Given a closed surface Sg of genus g, a mapping class f in \MCG(Sg) is said to be pseudo-Anosov if it preserves a pair of transverse measured foliations such that one is expanding and the other one is contracting by a number \lambda(f). The number \lambda(f) is called a stretch factor (or dilatation) of f. Thurston showed that a stretch factor is an algebraic integer with degree bounded above by 6g-6. However, little is known about which degrees occur. Using train tracks on surfaces, we explicitly construct pseudo-Anosov maps on Sg with orientable foliations whose stretch factor \lambda has algebraic degree 2g. Moreover, the stretch factor \lambda is a special algebraic number, called Salem number. Using this result, we show that there is a pseudo-Anosov map whose stretch factor has algebraic degree d, for each positive even integer d such that d≤g. Our examples also give a new approach to a conjecture of Penner.

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

Ziel der vorliegenden Studie war es, die Veränderungen der komplexen dreidimensionalen Infarktanatomie im Verlauf der Infarktheilung zu untersuchen. Material und Methoden: Mit Hilfe kernspintomographischer Late Enhancement (LE) Untersuchungen ist es möglich, den Myokardinfarkt im Verlauf der gesamten Infarktheilung abzubilden und exakt zu vermessen. Insgesamt wurden 74 LE Untersuchungen bei 30 Patienten nach erstmals aufgetretenem Myokardinfarkt durchgeführt. Alle Patienten waren einer Reperfusionstherapie unterzogen worden. Die Untersuchungszeitpunkte waren Tag 5±2 nach Myokardinfarkt (Mittelwert ± Standardabweichung, Zeitpunkt A), Tag 12±3 nach Myokardinfarkt (Zeitpunkt B), und nach 3 Monaten (Zeitpunkt C). 14 Patienten wurden zu allen drei Zeitpunkten untersucht, bei 10 Patienten wurden Messungen zu den Zeitpunkten A und C durchgeführt und bei 6 Patienten Messungen zu den Zeitpunkten B und C. In den LE Untersuchungen wurde der linke Ventrikel jeweils mit Hilfe von doppelt angulierten Kurzachsenschnitten (Schichtdicke 8 mm, ohne Zwischenschichtabstand) vollständig abgebildet. Die Bildauswertung erfolgte geblindet. In jedem Kurzachsenschnitt eines Infarkts wurden folgende Parameter gemessen: Die Infarktquerschnittsfläche (MI, in mm2), die größte zirkumferentielle Ausdehnung des Myokardinfarkts (Z, in mm) und die Infarktdicke (D, in mm). Aus diesen Parametern und der gegebenen Schichtdicke von 8 mm konnten das Infarktvolumen (IV, in mm3), die Infarktausdehnung (IA, in mm2), die mittlere Infarktdicke (MID, in mm) und die mittlere zirkumferentielle Ausdehnung des Infarkts (MIZ, in mm) berechnet werden. Die Infarktausdehnung ist hierbei eine Fläche und beschreibt den Infarkt in seiner longitudinalen und zirkumferentiellen Ausdehnung. Eine Zunahme der Infarktausdehnung ist gleichbedeutend mit einer Dilatation bzw. Expansion des Infarkts. Alle Parameter können unabhängig vom vitalen Restmyokard bestimmt werden. In einer zusätzlichen zweidimensionalen Analyse wurden außerdem die Veränderungen der Infarktanatomie am Ort der maximalen Infarktdicke zum Zeitpunkt der ersten Messung und die Veränderungen der Infarktanatomie am Ort der maximalen zirkumferentiellen Ausdehnung zum Zeitpunkt der ersten Messung untersucht. Die Ergebnisse werden als Mittelwerte mit dazugehörigen Standardfehlern berichtet. Zur Verlaufsbeurteilung wurden die Parameter der Zeitpunkte B und C als Prozentsatz der vorangegangenen Messungen berechnet. Ergebnis: Innerhalb der ersten drei Monate nach Infarkt wurde eine Verringerung des Infarktvolumens im Mittel auf 69±5% des Ausgangswertes beobachtet. Die Volumenabnahme war hierbei zu einem größeren Anteil auf die Abnahme der Infarktdicke und zu einem kleineren Anteil auf die Abnahme der Infarktausdehnung zurückzuführen. Die mittlere Infarktdicke nahm innerhalb von 3 Monaten im Mittel auf 79±3% und die Infarktausdehnung im Mittel auf 88±4% ab. Diese Veränderungen waren signifikant (p<0,05). Die Infarktausdehnung veränderte sich jedoch innerhalb des untersuchten Kollektivs unterschiedlich. Bei 75% der untersuchten Infarkte wurde die Infarktausdehnung im Verlauf der Untersuchung geringer, bei 25% nahm die Infarktausdehnung jedoch zu. Eine Abnahme der Infarktdicke wurde in 92% der Fälle beobachtet. Sie kam unabhängig von der Dilatation eines Infarkts vor. Die Infarktdicke verringerte sich zwischen dem Zeitpunkt A und C bei 5 von 6 Patienten mit einer Zunahme der Infarktausdehnung, aber auch bei 17 von 18 Patienten ohne Infarktdilatation. In der zweidimensionalen Analyse zeigte sich, dass die Veränderungen der Infarktdicke und der zirkumferentiellen Ausdehnung innerhalb eines Infarkts regional unterschiedlich stark ausgeprägt waren. / Objective: To analyze the changes of infarct size and infarct anatomy during the course of infarct healing. Materials and Methods: MRI Late Enhancement (LE) studies can be used to visualize myocardial infarctions during the course of infarct healing. It is also possible to use these studies to accurately measure the size and shape of myocardial infarctions. For this study a total of 74 LE studies were performed in 30 patients following their first myocardial infarction. All patients were treated with a reperfusion therapy. The studies were performed on day 5±2 (mean ± standard deviation) post myocardial infarction (point A), day 12 ± 3 post myocardial infarction (point B) and after 3 months (point C). Of the 30 patients in this study 14 patients were measured at all three points, 10 patients were measured at point A and C and 6 patients were measured at point B and C. The left ventricle was imaged completely from base to apex using consecutive double oblique imaging planes (slice thickness 8mm, no slice spacing) during the LE studies. Image analysis was performed in a blinded fashion. In every short axis view the cross section surface (MI, in mm2), the circumferential extent (Z, in mm) and the infarct thickness (D, in mm) were measured. Using these parameters and the given slice thickness of 8mm, the infarct volume (IV, in mm3), the infarct extent (IA, in mm2), the mean infarct thickness (MID, in mm) and the mean circumferential extent (MIZ, in mm) were calculated. The infarct extent was defined as an area which described the myocardial infarction in both the longitudinal and circumferential extent. An increase of the infarct extent was equivalent to a dilatation or expansion of the myocardial infarct. All parameters were able to be determined independently from the vital rest of the myocardium. In an additional two-dimensional analysis, the changes of the infarct anatomy were studied using two different slices. One slice where the maximum infarct thickness was localized and the other, where the maximum circumferential extent was localized. Results were reported as means with corresponding standard errors. All parameters of Point B and C were calculated as a percentage of prior measurements. Results: Within the first three months post myocardial infarction, a decrease of infarct volume to 69±5% of the initial volume was found. The shrinkage of volume was mainly due to a decrease of the infarct thickness and to a lesser extent, to a decrease of the infarct extent. The mean infarct thickness decreased within three months to 79±3% and the infarct extent to 88±4%. These changes were statistically significant (p< 0.05). However, the changes of infarct extent in the study group were inconsistent. In 75% of the evaluated patients infarct extent decreased between point A and C but in 25% of the patients, the infarct extent increased in the same period of time. Infarct thinning was observed in 92% of all cases and occurred independently from infarct dilatation. The mean infarct thickness decreased between point A and C in 5 out of 6 patients with an increase of infarct extent. However, the infarcts thinned in 17 out of 18 patients without infarct dilatation as well. The two-dimensional analysis showed that the changes of infarct thickness and circumferential extent were regionally different within one myocardial infarction.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, 2016. / The AdS/CFT correspondence is a conjectured exact duality between type IIB string theory on the AdS5 S5 background and N = 4 Super Yang-Mills theory, a conformal eld theory (CFT), on the boundary of the AdS space. A speci c observable of the CFT, which can be read from the two point correlation function, is the anomalous dimension. In this dissertation we will compute spectra of anomalous dimensions of excited giant gravitons up to two loops in a speci c limit. We are interested in the anomalous dimensions because the AdS/CFT correspondence associates them with energies of states in quantum gravity. We study operators constructed using n Z elds and m Y elds with n << m: In this case m n is a small parameter. At the leading order in m n and at large N, the problem of determining the anomalous dimensions can be mapped into the dynamics of m non-interacting magnons. The subleading terms at two loops, computed for the rst time in this dissertation, induce interactions between the magnons. Even after including this new correction, we nd the BPS operators remain BPS. / MT2016

Orientador: Manoel Ferreira Borges Neto / Banca: Masayoshi Tsuchida / Banca: Siovani Felipussi / Resumo: Neste trabalho estudamos transformações quaseconformes no contexto dos octônios, que são hipercomplexos de oito dimensões. Por não preservar a magnitude dos ângulos, mapeamentos quaseconformes causam uma dilatação linear. A partir da definição métrica de quaseconformidade, utilizamos a forma binomial para mostrar que a distância jf(y) ¡ f(x)j pode ser escrita como um polinômio em r. Com isso, pudemos desenvolver não são um conjunto de fórmulas como também um método computacional simplificado para o cálculo analítico da dilatação. Posteriormente, utilizamos ferramentas gráficas para vizualizar as consequências da dilatação. / Abstract: In this work we study quasiconformal mappings related to octonionic algebra. Since quasicon- formal mappings do not preserve the magnitude of the angles they cause a linear dilatation. We show that it also happens to 8-dimensional hipercomplex. Based on the metric de¯nition of quasiconformal mapping we show that the distance jf(y)¡f(x)j is a polynomial of variable r. Then it¶s possible to make not only a set of formulas but also a computacional method to calculate the dilatation. We also use some graphical tools to visualize the consequences of dilatation. / Mestre

A Morfologia Matemática (MM) é um arcabouço geral para o estudo de mapeamentos entre imagens binárias. Estes estudos são de especial interesse na área de Processamento de Imagens. Tais mapeamentos entre imagens binárias são conhecidos como operadores de conjunto. Um aspecto importante da MM é a representação destes operadores em termos de dilatações, erosões e outras operações usuais de conjunto (interseção, união, complemento e diferença). Por este motivo, a dilatação e a erosão são ditos operadores morfológicos elementares. Este trabalho visa propor novos métodos para calcular a erosão e a dilatação morfológica binária rapidamente. Tais métodos se fundamentam em conceitos e técnicas de pré-processamento (em tempo linear) introduzidas por este trabalho, como a Transformada da Densidade, ou ainda, um Conjunto de Cascas. O resultado destes pré-processamentos é traduzido em ganho de velocidade dos algoritmos de erosão e dilatação, além de apresentar uma representação compacta dos conjuntos operandos. O consumo de tempo dos métodos propostos é no pior caso quadrático, porém, num estudo experimental preliminar, o algoritmo se comporta eficientemente, chegando a ser até mesmo linear em alguns casos. Além disso, um levantamento sucinto de outros métodos de erosão e dilatação morfológica binária conhecidos pela literatura atual é apresentado. Algumas simulações e uma breve análise de complexidade mostram que os métodos propostos são boas alternativas para implementação de erosão e dilatação morfológica eficiente. / A Mathematical Morphology (MM) is a general framework for the study of mappings between binary images. These studies are of particular interest in the area of Image Processing. Such mappings between binary images are known as set operators. An important aspect of MM is the representation of these operators in terms of dilations, erosions and other usual set operations (intersection, union, complement and difference). For that reason, the dilation and erosion are called elementary morphological operators. This work aims to propose new methods to calculate the morphological binary erosion and dilation quickly. Such methods are based on concepts and techniques of preprocessing (in linear time) introduced by this work, as the density transformed, or even a set of shells. The result of these preprocessing translates into speedup of erosion and dilation algorithms, and present a compact representation of the operands sets. The time complexity of the proposed methods is quadratic in the worst case, however, a preliminary experimental study, the algorithm behaves efficiently, becoming even linear in some cases. Furthermore, a brief survey of other methods of morphological erosion and binary dilation known by current literature is presented. Some simulations and a brief complexity analysis shows that our methods are a good alternative for implementation of erosion and dilation morphological efficient.

"2+" in the title is superscript. / "December 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 179-204) / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Common risk factors for CVD such as hyperlipidaemia, hypertriglyceridemia, low HDL-C, obesity, insulin resistance, impaired glucose tolerance, inflammation and hypertension may increase the risk of atherosclerosis through altering vascular function. Modification of dietary intake and weight loss can ameliorate these risk factors and may impede the development of atherosclerosis. CVD risk can be assessed by measurement of both traditional e.g. lipid levels, glucose and blood pressure and novel risk markers of CVD e.g. FMD, levels of adhesion molecules, inflammatory markers and adipokines. Changes in these measurements are used to determine effects, if any, of dietary interventions. The studies in this thesis focus on the relationship between nutrition and vascular function and the effects of modifying dietary composition either with, or without weight loss. The primary hypotheses addressed were that a high saturated fat diet would have adverse effects on markers of CVD risk., that short and long term weight loss would have beneficial effects on these markers, that a conventional low fat, high glycaemic load diet would also have adverse effects on these markers and that weight loss would attenuate the BP response to salt. Six studies were conducted to address these hypotheses. The effects of saturated fat were investigated in chapters 3 and 6. In chapter 3, a high saturated fat diet impaired FMD and increased the level of the adhesion molecule Pselectin compared with a high MUFA, a high PUFA, or a low fat, high glycaemic load diet in weight stability. The high fat, high glycaemic load caused increases of 23-39% in TG and decreases of 10-15% in HDL-C but despite these adverse effects there was no change in FMD. In chapter 6, subjects on a very low carbohydrate/high saturated fat diet lost approximately 1 kg more weight over 8 weeks than those on a conventional low fat diet. While other CVD risk factors, glucose, insulin, E and P-selectin, ICAM-1 and PAI-1 levels all improved FMD did not change in either diet. Reductions in LDL-C and CRP were greater on the conventional diet. The effects of weight loss on CVD risk factors were also investigated in the studies in chapters 4, 5, 7 & 8. In chapter 4, moderate weight loss using 2 different low fat diets resulted in improvements in PAI-1 and sICAM-1 but there was no change in FMD. Similarly in chapter 5 weight loss on a low carbohydrate/low saturated fat diet did not change FMD but there were other benefits including reductions in glucose and insulin, LDL-C, adhesion molecules, VCAM1 and ICAM1. Adiponectin did not change after short term weight loss in either of the studies in chapters 5 or 6. In chapter 7 salt loading increased ambulatory day time BP and this response was not altered by short term moderate weight loss. The long term effects of weight loss were investigated in chapters 5, 7 and 8. In chapter 5, after 52 weeks, there was sustained weight loss of 5% but no change in FMD while adiponectin levels increased and LDL-C and insulin were substantially reduced. In chapter 7 the BP response to salt loading remained unchanged despite weight loss maintenance. Finally in chapter 8 weight loss was predicted by protein intake and there were reductions in CVD risk demonstrated by decreases in insulin, TG and CRP and increases in HDL-C. The studies in this thesis demonstrate that moderate weight loss has beneficial effects on traditional and novel cardiovascular disease risk markers but does not have a beneficial effect on FMD regardless of dietary composition. A high saturated fat diet has detrimental effects on novel CVD risk markers in weight stability but weight loss attenuates this effect. A high saturated fat diet may have detrimental effects on adhesion molecules in weight stability and may attenuate the beneficial effects of weight loss on LDL-C and CRP. Moderate long term weight loss maintenance has beneficial effects on most but not all CVD risk markers. / http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1293779 / Thesis (Ph.D.) -- School of Medicine, 2007

La modélisation des formes naturelles reste un enjeu majeur pour le réalisme en synthèse d'images. Ces formes sont souvent complexes et leur modélisation avec les outils classiques nécessitent généralement une masse de travail considérable pour le graphiste. Les phénomènes de croissance sont très courants dans la nature. Ils engendrent souvent des formes complexes, même quand le mécanisme mis en jeu reste simple. Recréer de telles formes par des simulations physiques n'est pas toujours très pratique, du fait du manque de contrôle sur le résultat. Nous proposons dans cette thèse un nouveau genre de modeleur, basé sur la croissance d'une surface, qui permet de recréer des formes de croissance. Le modeleur présente des contrôles supplémentaires par rapport à un simulateur physique, et il n'est pas uniquement limité à la simulation de phénomènes naturels : il permet de rajouter interactivement des détails à une surface, tel que des plis des cloques, et même des branches.

Dans l'étude du comportement du béton au jeune âge dans les structures massives, les retraits endogène et thermique apparaissent comme des phénomènes majeurs, qui sont responsables du fluage lorsque le retrait est empêché. La réaction chimique du ciment avec l'eau est exothermique et thermo-activée, ce qui induit des déformations de dilatation puis de contraction. La chaleur d'hydratation peut créer des déformations différentielles entre la peau et le cœur d'une structure, ceci peut causer des fissurations traversantes au jeune âge. Dans ce contexte, cette thèse est dédiée à l'étude du comportement visco-élastique du béton au jeune âge dans les structures massives. L'idée est de développer un modèle numérique qui décrive le comportement visco-élastique du béton au jeune âge, et qui permette de prédire les contraintes au jeune âge et le risque de fissuration.. Une méthode d'identification des paramètres du modèle est proposée à partir d'essais simples développés au laboratoire et sur chantier. Une validation sera réalisée par confrontation à des essais réalisés. Enfin le modèle développé est appliqué à des simulations sur des structures réelles, qui sont confrontées aux mesures de température et de déformations réalisées sur site.