<p>This thesis consists of four papers, all concerning random iteration of isometries. The papers are:</p><p>I. Ambroladze A, Ådahl M, Random iteration of isometries in unbounded metric spaces. Nonlinearity 16 (2003) 1107-1117.</p><p>II. Ådahl M, Random iteration of isometries controlled by a Markov chain. Manuscript.</p><p>III. Ådahl M, Melbourne I, Nicol M, Random iteration of Euclidean isometries. Nonlinearity 16 (2003) 977-987.</p><p>IV. Johansson A, Ådahl M, Recurrence of a perturbed random walk and an iterated function system depending on a parameter. Manuscript.</p><p>In the first paper we consider an iterated function system consisting of isometries on an unbounded metric space. Under suitable conditions it is proved that the random orbit {<i>Z</i>n} ^∞_n=0, of the iterations corresponding to an initial point Z₀, “escapes to infinity" in the sense that <i>P</i>(<i>Z</i>n Є <i>K)</i> → 0, as <i>n</i> → ∞ for every bounded set <i>K</i>. As an application we prove the corresponding result in the Euclidean and hyperbolic spaces under the condition that the isometries do not have a common fixed point.</p><p>In the second paper we let a Markov chain control the random orbit of an iterated function system of isometries on an unbounded metric space. We prove under necessary conditions that the random orbit \escapes to infinity" and we also give a simple geometric description of these conditions in the Euclidean and hyperbolic spaces. The results generalises the results of Paper I.</p><p>In the third paper we consider the statistical behaviour of the reversed random orbit corresponding to an iterated function system consisting of a finite number of Euclidean isometries of <b>R</b>n. We give a new proof of the central limit theorem and weak invariance principles, and we obtain the law of the iterated logarithm. Our results generalise immediately to Markov chains. Our proofs are based on dynamical systems theory rather than a purely probabilistic approach.</p><p>In the fourth paper we obtain a suficient condition for the recurrence of a perturbed (one-sided) random walk on the real line. We apply this result to the study of an iterated function system depending on a parameter and defined on the open unit disk in the complex plane. </p>

Lorsqu'un gaz bosonique ultrafroid est fortement confiné selon une direction de l'espace, les degrés de liberté correspondants sont « gelés » et le gaz devient effectivement bidimensionnel. Le sujet principal de ce manuscrit de thèse est la production de ces gaz quasi-bidimensionnels avec un nouveau dispositif expérimental ainsi que leur étude subséquente. Le manuscrit se divise en deux parties dont la première est consacrée à la description du dispositif expérimental et des techniques qui nous permettent la production des gaz de Bose ultrafroids. Le cas particulier de la production (pour laquelle on se sert d'une lame de phase holographique) et l'étude des gaz de Bose quasi-bidimensionnels est discuté en détail dans la deuxième partie. Le but original des expériences décrites ici était de mesurer l'équation d'état du gaz de Bose quasi-bidimensionnel. Il s'est avéré que la méthode de l'imagerie par absorption, appliquée sur un tel gaz, donne naissance à des effets inattendus. Nous donnons une caractérisation détaillée ainsi que des éléments d'explication possibles de ces effets.

Switched electronic systems are used in a huge number of everyday domestic and industrial utilities: liquid crystal displays, home appliances, lighting, personal computers, power plants, transportation vehicles and so on. Efficient operations of all such applications depend on the essential "hidden work" done by switched electronic systems, whose behavior is determined by a suitable interconnection and control of analog and digital devices. As a motivation of this work, we consider the DC-DC power converters. This thesis contributes to provide hybrid and nonlinear control problem solutions to several types of power converters. In the first part we are interested in the problem of voltage regulation of power converters operating in discontinuous conducting mode. Two power converters are considered: the boost converter and the buck-boost converter. The system does not admit a (continuous--time) average model approximation, hence is a hybrid system where the control objective is the generation of a periodic orbit and the actuator commands are switching times. Our main contribution is a simple robust algorithm that gives explicit formulas for the switching times without approximations. Simulation and experimental results that illustrate the robustness of the scheme to parameter uncertainty, as well as performance comparisons with current practice, are presented. In the second part a class of power converters that can be globally stabilized with an output-feedback PI controller has been identified. Moreover, we will prove that the I&I observer can be combined with the PI controller preserving the GAS properties of the closed-loop. The class is characterized by a simple linear matrix inequality. The new controller is illustrated with the widely-popular, and difficult to control, single-ended primary inductor converter, for which simulation and experimental results are presented.

This thesis consists of four papers, all concerning random iteration of isometries. The papers are: I. Ambroladze A, Ådahl M, Random iteration of isometries in unbounded metric spaces. Nonlinearity 16 (2003) 1107-1117. II. Ådahl M, Random iteration of isometries controlled by a Markov chain. Manuscript. III. Ådahl M, Melbourne I, Nicol M, Random iteration of Euclidean isometries. Nonlinearity 16 (2003) 977-987. IV. Johansson A, Ådahl M, Recurrence of a perturbed random walk and an iterated function system depending on a parameter. Manuscript. In the first paper we consider an iterated function system consisting of isometries on an unbounded metric space. Under suitable conditions it is proved that the random orbit {Zn} ∞n=0, of the iterations corresponding to an initial point Z0, “escapes to infinity" in the sense that P(Zn Є K) → 0, as n → ∞ for every bounded set K. As an application we prove the corresponding result in the Euclidean and hyperbolic spaces under the condition that the isometries do not have a common fixed point. In the second paper we let a Markov chain control the random orbit of an iterated function system of isometries on an unbounded metric space. We prove under necessary conditions that the random orbit \escapes to infinity" and we also give a simple geometric description of these conditions in the Euclidean and hyperbolic spaces. The results generalises the results of Paper I. In the third paper we consider the statistical behaviour of the reversed random orbit corresponding to an iterated function system consisting of a finite number of Euclidean isometries of <b>R</b>n. We give a new proof of the central limit theorem and weak invariance principles, and we obtain the law of the iterated logarithm. Our results generalise immediately to Markov chains. Our proofs are based on dynamical systems theory rather than a purely probabilistic approach. In the fourth paper we obtain a suficient condition for the recurrence of a perturbed (one-sided) random walk on the real line. We apply this result to the study of an iterated function system depending on a parameter and defined on the open unit disk in the complex plane.

This thesis investigates a technique to estimate the risk of the mean-variance (MV) portfolio optimization problem. We call this technique the Scaling technique. It provides a better estimator of the risk of the MV optimal portfolio. We obtain this result for a general estimator of the covariance matrix of the returns which includes the correlated sampling case as well as the independent sampling case and the exponentially weighted moving average case. This gave rise to the paper, [CMcS]. Our result concerning the Scaling technique relies on the moments of the inverse of compound Wishart matrices. This is an open problem in the theory of random matrices. We actually tackle a much more general setup, where we consider any random matrix provided that its distribution has an appropriate invariance property (orthogonal or unitary) under an appropriate action (by conjugation, or by a left-right action). Our approach is based on Weingarten calculus. As an interesting byproduct of our study - and as a preliminary to the solution of our problem of computing the moments of the inverse of a compound Wishart random matrix, we obtain explicit moment formulas for the pseudo-inverse of Ginibre random matrices. These results are also given in the paper, [CMS]. Using the moments of the inverse of compound Wishart matrices, we obtain asymptotically unbiased estimators of the risk and the weights of the MV portfolio. Finally, we have some numerical results which are part of our future work.

L'utilisation des convertisseurs de puissance pour des applications de la vie quotidienne devient de plus en plus importante. Les applications technologiques actuelles demandent simultanément un haut niveau de précision et de performance, ainsi les convertisseurs DC-DC ont un rôle très important dans les systèmes nécessitant la conversion et l'adaptation du niveau d'énergie. Nous nous intéressons dans le cadre des travaux de cette thèse à une analyse des approches de modélisation et de synthèse de loi de commande permettant d'assurer la stabilité et un certain niveau de performances dans l'ensemble du domaine de fonctionnement défini par un cahier des charges tout en prenant en compte la problématique de leur application dans un environnement industriel. L'objectif de nos travaux de recherche est donc de proposer des lois de commandes dont la synthèse est fondée sur une approche formalisé {modélisation + commande} en vue d'obtenir des lois de commande adaptées au point de fonctionnement. Les principes exploités sont fondés sur la commande et l'observation par modes glissants d'une part, et sur la théorie de passivité pour la synthèse des lois de commande, complétées par un couple {observateur d'état + estimateur de charge} dont la synthèse est fondée sur l'exploitation des principes d'immersion et invariance, d'autre part. Le souci de la validation expérimentale et de l'implantation des structures de commande avec du matériel disponible industriellement a été en permanence un fil conducteur. Pour démontrer l'efficacité des méthodes proposées, leur application expérimentale a été effectuée sur un convertisseur de type SEPIC. Ce convertisseur présente plusieurs avantages par rapport à autres convertisseurs. Cependant, il reste peu exploité, en dépit de ces avantages, en raison des difficultés pour obtenir des lois commande performantes permettant la stabilisation de sa tension de sortie dans tout l'ensemble du domaine de fonctionnement.

In this thesis, the performance of four state-of-the-art feature detectors along with SIFT and SURF descriptors in matching object features of mid-wave infrared, long-wave infrared and visual-band images is evaluated across viewpoints and changing distance conditions. The utilized feature detectors are Scale Invariant Feature Transform (SIFT), multiscale Harris-Laplace, multiscale Hessian-Laplace and Speeded Up Robust Features (SURF) detectors, all of which are invariant to image scale and rotation. Features on different blackbodies, human face and vehicle images are extracted and performance of reliable matching is explored between different views of these objects each in their own category. All of these feature detectors provide good matching performance results in infrared-band images compared with visual-band images. The comparison of matching performance for mid-wave and long-wave infrared images is also explored in this study and it is observed that long-wave infrared images provide good matching performance for objects at lower temperatures, whereas mid-wave infrared-band images provide good matching performance for objects at higher temperatures. The matching performance of SURF detector and descriptor for human face images in long-wave infrared-band is found to be outperforming than other detectors and descriptors.

The Irrational Beliefs Inventory (IBI) was built to measure self-defeating beliefs as conceptualized in Rational-Emotive Behavior Therapy. The IBI has five factors: worrying, rigidity, problem avoidance, need for approval, and emotional irresponsibility. A three-phase cross-cultural study was conducted to translate and adapt the IBI from English to Icelandic, and a Confirmatory Factor Analysis (CFA) approach was used for a test of factorial validity and cross-cultural invariance. In Phase 1, the IBI was translated from English to Icelandic, using a forward-translation and back-translation. Two forward-translators and two back-translators were recruited. In Phase 2, qualitative interview methods were used in both the U.S. and Iceland to gain insights into the meaning of the items on the IBI. In the U.S., 21 university students provided insights in a group discussion, and four students were individually interviewed in depth about individual items on the IBI. In Iceland, four university students were interviewed in depth about the meaning of individual items. Three Icelandic psychology professionals were recruited to evaluate the appropriateness of the IBI for the Icelandic culture. In Phase 3, a Confirmatory Factor Analysis (CFA) was conducted to check factorial validity and cross-cultural invariance of the IBI. The total sample size in Phase 3 was N=1547, all college students, with n=827 in the U.S. and n=720 in Iceland. Overall, the CFA did not support the fit of the IBI's original five-factor model, although the fit was slightly better in the Icelandic version. Fit indices conflicted; the chi-square and comparative fit index (CFI) showed poor fit, while the RMSEA and SRMR showed acceptable fit. Correlated error was found between 85 item pairs in the U.S. model, and between 68 item pairs in the Icelandic model. Modifications were attempted to the original model by including the correlated errors, and a multigroup CFA was conducted. Adding the correlated errors slightly improved the fit of both models, but only 11 out of the IBI's 50 items were found to have equivalent item factor loadings and intercepts between the countries. Results from the psychometric analysis and qualitative interviews indicated that the IBI needs to be rewritten if the measure is to be used for research in Iceland. The results were discussed in light of a recent analysis of REBT-based measurement instruments, and implications for cross-cultural research on highly abstract constructs such as irrationality were discussed.

The Study Anxiety Inventory (SAI), consisting of the factors of worry and emotionality, was developed to measure college students' self-reported levels of anxiety while studying for an exam. Data from 2002 undergraduate students from four colleges (Arts and Sciences, Engineering, Business, and Education) at a southeastern state university were used to evaluate the validity of the scores from the 16-item Study Anxiety Inventory. Results of confirmatory factor analyses for the two factor model, conducted separately for each college, indicated marginally acceptable fit for the data (median fit measures across the four colleges: CFI =.915, SRMR=.049, RMSEA=.098), a pattern that was repeated for both males and females. Multigroup CFA was used to evaluate the factorial invariance of the SAI across gender within each college. Factor loadings (i.e., pattern coefficients) for the SAI items were not found to be significantly different between males and females (p > .05). Error variances for four items were found to be significantly different between males and females, indicating that there may be some difference in scale reliability by gender. Factor covariances were invariant for all four colleges (p > .05) and factor variances were invariant for all but the worry component for the College of Arts and Sciences where females had significantly greater variability on the worry factor. As was hypothesized, the SAI scores were positively correlated with scores on measures of test anxiety (median r=.74), trait anxiety (median r=.46), active procrastination (median r=.23), and passive procrastination (median r=.29), but negatively correlated with trait curiosity (median r=-.19). Contrary to what was hypothesized, no relationship was demonstrated between study anxiety and study skills and habits (median r=-.03). The nomological network was extended in this study by examining relationships between scores obtained from students on the SAI and measures of active and passive procrastination. This is the first study that systematically examines the factorial invariance of the SAI by gender, which is important because previous research using the SAI has shown men's scores to be consistently lower than women's scores. The results obtained in the current study provide support for gender invariance in a nonclinical population in the situation specific level of anxiety while studying. There is sufficient evidence of validity and reliability (median Cronbach alphas for males and females for the total score were .978 and .980, for worry were .968 and .973, and for emotionality were .947 and .951, respectively) that a researcher should feel confident that the SAI is a psychometrically sound research tool that holds up fairly well across a number of different types of students and that making mean comparisons on the SAI by gender is acceptable.

In the doctoral dissertation, we consider problems of testing and estimating changed segment with unknown starting position and duration of epidemic state in the autoregressive first-order model. The proposed tests are based on partial sums of model residuals and model-parameter partial-estimator polygonal line processes. We derive asymptotic results for these processes in Holder spaces. The behavior of test statistics under the null hypothesis of no change and alternative is provided. Empirical power analysis has shown that tests are more powerful when absolute values of model parameter are quite large or autoregressive process changes from a stationary state to a nonstationary one. We prove the consistency of the least square changed-segment estimators and provide their convergence rates. / Disertacijoje nagrinėjamas pirmos eilės autoregresinio modelio pasikeitusio segmento testavimo ir vertinimo uždavinys. Aprašomo modelio epideminio pasikeitimo pradžia ir ilgis nėra žinomi. Pasiūlyti kriterijai pasikeitusio segmento testavimui, kurie pagrįsti modelio paklaidų įvertinių dalinių sumų ir modelio parametro dalinių įvertinių laužčių procesais. Šiems procesams gautos ribinės teoremos Hiolderio erdvėse. Nurodomas testų statistikų ribinis elgesys esant teisingai nulinei ir alternatyviajai hipotezėms. Iš empirinio kriterijų galios tyrimo rezultatų matyti, kad pasiūlytų testų galia didžiausia aptinkant pasikeitimus iš stacionarios būklės į nestacionarią arba esant artimoms vienetui modelio parametro reikšmėms. Taip pat įrodoma, kad mažiausių kvadratų metodu gauti pasikeitusio segmento pradžios ir ilgio įverčiai bei autoregresinio modelio su pasikeitusiu segmentu parametrų įverčiai yra suderintieji bei pateikiamas jų konvergavimo greitis.