impact testing. Generally the mechanical disruption in the materials produces a power dissipation forming cracks and fracture surfaces having an irregular geometry. The main objective of this work was to characterize the microstructure and the fractal fracture surface in porcelains. For comparison, the impact tests were also performed on commercial glass and acrylic. The evaluation of the fracture surface and the fractal dimension of rupture was performed by analyzing the fraction of the fragments as a function of the probability of fracture. The samples were prepared in the form of cylindrical disks with a thickness and fixed diameters. Mechanical impact test was made on the center of the disks for different materials, maintaining the same test conditions. The results of the size and mass of the fragments were obtained as a function of the impact energy, thickness, diameter and kind of material. Thus, it was possible to obtain a correlation between the test conditions and the composition of the material with the fractal pattern breakage. It has been found that the compositions used in porcelain, has a fracture toughness which is between the glass and acrylic. A correlation between strength properties to the patterns of formed crack was made. It was noticed that the number, the shape of cracks and the branches form a pattern that is associated with the impact energy and material type. / As porcelanas são cerâmicas produzidas a partir de matérias primas naturais (sílica, feldspato e caulim). Em algumas aplicações são adicionadas outras matérias primas para o aumento da resistência mecânica e dielétrica. Elas são usadas na fabricação de variados produtos. Portanto, elas são muito estudadas e vêm sendo desenvolvidas há muito tempo. Neste trabalho, porcelanas com diferentes composições foram caracterizadas e submetidas à fragmentação por ruptura mecânica em um ensaio de impacto balístico. A ruptura mecânica nos materiais em geral produz uma dissipação de energia formando trincas e superfícies de fratura que tem uma geometria irregular. O principal objetivo deste trabalho foi a caracterização da microestrutura e a caracterização fractal da superfície de fratura de porcelanas. Para comparação, os ensaios de impacto também foram feitos em vidro e acrílico comercial. A avaliação da superfície de fratura e da dimensão fractal de ruptura foi feita pela análise da fração de fragmentos em função da probabilidade de fratura. Os corpos de prova foram preparados na forma de discos cilíndricos, com espessura e diâmetros fixos. O ensaio de impacto mecânico foi feito sobre o centro dos discos, para os diferentes materiais, mantendo-se as mesmas condições de ensaios. Os resultados, do tamanho e massa dos fragmentos, foram obtidos em função da energia, espessura, diâmetro e do tipo de material. Desta forma, foi possível obter uma correlação entre as condições de ensaio e a composição do material com o padrão de ruptura fractal. Verificou-se que a porcelana nas composições usadas possui uma tenacidade à fratura que se situa entre a do vidro a do acrílico. Finalmente foi feita uma correlação entre as propriedades de resistência mecânica com os padrões de trinca formado. Percebeu-se que o número, a forma das trincas e as ramificações formam um padrão que está relacionado com a energia de impacto e o tipo de material.

A city consists of many elements such as humans, buildings, and roads. The complexity of cities is difficult to measure using Euclidean geometry. In this study, we use fractal geometry (scaling analysis) to measure the complexity of urban areas. We observe urban development from different perspectives using the bottom-up approach. In a bottom-up approach, we observe an urban region from a basic to higher level from our daily life perspective to an overall view. Furthermore, an urban environment is not constant, but it is complex; cities with greater complexity are more prosperous. There are many disciplines that analyze changes in the Earth’s surface, such as urban planning, detection of melting ice, and deforestation management. Moreover, these disciplines can take advantage of remote sensing for research. This study not only uses satellite imaging to analyze urban areas but also uses check-in and points of interest (POI) data. It uses straightforward means to observe an urban environment using the bottom-up approach and measure its complexity using fractal geometry.   Web 2.0, which has many volunteers who share their information on different platforms, was one of the most important tools in this study. We can easily obtain rough data from various platforms such as the Stanford Large Network Dataset Collection (SLNDC), the Earth Observation Group (EOG), and CloudMade. The check-in data in this thesis were downloaded from SLNDC, the POI data were obtained from CloudMade, and the nighttime lights imaging data were collected from EOG. In this study, we used these three types of data to derive natural cities representing city regions using a bottom-up approach. Natural cities were derived from open geographic data without human manipulation. After refining data, we used rough data to derive natural cities. This study used a triangulated irregular network to derive natural cities from check-in and POI data.   In this study, we focus on the four largest US natural cities regions: Chicago, New York, San Francisco, and Los Angeles. The result is that the New York City region is the most complex area in the United States. Box-counting fractal dimension, lacunarity, and ht-index (head/tail breaks index) can be used to explain this. Box-counting fractal dimension is used to represent the New York City region as the most prosperous of the four city regions. Lacunarity indicates the New York City region as the most compact area in the United States. Ht-index shows the New York City region having the highest hierarchy of the four city regions. This conforms to central place theory: higher-level cities have better service than lower-level cities. In addition, ht-index cannot represent hierarchy clearly when data distribution does not fit a long-tail distribution exactly. However, the ht-index is the only method that can analyze the complexity of natural cities without using images.

The objective is to contribute to several issues regarding the traditional view of the local structure of passive scalar fields: (1) probability density function (PDF) of the scalar concentration and scalar gradient, (2) the scalar power spectrum, (3) the structure functions, and (4) correlation functions and multi-point correlators. In addition, the research provides a geometric description of two-dimensional transects of the passive scalar iso-surfaces using the tools of fractal geometry. The local structure is analyzed as a function of large-scale anisotropy, intermittency factor, Reynolds number, and initial condition of the scalar injection. Experiments were performed in the bed boundary layer produced by a uniform depth open channel flow of water in a tilting flume for Re_lamda = 63, 94, and 120. A small nozzle iso-kinetically delivers a passive scalar of high Schmidt number ( Sc = 1000) at mid-depth to generate the turbulent scalar field. Three nozzle diameters are used to study the effects of the injection length scale. High-resolution planar laser induced fluorescence (PLIF) technique is used to measure the scalar field. The local structure far from isotropic and is influenced even at the smallest scales by large-scale anisotropy, initial injection length scale and the Reynolds number of the flow. The PDF of the scalar fluctuations is non-Gaussian and dependent on large-scale anisotropy. The PDF of scalar gradients show the influence of large-scale anisotropy on the structure at the smallest scales. The spectrum of the scalar field deviates from the in the inertial convection regime and is dependent on large-scale anisotropy, external intermittency, and low Reynolds number. There is no evidence of Batchelors k^-1 scaling law. The scaling exponents of the even-ordered structure functions appear to be inversely correlated with the kurtosis of the scalar fluctuations. The fractal geometry of the two dimensional transects of passive scalar iso-surfaces is scale dependent. The fractal dimension is 1.0 at the smallest length scale and increases in a universal manner in the viscous-convective regime. The coverage length underestimate reflects this universal behavior with practical significance. The lacunarity function shows that the instantaneous scalar field is most in-homogenous around the Kolmogorov scale.

Forty songs are randomly selected from four randomly selected maqams. Songs are restricted to be in sofyan us&uuml / l (sofyan rhythmic form) to check the statistical significance. Next, fractal dimensions of the these songs are calculated by using two different method and two different scattering diagrams. In the first method, fractal dimensions are calculated via two different box sizes. As for second method, successively decreased box sizes are used. In addition, standard deviation and mean values of the fractal dimensions are calculated to check the relation between fractal dimension and maqam. T test and F test are applied to check the statistical significance. After these calculations, it is verified that fractal dimension can be used as an information source concerning the Turkish art music songs which are nonlinear dynamical systems. Moreover, it is showed that maqams can have their own fractal dimension for low resolutions. On the other hand, it is seen that for high resolutions all songs have almost same fractal dimension.

The response of geological materials at the scale of meters and the response of buried targets of different shapes and sizes using controlled-source electromagnetic induction (CSEM) is investigated. This dissertation focuses on three topics; i) frac- tal properties on electric conductivity data from near-surface geology and processing techniques for enhancing man-made target responses, ii) non-linear inversion of spa- tiotemporal data using continuation method, and iii) classification of CSEM transient and spatiotemporal data. In the first topic, apparent conductivity profiles and maps were studied to de- termine self-affine properties of the geological noise and the effects of man-made con- ductive metal targets. 2-D Fourier transform and omnidirectional variograms showed that variations in apparent conductivity exhibit self-affinity, corresponding to frac- tional Brownian motion. Self-affinity no longer holds when targets are buried in the near-surface, making feasible the use of spectral methods to determine their pres- ence. The difference between the geology and target responses can be exploited using wavelet decomposition. A series of experiments showed that wavelet filtering is able to separate target responses from the geological background. In the second topic, a continuation-based inversion method approach is adopted, based on path-tracking in model space, to solve the non-linear least squares prob- lem for unexploded ordnance (UXO) data. The model corresponds to a stretched- exponential decay of eddy currents induced in a magnetic spheroid. The fast inversion of actual field multi-receiver CSEM responses of inert, buried ordnance is also shown. Software based on the continuation method could be installed within a multi-receiver CSEM sensor and used for near-real-time UXO decision. In the third topic, unsupervised self-organizing maps (SOM) were adapted for data clustering and classification. The use of self-organizing maps (SOM) for central- loop CSEM transients shows potential capability to perform classification, discrimi- nating background and non-dangerous items (clutter) data from, for instance, unex- ploded ordnance. Implementation of a merge SOM algorithm showed that clustering and classification of spatiotemporal CSEM data is possible. The ability to extract tar- get signals from a background-contaminated pattern is desired to avoid dealing with forward models containing subsurface response or to implement processing algorithm to remove, to some degree, the effects of background response and the target-host interactions.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O caos determinístico é um dos aspectos mais interessantes no que diz respeito à teoria moderna dos sistemas dinâmicos, e está intrinsecamente associado a pequenas variações nas condições iniciais de um dado modelo. Neste trabalho, é feito um estudo acerca do comportamento caótico em dois casos específicos. Primeiramente, estudam-se modelos préinflacionários não-compactos de Friedmann-Robertson-Walker com campo escalar minimamente acoplado e, em seguida, modelos anisotrópicos de Bianchi IX. Em ambos os casos, o componente material é um fluido perfeito. Tais modelos possuem constante cosmológica e podem ser estudados através de uma descrição unificada, a partir de transformações de variáveis convenientes. Estes sistemas possuem estruturas similares no espaço de fases, denominadas centros-sela, que fazem com que as soluções estejam contidas em hipersuperfícies cuja topologia é cilíndrica. Estas estruturas dominam a relação entre colapso e escape para a inflação, que podem ser tratadas como bacias cuja fronteira pode ser fractal, e que podem ser associadas a uma estrutura denominada repulsor estranho. Utilizando o método de contagem de caixas, são calculadas as dimensões características das fronteiras nos modelos, o que envolve técnicas e algoritmos de computação numérica, e tal método permite estudar o escape caótico para a inflação. / Deterministic chaos is the most interesting aspect with regard to the modern theory of dynamical systems, and is intrinsically associated with small changes in initial conditions of a given model. This paper is a study about the chaotic behavior in two specific cases. First, we study non compact pre-inflationary FRW models with a minimally coupled scalar field, and then anisotropic models of Bianchi IX. In both cases the material component is a perfect fluid. Such models have a cosmological constant and can be studied via a unified description using suitable transformations of variables. These systems have similar structures in phase space, called saddle-centers, which make the solutions to be contained in hypersurfaces whose topology is cylindrical. These structures dominate the relationship between collapse and escape to inflation, which can be treated as basins whose boundary can be fractal, and can be associated with a structure called a strange repeller. Using the boxcounting method, which involves methods and algorithms for numerical computation, we calculate the characteristic dimension of their sets. This method allows to study the chaotic escape to inflation.

Orientador: Prof. Dr. Marcelo Zanchetta do Nascimento / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Engenharia da Informação, 2015. / O câncer de próstata é o segundo que provoca o maior número de vítimas fatais entre os homens, atingindo principalmente a população mundial com idades superiores a 60 anos. Entre os métodos empregados para o diagnóstico médico estão os exames clínicos, laboratoriais e o diagnóstico por imagem, o que pode indicar a necessidade da biópsia da próstata. As biópsias são avaliadas por especialistas para auxiliar na conduta mais adequada de tratamento, desta forma o estudo por imagem histológica é realizado e se destaca como um dos métodos utilizados devido a facilidade de diagnosticar a doença. Porém, ainda existem problemas que precisam ser solucionados para reduzir o número de falsos positivos. Este trabalho apresenta um conjunto de técnicas para identificar e quantificar as regiões de interesse em imagens histológicas da próstata. As análises foram realizadas com dimensão fractal de imagens coloridas e classificadas com SVM com os kernels linear, polinomial e RBF. As regiões de interesses foram segmentadas em núcleos da célula cuboide, lúmens glandulares e tecido estromal e aplicado o cálculo da dimensão fractal. A avaliação de desempenho foi baseada na área sob a curva ROC (AUC) e pela acurácia. Os resultados obtidos com essas ferramentas mostram que o grupo de imagens segmentadas por estroma com magnificação de 100x obtiveram melhores resultados de classificação, obtendo valores de AUC de 92,21% e 86,77% de acurácia para os grupos de tecido normal versus tecido tumoral, obteve 73,53% de acurácia para o grupo tecido normal versus tecido hiperplásico e de 80,00% para o grupo de tecido hiperplásico versus tecido tumoral. O método proposto quantificou tecidos histológicos da próstata com descritores baseados em técnicas não lineares multi-escala. O uso de informações dos canais de cores em conjunto com a segmentação das estruturas foi mais relevante para um sistema de apoio ao diagnóstico. / Prostate cancer is the second type of cancer that causes more deaths between men. It affects mainly the population over the age of 60. Laboratory exams and diagnostic imaging are among the methods used for medical diagnosis, which may indicate the need for a prostrate biopsy. Biopsies are evaluated by experts in order to indicate the most appropriate treatment strategy. Hence, the study of histological images stands out as one of the most used methods as it allows an easier diagnosis. However, there are still problems that need to be addressed to reduce the number of false positives. This work presents a set of techniques to identify and quantify regions of interest in histological images of the prostate. Color and greyscale images were analysed using fractal dimension then classified in SVM with linear, polynomial and RBF kernels. Regions of interest were segmented in basal cell cuboid, glandular lumens and stromal tissue and then a fractal dimension was applied. Performance evaluation was based on the area under the ROC curve(AUC) and accuracy. The results obtained by applying these tools show that images segmented by stroma with a magnification of 100x had better classification results, achieving AUC values of 92.21% and 86.77% accuracy for the normal tissue groups versus tumor tissue. Also, in this group of images a level of accuracy of 73.53% for hyperplastic tissue versus normal tissue and 80.00% for hyperplastic tissue versus tumor tissue. The method quantified histological prostate tissue with multi-scale techniques based on nonlinear descriptors. Therefore, the use of information from color channels together with the segmented structures are most relevant to a diagnostic support system.

Orientador: Rafael Ribeiro Dias Vilela de Oliveira / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Matemática , 2016. / No espaço de fases de sistemas dinâmicos, podem existir diferentes regiões as quais correspondem a diferentes comportamentos futuros do sistema: as bacias de atração. Separando essas regiões, há um conjunto de pontos, o qual chamamos de fronteira, que pode possuir uma geometria regular ou fractal, essa última caracterizada por uma dimensão D não inteira. A principal consequência de um sistema dinâmico possuir uma fronteira fractal em seu espaço de fases está na dificuldade em se determinar o comportamento futuro do sistema. De fato, dado que a precisão com a qual conseguimos medir um ponto é finita, existe uma área no espaço de fases em que não sabemos ao certo a qual bacia de atração o ponto pertence. Em especial, caso a fronteira seja fractal, essa área é proporcional a N..D, onde é o erro de medição e N é a dimensão do sistema. Dessa forma, percebemos a importância de conseguirmos calcular a dimensão D da fronteira fractal. Nesse trabalho, primeiro apresentamos os principais conceitos de sistemas dinâmicos e geometria fractal, relacionando essas estruturas geométricas ao comportamento dinâmico caótico. Em seguida, definimos as fronteiras e estendemos a elas o conceito de geometria fractal. Por último, apresentamos os métodos vigentes para o cálculo numérico da dimensão de fronteiras fractais, a saber, o método da incerteza e o método da avaliação da função de saída e, baseados no primeiro método, desenvolvemos um método alternativo: o método da incerteza condicional. Observamos que o método desenvolvido nesse trabalho é válido como um novo método para o cálculo da dimensão de fronteiras fractais, podendo ser utilizado tanto em sistemas de tempo contínuo quanto discreto. / In the phase space of dynamical systems there may exist different regions which correspond to different final states: the basins of attraction. Between different basins of attraction, there is a set of points which we call basin boundary. Basin boundaries can be either smooth or fractal, the latter being characterized by a non-integer dimension D. The main consequence of fractal basin boundaries in the phase space of a dynamical system is the difficulty of determining the system¿s final state. Indeed, knowing that we can only measure a point with a finite precision, there is a phase space region where we cannot know in which of the basins of attraction the point really is by looking at the system¿s final state alone. In particular, for a fractal basin boundary, the area of the phase space where we cannot predict the final state with certainty is proportional to N..D, with being the measurement error and N the system¿s dimension. Therefore, it is important to know the dimension D of the fractal basin boundary. In this work, we first present the main concepts of dynamical systems and fractal geometry, linking these geometric structures to chaotic behavior in the system. Later, we define basin boundaries, both regular and fractal. At last, we present the two methods currently available to calculate the dimension of fractal basin boundaries in dynamical systems, namely the uncertainty method and the output function evaluation method. We propose a new method that is based on the former one called the conditional uncertainty method and we show that this method can calculate fractal dimensions of basin boundaries to a good accuracy either on continuous or discrete-time dynamics.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O caos determinístico é um dos aspectos mais interessantes no que diz respeito à teoria moderna dos sistemas dinâmicos, e está intrinsecamente associado a pequenas variações nas condições iniciais de um dado modelo. Neste trabalho, é feito um estudo acerca do comportamento caótico em dois casos específicos. Primeiramente, estudam-se modelos préinflacionários não-compactos de Friedmann-Robertson-Walker com campo escalar minimamente acoplado e, em seguida, modelos anisotrópicos de Bianchi IX. Em ambos os casos, o componente material é um fluido perfeito. Tais modelos possuem constante cosmológica e podem ser estudados através de uma descrição unificada, a partir de transformações de variáveis convenientes. Estes sistemas possuem estruturas similares no espaço de fases, denominadas centros-sela, que fazem com que as soluções estejam contidas em hipersuperfícies cuja topologia é cilíndrica. Estas estruturas dominam a relação entre colapso e escape para a inflação, que podem ser tratadas como bacias cuja fronteira pode ser fractal, e que podem ser associadas a uma estrutura denominada repulsor estranho. Utilizando o método de contagem de caixas, são calculadas as dimensões características das fronteiras nos modelos, o que envolve técnicas e algoritmos de computação numérica, e tal método permite estudar o escape caótico para a inflação. / Deterministic chaos is the most interesting aspect with regard to the modern theory of dynamical systems, and is intrinsically associated with small changes in initial conditions of a given model. This paper is a study about the chaotic behavior in two specific cases. First, we study non compact pre-inflationary FRW models with a minimally coupled scalar field, and then anisotropic models of Bianchi IX. In both cases the material component is a perfect fluid. Such models have a cosmological constant and can be studied via a unified description using suitable transformations of variables. These systems have similar structures in phase space, called saddle-centers, which make the solutions to be contained in hypersurfaces whose topology is cylindrical. These structures dominate the relationship between collapse and escape to inflation, which can be treated as basins whose boundary can be fractal, and can be associated with a structure called a strange repeller. Using the boxcounting method, which involves methods and algorithms for numerical computation, we calculate the characteristic dimension of their sets. This method allows to study the chaotic escape to inflation.

Submitted by Jordan (jordanbiblio@gmail.com) on 2017-05-04T14:04:39Z No. of bitstreams: 1 DISS_2015_Guilherme Falcão da Silva Campos.pdf: 3678965 bytes, checksum: 16184b756c14ab6fc7eb19e95ff445d4 (MD5) / Approved for entry into archive by Jordan (jordanbiblio@gmail.com) on 2017-05-04T15:41:39Z (GMT) No. of bitstreams: 1 DISS_2015_Guilherme Falcão da Silva Campos.pdf: 3678965 bytes, checksum: 16184b756c14ab6fc7eb19e95ff445d4 (MD5) / Made available in DSpace on 2017-05-04T15:41:39Z (GMT). No. of bitstreams: 1 DISS_2015_Guilherme Falcão da Silva Campos.pdf: 3678965 bytes, checksum: 16184b756c14ab6fc7eb19e95ff445d4 (MD5) Previous issue date: 2015-11-23 / Pesquisas ambientais dependem de dados de sensores para a criação das séries temporais referentes às variáveis analisadas. A quantidade de dados tende a aumentar, cada vez mais, à medida que novos sensores são criados e instalados. Com o passar do tempo os conjuntos de dados se tornam massivos, requerendo novas formas de armazenamento e processamento. Este trabalho busca meios de se contornar esses problemas utilizando uma solução tecnológica capaz de armazenar e processar grandes quantidades de dados. A solução tecnológica utilizada é o Apache Hadoop, uma ferramenta voltada a problemas de Big Data. Com a finalidade de avaliar a ferramenta foram utilizados diferentes conjuntos de dados e adaptados diferentes algoritmos usados na análise de séries temporais. Foram implementados analises de séries caóticas e não caóticas. As implementações foram a transformada de wavelet, uma busca por similaridade usando a função de distância Euclidiana, cálculo da dimensão box-counting e o cálculo da dimensão de correlação. Essas implementações foram adaptadas para utilizar o paradigma de processamento distribuído MapReduce. / Environmental research depend on sensor generated data to create time series regarding the variables that are being analyzed. The amount of data tends to increase as more and more sensors are created and installed. After some time the datasets become huge and requires new ways to process and store the data. This work seeks to find ways to avoid these issues using a technological solution able to store and process large amounts of data. The solution used is Apache Hadoop, a tool which purpose is to solve Big Data problems. In order to evaluate the tool were used different datasets and time series analysis algorithms. The analysis of chaotic and non-chaotic time series were implemented. These implementations were: the wavelet transform, similarity search using Euclidean distance function, the calculus of the box-counting dimension and the calculus of the correlation dimension. Those implementations were adapted for the MapReduce parallel processing paradigm.