Typescript (photocopy). / Digitized by Kansas Correctional Industries

University of Macau / Faculty of Science and Technology. / Department of Computer and Information Science

Choi, Yuet Kei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 68-72). / Abstracts in English and Chinese. / Acknowledgement --- p.i / Abstract --- p.ii / Contents --- p.vi / List of Figures --- p.viii / Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Previous Works --- p.3 / Chapter 1.1.1 --- Template deformation --- p.3 / Chapter 1.1.2 --- Mesh partitioning --- p.3 / Chapter 1.1.3 --- Mesh Smoothing --- p.4 / Chapter 1.2 --- Overview of the approach --- p.5 / Chapter 1.3 --- Thesis outline --- p.7 / Chapter 2. --- Global Deformation --- p.8 / Chapter 2.1 --- The closet point method --- p.10 / Chapter 2.1.1 --- Computational complexity --- p.11 / Chapter 2.2 --- Deformation Techniques --- p.12 / Chapter 2.2.1 --- Existing deformation method --- p.12 / Chapter 2.2.2 --- Radial Basis Functions (RBFs) --- p.14 / Chapter 2.2.2.1 --- Computational complexity --- p.18 / Chapter 2.2.3 --- Result --- p.18 / Chapter 2.3 --- Face flip prevention --- p.20 / Chapter 2.3.1 --- Detection of the flipped face --- p.22 / Chapter 2.3.1.1 --- Common approach: --- p.22 / Chapter 2.3.1.2 --- Our Approach --- p.23 / Chapter 2.3.1.3 --- Comparisons of the face flip detection method: --- p.26 / Chapter 2.3.2 --- Local Subdivision --- p.27 / Chapter 3. --- Partitioning of the mesh --- p.29 / Chapter 3.1 --- Existing method --- p.29 / Chapter 3.2 --- Our approach --- p.31 / Chapter 3.3 --- Computational complexity --- p.34 / Chapter 4. --- Mesh smoothing algorithm --- p.35 / Chapter 4.1 --- The Laplacian flow method --- p.36 / Chapter 4.2 --- The mean-curvature method --- p.40 / Chapter 4.3 --- Our Approach --- p.43 / Chapter 4.3.1 --- The modified mean-curvature method --- p.43 / Chapter 4.3.2 --- The modified Laplacian flow method --- p.45 / Chapter 4.3.3 --- Feature constraints --- p.47 / Chapter 4.3.4 --- Computational complexity --- p.47 / Chapter 4.4 --- Comparison of the mesh smoothing approach --- p.48 / Chapter 5. --- Implementation and Results --- p.51 / Chapter 5.1 --- Construction of the template mesh and boundary curves --- p.51 / Chapter 5.2 --- Selection of the corresponding vertex pairs --- p.52 / Chapter 5.3 --- Results --- p.54 / Chapter 6. --- Conclusions --- p.63 / Chapter 6.1 --- Future development --- p.65 / Appendix A --- p.66 / Determination of the projected path on a mesh: --- p.66 / Reference --- p.68

The predominant model of the human hip is a mechanical ball-and-socket joint. This description has two key implications: that the motion of the hip is purely rotational, and that the rigid articulating geometry of the hip is a sphere-on-sphere contact. Since the widespread adoption of this model, in the late 1960s, there has however been a persistent thread of literature suggesting that the articulating geometry of the hip is aspherical. The recent widespread availability of three-dimensional medical imaging now makes it possible to empirically assess the applicability of the predominant model. For this research dissertation, two arthritic groups were examined: patients either had primary early-life osteoarthritis of the hip, or hip dysplasia with secondary osteoarthritis. Computed tomography scans, taken as part of routine preoperative preparation, served as the source data for this work. The scans were manually segmented to produce 3D models of the bones of the hip, which were further refined to isolate the bony articular surfaces. These surfaces were fit to general ellipsoids and to spheres, the latter being the ball-and-socket model. The arthritic hips examined had comparable fitting accuracy for both ellipsoids and spheres; however, sixteen of nineteen hips formed geometrically incompatible ball-and-socket joints. The dysplastic hips examined had a notable difference in fitting accuracy, with ellipsoids being a statistically significantly better fit to the hip geometry. The ellipsoid shapes in all cases were aspherical, and in each population formed a statistically significantly aspherical group. There were no trends relating the ellipsoid shapes of bones of an individual joint, nor were there practical differences between the ellipsoid shapes between the two populations. Despite patient groups not being controlled for age, sex, or race, and accounting for typical manual segmentation errors, these results suggest that the hip is aspherically shaped. Thus, the geometric foundation of the ball-and-socket motion may be unsupported, and the conventional kinematic description of the hip may be called into question. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2011-09-28 09:41:29.114

The purpose of this study was to investigate the relationship between live and recorded determinations of most comfortable loudness levels (MCL's) and to determine if a relationship existed between MCL's, tolerance levels (TL's), and acoustic reflex thresholds so that further research might be conducted regarding the use of acoustic impedance measures in hearing aid fitting.Thirty normal hearing female subjects were tested in this investigation. MCL's using live and recorded stimuli, TL's, and contralateral and ipsilateral acoustic reflex thresholds were obtained for each subject. Correlation coefficients were computed to determine if a relationship existed between any of the measurements.It was concluded that live voice stimuli yielded highly equivalent results to recorded stimuli in finding MCL's. Acoustic reflex thresholds were found to be poor predictors of MCL's and TL's. Before acoustic reflex measurements can be used in hearing aid fitting procedures, further research is warranted.

Computational geometry is the study of algorithms for manipulating sets of points, lines, polygons, planes and other geometric objects. For many problems in this realm, the sets considered are static and the data structures representing them do not permit efficient insertion and deletion of objects (e.g. points). Dynamic problems, in which the set and the geometric data structure change over time, are also of interest. The topic of this thesis is the presentation of fast algorithms for fully dynamic maintenance of some common geometric structures. The following configurations are examined: planar nearest-point and farthest-point Voronoi diagrams, convex hulls (in two and three dimensions), common intersection of halfspaces (2-D and 3-D), and contour of maximal vectors (2-D and 3-D). The principal techniques exploited are fast merging of substructures, and the use of extra storage. Dynamic geometric search structures based upon the configurations are also presented. / Science, Faculty of / Computer Science, Department of / Graduate

The main problems of numerical analysis involve performing analytical operations, such as integration, differentiation, finding zeroes, interpolation, and so forth, of a function when all the data available are some samples of the function. Therefore, the purpose of this paper is to investigate the following problem: given a set of data points (x[sub i], y[sub i]) which are samples of some function, determine an approximating function. Further, extend the problem to that of determining an approximating function for a surface given some samples (x[sub i], y[sub j], z[sub ij]) of the surface.

O primeiro objetivo deste trabalho é um estudo dos invariantes necessários para determinar condições de Whitney equisingularidade ou trivialidade topollógica para germes de aplicações f : (\'C POT.n+3\' ,0) \'SETA\' (\'C POT.3\',0). São obtidas relações entre os invariantes sem considerar a hipótese de que o germe tenha co-posto 1 e o desdobramento ser excelente, generalizando os resultados obtidos por Jorge Pèrez para germes f : (\'C POT.3\' ,0) \' SETA\' !(\'C POT.3\' ,0) de co-posto 1. Outro problema interessante em teoria de singularidades é encontrar fórmulas para calcular invariantes 0-estáveis que podem surgir no discriminante de uma deformaçãao estável de um germe finitamente determinado. Neste contexto são desenvolvidos métodos de contagem dos invariantes 0-estáveis a partir dos ideais de Fitting associados ao conjunto discriminante de f . Por último, implementamos um algoritmo no software Maple, para determinar a matriz de uma apresentação do \'O IND.m\' módulo finitamente gerado \'O IND.SIGMA( f ). Desta matriz, podemos obter os ideais de definição de todos os conjuntos de pontos múltiplos de f . Além disto apresentamos uma aplicação deste algoritmo no cálculo do número de pontos múltiplos em germes finitamente determinados de \'C POT.2\' em \'C POT.2\' / In the first of this work we study the necessary invariants to give conditions for the Whitney equissingularity or the topological triviality in families of map germs f : (\'C POT. n+3\', 0) \'ARROW\' (\'C POT.3\' ,0). We obtain relations between these invariants without the hypothesis of the germ to be of co-rank 1 and the unfolding to be excelent. We generalize the results given by Jorge Perez in the case co-rank one map germs f : (\'C POIT.3\', 0)!(\'C POT.3\' ,0). Other interesting problem in Singularity Theory is to find formulae which allow us to count the 0-stable singularities which appear in the discriminant of a stable deformation of a finitely determibed germ. In this context are developed methods of calculation of invariant 0-stable from the ideals of fitting associated with the discriminant set of f . Last, but not least we implement an algorithm using Maple to obtain the representation matrix of the finitely generated \'O IND.m\' module \'O IND. SIGMA\'( f ). From this matrix we obtain all Fitting ideals related with the multiple points. Moreover we show how to apply this algorithm to obtain the multiple points of finitely determined map germs f : (\'C POT.2\' ,0) \'ARROW\' (\'C POT.2\', 0)

O primeiro objetivo deste trabalho é um estudo dos invariantes necessários para determinar condições de Whitney equisingularidade ou trivialidade topollógica para germes de aplicações f : (\'C POT.n+3\' ,0) \'SETA\' (\'C POT.3\',0). São obtidas relações entre os invariantes sem considerar a hipótese de que o germe tenha co-posto 1 e o desdobramento ser excelente, generalizando os resultados obtidos por Jorge Pèrez para germes f : (\'C POT.3\' ,0) \' SETA\' !(\'C POT.3\' ,0) de co-posto 1. Outro problema interessante em teoria de singularidades é encontrar fórmulas para calcular invariantes 0-estáveis que podem surgir no discriminante de uma deformaçãao estável de um germe finitamente determinado. Neste contexto são desenvolvidos métodos de contagem dos invariantes 0-estáveis a partir dos ideais de Fitting associados ao conjunto discriminante de f . Por último, implementamos um algoritmo no software Maple, para determinar a matriz de uma apresentação do \'O IND.m\' módulo finitamente gerado \'O IND.SIGMA( f ). Desta matriz, podemos obter os ideais de definição de todos os conjuntos de pontos múltiplos de f . Além disto apresentamos uma aplicação deste algoritmo no cálculo do número de pontos múltiplos em germes finitamente determinados de \'C POT.2\' em \'C POT.2\' / In the first of this work we study the necessary invariants to give conditions for the Whitney equissingularity or the topological triviality in families of map germs f : (\'C POT. n+3\', 0) \'ARROW\' (\'C POT.3\' ,0). We obtain relations between these invariants without the hypothesis of the germ to be of co-rank 1 and the unfolding to be excelent. We generalize the results given by Jorge Perez in the case co-rank one map germs f : (\'C POIT.3\', 0)!(\'C POT.3\' ,0). Other interesting problem in Singularity Theory is to find formulae which allow us to count the 0-stable singularities which appear in the discriminant of a stable deformation of a finitely determibed germ. In this context are developed methods of calculation of invariant 0-stable from the ideals of fitting associated with the discriminant set of f . Last, but not least we implement an algorithm using Maple to obtain the representation matrix of the finitely generated \'O IND.m\' module \'O IND. SIGMA\'( f ). From this matrix we obtain all Fitting ideals related with the multiple points. Moreover we show how to apply this algorithm to obtain the multiple points of finitely determined map germs f : (\'C POT.2\' ,0) \'ARROW\' (\'C POT.2\', 0)

<p> The work in this thesis is to develop a tool for calculating the parameters corresponding to certain theoretical model of dielectric relaxation phenomena and then doing the curve fitting using the result after fetching the data from the user. To our best knowledge, this the first such tool to calculate the parameters corresponding to certain theoretical model of dielectric relaxation phenomena while the user only need to provide the experimental data. The parameters are calculated by using a nonlinear least square algorithm implemented in Matlab and a nonlinear function minimizer available in Matlab. The way to do the curve fitting is not by the traditional way such as cubic spline but by calculating the simulated data using the chosen model and the calculated result for the parameters. </p> <p> The available mathematical models include all of popular theoretical models, the Cole-Davidson (DC), the Kohlrausch-Williams-Watts (KWW), the Havriliak-Negami (HN) and the model proposed by R. Hilfer (FD). </p> <p> There are two ways to calculate the parameters for each model as mentioned before. The result returned by this system may not be unique. Especially if the frequency range of data is not wide enough, the result would most likely be non-unique. Since the iterative method is used in the system, it is suggested that the user provides the initial values for the system with his best knowledge or background for the data and the tested sample related to dielectric relaxation process. </p> <p> It is normal if there is a part having worse fitting than the other parts. One of reasons could be the mathematical model's defect, which the model does not work for that part. For the further information, please contact me by email at zouhaijun at yahoo.com. </p> / Thesis / Master of Science (MSc)