Mannheim, Universiẗat, Diss., 2003.

Hannover, Universiẗat, Diss., 2001.

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

No description available.

No description available.

Inverse problems arise in many branches of natural science, medicine and engineering involving the recovery of a whole function given only a finite number of noisy measurements on functionals. Such problems are usually ill-posed, which causes severe difficulties for standard least-squares or maximum likelihood estimation techniques. These problems can be solved by a method of regularization. In this dissertation, we study various problems in the method of regularization. We develop asymptotic properties of the optimal smoothing parameters concerning levels of smoothing for estimating the mean function and an associated inverse function based on Fourier analysis. We present numerical algorithms for an approximated method of regularization estimator computation with linear inequality constraints. New data-driven smoothing parameter selection criteria are proposed in this setting. In addition, we derive a Bayesian credible interval for the approximated method of regularization estimators.

This study deals specifically with classical cubic splines. Based on a lemma of John Rice, best approximation in the uniform norm by cubic splines is explored. The purpose of this study is to characterize the best approximation to a given continuous function f(x) by a cubic spline with fixed knots by counting alternating extreme points of its error function E(t). / Graduation date: 1991

Various proteins with specific properties and functions exist in organisms, they perform all important biochemical activities. The biochemical functions of proteins are determined by their structures. One of the most important issues in the life science is to predict the three-dimensional structures with protein sequences, and then to deduce their biochemical functions. To predict protein structure precisely will accelerate biochemical research. However, it is a challenge task to obtain the real structure of a protein. The objective of this study is to develop a protein structure prediction methodology based on a structure-known protein (such as the proteins in the PDB database), where the two protein sequences are extremely similar. Some folding algorithms, such as U-fold and S-fold, have been developed to predict protein structures. However, the folding algorithms work on a grid lattice, which is very different from the real structure of a protein. Here we use the curve fitting technique, such as B-splines, to convert the lattice model and a real structure to the same domain, that is, the curve. We therefore perform curve (structure) alignment on them. The curve alignment can also be used to evaluate the similarity between two structures. By the experimental results, our protein structure prediction method performs well when we get two protein sequences with similarity that is not too high.

Inverse problems arise in many branches of natural science, medicine and engineering involving the recovery of a whole function given only a finite number of noisy measurements on functionals. Such problems are usually ill-posed, which causes severe difficulties for standard least-squares or maximum likelihood estimation techniques. These problems can be solved by a method of regularization. In this dissertation, we study various problems in the method of regularization. We develop asymptotic properties of the optimal smoothing parameters concerning levels of smoothing for estimating the mean function and an associated inverse function based on Fourier analysis. We present numerical algorithms for an approximated method of regularization estimator computation with linear inequality constraints. New data-driven smoothing parameter selection criteria are proposed in this setting. In addition, we derive a Bayesian credible interval for the approximated method of regularization estimators.

Thesis--Auburn University, 2009. / Abstract. Vita. Includes bibliographic references (p.36).