Submitted by Marcele Costal de Castro (costalcastro@gmail.com) on 2017-10-05T18:23:55Z No. of bitstreams: 1 ZELMO RODRIGUES LIMA D.pdf: 3728947 bytes, checksum: d4f0e5497c077a0005967eacce6eee3c (MD5) / Made available in DSpace on 2017-10-05T18:23:55Z (GMT). No. of bitstreams: 1 ZELMO RODRIGUES LIMA D.pdf: 3728947 bytes, checksum: d4f0e5497c077a0005967eacce6eee3c (MD5) Previous issue date: 2005-10 / A proposta deste trabalho é desenvolver um método modal com base na teoria dos pseudo-harmônicos para tratar problemas da cinética espacial. Os pseudo-harmônicos são as autofunções associadas ao operador da fuga + remoção em cada grupo de energia da equação de difusão multigrupo estacionária. O método modal desenvolvido aproxima o fluxo dependente do tempo em uma expansão em pseudo-harmônicos onde os coeficientes são dependentes do tempo. A dedução do sistema cujas soluções são os coeficientes da expansão modal é feita com auxílio de funções de peso. Para fins de comparação também é desenvolvido um método direto da cinética espacial. Este método trata a dependência espacial empregando o método de diferenças finitas de malha grossa (DFMG) acoplado com o método de expansão nodal (NEM). Na solução da parte dependente do tempo o método modal e o método direto utilizam a integração analítica da equação dos precursores e um esquema semi-implícito na equação de difusão. Os resultados obtidos mostraram que o método proposto tem uma boa acurácia.

Submitted by Marcele Costal de Castro (costalcastro@gmail.com) on 2017-11-06T15:19:18Z No. of bitstreams: 1 ZELMO RODRIGUES DE LIMA M.pdf: 1314418 bytes, checksum: 295c04b222fa836626b95e9f84cca5ae (MD5) / Made available in DSpace on 2017-11-06T15:19:18Z (GMT). No. of bitstreams: 1 ZELMO RODRIGUES DE LIMA M.pdf: 1314418 bytes, checksum: 295c04b222fa836626b95e9f84cca5ae (MD5) Previous issue date: 2000-10 / A equação da difusão de nêutrons, em geometria Cartesiana bidimensional para dois grupos de energia, com a presença de fonte fixa é resolvida aplicando-se um método de expansão em pseudo-harmônicos, com suporte na discretização nodal pelo método de expansão de fluxo (FEM) para grandezas médias. Para fins de comparação, o mesmo problema de fonte fixa foi resolvido através da discretização por diferenças finitas e, também para efeito de comparação, o cálculo do fluxo de nêutrons (problema de autovalor) foi feito tanto com o FEM quanto por diferenças finitas. O método de expansão em pseudo-harmônicos utilizado é parte da chamada versão alternativa do método perturbativo de pseudo-harmônicos e o problema de fonte fixa testado foi o de função auxiliar. Os resultados obtidos, para os casos testes realizados, mostram que o método desenvolvido para resolver problemas de fonte fixa é bastante preciso, quando comparado com diferenças finitas. / The two-group neutron diffusion equation, in two dimensional cartesian geometry, with fixed source is solved by using a pseudo-harmonics expansion method in connection to the flux expansion method of nodal discretization, based on average value. The same fixed source problem was solved by finite difference discretization and the results obtained were compared. The neutron flux associated with the eigenvalue problem was also solved by both methods (FEM and Finite Difference). The pseudo-harmonics expansion method employed is part of the alternative version of the pseudo-harmonics perturbation method and the fixed source problem tested was the “auxiliary function” problem. Results obtained for the test cases show that the method developed for solving fixed source problems is very accurate when compared to the finite difference method.

In this thesis we are interested in generalized estimating equations (GEE). First, we introduce the term of generalized linear model, on which generalized estimating equations are based. Next we present the methos of pseudo maximum likelyhood and quasi-pseudo maximum likelyhood, from which we move on to the methods of generalized estimating equations. Finally, we perform simulation studies, which demonstrates the theoretical results presented in the thesis. 1

Thesis advisor: Kathryn Lindsey / We use interval maps to construct pseudo-Anosovs and relate important invariants of each regime. This work builds on techniques of André de Carvalho, Toby Hall, Bill Thurston, and others. We introduce a new perspective on the pseudo-Anosovs created in this way, showing how they constitute the vertices of a tree whose edges encode relations between them. We also characterize the pseudo-Anosovs arising from interval maps, and use this result to reprove a universal lower bound on their stretch factors originally due to Boissy-Lanneau. / Thesis (PhD) — Boston College, 2023. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

This study attempts to list subjects in the field of Science, in which Poe had an interest. For the purpose of this study, the writer has divided the field of Science into the following heads: medicine, chemistry, biology, navigation, metrology, astronomy, physics, mathematics, and invention. Pseudo-sciences classified as: psychology, metphysics, phrenolgy, astrology, galvanism, mesmerism, logic reasoning, cryptography, and graphology.

This research study investigated how professional mathematicians understand and operate with highly-abstract, advanced mathematical concepts in their own work. In particular, this study examined how professional mathematicians operated with mathematical concepts at different levels of understanding. Moreover, this study aimed to capture what factors influence professional mathematicians' level of understanding for particular mathematical concepts. To frame these research goals, three theoretical levels of understanding were proposed, process-level, pseudo-object-level, object-level, leveraging two ways that Piaget (1964) described what it meant to know or understand a mathematical concept. Specifically, he described understanding an object as being able to "act on it," and also as being able to "understand the process of this transformation" (p. 176). Process-level understanding corresponds to only understanding the underlying processes of the concept. Pseudo-object-level understanding corresponds to only being able to act on the concept as a form of object. Object-level understanding corresponds to when an individual has both of these types of understanding. This study is most especially concerned with how professional mathematicians operate with a pseudo-object-level understanding, which is called pseudo-objectification. For this study, six professional mathematicians with research specializing in a subfield of algebra were each interviewed three times. During the first interview, the participants were given two mathematical tasks, utilizing concepts in category theory which were unfamiliar to the participants, to investigate how they operate with mathematical concepts. The second interview utilized specific journal publications from each participant to generate discussion about influences on their level of understanding for the concepts in that journal article. The third interview utilized stimulated recall to triangulate and support the findings from the first two interviews. The findings and analysis revealed that professional mathematicians do engage in pseudo-objectification with mathematical concepts. This demonstrates that pseudo-objectification can be productively leveraged by professional mathematicians. Moreover, depending on their level of understanding for a given concept, they may operate differently with the concept. For example, when participants utilized pseudo-objects, they tended to rely on figurative material, such as commutative diagrams, to operate on the concepts. Regarding influences on understanding, various factors were shown to influence professional mathematicians' level of understanding for the concepts they use in their own work. These included factors pertaining to the mathematical concept itself, as well as other sociocultural or personal factors. / Doctor of Philosophy / In this research study, I investigated how professional mathematicians utilize advanced mathematical concepts in their own work. Specifically, I examined how professional mathematicians utilize mathematical concepts that they do not fully understand. I also examined what factors might influence a professional mathematician to fully understand or choose not to fully understand a mathematical concept they are using. To address these goals, six research-active mathematicians were each interviewed three times. In these interviews, the mathematicians engaged with mathematical concepts that were unfamiliar to them, as well as concepts from one of their own personal research journal publications. The findings demonstrated that professional mathematicians sometimes utilize mathematical concepts in different ways depending on how well they understand the concepts. Moreover, even if mathematicians do not have a full understanding of the concepts they are using, they can still sometimes productively leverage this amount of understanding to successfully reach their goals. I also demonstrate that various factors can and do influence how well a professional mathematician understands a given mathematical concept. Such influences could include the purpose of use for the concept, or what a mathematician's research community values.

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In dieser Arbeit untersuchen wir die Interaktion von Holonomie und der globalen Geometrie von Lorentzmannigfaltigkeiten und pseudo-Riemannschen Untermannigfaltigkeiten in Räumen konstanter Krümmung. Insbesondere konstruieren wir schwach irreduzible, reduzible Lorentzmetriken auf den Totalräumen von gewissen Kreisbündeln, was zu einer Konstruktionsmethode von Lorentzmannigfaltigkeiten mit vorgegebener Holonomiedarstellung führt. Danach führen wir eine Bochnertechnik für die Lorentzmannigfaltigkeiten ein, die ein nirgends verschwindendes, paralleles, lichtartiges Vektorfeld zulassen, dessen orthogonale Distribution kompakte Blätter hat. Schließlich klassifizieren wir normale Holonomiedarstellungen von raumartigen Untermannigfaltigkeiten in Räumen konstanter Krümmung und verallgemeinern die Klassifikation eine größere Klasse von Untermannigfaltigkeiten. / In this thesis we study the interaction of holonomy and the global geometry of Lorentzian manifolds and pseudo-Riemannian submanifolds in spaces of constant curvature. In particular, we construct weakly irreducible, reducible Lorentzian metrics on the total spaces of certain circle bundles leading to a construction of Lorentzian manifolds with specified holonomy representations. Then we introduce a Bochner technique for Lorentzian manifolds admitting a nowhere vanishing parallel lightlike vector field whose orthogonal distribution has compact leaves. Finally, we classify normal holonomy representations of spacelike submanifolds in spaces of constant curvature and extend the classification to more general submanifolds.

Dans le domaine de l’oncogénomique, l’un des axes actuels de recherche est l’identification de nouveaux marqueurs génétiques permettant entre autres de construire des règles prédictives visant à classer les patients selon le risque d’apparition d’un événement d’intérêt (décès ou récidive tumorale). En présence de telles données de haute dimension, une première étape de sélection parmi l’ensemble des variables candidates est généralement employée afin d’identifier les marqueurs ayant un intérêt explicatif jugé suffisant. Une question récurrente pour les biologistes est le choix de la règle de sélection. Dans le cadre de l’analyse de survie, les approches classiques consistent à ranger les marqueurs génétiques à partir du risque relatif ou de quantités issues de test statistiques (p-value, q-value). Cependant, ces méthodes ne sont pas adaptées à la combinaison de résultats provenant d’études hétérogènes dont les tailles d’échantillons sont très différentes.Utiliser un indice tenant compte à la fois de l’importance de l’effet pronostique et ne dépendant que faiblement de la taille de l’échantillon permet de répondre à cette problématique. Dans ce travail, nous proposons un nouvel indice de capacité de prédiction afin de sélectionner des marqueurs génomiques ayant un impact pronostique sur le délai de survenue d’un évènement.Cet indice étend la notion de pseudo-R2 dans le cadre de l’analyse de survie. Il présente également une interprétation originale et intuitive en terme de « séparabilité ». L’indice est tout d’abord construit dans le cadre du modèle de Cox, puis il est étendu à d’autres modèles plus complexes à risques non-proportionnels. Des simulations montrent que l’indice est peu affectée par la taille de l’échantillon et la censure. Il présente de plus une meilleure séparabilité que les indices classiques de la littérature. L’intérêt de l’indice est illustré sur deux exemples. Le premier consiste à identifier des marqueurs génomiques communs à différents types de cancers. Le deuxième, dans le cadre d’une étude sur le cancer broncho-pulmonaire, montre l’intérêt de l’indice pour sélectionner des facteurs génomiques entraînant un croisement des fonctions de risques instantanés pouvant être expliqué par un effet « modulateur » entre les marqueurs. En conclusion, l’indice proposé est un outil prometteur pouvant aider les chercheurs à identifier des listes de gènes méritant des études plus approfondies. / In oncogenomics research, one of the main objectives is to identify new genomic markers so as to construct predictive rules in order to classify patients according to time-to-event outcomes (death or tumor relapse). Most of the studies dealing with such high throughput data usually rely on a selection process in order to identify, among the candidates, the markers having a prognostic impact. A common problem among biologists is the choice of the selection rule. In survival analysis, classical procedures consist in ranking genetic markers according to either the estimated hazards ratio or quantities derived from a test statistic (p-value, q-value). However, these methods are not suitable for gene selection across multiple genomic datasets with different sample sizes.Using an index taking into account the magnitude of the prognostic impact of factors without being highly dependent on the sample size allows to address this issue. In this work, we propose a novel index of predictive ability for selecting genomic markers having a potential impact on timeto-event outcomes. This index extends the notion of "pseudo-R2" in the ramework of survival analysis. It possesses an original and straightforward interpretation in terms of "separability". The index is first derived in the framework of the Cox model and then extended to more complex non-proportional hazards models. Simulations show that our index is not substantially affected by the sample size of the study and the censoring. They also show that its separability performance is higher than indices from the literature. The interest of the index is illustrated in two examples. The first one aims at identifying genomic markers with common effects across different cancertypes. The second shows, in the framework of a lung cancer study, the interest of the index for selecting genomic factor with crossing hazards functions, which could be explained by some "modulating" effects between markers. The proposed index is a promising tool, which can help researchers to select a list of features of interest for further biological investigations.