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Thesis (M.S. in Math.)--School of Mathematics, Georgia Institute of Technology, 2004. Directed by Yang Wang. / Includes bibliographical references (leaves 37-38).

Thesis (Ph. D.)--University of Hawaii at Manoa, 2005. / Includes bibliographical references (leaves 125-129). / Also available by subscription via World Wide Web / xi, 129 leaves, bound ill. 29 cm

Thesis (Ph. D.)--University of Hawaii at Manoa, 2005. / Includes bibliographical references (leaves 125-129).

L’objectif de ce travail de thèse est d’enrichir la formulation du Lancer de Faisceaux Gaussiens (LFG) et de tester sa capacité à répondre à certains des besoins actuels en calculs de propagation dans le domaine du Radar terrestre. Le LFG est envisagé comme une alternative possible aux méthodes classiques (Equation Parabolique, méthodes de rayons) en environnement complexe urbanisé, en particulier en présence d’obstacles latéraux, avec une cible située en non visibilité. La méthode de LFG "de base", qui utilise des expressions analytiques obtenues par approximation paraxiale, permet des calculs de propagation rapides en environnements complexes, sans problèmes de caustiques. Elle conduit à des résultats de précision satisfaisante dans le domaine millimétrique, par exemple pour des calculs de champs intra-bâtiments. Aux fréquences plus basses comme celles utilisées en Radar terrestre, elle est limitée par une prise en compte trop approximative des effets de diffraction et par l’élargissement spatial des faisceaux gaussiens au regard des dimensions des obstacles. La théorie des frames est utilisée dans cette thèse pour dépasser ces limites. La théorie des frames fournit un cadre rigoureux pour la décomposition initiale du champ rayonné en faisceaux gaussiens, et permet de calibrer le nombre et les directions des faisceaux à lancer. Dans ce travail de thèse, l’emploi de frames de fenêtres gaussiennes pour décomposer des distributions de champs ou de sources équivalentes est généralisé aux distributions de champs incidents sur des plans ou des portions de plans, choisis en fonction des obstacles rencontrés et des distances parcourues. Les champs rayonnés à partir de ces plans sont alors obtenus par sommation des faisceaux gaussiens lancés depuis ces frames dits de "re-décomposition". Les transformations de faisceaux gaussiens par des obstacles de taille limitée sont ainsi traitées par redécomposition : les faisceaux incidents partiellement interceptés par des surfaces limitées sont "re-décomposés" successivement sur deux frames de re-décomposition, à fenêtres "étroites" puis "larges", définis dans les plans de ces surfaces. Le frame à fenêtres "étroites" permet de traiter les discontinuités physiques, tandis que le frame à fenêtres "larges" permet de propager les champs transformés sous la forme de faisceaux "collimatés". Dans cette thèse, nous présentons une formulation de ces re-décompositions permettant une mise en œuvre numériquement efficace, grâce à des expressions analytiques approchées des coefficients de frame pour la première décomposition, et des éléments de la matrice de changement de frame pour la seconde. Cette formulation est mise en œuvre numériquement, et l’influence de différents paramètres sur la précision des re-décompositions est analysée. Finalement, l’algorithme de LFG enrichi de ces re-décompositions successives est utilisé dans un scénario simplifié proche de situations rencontrées en propagation Radar terrestre. / In this work the Gaussian Beam Shooting (GBS) algorithm is complemented with new original formulations, and the ability of this "augmented" GBS algorithm to address specific problems encountered in electromagnetic field computations for ground-based Radar applications is tested. GBS is considered as an alternative to methods (Parabolic Equation, ray based methods) currently used for such computations in complex urban environments, especially when lateral obstacles and Non-Line-Of-Sight (NLOS) targets are involved. The "basic" GBS algorithm makes use of analytical expressions obtained through paraxial approximations. It allows to perform fast computations in complex environments, without suffering from any caustics problems. Reasonably accurate results have been obtained with this method in the millimetric range, e.g. for indoor field calculations. At lower frequencies, such as used in ground Radar systems, "basic" GBS cannot model diffraction effects accurately enough, and Gaussian beam width with respect to obstacle dimensions becomes a problem after some propagation distance. Frame theory is used in this PhD to overcome these limitations. Frame theory provides a rigorous framework for the initial decomposition of radiated fields into a set of Gaussian beams, providing flexible rules to adjust the number and directions of the launched beams. In this thesis, frame theory is used to discretize not only the source field distribution but also incident field distributions over planes or parts of planes of interest, according to encountered obstacles and propagation distances. The radiated fields are then obtained by summation of Gaussian beams launched from these frames called "reexpansion frames". Gaussian beam transformations by finite sized obstacles are addressed by this re-expansion scheme : the incident beams partially impinging on limited areas are successively "re-expanded" on two re-expansion frames, the first one composed of "narrow" windows and the second one of "wide" windows, both defined in the plane containing the limited area. Spatially narrow window frames allow to take into account abrupt transitions in space, and spatially wide window frames radiate in the form of collimated Gaussian beams. The re-expansion formulation proposed in this work is designed for efficient numerical implementation. Approximate analytical expressions are established for expansion coefficients on narrow window frames, and for frame change matrix elements. This formulation has been implemented, and the influence of frame parameters on re-expansion accuracy is analyzed. Finally, the GBS algorithm augmented with successive re-expansions is used to compute fields in simplified scenarios similar to situations encountered in ground-based Radar propagation problems.

In this thesis we propose an automated process for the removal of non-precipitation echoes present in weather radar signals and accurate detection of rainfall. The process employs multifractal analysis using directional Gabor wavelets for accurate detection of the rain events. An optoelectronic joint transform correlator is proposed to provide ultra fast processing and wavelet analysis. Computer simulations of the proposed system show that the proposed algorithm is successful in the detecting rainfall accurately in radar images. The accuracy of the algorithms proposed are compared to accurate results that were generated under expert supervision. Results of the proposed system are also compared to results of QC algorithm for the ground validation software (GVS) used by TRMM ground validity Project and a previous QC algorithm. Several statistical measures computed for different reflectivity ranges show that the proposed algorithm gives accuracy as high as 98.95%, which exceed the 97.46% maximum accuracy for the GVS results. Also, the minimum error rate obtained by the proposed algorithm for different dB ranges decreases to 1.09% whereas the GVS results show a minimum error rate of 1.80%. The rain rate accumulation confirms the success of the proposed algorithm in the accurate removal of nonprecipitation echoes and a higher precision in rain accumulation estimates.

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Understanding how organisms learn perceptual categories on the basis of experience has been an important goal for researchers in a number of subdisciplines of psychology, including behavior analysis, experimental psychology, and comparative cognition. The primary aim of this thesis is to investigate how nonhumans (pigeons) and humans learn to make visual category judgments when stimuli vary quantitatively along two dimensions, particularly when accurate responding requires integration of information from both dimensions. The thesis consists of four chapters and a technical appendix. Chapter 1 is a literature review which provides a broad overview of studies on categorization by nonhumans and humans, as well as specific background for the current research. Chapters 2 and 3 constitute the empirical portion of this thesis. Four experiments are described, using a category task based on the ‘randomization’ procedure developed originally by Ashby and Gott (1988) with human participants and employed in subsequent research by Ashby, Maddox and their colleagues (see Ashby & Maddox, 2005; Maddox & Ashby, 2004, for review). Stimuli were Gabor patches that varied in frequency and orientation. Our primary goals were to determine whether pigeons could respond accurately in an information integration task with dimensionally-separable stimuli, and to compare performances of pigeons and humans. Chapter 2 reports two experiments with pigeons. Experiment 1 compared performance in two conditions which varied in terms of whether accurate performance required control by both dimensions (“information integration; II) or by a single dimension (“rule based”; RB). Results showed that pigeons learned both category tasks,with an average percentage of correct responses of 85.5% and 82% in the II and RB conditions, respectively. Although perfect performance was possible, responding for all pigeons fell short of optimality. Model comparison analyses showed that the General Linear Classifier (GLC; Ashby, 1992), which has been proposed to account for category learning in similar tasks with humans, provided a better account of responding in the II conditions, but a unidimensional model that assumed control only by frequency provided a better account of results from the RB condition. Thus results show that pigeons can respond accurately in an information integration task based on dimensionally-separable stimuli. However, analysis of residuals showed that systematic deviations of GLC predictions from the obtained data were present in both II and RB conditions. Specifically, accuracy for one category (A) was an inverted-U shaped function of orientation, whereas accuracy for the other category (B) did not vary systematically with orientation. Results from the RB condition showed evidence of an interaction between frequency and orientation, such that accuracy was higher for orientation values that were relatively low (i.e. close to horizontal) than high (i.e., close to vertical). Experiment 2 compared responding in two RB conditions which differed in terms of whether frequency or orientation was the relevant dimension. Pigeons again responded accurately in the task. Results from the frequency-relevant condition replicated the interaction obtained in Experiment 1, whereas results from the orientation-relevant condition gave no evidence of an interaction. Chapter 3 reports two experiments which compare performances of pigeons (Experiment 1) and humans (Experiment 2) in category tasks using identical stimuli. In each experiment there were two conditions, both based on the information-integration task in which the range of orientation values was wide or narrow. There were two primary goals. First, we wanted to test whether the inverted-U shaped pattern for Category A accuracy as a function of orientation would be replicated with different pigeons and stimulus values. Second, we wanted to compare responding of pigeons and humans. A secondary aim was to test whether restriction of range would affect control by orientation. Results from the condition with a wide orientation range were similar to those from Chapter 2, and showed that the inverted-U shaped pattern was replicated for both pigeons and humans. When the range of orientation values was narrow, responding for both pigeons and humans was exclusively controlled by orientation. Overall, results for pigeons and humans were similar and suggest that a common process may underlie information-integration category learning in both species. Chapter 4 provides a summary of the empirical results from Chapters 2 and 3, and shows that the inverted-U shaped pattern of accuracy for Category A as a function of orientation is unanticipated by current models for category learning, such as the GLC, prototype theory, and exemplar theory. A new ‘fuzzy prototype’ model is described which provides a good account of the results and predicts the inverted-U shaped pattern. According to the new model, subjects associate a linear segment in the stimulus space (‘fuzzy prototype’) with one of the category responses. When a stimulus is presented on a trial, subjects are assumed to use an ‘A/Not-A’ decision rule, with the probability of a Category A response determined as a function of the minimum distance of the stimulus from the fuzzy prototype. Possible directions for future research are considered. The thesis concludes with a technical appendix which describes the experimental chambers, interface hardware, and computer software developed to conduct the research,and a detailed user’s manual for the software. The system allows the same control procedure for both human and pigeon experiments, and should be useful for future research on categorization

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