Les points critiques d’une fonction scalaire (minima, points col et maxima) sont des caractéristiques importantes permettant de décrire de gros ensembles de données, comme par exemple les données topographiques. L’acquisition de ces données introduit souvent du bruit sur les valeurs. Un grand nombre de points critiques sont créés par le bruit, il est donc important de supprimer ces points critiques pour faire une bonne analyse de ces données. Le complexe de Morse-Smale est un objet mathématique qui est étudié dans le domaine de la Visualisation Scientifique car il permet de simplifier des fonctions scalaires tout en gardant les points critiques les plus importants de la fonction étudiée, ainsi que les liens entre ces points critiques. Nous proposons dans cette thèse une méthode permettant de construire une fonction qui correspond à un complexe de Morse-Smale d’une fonction définie sur R^2 après suppression de paires de points critiques dans celui-ci.Tout d’abord, nous proposons une méthode qui définit une surface interpolant des valeurs de fonction aux points d’une grille de façon monotone, c’est-à-dire en ne créant pas de point critique. Cette surface est composée d’un ensemble de patchs de Bézier triangulaires cubiques assemblés de telle sorte que la surface soit globalement C^1. Nous donnons des conditionssuffisantes sur les valeurs d fonction et les valeurs de dérivées partielles aux points de la grille afin que la surface soit croissante dans la direction (x+y). Il n’est pas évident de créer des valeurs de dérivées partielles en chaque point de la grille vérifiant ces conditions. C’est pourquoi nous introduisons deux algorithmes : le premier permet de modifier des valeurs de dérivées partielles données en entrée afin que celles-ci vérifient les conditions et le second calcule des valeurs de dérivées partielles à partir des valeurs de fonctions aux points de la grille.Ensuite, nous décrivons une méthode de reconstruction de champs scalaires à partir de complexes de Morse-Smale simplifiés. Pour cela, nous commençons par approximer les 1-cellules (les liens entre les points critiques dans le complexe de Morse-Smale, ceux-ci sont décrits par des polylignes) par des courbes composées de courbes de Bézier cubiques. Nous décrivons ensuite comment notre interpolation monotone de valeurs aux points d’une grille est utilisée pour construire des surfaces monotones interpolant les courbes construites précédemment. De plus, nous montrons que la fonction reconstruite contient tout les points critiques du complexe de Morse-Smale simplifié et n’en contient aucun autre. / Critical points of a scalar function (minima, saddle points and maxima) are important features to characterize large scalar datasets, like topographic data. But the acquisition of such datasets introduces noise in the values. Many critical points are caused by the noise, so there is a need to delete these extra critical points. The Morse-Smale complex is a mathematical object which is studied in the domain of Visualization because it allows to simplify scalar functions while keeping the most important critical points of the studied function and the links between them. We propose in this dissertation a method to construct a function which corresponds to a Morse-Smale complex defined on R^2 after the suppression of pairs of critical points.Firstly, we propose a method which defines a monotone surface (a surface without critical points).This surface interpolates function values at a grid points. Furthermore, it is composed of a set of triangular cubic Bézier patches which define a C^1 continuous surface. We give sufficient conditions on the function values at the grid points and on the partial derivatives at the grid points so that the surface is increasing in the (x+y) direction. It is not easy to compute partial derivatives values which respect these conditions. That’s why we introduce two algorithms : the first modifies the partial derivatives values on input such that they respect the conditions and the second computes these values from the function values at the grid points.Then, we describe a reconstruction method of scalar field from simplified Morse-Smale complexes. We begin by approximating the 1-cells of the complex (which are the links between the critical points, described by polylines) by curves composed of cubic Bézier curves. We then describe how our monotone interpolant of values at grid points is used to construct monotone surfaces which interpolate the curves we computed before. Furthermore, we show that the function we compute contains all the critical points of the simplified Morse-Smale complex and has no others.

Neste trabalho, estudamos a existˆencia e multiplicidade de solu¸c˜oes de certos problemas p-sublineares envolvendo o operador p-laplaciano usando teoria de Morse. / The purpose of this text is to provide a didactic exposition of the paper “Solutions of p-sublinear p-Laplacian equation via Morse theory” by Yuxia Guo and Jiaquan Liu [8]. This paper addresses the existence and multiplicity of solutions for the problem where is a smooth, bounded domain of RN, p is the p-Laplacian operator and f satisfies certain conditions, in particular f is p-sublinear at 0. Morse theory is used to infer the existence of critical points of a functional associated to this problem. In Chapter 2, we introduce the necessary Morse theoretic concepts, assuming basic knowledge of singular homology theory. In Chapter 3, we introduce basic properties of the p-Laplacian operator, assuming knowledge of Sobolev spaces, including imbedding and compactness results. Finally, in Chapter 4, we follow Guo and Liu’s paper itself.

Orientadora: Profa. Dra. Ilma Aparecida Marques Silva / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Matemática , 2015.

Neste trabalho, estudamos a existˆencia e multiplicidade de solu¸c˜oes de certos problemas p-sublineares envolvendo o operador p-laplaciano usando teoria de Morse. / The purpose of this text is to provide a didactic exposition of the paper “Solutions of p-sublinear p-Laplacian equation via Morse theory” by Yuxia Guo and Jiaquan Liu [8]. This paper addresses the existence and multiplicity of solutions for the problem where is a smooth, bounded domain of RN, p is the p-Laplacian operator and f satisfies certain conditions, in particular f is p-sublinear at 0. Morse theory is used to infer the existence of critical points of a functional associated to this problem. In Chapter 2, we introduce the necessary Morse theoretic concepts, assuming basic knowledge of singular homology theory. In Chapter 3, we introduce basic properties of the p-Laplacian operator, assuming knowledge of Sobolev spaces, including imbedding and compactness results. Finally, in Chapter 4, we follow Guo and Liu’s paper itself.

Problemas com desenho de conexões protéticas sobre implantes, microfendas, afrouxamento e, consequentemente, perdas das estruturas protéticas reabilitadoras são tópicos frequentes do estudo odontológico. Conexões do tipo Cone Morse, devido às suas características, diminuíram o índice desses problemas, abrindo uma nova perspectiva para o sucesso da prótese sobre implante. Contudo, ainda é frequente encontrar componentes que falham no desempenho, levando à falência da restauração, especialmente quando esses componentes não são bem ajustados, bem fixados ou, ainda, não possuem, na sua geometria, características suficientes para suportar as forças laterais e oclusais de um ciclo mastigatório. O objetivo deste estudo é avaliar a influência do jateamento com óxido de alumínio sobre a superfície externa dos componentes protéticos, separadamente e em conjunto, com um adesivo industrial, em uma tentativa de aumentar os valores de torque de abertura de componentes apertados em seu torque recomendado, pelo fabricante ou menor. Neste ensaio, foram utilizados 36 implantes da marca Straumann®, de 10mm de comprimento com diâmetro de 4,8 mm, os quais foram divididos em 6 grupos: Grupo 1 = controle, torque de 35 N.cm; Grupo 2 = superfície jateada com óxido de alumínio (# 320) e torque de 35 N.cm; Grupo 3 = superfície jateada com óxido de alumínio (# 320) e torque de 25 N.cm; Grupo 4 = superfície jateada com óxido de alumínio (# 100) e torque de 25 N.cm; Grupo 5 = superfície jateada com óxido de alumínio (# 320), aplicação de adesivo e torque de 25 N.cm; Grupo 6 = superfície jateada com óxido de alumínio (# 100), aplicação de adesivo e torque de 25 N.cm, que receberam componentes protéticos sólidos de 5,5 mm de altura, regulares e alterados. As modificações incluídas foram o jateamento com partículas de óxido de alumínio (100 e 320 micra) e o uso de Loctite® 277 como adesivo industrial. Os conjuntos implante-componente foram levados até uma máquina de controle de tração, Instron®, e, após a sua calibração, as amostras dos grupos foram apertadas em 35 e 25 N.cm, com um conjunto catraca-torquímetro, com checagem visual e registro no software acoplado à máquina de ensaio. Após trinta dias, os grupos foram levados à máquina novamente e o conjunto abutment-implante foi desapertado, agora somente com registro no software da máquina de ensaio. Os valores e porcentagens da diferença entre torque de aperto e desaperto foram avaliados estatisticamente, e comparados entre os grupos. Para todas as associações, o valor de p deveria ser menor ou igual 0,05, para relevância. O grupo Jateado 35 N.cm, 320 micra, não apresentou valores mais altos do que o grupo Controle no momento do torque de desaperto, assim como os grupos Jateados 25 N.cm 100 e 320 micra. Os grupos Jateados 25 N.cm, 100 e 320 micra, com adesivo, mostraram uma resistência por volta de uma vez e meia maior, no torque de desaperto do que o grupo Controle 35 N.cm. / Problems with design of prosthetic implant connections, microleakage,! loosening which leads to loss of rehabilitative prosthetic structures are frequent topics of dental study. Morse taper connections, due to its characteristics, decreased the rate of these problems opening a new perspective to the success of the prosthesis supported over implant. However, it is still frequent to find components that fail in performance leading to failure of restoration especially when these components are not well adjusted, tightened or do not have in its geometry enough characteristics to support the occlusal and lateral forces in a masticatory cycle. The aim of this study is to evaluate the influence of blasting with aluminum oxide on the outer surface of the prosthetic components separately and in conjunction with an industrial adhesive in an attempt to increase the opening torque values of components tightened on their recommended torque by the manufacturer or less, therefore allowing the dentist an early intervention in the prosthetic rehabilitation. In this test, 36 Straumann® implants of 10mm high and 4,8mm wide were used. They were divided into six groups: Group 1 Solid abutments control group - 35 N.cm tightened; Group 2 - Solid sandblasted abutments, 35 N.cm aluminum oxide 320 microns size particles; Group 3 - Solid sandblasted abutments, 25 N.cm aluminum oxide 320 microns size particles; Group 4 - Solid sandblasted abutments, 25 N.cm aluminum oxide 100 microns size particles; Group 5 - Solid sandblasted abutments, 25 N.cm aluminum oxide 320 microns size particles with glue application; Group 6 - Solid sandblasted abutments, 25 N.cm aluminum oxide 100 microns size particles with glue application, which received 5,5 mm high regular and modified solid abutments. The included modifications were sandblasting with aluminum oxide particles (100 and 320 microns) and the use of Loctite® 277 as an industrial adhesive. The samples were taken to a traction control test machine, Instron ®, and after calibration the group samples were tightened on 35 and 25 N.cm with a ratchet-wrench set with visual check. The data was recorded in a software coupled to the test machine. After thirty days the groups were brought again to the test machine and the samples were untightened. At this point the resulting data was recorded only in the testing machine software. The values and percentages of the changes between the tightening and loosening torques were recorded and compared among the study groups. For all associations a p-value < 0.05 was considered significant. The group blasted 35 N.cm, 320 microns did not show higher values than the control group at the time of loosening torque as well as groups blasted 25 N.cm 100 and 320 microns. The groups blasted 25 N.cm, 100 and 320 microns with adhesive showed a resistance around one and a half times greater in the loosening torque than the control group 35 N.cm.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-04-05T15:21:09Z No. of bitstreams: 1 marianeambrosiocosta.pdf: 734174 bytes, checksum: 22ce1acc06b5bfd3d6d42c5ab4dfd730 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-04-24T03:49:10Z (GMT) No. of bitstreams: 1 marianeambrosiocosta.pdf: 734174 bytes, checksum: 22ce1acc06b5bfd3d6d42c5ab4dfd730 (MD5) / Made available in DSpace on 2016-04-24T03:49:10Z (GMT). No. of bitstreams: 1 marianeambrosiocosta.pdf: 734174 bytes, checksum: 22ce1acc06b5bfd3d6d42c5ab4dfd730 (MD5) Previous issue date: 2013-11-29 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A presente dissertação estabelece um diálogo entre as ideias do historiador norte-americano Richard Morse (1922-2001) e do sociólogo brasileiro Gilberto Freyre (1900-1987), analisando a influência recebida por Morse do pensador pernambucano em sua formação acadêmica, tanto nos Estados Unidos quanto no Brasil. Utiliza como fontes principais textos acadêmicos publicados por Morse enquanto estudante de pós-graduação e textos de Freyre publicados no Brasil e nos Estados Unidos. Para tal, o contexto das produções também é mostrado como forma de, localizar temporal e espacialmente suas interpretações. Considerando as propostas metodológicas da História Comparada – que consistem em examinar sistematicamente duas realidades (no caso deste trabalho, duas formas de pensar), assinalando não apenas as semelhanças, mas também, as diferenças de pensamento – o trabalho analisa de que forma o norte-americano se apropriou de ideias difundidas pelo brasileiro, e as apropriou em seus escritos de juventude utilizando-se de temáticas e métodos semelhantes. / This essay establishes a dialogue between the ideias of the north American historian Richard Morse (1922-2001) and the Brazilian sociologist Gilberto Freyre (1900 – 1987), analyzing the influence received by Morse from the Brazilian scholar in his academic studies, both in the United States and Brazil. Used as primary sources for scholarly text published Morse while graduate student, texts that Freyre published in Brazil and in the United States. For this , the context of production is also shown as a way to locate temporally and spatially their interpretations. Considering the methodological proposals of Comparative History - consisting of systematically examine two realities ( in the case of this work , two ways of thinking ) , indicating not only the similarities but also the differences of thought - the work examines how the north American appropriated ideas spread by the Brazilian , and appropriated in his early writings using thematic and similar methods .

Submitted by Renata Lopes (renatasil82@gmail.com) on 2015-12-08T11:13:05Z No. of bitstreams: 1 caiomarceluspaislevasseur.pdf: 4546598 bytes, checksum: be57e1ab62ac45ae2f9ffe3e165c9e75 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2015-12-09T13:38:24Z (GMT) No. of bitstreams: 1 caiomarceluspaislevasseur.pdf: 4546598 bytes, checksum: be57e1ab62ac45ae2f9ffe3e165c9e75 (MD5) / Made available in DSpace on 2015-12-09T13:38:24Z (GMT). No. of bitstreams: 1 caiomarceluspaislevasseur.pdf: 4546598 bytes, checksum: be57e1ab62ac45ae2f9ffe3e165c9e75 (MD5) Previous issue date: 2015-04-30 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Os sistemas de implantes osseointegráveis se apresentam em um ou mais componentes, e a correta inter-relação, passividade de assentamento e resistência biomecânica, definem a resistência / vulnerabilidade do mesmo frente aos fatores bacterianos e oclusais. Objetivo: Avaliar as deformações inerentes ao processamento laboratorial dos pilares calcináveis de corpo único para o sistema de implantes Cone Morse. Materiais e métodos: Utilizou-se 20 implantes Cone Morse da marca SIN, 10 componentes protéticos calcináveis e 10 não calcináveis. Após os processos laboratoriais, os conjuntos foram submetidos à Microscopia eletrônica de varredura (MEV) da interface pilar/implante, para análise qualitativa e quantitativa da desadaptação gerada. Os conjuntos foram levados a ciclos térmicos (1.000 ciclos) e de fadiga mecânica (500.000 ciclos) e novamente foi realizada a MEV. Os resultados foram comparados através de análise estatística de Mean-Whitmann. Resultados: O grupo de teste (G1) apresentou os maiores valores iniciais, com média de 34, 55 μm e 11,17 μm, para a subdivisões A (fundição) e B (aplicação de porcelana) respectivamente. A subdivisão B do grupo teste apresentou a maior alteração pós testes, com média de 19,28 μm de aumento da desadaptação protética. As subdivisões G1.A, G2.A, G2.B mostraram tendência à diminuição da desadaptação de -1,03 μm, - 1,64 μm, e -0,49 μm, respectivamente. Pilares Cone Morse não calcináveis apresentam-se com alta estabilidade e baixa taxa de desadaptações. Para o grupo teste pode-se afirmar que o processo de fundição nitidamente criou as maiores dilatações e desadaptações das estruturas. O processo de sinterização da porcelana em teste, criou uma redução da desadaptação medida, porém esta voltou a aumentar após os testes em laboratório. Para o grupo controle, houve a manutenção das taxas de desadaptações menores ao limite de 10 μm, e com tendência de redução após os testes. Conclusão: O pilar calcinável Cone Morse de corpo único mostrou-se como desfavorável quanto à biomecânica, e o processo de fundição gerou as maiores desadaptações. / The system of dental implants present in one or more components, and the correct interrelationship, settling and passive biomechanical strength, defining the strength / vulnerability of the same to the forward occlusal and bacterial factors.Objective: To evaluate the defects associated to laboratory processing of abutments of unique body to the system of Cone Morse implants. Methods: We used 20 Cone Morse implants SIN brand, prosthetic components 10 and 10 calcinable not calcinable. After the laboratory processes the sets were subjected to scanning electron microscopy (SEM) of the pillar / implant interface, for qualitative and quantitative analysis of the generated misfit. The samples were taken to alternated thermal cycles (1000 – 50 and 550) and mechanical fatigue (500,000 - 120 N/cm2) and again was carried out by SEM. The results were compared by statistical analysis Mean-Whitmann (P>0,05). Results: The test group (G1) showed the highest initial values, averaging 34.55 and 11.17 micrometres for subdivisions A (casting) and B (porcelain application) respectively. The B subdivision of the test group showed the greatest change after tests, averaging 19.28 mm of increasing prosthetic misfit. The G1.A subdivisions, G2.A, G2.B showed a tendency to decrease the mismatch of -1.03 micrometres - 1.64 micrometres and -0.49 micrometres respectively. Pillars Cone Morse calcinable not present with high stability and low rate misfits. For the test group it can be said that the casting process clearly created the largest expansion and mismatches of structures. The porcelain sintering process under test, created a reduction of the mismatch measure, however this increased again after the tests in the laboratory. For the control group, there was the maintenance of rates of minor mismatches to 10 micrometres limit, and with downward trend after the tests. Conclusion: Cone Morse castable pillars proved to be unfavorable on the biomechanics, and the casting process generated the biggest misfits.

Sistemas de Transportes Inteligentes representam um imenso impacto social e aos poucos tem modificado o paradigma de mobilidade atual. Desde a década de 80, veículos autônomos vêm sendo desenvolvidos e estudados pela comunidade científica e hoje atrai o interesse de grandes empresas automobilísticas. Esses sistemas têm como objetivo a redução do número de acidentes de trânsito, aumento da eficiência dos transportes e inclusão social, sendo que neste contexto surge o projeto CaRINA. Através do desenvolvimento de uma plataforma robótica móvel pretende-se realizar a navegação completamente autônoma em ambiente urbano. Contudo, os experimentos realizados com a plataforma real são custosos, demorados e perigosos. A logística dos testes é complexa, uma vez que necessitam de local apropriado e disponibilidade de recursos. Portanto, o objetivo deste trabalho é desenvolver uma arquitetura de simulação para veículos autônomos que seja capaz de realizar experimentos em laboratório e facilite a portabilidade dos programas desenvolvidos em simulação para o veículo real. A flexibilidade da arquitetura do simulador também permite realizar experimentos utilizando múltiplos veículos. / Intelligent Transportation Systems represent a huge social impact and has gradually modified the current mobility paradigm. Since the1980s, autonomous vehicles have been developed and investigated by the scientific community and today attracts the interest of major automotive companies. These systems aims to reduce the number of traffic accidents, increase the transports efficiency and social inclusion, in this context the CaRINA project started. Through the development of amobile robotic platformis intended to performa fully autonomous navigation in urban environments. However, the experiments with the platform are costly, time-consuming and dangerous. The logistics of the tests are complex, since that require the appropriate location and availability of resources. Therefore, the purpose of this work is to develop a simulation architecture for autonomous vehicles to be able to perform experiments in the laboratory and to facilitate the portability of programs developed in simulation to the real vehicle. The flexibility of the simulator architecture also allows to perform experiments using multiple vehicles.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

In recent decades, scientific data has become available in increasing sizes and precision. Therefore techniques to analyze and summarize the ever increasing datasets are of vital importance. A common form of scientific data, resulting from simulations as well as observational sciences, is in the form of scalar-valued function on domains of interest. The Morse-Smale complex is a topological data-structure used to analyze and summarize the gradient behavior of such scalar functions. This thesis deals with efficient parallel algorithms to compute the Morse-Smale complex as well as its application to datasets arising from cosmological sciences as well as structural biology. The first part of the thesis discusses the contributions towards efficient computation of the Morse-Smale complex of scalar functions de ned on two and three dimensional datasets. In two dimensions, parallel computation is made possible via a paralleizable discrete gradient computation algorithm. This algorithm is extended to work e ciently in three dimensions also. We also describe e cient algorithms that synergistically leverage modern GPUs and multi-core CPUs to traverse the gradient field needed for determining the structure and geometry of the Morse-Smale complex. We conclude this part with theoretical contributions pertaining to Morse-Smale complex simplification. The second part of the thesis explores two applications of the Morse-Smale complex. The first is an application of the 3-dimensional hierarchical Morse-Smale complex to interactively explore the filamentary structure of the cosmic web. The second is an application of the Morse-Smale complex for analysis of shapes of molecular surfaces. Here, we employ the Morse-Smale complex to determine alignments between the surfaces of molecules having similar surface architecture.