This thesis uses methods from functional data analysis (FDA) to solve problems from three scientific areas of study. While the areas of application are quite distinct, the common thread of functional data analysis ties them together. The first chapter describes interactive open-source software for explaining and disseminating results of functional data analyses. Chapters two and three use curve alignment, or registration, to solve common problems in accelerometry and neuroimaging, respectively. The final chapter introduces a novel regression method for modeling functional outcomes that are trajectories over time. The first chapter of this thesis details a software package for interactively visualizing functional data analyses. The software is designed to work for a wide range of datasets and several types of analyses. This chapter describes that software and provides an overview ofFDA in different contexts. The second chapter introduces a framework for curve alignment, or registration, of exponential family functional data. The approach distinguishes itself from previous registration methods in its ability to handle dense binary observations with computational efficiency. Motivation comes from the Baltimore Longitudinal Study on Aging, in which accelerometer data provides valuable insights into the timing of sedentary behavior. The third chapter takes lessons learned about curve registration from the second chapter and use them to develop methods in an entirely new context: large multisite brain imaging studies. Scanner effects in multisite imaging studies are non-biological variability due to technical differences across sites and scanner hardware. This method identifies and removes scanner effects by registering cumulative distribution functions of image intensities values. In the final chapter the focus shifts from curve registration to regression. Described within this chapter is an entirely new nonlinear regression framework that draws from both functional data analysis and systems of ordinary equations. This model is motivated by the neurobiology of skilled movement, and was developed to capture the relationship between neural activity and arm movement in mice.

No description available.

This thesis examines the existing theories and applications of Multivariate Statistical Process Control, outlines areas of difficulty and proposes a new technique of multivariate process control chart with input-output relationship for optimal process control. The process control techniques developed up to the present time focused on the fast detection of out-of-control signals, and achieved considerable success in that respect. The techniques reported on multivariate process control thus far include extensions of univariate process control charts to their multivariate counterparts, ranging from classical Shewharts charts to modern Cumulative Sum Process Control charts. Alternative approaches in this area include Principal Component Approach, Partial Regression approach, Baysian modelling and sequential tests on detection of change points. Although each method has its own limitation, these new developments have significantly contributed to the achievement of a constant high quality of products and services. The techniques of process control are yet incomplete. They require continuous attention, as production and service technologies are being continuously developed.In particular, the level of automation, re-engineering of production processes and ever demanding economic optimality of technology demand the re-engineering of statistical process control. The CFM chart developed in this thesis would open the door to this area of science and lays a critical foundation for future research / Doctor of Philosophy (PhD)

Includes bibliographical references. / 1 v. : / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis investigates the nature and origins of minerals of a group known as layer (sheet) silicates or phyllosilicates. It consists of a collection of research papers grouped into 3 categories: modulated layer silicates, clay silicates and the weathering of rocks and minerals, including the formation of clay minerals. Central to the research has been the use of X-ray diffraction (XRD) and high resolution transmission electron microscopy (HRTEM). All three research categories were carried out simultaneously. / Thesis (D.Sc.)--University of Adelaide, Dept. of Geology and Geophysics, 1999

<p>The analysis of the health condition in Rheumatoid Arthritis (RA) remains a qualitative process dependent on visual inspection by a clinician. Fully automatic techniques that can accurately classify the health of the muscle have yet to be developed. The intended purpose of this work is to develop a novel spatio-temporal technique to assist in a rehabilitation program framework, by identifying motion features inherited in the muscles in order to classify them as either healthy or diseased. Experiments are based on ultrasound image sequences during which the muscles were undergoing contraction. The proposed system uses an optical flow technique to estimate the velocity of contraction. Analyzing and manipulating the velocity vectors reveal valuable information which encourages the extraction of motion features to discriminate the healthy against the sick. Experimental results for classification prove helpful in essential developments of therapy processes and the performance of the system has been validated by the cross-validation technique “leave-one-out”. The method leads to an analytical description of both the global and local muscle’s features in a way which enables the derivation of an appropriate strategy for classification. To our knowledge this is the first reported spatio-temporal method developed and evaluated for RA assessment. In addition, the progress of physical therapy to improve strength of muscles in RA patients has also been evaluated by the features used for classification.</p>

<p>This thesis consists of four papers about the Minkowski measure of asymmetry and the Minkowski (or Banach-Mazur) distance for convex bodies.We relate these two quantities by giving estimates for the Minkowski distance in terms of the Minkowski measure. We also investigate some properties of the Minkowski measure, in particular a stability estimate is given. More specifically, let <i>C</i> and <i>D</i> be n-dimensional convex bodies. Denote by As(<i>C</i>) and As(<i>D</i>) the Minkowski measures of asymmetry of <i>C</i> and <i>D </i>resp. and by <i>d</i>(<i>C,D</i>) the Minkowski distance between <i>C</i> and <i>D</i>.</p><p>In Paper I, by using a linearisation method for affine spaces and affine maps and using a generalisation of a lemma of D.R. Lewis, we proved that <i>d</i>(<i>C</i>,<i>D</i>) < <i>n</i>(As(<i>C</i>) + As(<i>D</i>))/2 for all convex bodies <i>C,D</i>.</p><p>In Paper II, by first proving some general existence theorems for a class of volume-increasing affine maps, we obtain the estimate that under the same conditions as in paper I, <i>d</i>(<i>C,D</i>) < (<i>n</i>-1) min(As(<i>C</i>),As(<i>D</i>)) + <i>n</i>.</p><p>In Paper III we consider the Minkowski measure itself. We determine the Minkowski measures for convex hulls of sets of the form <i>conv</i>(<i>C,p</i>) where <i>C</i> is a convex set with known measure of asymmetry and <i>p</i> is a point outside <i>C</i>.</p><p>In Paper IV, we focus on estimating the deviation of a convex body C from the simplex S if the Minkowski measure of C is close to the maximum value n (known to be attained only for the simplex). We prove that if As(C) > n - ε for 0 < ε < 1/δ where δ = 8(n+1), then d(C,S) < 1 + 8(n+1) ε .</p>

<p>This thesis consists of three papers on topics related to optimization and estimation of solutions of Riccati equations. We are concerned with the initial value problem</p><p><i>f</i>'+<i>f</i>² =<i>r</i>², <i>f</i>(0)=0, (*)</p><p>and we want to optimise</p><p><i>F</i>(<i>T</i>)= ∫₀^T <i>f</i>(<i>t</i>) <i>dt</i></p><p>when <i>r</i> is allowed to vary over the set <i>R</i>(φ ) of all <i>equimeasurable</i> rearrangements of a decreasing function φ and its convex hull <i>CR</i>(φ). </p><p>In the second paper we give a new proof of a lemma of Essén giving lower and upper bounds for the solution to the above equation, when <i>r</i> is increasing. We also generalize the lemma to a more general equation.</p><p>It was proved by Essén that the infimum of <i>F</i>(<i>T</i>) over <i>R</i>(φ) and <i>RC</i>(φ) is attained by the solution <i>f</i> of (*) associated to the increasing rearrangement of an element in <i>R</i>(φ). The supremum of <i>F</i>(<i>T</i>) over <i>RC</i>(φ) is obtained for the solution associated to a decreasing function <i>p</i>, though not necessarily the decreasing rearrangement φ, of an element in <i>R</i>(φ). By changing the perspective we determine the function <i>p </i>that solves the supremum problem.</p>

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 110-114).

Thesis (M. A.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

Author's thesis (Ph. D.)--Technische Universiteit Delft, 2006. / Includes bibliographical references.