Asymptotic Methods in Change-Point Analysis

This thesis is focussed on two areas of statistics, change-point analysis and functional data analysis, and the intersection of these two areas, i.e., the detection of structural breaks in functional stochastic models. The considered problems from (scalar) change-point analysis result from criticism of already existing sequential change-point procedures. The subject of this criticism was a lack of stability of these procedures regarding the time of occurrence of a change. As a possible solution to this criticism sequential methods are presented in this thesis in the framework of a linear regression model on the basis of the so-called Page CUSUM. To prove the desired properties of these procedures theoretically the asymptotic distribution of the delay time in the detection of structural breaks is derived in the special case of a location model. The notion "functional data analysis" represents an area of statistics that considers functions (in general defined on a compact interval) as "data points". Examples for such data are temperature curves or the path of a stock price on one trading day. To derive statistical procedures for this class of data dimension reduction techniques play a key role. The methods presented in this thesis are based on one of those techniques, the functional principal component analysis. They illustrate the construction of two-sample tests as well as change-point tests exploiting the properties of these functional principal components. In particular the problem of an adequate choice of the dimension of the space to project on in order to reduce the dimension is addressed and included in the construction of the respective testing procedures

Doctor of Philosophy

dissertationThis work presents the results of various investigations using various techniques of hyperpolarizing the nuclei of atoms. Hyperpolarization implies magnetic order in excess of the thermal order obtained naturally as described by Curie's law. The main portion of this work presents the results of a detailed experimental exploration of predictions arising from a new model of transverse nuclear spin relaxation in quantum systems, based on possible manifestations of microscopic chaos in quantum systems. Experiments have been carried out on a number of hyperpolarized xenon samples, each di ering in its relative percentage of xenon isotopes in order to vary the homonuclear and heteronuclear dipole couplings in the spin system. The experiments were performed under a variety of conditions in an attempt to observe the behaviors predicted by the model. Additionally, much more extensive measurements were made on a number of samples of solid CaF2 in both single crystal and powder forms. These samples, although thermally polarized, were observed with superior signal to noise ratios than even the hyperpolarized xenon solids, allowing for more precise measurements for comparison to the theory. This work thus contains the rst experimental evidence for the majority of the model's predictions. Additionally, this work contains the rst precise measurements of the frequency-shift enhancement parameters for 129Xe and krypton in the presence of spin-polarized Rb. The determination of these important numbers will be useful to many groups who utilize spinexchange optical pumping in their labs. This work built on the prior knowledge of a precise number for the frequency-shift enhancement parameter of 3He in Rb vapor. Finally, I detail work using NMR to detect nuclear-spin polarization enhancement in silicon phosphorus by a novel, photo-induced hyperpolarization technique developed by the Boehme research group at the University of Utah. Signiif cant nuclear polarization enhancements were observed by the Boehme group due to electron-photon interactions in semiconductor soilds; these enhancements were observed by their e ffects on the ambient electrons and measured with electron spin resonance techniques. The work described here details experiments to observe the enhanced nuclear polarization by directly measuring the intensity increase in an NMR measurement

Dynamics of Macrosystems; Proceedings of a Workshop, September 3-7, 1984

There is an increasing awareness of the important and persuasive role that instability and random, chaotic motion play in the dynamics of macrosystems. Further research in the field should aim at providing useful tools, and therefore the motivation should come from important questions arising in specific macrosystems. Such systems include biochemical networks, genetic mechanisms, biological communities, neutral networks, cognitive processes and economic structures. This list may seem heterogeneous, but there are similarities between evolution in the different fields. It is not surprising that mathematical methods devised in one field can also be used to describe the dynamics of another. IIASA is attempting to make progress in this direction. With this aim in view this workshop was held at Laxenburg over the period 3-7 September 1984. These Proceedings cover a broad canvas, ranging from specific biological and economic problems to general aspects of dynamical systems and evolutionary theory

VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts

The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)