This research attempt further analyzes implications of statistical correlations regarding specific relationships between the extremity-intensity variables, as defined by the social judgment instrument, and the polarity variable, as defined by the semantic differential scale.

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Ce travail porte sur la modélisation et la commande de la machine synchrone à réluctance variable, l’objectif étant de réduire les ondulations de couple. La méthodologie adoptée consiste à agir à la fois sur la structure de la machine et sur ses courants d’alimentation. Un état de l’art des techniques de réduction des ondulations de couple dans les machines électriques est d’abord dressé. Un modèle électromagnétique qui tient compte des harmoniques d’espace, basé sur l’approche par les fonctions de bobinage, est ensuite élaboré dans le but de caractériser et de quantifier les ondulations de couple. La pertinence du modèle est faite à travers la confrontation avec des résultats obtenus par calcul de champ par éléments finis. Ce modèle est alors utilisé pour l’optimisation des paramètres géométriques de la machine. Il a conduit à la définition d’un prototype de machine optimisée au sens du maximum de couple moyen et du minimum d’ondulations de couple. La deuxième partie de ce travail porte sur la commande de la machine en vue de compenser les ondulations de couple. Pour les simulations dynamiques de la machine pilotée par un onduleur de tension à commande vectorielle, le modèle élaboré demandant des temps de calcul raisonnables est utilisé sans difficulté particulière. Deux méthodes de compensation des ondulations de couple sont ensuite proposées. La première consiste à déterminer les courants qui produisent un couple constant en optimisant un autre critère tel que les pertes Joule ou le facteur de puissance. Une méthode de calcul systématique de ces courants est élaborée en utilisant les multiplicateurs de Lagrange. La deuxième méthode consiste à estimer en temps réel le couple résistant, puis à injecter un courant supplémentaire dans la boucle de régulation du couple. Les simulations numériques des deux méthodes ont donné des résultats probants. La validation expérimentale des calculs est effectuée sur un prototype de machine que nous avons calculé et réalisé. Les résultats des calculs, comparés aux mesures effectuées, sont satisfaisants. / This work deals with the modelling and control of synchronous reluctance machine in order to attenuate the torque ripple. The adopted methodology concerns both the electromagnetic structure of the machine and its feeding currents waveshapes. Firstly, a state of the art of torque ripple minimisation techniques in electrical machines is drawn up. Then, an electromagnetic model, taking into account all the space harmonics, based on winding functions approach, is proposed in order to compute the electromagnetic torque with its whole harmonic spectrum. The results of this model are compared with finite elements analysis ones and a good agreement between them is obtained. A parametric analysis of the machine is then done with the goal of maximizing the mean torque and minimizing the torque ripple. An optimal structure is then defined. The second part of this work is interested in the control in order to compensate the torque ripple. For the dynamic simulations of the vector controlled machine, the proposed model being low time consuming, is favourably and easily used. Two methods for torque ripple compensation are then proposed. The first one consists to determine the feeding currents that produce a constant torque by optimizing another criterion such as Joule losses or power factor. A systematic method of calculation of these currents is developed using Lagrange’s multipliers. In the second method the load torque is tracked and corrected by the injection of an additional current into the torque control loop. Numerical simulations of the two methods give good results. The experimental validation of the calculation is performed on a prototype machine that we have calculated and realized. The results of the calculations are favourably compared to measurements.

Master of Science / Department of Agronomy / J. Anita Dille / Variable-rate (VR) nitrogen (N) applications have the potential to improve efficiency of grain sorghum production. Field experiments were conducted in 2010 and 2011 in Stockton and Manhattan, KS. Four VR-N prescriptions were generated using various combinations of grid soil sampling data, soil electrical conductivity (EC) data, and yield maps, and were compared in the field with a uniform application based on a composite soil sample and whole field average yield goal. Soil EC data were used to create management zones that were individually soil sampled. Prescriptions were applied before planting and grain sorghum was harvested and recorded with a yield monitor in the fall. Grain sorghum yields responded to N at both sites with a higher response in 2010 due to more precipitation during the growing season. At Stockton in both years, greatest yields and returns were realized with prescription 4, a combination of management zone soil data and spatially-variable yield goal, while the smallest yields were realized with prescription 2 based on management zone soil data and field average yield goal. Prescription 5, which used grid-soil sampling and a spatially-variable yield goal, and prescription 2 resulted in the lowest returns in both years. At Manhattan in both years, greatest yields and returns were realized with prescription 3, combining a composite soil sample with spatially-variable yield goal. Prescription 5 was among the lowest returning treatments in both years. At Stockton, there was no correlation between yield and soil EC during the 2010 growing season, however there was a significant correlation between yield and shallow EC during the drier 2011 season. At Manhattan, yield was correlated to deep EC in 2010 and to shallow EC in 2011. Overall, increasing spatial intensity of data to develop the prescriptions did not necessarily result in an increased yield response to the application. Prescriptions that included a variable yield goal component tended to perform better across both sites and years.

The new outcomes based education (OBE) in the form of the Revised National Curriculum Statements (RNCS, 2002) advocates for the use of contexts in the teaching and learning of mathematics. The motivation for this advocacy is the expectation of the promotion of understanding of the subject. Such expectations however cannot be achievable without consideration of factors such as what contexts are appropriate for use in the teaching and learning of mathematics, how the contexts have to be used in order to promote understanding and more importantly how are teachers involved in this process. The study explores the ways in which a Grade 7 teacher selects contexts in the learning support materials or in any other source for use in order to promote understanding of the concept of variable among learners. It draws on socio-cultural theories and is underpinned by the notion that understanding of a concept presupposes and is presupposed by the formation of the concept. The research method employed was a case study and data was mainly collected through interviews as well as materials that were availed by the teacher. The following three key issues emerged from the study and were taken up for discussion: a) what does it take to make the transition from context to mathematics in terms of the promotion of the understanding of the concept of variable? b) to what extent were the materials selected by the teacher adequate to deal with issues of transition from context to mathematics in terms of the promotion of the understanding of the concept of variable? and c) what possibilities were available for the teacher to use context in order to promote understanding of the concept of variable? This study further explores the extent to which the notions of mathematisation and transition from context to mathematics may be used as the means by which the selection and use of contexts in the learning and teaching of the concept of variable may facilitate the promotion of understanding of the concept variable.

El objetivo principal de la presente tesis es presentar la teoría de las familias normales y mostrar su importancia en la teoría de grupos discontinuos y discretos. Primero haremos un estudio de las propiedades de las transformaciones de Moebius y luego su clasificación por conjugación. Para así introducirnos en la teoría de familias normales para funciones holomorfas y meromorfas. A partir de ello probaremos algunos resultados de normalidad para transformaciones de Moebius en especial el teorema fundamental de normalidad para transformaciones de Moebius. Finalmente veremos que un grupo Γ de transformaciones de Moebius es discontinuo en un punto α si y solo si Γ es discreto y forma una familia normal en α. / Tesis

Feature Selection is central to modern data science, from exploratory data analysis to predictive model-building. The "stability"of a feature selection algorithm refers to the robustness of its feature preferences, with respect to data sampling and to its stochastic nature. An algorithm is "unstable" if a small change in data leads to large changes in the chosen feature subset. Whilst the idea is simple, quantifying this has proven more challenging---we note numerous proposals in the literature, each with different motivation and justification. We present a rigorous statistical and axiomatic treatment for this issue. In particular, with this work we consolidate the literature and provide (1) a deeper understanding of existing work based on a small set of properties, and (2) a clearly justified statistical approach with several novel benefits. This approach serves to identify a stability measure obeying all desirable properties, and (for the first time in the literature) allowing confidence intervals and hypothesis tests on the stability of an approach, enabling rigorous comparison of feature selection algorithms.

Random Forests (RF) (Breiman 2001; Breiman and Cutler 2004) is a completely nonparametric statistical learning procedure that may be used for regression analysis and. A feature of RF that is drawing a lot of attention is the novel algorithm that is used to evaluate the relative importance of the predictor/explanatory variables. Other machine learning algorithms for regression and classification, such as support vector machines and artificial neural networks (Hastie et al. 2009), exhibit high predictive accuracy but provide little insight into predictive power of individual variables. In contrast, the permutation algorithm of RF has already established a track record for identification of important predictors (Huang et al. 2005; Cutler et al. 2007; Archer and Kimes 2008). Recently, however, some authors (Nicodemus and Shugart 2007; Strobl et al. 2007, 2008) have shown that the presence of categorical variables with many categories (Strobl et al. 2007) or high colinearity give unduly large variable importance using the standard RF permutation algorithm (Strobl et al. 2008). This work creates simulations from multiple linear regression models with small numbers of variables to understand the issues raised by Strobl et al. (2008) regarding shortcomings of the original RF variable importance algorithm and the alternatives implemented in conditional forests (Strobl et al. 2008). In addition this paper will look at the dependence of RF variable importance values on user-defined parameters.

This thesis is concerned with the problem of selection of important variables in Principal Component Analysis (PCA) in such a way that the selected subsets of variables retain, as much as possible, the overall multivariate structure of the complete data. Throughout the thesis, the criteria used in order to meet this requirement are collectively referred to as measures of Multivariate Association (MVA). Most of the currently available selection methods may lead to inappropriate subsets, while Krzanowskis (1987) M(subscript)2-Procrustes criterion successfully identifies structure-bearing variables particularly when groups are present in the data. Our major objective, however, is to utilize the idea of multivariate association to select subsets of the original variables which preserve any (unknown) multivariate structure that may be present in the data.The first part of the thesis is devoted to a study of the choice of the number of components (say, k) to be used in the variable selection process. Various methods that exist in the literature for choosing k are described, and comparative studies on these methods are reviewed. Currently available methods based exclusively on the eigenvalues of the covariance or correlation matrices, and those based on cross-validation are unsatisfactory. Hence, we propose a new technique for choosing k based on the bootstrap methodology. A full comparative study of this new technique and the cross-validatory choice of k proposed by Eastment and Krzanowski (1982) is then carried out using data simulated from Monte Carlo experiment.The remainder of the thesis focuses on variable selection in PCA using measures of MVA. Various existing selection methods are described, and comparative studies on these methods available in the literature are reviewed. New methods for selecting variables, based of measures of MVA are then proposed and compared ++ / among themselves as well as with the M(subscript)2-procrustes criterion. This comparison is based on Monte Carlo simulation, and the behaviour of the selection methods is assessed in terms of the performance of the selected variables.In summary, the Monte Carlo results suggest that the proposed bootstrap technique for choosing k generally performs better than the cross-validatory technique of Eastment and Krzanowski (1982). Similarly, the Monte Carlo comparison of the variable selection methods shows that the proposed methods are comparable with or better than Krzanowskis (1987) M(subscript)2-procrustes criterion. These conclusions are mainly based on data simulated by means of Monte Carlo experiments. However, these techniques for choosing k and the various variable selection techniques are also evaluated on some real data sets. Some comments on alternative approaches and suggestions for possible extensions conclude the thesis.

Over the last decade, 135 extrasolar planets have been discovered, the vast majority found by ongoing radial velocity searches. Of the stars sampled in these searches, 1% have `Hot Jupiter' planets associated with them. Having masses equivalent to Jupiter yet orbital periods of only a few days, this new class of planet is clearly unlike anything in our Solar System.¶ Hot Jupiters present us with an intriguing prospect. If the orientation of the planetary orbit is close to edge-on, the planet will periodically transit across the face of its star, resulting in a small drop in brightness. This transit phenomenon has been successfully used for planet detection over the last couple of years, allowing determination of the planetary radius and accurate mass estimates when coupled with radial velocity observations.¶ To aid understanding of the effect stellar environment plays on Hot Jupiter formation and survivability, this thesis presents the results of a wide-field search for transiting Hot Jupiters in the globular cluster 47 Tucanae. This cluster presents many thousands of stars in a moderate field of view and provides the perfect target for a search of this nature. One previous transit search has been made in the central core of 47 Tuc; using the HST for 8.3 continuous days, Gilliland et.al (2000) expected 17 transits yet found none. This null result suggests that either system metallicity or stellar density may be inhibiting Hot Jupiter formation or survivability in the cluster.¶ This thesis presents a search for transits with a field of view 250 times larger than the HST search and samples the uncrowded outer halo of the cluster (previously unsampled for transits), providing important constraints on the effect of environment on Hot Jupiter formation. If planets are found, then stellar density would seem responsible for the Gilliland et.al (2000) core null result. If no planets are found to a significant level, the survey would provide strong evidence that system metallicity is the dominant factor. Using the ANU 40'' (1m) telescope at Siding Spring Observatory, a 30.4 night observing run was executed and photometry was derived via differential imaging. The dataset numbers 109,000 cluster (and field) stars for photometric analysis, of which 22,000 are suitable for the transit search. With a custom-written transit detection algorithm and extensive Monte Carlo simulations to model the dataset, seven planets should be detectable if the occurrence rate of Hot Jupiters is the same in the cluster as in the Solar Neighbourhood.¶ Despite a detailed search, no transit signatures were identified. This result strongly indicates that the low metallicity of the cluster is the dominant factor inhibiting planet formation in 47 Tuc. Current results in the Solar Neighbourhood show that planet frequency is strongly biased towards stars of high metallicity. This thesis shows that the metallicity trend is likely a universal phenomenon, not only limited to the immediate Solar Neighbourhood and raises questions of whether planets were much rarer in the earlier Universe.¶ As a side result of the search, 100 variable stars were identified in the field, 69 of which are new discoveries. Subsequent analysis reveals a strong period segregation among the cluster eclipsing binaries, indicating previously unobserved dynamical effects in the cluster. Distance estimates for both 47 Tuc and the SMC are in agreement with previously published values and an independent identification of the binary period-colour relation was observed. Two binaries seem to have low-luminosity companions worthy of followup and one variable is likely a star in the early phases of planetary nebula formation. All of the results presented in this thesis have been published in three separately refereed research papers.