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.

Zugl.: Kaiserslautern, Techn. Univ., Diss., 2009

Thesis (M.S.)--Rochester Institute of Technology, 2010. / Typescript. Includes bibliographical references (leaves 94-99).

迴歸分析中，若變數間有非線性(nonlinear)的關係，此時我們可以用B-spline線性迴歸，一種無母數的方法，建立模型。Penalized spline是B-spline方法的一種改良，其想法是增加一懲罰項，避免估計函數時出現過度配適的問題。本文中，考慮三種方法:(a) Marginal Mixed Model approach, (b) Conditional Mixed Model approach, (c) 貝氏方法建立信賴帶，其中，我們對第一二種方法內的估計式作了一點調整，另外，懲罰項中的平滑參數也是我們考慮的問題。我們發現平滑參數確實會影響信賴帶，所以我們使用cross-validation來選取平滑參數。在調整的cross-validation下，Marginal Mixed Model的信賴帶估計不平滑的函數效果較好，Conditional Mixed Model的信賴帶估計平滑函數的效果較好，貝氏的信賴帶估計函數效果較差。 / In regression analysis, we can use B-spline to estimate regression function nonparametrically when the regression function is nonlinear. Penalized splines have been proposed to improve the performance of B-splines by including a penalty term to prevent over-fitting. In this article, we compare confidence bands constructed by three estimation methods: (a) Marginal Mixed Model approach, (b) Conditional Mixed Model approach, and (c) Bayesian approach. We modify the first two methods slightly. In addition, the selection of smoothing parameter of penalization is considered. We found that the smoothing parameter affects confidence bands a lot, so we use cross-validation to choose the smoothing parameter. Finally, based on the restricted cross-validation, Marginal Mixed Model performs better for less smooth regression functions, Conditional Mixed Model performs better for smooth regression functions and Bayesian approach performs badly.

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Thesis (M.S.)--Rochester Institute of Technology, 1989. / Includes bibliographical references (leaves 72-73).

Thesis (M.S.)--Ohio University, June, 1999. / Title from PDF t.p.

Thesis (M.S.)--Ohio University, August, 1999. / Title from PDF t.p.