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Accurate segmentation of brain tissue in magnetic resonance images (MRI) is a difficult task due to different types of brain abnormalities. In this paper, we review the deformation method focus on the construction of diffeomorphisms to generate the 2D MRI image grids and extend it to the 3D MRI images, address clearly a new formation of the deformation problem for moving domains and construction of diffeomorphisms through a completely different approach. The idea is to control directly the first order differential operators including the Jacobian determinant (JD), divergence (DIV), and curl vector (CV) generated by the 2D and 3D MRI image grids and use them as CNN channels with other modalities (T1-weighted, T1-IR, and T2-FLAIR) or single T1-weighted modality to improve the performance of brain segmentation. More importantly, we discuss the influence of three optimization parameters to the generation of the 2D and 3D MRI image grids by both theoretical analysis and the numerical experiments. We test this method on the IBSR dataset and MRBrainS18 dataset based on VoxResNet and verify the influence of three parameters on the accuracy of MRI brain segmentation. Finally, we also compare the segmentation performance of our method in three networks, including 2D U-Net, 3D U-Net, and VoxResNet. We believe the proposed method can advance the performance in brain segmentation and clinical diagnosis.

This dissertation constitutes a study on Classical Field Theory, with a specific approach for scalar fields. Initially, the equations of motion, the energy, and the stability conditions of the solutions are presented. These solutions which present topological features are, called kinks, besides the non-topological ones are, named lumps. Moreover, important models are going to be discussed, for instance, models f4, f6, sine-Gordon and double sine-Gordon. The phenomenon of spontaneous symmetry breaking, the Bogomol’nyi method, and the construction of Field Theory based on potentials of quantum mechanics also are going to be addressed. Subsequently, the deformation method is presented, which allows us to build analytic Field Theory models. Finally, we proceed with the application of the method, to obtain new families of sine-Gordon models, and polynomial potentials, that allow are to explore long-range interactions between kinks. Fundação de Apoio à Pesquisa do Estado da Paraíba - FAPESQ Esta dissertação constitui um estudo sobre Teoria Clássica de Campos, com uma abordagem específica para campos escalares. Inicialmente são apresentados as equações de movimentos, energias e condições de estabilidade das soluções, que podem ter características topológicas, denominadas por kinks ou não topológicas, nomeadas por lumps. Em seguida, serão discutidos importantes modelos como, por exemplo, os modelos f4, f6, seno-Gordon e seno-Gordon duplo. Será também estudado o fenômeno de quebra espontânea de simetria, o método de Bogomol’nyi e a construção de Teoria de Campos a partir de potenciais da mecânica quântica. Posteriormente é apresentado o método da deformação, que permite construir novos modelos de Teoria de Campos solúveis. Prosseguimos com a aplicação do método, para obter novas famílias de modelos seno-Gordon e de potenciais polinomiais, que permitem explorar interações de longo alcance entre kinks.

Дослідження стосуються бетонних порожнистих блоків стін підвалів, які широко використовували і використовують в практиці будівництва. Показано, що навіть для середньоповерхових і багатоповерхових будівель міцність бетонних блоків використовуються лише на 10–30 %. Тому масивні фундаментні блоки доцільно виготовляти порожнистими. За конструкцією оптимізовані блоки можна об’єднати в такі групи: з крупними порожнинами, відкритими знизу, з вертикальними закритими і наскрізними порожнинами, горизонтальними порожнинами і ребристі. Розроблені конструкції ефективних блоків стін підвалів потенційно дають можливість значно облегшити їх і зекономити бетон. Проте майже всі запропоновані рішення не знайшли широкого використання на практиці – в основному внаслідок технологічних проблем. Необхідно продовжити пошук ефективних конструктивно- технологічних рішень блоків стін підвалів, та їх дослідження. У статті відображено результати експериментально-теоретичних досліджень фундаментних блоків двох типів: з двома відкритими зверху порожнинами марки ФБП-1 та з 4-ма закритими порожнинами марки ФБП-2. В блоці ФБП-2 порожнини улаштовані з використанням арболітових вставок. Така конструкція блоків є доцільною для зовнішніх стін підвалів, оскільки покращує теплотехнічні характеристики стіни. Випробовували блоки у складі 3-х ярусної стінки загальною висотою 1,8 м на позацентрово прикладене навантаження. Натурні випробування блоків дозволили отримати їхні фактичні значення міцності і тріщиностійкості. Розрахункова несуча здатність і тріщиностійкість блоків визначали за деформаційною методикою згідно з чинними нормативними документами з врахуванням і ідеалізованої діаграми деформування бетону за розтягу. Розрахунок за розробленою методикою натурних порожнистих блоків показав задовільну збіжність з експериментальними даними за показниками несучої здатності і тріщиностійкості The research is about concrete hollow blocks that have been and still are used widely in basement wall construction. It shows that only 10–30 % of their strength is used even for mid and high-rise construction. Therefore massive foundation blocks should be made with hollows. By design, optimized blocks can be combined into the following groups: with large cavities, open from below, with vertical closed and through cavities, horizontal cavities and ribbed. The developed designs of effective blocks of walls of basements potentially give the chance to facilitate them considerably and to save concrete. However, almost of the proposed solutions have not been widely used in practice - mainly due to technological problems. It is necessary to continue the search for effective structural and technological solutions of basement wall blocks and their research. The article shows the result of experimental and theoretic research of two types of concrete blocks: FBH-1 with two top opened hollows and FBH-2 with 4 enclosed hollows. FBH-2 block has hollows with arbolite insertions. His type is efficient for basement external wall due superior thermal performance. The blocks were texted as a part of 3-storey masonry of 1.8 m height applying off-centric loads to it. Those texts allowed to get its actual strength capacity as well as cracking resistance. The load bearing capacity and cracking resistance have been calculated using a deformation method according to current codes. The method takes into account an idealized diagram of concrete stretching.The calculations according to developed method showed satisfactory matching with experimental data of load bearing capacity and cracking resistance.

In this paper, original extension of classic deformation method for global elastic analysis of steel construction with semi-rigid connections is developed. The original calculation for steel frame structures with semi-rigid connections as a function of rotational rigidity of connection, a realistic parameter for determination of both tension and deformation fields of connection as well as entire construction, has been derived in detail. Due to its generality, simplicity and straight-forward calculation, the method developed in this paper is convenient for both computational utilization and hand calculations. For introduced rotational rigidity of realistic connections, the expressions for determination of bending moments at ends of semi-rigidly connected elements have been derived as well as conditional equations for determination of deformation-unspecified values at static load by first-order theory. The obtained results are illustrated in detail on a numerical example. Their comparison with the results of FEM analysis was provided.

Resumo O método de deformação tem gerado inúmeros resultados satisfatórios dentro da teoria de campos, uma vez que o mesmo fornece uma maneira simples e até mesmo didática de descrever a estrutura de defeitos topológicos em diversos cenários. Ele consiste em gerar novos modelos a partir do potencial e da solução de um modelo conhecido, com o auxílio de uma função deformadora apropriada, gerando soluções analíticas sem precisar recorrer a métodos computacionais ou análise numérica. Neste trabalho demonstramos as diversas aplicações do método de deformação na teoria de campos escalares reais, estendendo-se desde a obtenção de potenciais polinomiais passando por modelos de dinâmica periódica até, resolução de equações diferencias não-lineares e o estudo de modelos de inflação cósmica no regime slow-roll. Abstract The deformation method has generated many satisfactory results within the field theory, since it provides a simple and even didactic way of describing the structure of topological defects in several scenarios. It consists of generating new models from the potential and solution of a known model, with the aid of an appropriate deformation function, generating analytical solutions without having to resort to computational methods or numerical analysis. In this work, we demonstrate the different applications of the deformation method in real scalar field theory, ranging from the obtaining of potential polynomials through periodic dynamics models until, solving nonlinear differential equations and the study of cosmic inflation models in the slow-roll regime.

Submitted by Severina Oliveira (severina.sueli@ufcg.edu.br) on 2019-02-15T12:15:31Z No. of bitstreams: 1 MAXWELL MENSAH-OPOKU-DISSERTAÇÃO-PPGF 2017.pdf: 18011675 bytes, checksum: 9201dab61fdd4360350876474dfeeec6 (MD5) Made available in DSpace on 2019-02-15T12:15:31Z (GMT). No. of bitstreams: 1 MAXWELL MENSAH-OPOKU-DISSERTAÇÃO-PPGF 2017.pdf: 18011675 bytes, checksum: 9201dab61fdd4360350876474dfeeec6 (MD5) Previous issue date: 2017-09-01 Capes Este trabalho aplica um novo procedimento para determinar modelos analíticos de mundos-brana híbridos. É construído através de modelos de três campos acoplados à gravidade em um espaço-espaço (4 + 1) dimensional que geralmente são de difícil tratamento analítico. Aplicamos o método de extensão para construir modelos de três campos em cenários de braneworld. A ideia fundamental do método é combinar três sistemas de campo de uma maneira não trivial, para construir um modelo composto por três campos escalares efetivos. O princípio subjacente ao sucesso do método nesta dissertação reside no método de deformação. This work applies a new procedure to determine analytical hybrid braneworld models. It is constructed via three-field models coupled with gravity in a (4+1) dimensional space-time which in general is difficult to compute analytically. We apply the extension method to construct three-field models in braneworld scenarios. The fundamental idea of the method is to combine three-one field systems in a non-trivial way, to construct an effective three scalar field models. The underlying principle to the success of the method in this dissertation lies in the deformation method.

A mathematical problem arising from data set alignment is studied. For two given real-valued functions defined on two (2D or 3D) domains, separately, find a transformation between the two domains that optimizes a similarity functional between the functions. Our approach is based on optimal control with PDE (partial differential equation) constraints. Numerical examples are provided to demonstrate the effectiveness of the method.

Is studied in this work two classes of solutions of scalar field theories. The first chapter deals with one-dimensional static fields models that give rise to topological defects, having its stability assured by arguments topological. This type of solution has a simple mathematical approach, however have greatly interest physical. The second chapter discusses a field theory with stationary solutions which is associated the a Noether s charge, coming from an internal symmetry of the field. It is called Q-balls the objects described in the second chapter. The main objective will be to use the method of deformation to find new solutions type Q-ball. Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES Estuda-se neste trabalho duas classes de soluções de teorias de campos escalares. O primeiro capítulo aborda modelos de campos estáticos unidimensionais que dão origem a defeitos topológicos, tendo sua estabilidade assegurada por argumentos topológicos. Esse tipo de solução tem uma abordagem simples matematicamente, no entanto apresenta muito interesse físico. O segundo capítulo aborda uma teoria de campo com soluções estacionárias a qual está associada uma carga de Noether, provinda de uma simetria interna do campo. Chama-se de Q-balls os objetos descritos no segundo capítulo. O objetivo principal será utilizar o método de deformação para encontrar novas soluções tipo Q-ball.

Not available, La modélisation de surfaces complexes existantes passe par une décomposition de la surface physique en régions rectangulaires. Chaque région est approchée par un carreau mathématique (bezier, b-spline, nurbs), de telle sorte que la jonction entre carreau est d'ordre 0 (bores des carreaux communs). Cette thèse propose une méthode de raccordement à l'ordre 1 de carreaux composant une surface. La méthode est étudiée pour deux carreaux ayant un bord commun puis n carreaux ayant un sommet commun (appelé coin d'ordre n). Des conditions sur les carreaux de départ peuvent apparaitre lorsque la conservation des tangentes extérieurs est demandée ou lorsqu'un des carreaux doit rester inchangé. La déformation des carreaux selon leur normale est repartie sur tous les carreaux. Le raccordement donne l'amplitude de déformation pour chaque carreau. Ceux-ci sont définis par le carreau initial et cette fonction de déformation. La mise en œuvre de la méthode proposée donne de bons résultats tant que les carreaux initiaux n'ont pas de forte différence de plan tangent le long du bord commun