Le travail de recherche concrétisé par ce mémoire de thèse se trouve à l'intersection de deux domaines importants, la commande robuste des systèmes linéaires (LTI, LPV, en commutation) à temps discret affectés par des perturbations permanentes bornées et des contraintes et les ensembles invariants ellipsoïdaux maximal ou minimal. La première partie de ce mémoire se focalise sur l'analyse de la stabilité entrée-état (en anglais ISS) du système par rapport à une perturbation bornée et le calcul des ensembles invariants ellipsoïdaux minimal ou maximal (ou sous forme d'ellipsoïdes tronqués) satisfaisant les contraintes. La deuxième partie envisage la synthèse d'une commande par retour d'état ISS stable et robuste vis-à-vis de perturbations bornées, garantissant l'ellipsoïde invariant maximal satisfaisant les contraintes ; puis la synthèse d'une loi decommande par retour d'état et observateur ISS stable vis-à-vis de perturbations bornées, garantissant une certaine performance ; enfin la synthèse d'un paramètre de Youla afin de garantir la projection maximale sur le sous-espace de l'état initial. La projection obtenue possède alors un volume plus grand que celui obtenu sans le paramètre de Youla d'où une amélioration en termes de robustesse. Une dernière étape vise à obtenirun compromis entre la robustesse et la performance en utilisant des critères basés sur le placement de pôles ou sur la vitesse de décroissance de la fonction de Lyapunov. Tous les résultats théoriques obtenus sont exprimés sous forme d'inégalités matricielles et sont validés en simulation et de façon expérimentale dans le cadre de la commande d'un convertisseur de puissance.

Dans ce travail de thèse, on s'intéresse au problème de déplacement et de la localisation d'un robot mobile autonome dans son environnement local. La première partie du manuscrit les deux tâches de mouvement de base : c'est-à-dire, la stabilisation et le suivi de trajectoire. Deux stratégies de commande ont été traitées: le mode de glissement intégral, et la méthode dite "Immersion et Invariance". La deuxième partie porte sur l'asservissement visuel, les deux techniques 2D et 3D d'asservissement visuel ont été appliquées. Les moments d'image ont été choisis comme indices visuels car ils sont moins sensibles au bruit d'image et autres erreurs de mesure. Une nouvelle approche de l'asservissement visuel qui repose sur l'image est ici proposée. Elle est basée sur la génération de trajectoires sur le plan de l'image directement (calcul des valeurs des primitives d'image correspondantes à une trajectoire cartésienne donnée). Cette approche garantit que la robustesse et la stabilité bien connues de l'asservissement 2D ont été étendues en raison du fait que les emplacements initial et désiré de la caméra sont proches. Les trajectoires obtenues garantissent aussi que la cible reste dans le champ de vue de la caméra et que le mouvement du robot correspondant est physiquement réalisable. Des tests expérimentaux ont été effectués et des résultats satisfaisants ont été obtenus à partir des implémentations des stratégies de commande et d'asservissement visuel. Bien qu'ils soient développés et expérimentés dans le cadre spécifique d'un robot de type unicycle, ces travaux sont assez génériques pour être appliqués sur autres types de véhicules.

We consider a statistical theory as being invariant when the results of two statisticians' independent data analyses, based upon the same statistical theory and using effectively the same statistical ingredients, are the same. We discuss three aspects of invariant statistical theories. Both model checking and checking for prior-data conflict are assessments of single null hypothesis without any specific alternative hypothesis. Hence, we conduct these assessments using a measure of surprise based on a discrepancy statistic. For the discrete case, it is natural to use the probability of obtaining a data point that is less probable than the observed data. For the continuous case, the natural analog of this is not invariant under equivalent choices of discrepancies. A new method is developed to obtain an invariant assessment. This approach also allows several discrepancies to be combined into one discrepancy via a single P-value. Second, Bayesians developed many noninformative priors that are supposed to contain no information concerning the true parameter value. Any of these are data dependent or improper which can lead to a variety of difficulties. Gelman (2006) introduced the notion of the weak informativity as a comprimise between informative and noninformative priors without a precise definition. We give a precise definition of weak informativity using a measure of prior-data conflict that assesses whether or not a prior places its mass around the parameter values having relatively high likelihood. In particular, we say a prior Pi_2 is weakly informative relative to another prior Pi_1 whenever Pi_2 leads to fewer prior-data conflicts a priori than Pi_1. This leads to a precise quantitative measure of how much less informative a weakly informative prior is. In Bayesian data analysis, highest posterior density inference is a commonly used method. This approach is not invariant to the choice of dominating measure or reparametrizations. We explore properties of relative surprise inferences suggested by Evans (1997). Relative surprise inferences which compare the belief changes from a priori to a posteriori are invariant under reparametrizations. We mainly focus on the connection of relative surprise inferences to classical Bayesian decision theory as well as important optimalities.

Researchers have raised concerns about measurement equivalence in comparing personalities across cultures using personality assessments. The self-reported personality measurements often do not assess the same construct, trigger different response styles (i.e., extreme response style), or use behavioral exemplars that are inappropriate across cultures (Byrne&Watkins, 2003; Chen, 2008; Poortinga, van de Vijber,&van Hermert, 2002, van de Vijver&Leung, 1997). James et al. (2005) developed a new measurement system for aggression that is different from traditional personality assessment. It is referred to as the Conditional Reasoning Test for Aggression (CRT-A). The CRT-A is an indirect measure for assessing unconscious motives to be aggressive that was developed in the USA. It has not been studied with people from different cultures. Study 1 investigated the equivalences of the Aggression Questionnaire (AQ) and the CRT-A by administering both to groups of Americans (n=432) and Koreans (n=363). Results based on the exploratory and confirmatory factor analyses and DIF analyses showed that the AQ and CRT-A are not invariant across these cultures. Study 2 replicated LeBreton et al.(2007) study regarding faking issues of the CRT-A with the Korean population. Study 2 found that on the CRT-A, Koreans were able to identify aggressive alternatives when they were told to do so, and Korean students and employees did not score differently on the CRT-A. Implications and future directions of the study are discussed herein.

Children with mild disabilities are known to have difficulties with developing mathematical skills (Hoard, Geary, & Hamson, 1999). Yet, children with mild intellectual disabilities (MIDs) have rarely been included in rigorous scientific research. The present study has three goals. The first goal was to determine the structure of mathematics achievement in elementary aged children with MIDs and children with reading disabilities (RDs) without accompanying mathematics disabilities. The second goal was to establish the measurement stability of mathematics achievement. The third goal was to evaluate students’ response to a mathematics intervention. The participants were 265 children with MIDs and 137 children with RDs. Confirmatory factor analysis and measurement invariance evaluation was utilized to determine the structure of mathematics achievement and to ensure reliable and valid measurement of mathematics achievement between groups across three time points. The results of measurement invariance evaluation indicated that a joint model specification, characterized by two groups, both of which included children with MIDs and children with RDs who were differentiated according to intervention condition participation (not disability status), provided the best account of the underlying data structure. Further, the structure of mathematics achievement in the present sample was unidimensional, and the measurement of mathematics achievement was temporally stable between groups. Finally, latent mathematics achievement growth was evaluated. The results indicated that students in the mathematics intervention condition evidenced an advantage over those in a reading intervention condition at mid- and post-intervention evaluation, while also evidencing more growth in this conceptual domain. Instructional implications are discussed in terms of topic choice and pacing.

Let X be a real reflexive locally uniformly convex Banach space with locally uniformly convex dual space X* . Let G be a bounded open subset of X. Let T:X⊃ D(T)⇒ 2X* be maximal monotone and S: X ⇒ 2X* be bounded pseudomonotone and such that 0 notin cl((T+S)(D(T)∩partG)). Chapter 1 gives general introduction and mathematical prerequisites. In Chapter 2 we develop a homotopy invariance and uniqueness results for the degree theory constructed by Zhang and Chen for multivalued (S+) perturbations of maximal monotone operators. Chapter 3 is devoted to the construction of a new topological degree theory for the sum T+S with the degree mapping d(T+S,G,0) defined by d(T+S,G,0)=limepsilondarr 0+ dS+(T+S+ J,G,0), where dS+ is the degree for bounded (S+)-perturbations of maximal monotone operators. The uniqueness and homotopy invariance result of this degree mapping are also included herein. As applications of the theory, we give associated mapping theorems as well as degree theoretic proofs of known results by Figueiredo, Kenmochi and Le. In chapter 4, we consider T:X D(T)⇒ 2X* to be maximal monotone and S:D(S)=K⇒ 2X* at least pseudomonotone, where K is a nonempty, closed and convex subset of X with 0isinKordm. Let Phi:X⇒ ( infin, infin] be a proper, convex and lower-semicontinuous function. Let f* isin X* be fixed. New results are given concerning the solvability of perturbed variational inequalities for operators of the type T+S associated with the function f. The associated range results for nonlinear operators are also given, as well as extensions and/or improvements of known results by Kenmochi, Le, Browder, Browder and Hess, Figueiredo, Zhou, and others.

Caregivers of persons with dementia, who are often older adults, report sleep disturbance, high rates of depressive symptoms and may be at risk for impaired cognition. This dissertation examined sleep, depressive symptoms, and cognition in older adults and caregivers of persons with dementia. The aims of the review of literature were to understand, in community dwelling adults 60 years and older, the relationships among sleep parameters (sleep onset latency, wake after sleep onset, sleep efficiency, total sleep time, and general sleep complaints), and the domains of cognition (Executive Function, Attention, Episodic Memory, Working Memory, Processing Speed), and global cognition. Based on the findings, the research on the association of subjective sleep parameters and cognition is inconclusive and there is insufficient evidence to confirm or deny the existence of a relationship between objective sleep parameters and cognition. The methods section examined whether in adults 60 years and older, Radloff’s postulated 4-factor structure replicates across Afro-Caribbean Americans, African-Americans, Hispanic-Americans, and European-Americans and determine whether there is evidence for measurement invariance across the four ethnic groups in their responses to the Center for Epidemiological Depression Scale (CES-D) statements. Radloff’s postulated 4-factor model fit the data adequately and the results suggest that there is evidence for configural and partial metric invariance. The final section examined the relationships among subjective sleep parameters (Sleep Onset Latency, Wake After Sleep Onset, Total Sleep Time, Time in Bed, Sleep Efficiency, Sleep Quality), depressive symptoms, and, crystallized, fluid and total cognition in caregivers of persons with dementia with poor sleep. Based on the findings, depressive symptoms also did not mediate the ability of the sleep parameters to predict cognitive performance. With the knowledge that there are potential associations among sleep parameters, depressive symptoms and cognition in caregivers, healthcare providers should collect baseline assessments on sleep, depressive symptoms and cognition from caregivers and monitor them on an ongoing basis to identify changes and intervene in a timely manner. More research studies incorporating measures to capture sleep variability and similar cognitive measures, are needed to clarify the relationships both in older adults and caregivers of persons with dementia.

Several advancements related to the solution of 3D time-harmonic wave equations are presented, especially in the context of a parallel moving-PML sweeping preconditioner for problems without large-scale resonances. The main contribution of this dissertation is the introduction of an efficient parallel sweeping preconditioner and its subsequent application to several challenging velocity models. For instance, 3D seismic problems approaching a billion degrees of freedom have been solved in just a few minutes using several thousand processors. The setup and application costs of the sequential algorithm were also respectively refined to O(γ^2 N^(4/3)) and O(γ N log N), where N denotes the total number of degrees of freedom in the 3D volume and γ(ω) denotes the modestly frequency-dependent number of grid points per Perfectly Matched Layer discretization. Furthermore, high-performance parallel algorithms are proposed for performing multifrontal triangular solves with many right-hand sides, and a custom compression scheme is introduced which builds upon the translation invariance of free-space Green’s functions in order to justify the replacement of each dense matrix within a certain modified multifrontal method with the sum of a small number of Kronecker products. For the sake of reproducibility, every algorithm exercised within this dissertation is made available as part of the open source packages Clique and Parallel Sweeping Preconditioner (PSP). / text

Intelligence testing has had a relatively long and controversial history, beginning with what is generally considered the first formal measure of intelligence, the Binet-Simon Scales (1916). Questions regarding possible cultural bias in these measures arose virtually simultaneously (e.g. Burt, 1921; Stern, 1914). Over the course of the twentieth and early twenty-first centuries, an abundance of intelligence measures have been developed, with many of them having several revisions, but the issue of test bias remains an important one, both in the professional literature and in the popular press (Reynolds & Lowe, 2009). A current intelligence measure in use, the Differential Ability Scales, Second Edition (DAS-II, Elliott, 2007), is a test with growing popularity for assessment of children and youth, not only for its ease of use, but also for its appeal to young children and its nonverbal composite (among other things). Consequently, it is essential that there be empirical evidence supporting the use of the DAS-II as an appropriate measure of cognitive abilities for children of varying backgrounds. The test publishers conducted extensive research with a representative sample during test development in an effort to ensure that the measure met adequate reliability and validity criteria; however, the issue of test bias, particularly regarding cultural or racial/ethnic groups, was not explicitly addressed. This issue was raised and examined with the original DAS by Keith, Quirk, Schartzer, and Elliott (1999), but with the significant changes made from the first edition to the second, there is no guaranty that the evidence from the earlier would necessarily apply to the latter. The current study investigated whether the DAS-II demonstrates systematic construct bias toward children and youth of any of four ethnic groups: Black, Hispanic, Asian, and White. Multi-group confirmatory factor analysis using data from the DAS-II standardization sample was used to assess whether criteria for increasingly strict levels of invariance were met across groups. Outcomes of this research contribute to an existing body of literature on test bias, as well as provide evidence regarding cross-group construct validity in the DAS-II. Ultimately the results of this study can be used to evaluate the appropriateness of the DAS-II for clinical use with certain ethnic groups and will help to emphasize further the importance of exploring these issues with all standardized tests. / text

This thesis focuses on applications of classical tools from probability theory and convex analysis such as limit theorems to problems in theoretical computer science, specifically to pseudorandomness and learning theory. At first look, limit theorems, pseudorandomness and learning theory appear to be disparate subjects. However, as it has now become apparent, there's a strong connection between these questions through a third more abstract question: what do random objects look like. This connection is best illustrated by the study of the spectrum of Boolean functions which directly or indirectly played an important role in a plethora of results in complexity theory. The current thesis aims to take this program further by drawing on a variety of fundamental tools, both classical and new, in probability theory and analytic geometry. Our research contributions broadly fall into three categories. Probability Theory: The central limit theorem is one of the most important results in all of probability and richly studied topic. Motivated by questions in pseudorandomness and learning theory we obtain two new limit theorems or invariance principles. The proofs of these new results in probability, of interest on their own, have a computer science flavor and fall under the niche category of techniques from theoretical computer science with applications in pure mathematics. Pseudorandomness: Derandomizing natural complexity classes is a fundamental problem in complexity theory, with several applications outside complexity theory. Our work addresses such derandomization questions for natural and basic geometric concept classes such as halfspaces, polynomial threshold functions (PTFs) and polytopes. We develop a reasonably generic framework for obtaining pseudorandom generators (PRGs) from invariance principles and suitably apply the framework to old and new invariance principles to obtain the best known PRGs for these complexity classes. Learning Theory: Learning theory aims to understand what functions can be learned efficiently from examples. As developed in the seminal work of Linial, Mansour and Nisan (1994) and strengthened by several follow-up works, we now know strong connections between learning a class of functions and how sensitive to noise, as quantified by average sensitivity and noise sensitivity, the functions are. Besides their applications in learning, bounding the average and noise sensitivity has applications in hardness of approximation, voting theory, quantum computing and more. Here we address the question of bounding the sensitivity of polynomial threshold functions and intersections of halfspaces and obtain the best known results for these concept classes.