本論文探討了以廣義線性混合模式(GLMM)結合時間及空間效果的時間空間模式，以將地區特性、人口特徵等變數，及時間變數納入模式中。有關時間效果可用B-Spline方法建構固定或隨機的時間趨勢平滑函數，而空間效果則是將各地區的隨機效果以條件自我相關模式(CAR)描述。實證部份則是應用GLMM模式分析台灣本島350個鄉鎮市區自民國八十八年到九十一年的肝癌就診資料，依性別、年齡層加以整理，並將年齡層分為0~19歲、20~39歲、40 ~59歲、60歲以上，分別代表少、青、壯、老等四個年齡層；再採用GLMMGibbs結合R軟體各個資料集分別配適時間空間模式，估計各地區之相對風險並繪製疾病地圖，據以找出各年估計的相對風險高的地區。

Real-valued functions have wide applications in various areas within computer graphics. In this work, we examine three representation of shapes using functions. In particular, we study the classical B-spline representation of piece-wise polynomials in the univariate domain. We provide a generalization of B-spline to the bivariate domain using intuition gained from the univariate construction. We also study the popular scheme of representing 3D density distribution using a uniform, rectilinear grid, where we provide a novel contouring scheme that culls occluded inner geometries. Lastly, we examine a ray-based representation for 3D indicator functions called ray-rep, for which we present a novel meshing scheme with multi-material extensions.

Most of the work accomplished on surface blending is based on visual trimming. In the process of visual trimming, the unwanted portion of a surface is only hidden but not removed. Geometric trimming provides a complete mathematical description of the wanted portion of the trimming surface, and generates a new mathematical surface or sets of surface patches. The new surface is intended to resemble closely the corresponding portion of the original surface. A robust procedure is developed to geometrically trim the intersecting surfaces and blend the trimmed surface patches into one new surface. This research generates a filleting algorithm for surface blending of an aircraft fuselage shape and a wing shape at a closed trimming intersection curve, and verifies the properties of the newly created surface. In order to distinguish how well the new surface approximates the original, an error comparison tool developed in MATLAB has been employed. / Master of Science

Geometric trimming of a surface involves removal of unwanted portions of the surface and providing a new mathematical description for the trimmed patch. This entails creating a new geometry for the trimmed patch, which closely approximates the corresponding portion on the original patch. The procedure is shown to involve obtaining data points on the B-spline surface that lie within the region specified by the parameter values for the trimming curve and describing a new surface which interpolates this new set of data points. This research looks at optimizing the procedure described above by basing the choice of parameter values for the trimming curve, at points where curvature optima occur over the surface. A visualization tool kit has been developed using OpenGL, as a means to discern the difference between the two surfaces. In order to quantify and aid in minimizing the error (difference) in approximating the original surface with the trimmed patch, an error measurement tool developed in MATLAB has been employed. / Master of Science

Protein is a fundamental material of life. There are many kinds of proteins in the body. If one of them malfunctions, it will cause physical problems. Therefore, many scientists try to analyze the functions of proteins. It is believed that the protein structure determines its function. The more similar the structures are, the more similar their functions are. Therefore, the prediction and comparison of protein structures are important topics in bioinformatics. Typically, distance RMSD (Root Mean Square Deviation) is a method used by most scientists to measure the distance between two structures. In this thesis, we propose a new algorithm to compare two protein structures, which is based on the comparison of curves in the space. To test and verify our method, we randomly choose some families in the CATH database and try to identify them. Experimental results show that our method outperforms RMSD. Furthermore, we also use the SVM (Support Vector Machine) tool to help us to obtain the better classification.

The finite element method since its development in the 1950’s has been used extensively in solving complex problems involving partial differential equations. The conventional finite element methods use piecewise Lagrange interpolation functions for approximating displacements. The aim of this research is to explore finite element analysis using B-spline interpolation. B-splines are piecewise defined polynomial curves which provide higher continuity of derivatives than piecewise Lagrange interpolation functions. This work focuses on the implementation and comparison of the B-spline finite elements in contrast with the conventional finite elements. This thesis observes that the use of B-spline interpolation functions can reduce the computational cost significantly. It is an efficient technique and can be conveniently implemented into the existing finite element programs.

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Techn. Universiẗat, Diss., 2005--Darmstadt.

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No description available.