Doctor of Philosophy / Department of Statistics / Kun Chen and Weixin Yao / This proposal contains two projects that are related to robust mixture models. In the robust project, we propose a new robust mixture of regression models (Bai et al., 2012). The existing methods for tting mixture regression models assume a normal distribution for error and then estimate the regression param- eters by the maximum likelihood estimate (MLE). In this project, we demonstrate that the MLE, like the least squares estimate, is sensitive to outliers and heavy-tailed error distributions. We propose a robust estimation procedure and an EM-type algorithm to estimate the mixture regression models. Using a Monte Carlo simulation study, we demonstrate that the proposed new estimation method is robust and works much better than the MLE when there are outliers or the error distribution has heavy tails. In addition, the proposed robust method works comparably to the MLE when there are no outliers and the error is normal. In the second project, we propose a new robust mixture of linear mixed-effects models. The traditional mixture model with multiple linear mixed effects, assuming Gaussian distribution for random and error parts, is sensitive to outliers. We will propose a mixture of multiple linear mixed t-distributions to robustify the estimation procedure. An EM algorithm is provided to and the MLE under the assumption of t- distributions for error terms and random mixed effects. Furthermore, we propose to adaptively choose the degrees of freedom for the t-distribution using profile likelihood. In the simulation study, we demonstrate that our proposed model works comparably to the traditional estimation method when there are no outliers and the errors and random mixed effects are normally distributed, but works much better if there are outliers or the distributions of the errors and random mixed effects have heavy tails.

Doctor of Philosophy / Electrical and Computer Engineering / Sanjoy Das / Quantum circuit synthesis is one of the major areas of current research in the field of quantum computing. Analogous to its Boolean counterpart, the task involves constructing arbitrary quantum gates using only those available within a small set of universal gates that can be realized physically. However, unlike the latter, there are an infinite number of single qubit quantum gates, all of which constitute the special unitary group SU(2). Realizing any given single qubit gate using a given universal gate family is a complex task. Although gates can be synthesized to arbitrary degree of precision as long as the set of finite strings of the gate family is a dense subset of SU(2), it is desirable to accomplish the highest level of precision using only the minimum number of universal gates within the string approximation. Almost all algorithms that have been proposed for this purpose are based on the Solovay-Kitaev algorithm. The crux of the Solovay-Kitaev algorithm is the use of a procedure to decompose a given quantum gate into a pair of group commutators with the pair being synthesized separately. The Solovay-Kitaev algorithm involves group commutator decomposition in a recursive manner, with a direct approximation of a gate into a string of universal gates being performed only at the last level, i.e. in the leaf nodes of the search tree representing the execution of the Solovay-Kitaev algorithm. The main contribution of this research is in integrating conventional optimization procedures within the Solovay-Kitaev algorithm. Two specific directions of research have been studied. Firstly, optimization is incorporated within the group commutator decomposition, so that a more optimal pair of group commutators are obtained. As the degree of precision of the synthesized gate is explicitly minimized by means of this optimization procedure, the enhanced algorithm allows for more accurate quantum gates to be synthesized than what the original Solovay-Kitaev algorithm achieves. Simulation results with random gates indicate that the obtained accuracy is an order of magnitude better than before. Two versions of the new algorithm are examined, with the optimization in the first version being invoked only at the bottom level of Solovay-Kitaev algorithm and when carried out across all levels of the search tree in the next. Extensive simulations show that the second version yields better results despite equivalent computation times. Theoretical analysis of the proposed algorithm is able to provide a more formal, quantitative explanation underlying the experimentally observed phenomena. The other direction of investigation of this research involves formulating the group commutator decomposition in the form of bi-criteria optimization. This phase of research relaxed the equality constraint in the previous approach and with relaxation, a bi-criteria optimization is proposed. This optimization algorithm is new and has been devised primarily when the objective needs to be relaxed in different stages. This bi-criteria approach is able to provide comparably accurate synthesis as the previous approach.

Product line planning aims at optimal planning of product variety. In addition, the traditional product line planning problem develops new product lines based on product attributes without considering existing product lines. However, in reality, almost all new product lines evolve from existing product lines, which leads to the product line evolution problem. Product line evolution involves trade-offs between the marketing perspective and engineering perspective. The marketing concern focuses on maximizing utility for customers; the engineering concern focuses on minimizing engineering cost. Utility represents satisfaction experienced by the customers of a product. Engineering cost is the total cost involved in the process of the development of a product line. These two goals are in conflict since the high utility requires high-end product attributes which could increase the engineering cost and vice versa. Rather than aggregating both problems as one single level optimization problem, the marketing and engineering concerns entail a non-collaborative game per se. This research investigates a game-theoretic approach to the product line evolution problem. A leader-follower joint optimization model is developed to leverage conflicting goals of marketing and engineering concerns within a coherent framework of game theoretic optimization. To solve the joint optimization model efficiently, a bi-level nested genetic algorithm is developed. A case study of smart watch product line evolution is reported to illustrate the feasibility and potential of the proposed approach.

ITC/USA 2010 Conference Proceedings / The Forty-Sixth Annual International Telemetering Conference and Technical Exhibition / October 25-28, 2010 / Town and Country Resort & Convention Center, San Diego, California / Providing normal telemetry behavior predictions prior to and post launch will help to stop surprise catastrophic satellite and spacecraft equipment failures. In-orbit spacecraft fail from surprise equipment failures that can result from not having normal telemetry behavior available for comparison with actual behavior catching satellite engineers by surprise. Some surprise equipment failures lead to the total loss of the satellite or spacecraft. Some recovery actions from a surprise equipment failure increase spacecraft risk and involve decisions requiring a level of experience far beyond the responsible engineers.

Résumé: La mesure de l’équivalent en eau de la neige (EEN) sur le terrain permet de prédire la quantité d’eau libérée par la fonte de la neige. La télédétection dans les micro-ondes passives offre le potentiel d’estimer I’EEN et peut complémenter ces observations de façon synoptique pour l’ensemble du territoire. Un produit de cartographie de I’EEN couvrant l’ensemble du globe a été élaboré par le NSIDC basé sur le capteur AMSR-E. Cet instrument, lancé en 2002, a une résolution améliorée par rapport aux capteurs antérieurs. L’estimation de I’EEN se base sur la différence entre un canal peu affecté (19 GHz) et un canal affecté (37 GHz) par la diffusion de volume de la neige. La précision de ce produit a été évaluée pour la province de Québec à l’hiver 2003 et à l’hiver 2004 qui ont un EEN moyen de 170 mm. Des sous-estimations importantes ont été révélées et une certaine difficulté à détecter la présence de neige. Des modèles régionaux de régressions linéaires ont été développés pour le Québec. Des corrections pour la fraction d’eau et de forêt ont été appliquées à la combinaison T19v.37v et ont permis d’améliorer les résultats. Ces corrections sont basées sur la température de l’air du modèle GEM. Les meilleurs résultats sont pour la classe de neige taïga à l’hiver 2003 avec une erreur relative de 24 % tandis que l’erreur relative est d’environ 40 % pour la région maritime. Les erreurs élevées dans la classe taïga ont été attribuées à des couverts de neige plus épais que la capacité de pénétration des micro-ondes tandis que les erreurs de la classe maritime a des fractions forêt élevées et à la neige mouillée. La présence d’importante quantité de neige et la forêt dense de la province de Québec compliquent l’estimation de I’EEN au Québec avec un modèle de régression. || Abstract: Snow water equivalent (SWE) measurements in the field allow estimation of the quantity of released water from the melting of snow. This is useful to predict the water reserve available for production of hydro-electricity. Remote sensing with microwave can estimate SWE and complement those observations synoptically for whole territories. A SWE mapping products was developed by NSIDC based on the AMSR-E sensor launched in 2002 with an improved resolution compared to previous sensors. SWE estimation is based on difference between a channel weakly affected (19 GHz) and a channel strongly affected by volume scattering. The precision of this product was evaluated for the province of Quebec in winter 2003 and winter 2004 with a mean SWE of 170 mm. Important underestimation and some difficulty of detecting the snow was revealed. Regional linear regression models were developed for the province of Quebec. Corrections for forest and water fraction were applied on T19V-37V combination and permit to improve the results. Those corrections were based on air temperature from the GEM model. Best results were found for taiga snow class in winter 2003 with a relative error of 28% and approximately 40% for maritime snow class. High errors in the taiga region were attributed to snow depth higher than the penetration depth of the microwave and errors in the maritime region to high forest density and wet snow. The important snow amount and high density forest of the province of Quebec hampers the estimation of SWE with a regression model.

ITC/USA 2009 Conference Proceedings / The Forty-Fifth Annual International Telemetering Conference and Technical Exhibition / October 26-29, 2009 / Riviera Hotel & Convention Center, Las Vegas, Nevada / Providing normal telemetry behavior predictions prior to and post launch will help to stop surprise catastrophic satellite and spacecraft equipment failures. In-orbit spacecraft fail from surprise equipment failures that can result from not having normal telemetry behavior available for comparison with actual behavior catching satellite engineers by surprise. Some surprise equipment failures lead to the total loss of the satellite or spacecraft. Some recovery actions as a consequence of a surprise equipment failure are high risk and involve decisions requiring a level of experience far beyond the responsible engineers.

ITC/USA 2007 Conference Proceedings / The Forty-Third Annual International Telemetering Conference and Technical Exhibition / October 22-25, 2007 / Riviera Hotel & Convention Center, Las Vegas, Nevada / Robust adaptive beamforming using worst-case performance optimization is developed in recent years. It had good performance against array response errors, but it cannot reject strong interferences. In this paper, we propose a scheme for robust adaptive beamforming with broad nulls to reject strong interferences. We add a quadratic constraint to suppress the power of the array response over a spatial region of the interferences. The optimal weighting vector is then obtained by minimizing the power of the array output subject to quadratic constrains on the desired signal and interferences, respectively. We derive the formulations for the optimization problem and solve it efficiently using Newton recursive algorithm. Numerical examples are presented to compare the performances of the robust adaptive beamforming with no null constrains, sharp nulls and broad nulls. The results show its powerful ability to reject strong interferences.

Thesis (PhD (Mathematics))--University of Stellenbosch, 2010. / Contains bibliography. / ENGLISH ABSTRACT: See full text for summary. / AFRIKAANSE OPSOMMING: Sien volteks vir opsomming

Thesis (MSc)--University of Stellenbosch, 2001. / ENGLISH ABSTRACT: lP networks offer scalability and flexibility for rapid deployment of value added lP services. However, with the increased demand and explosive growth of the Internet, carriers require a network infrastructure that is dependable, predictable, and offers consistent network performance. This thesis examines the functionality, performance and implementation aspects of the MPLS mechanisms to minimize the expected packet delay in MPLS networks. Optimal path selection and the assignment of bandwidth to those paths for minimizing the average packet delay are investigated. We present an efficient flow deviation algorithm (EFDA) which assigns a small amount of flow from a set of routes connecting each OD pair to the shortest path connecting the OD pair in the network. The flow is assigned in such a way that the network average packet delay is minimized. Bellman's algorithm is used to find the shortest routes between all OD pairs. The thesis studies the problem of determining the routes between an OD pair and assigning capacities to those routes. The EFDA algorithm iteratively determines the global minimum of the objective function. We also use the optimal flows to compute the optimal link capacities in both single and multirate networks. The algorithm has been applied to several examples and to different models of networks. The results are used to evaluate the performance of the EFDA algorithm and compare the optimal solutions obtained with different starting topologies and different techniques. They all fall within a close cost-performance range. They are all within the same range from the optimal solution as well. / AFRIKAANSE OPSOMMING: lP-netwerke voorsien die skaleerbaarheid en buigsaamheid vir die vinnige ontplooing van toegevoegde-waarde lP-dienste. Die vergrote aanvraag en eksplosiewe uitbreiding van die Internet benodig betroubare, voorspelbare en bestendige netwerkprestasie. Hierdie tesis ondersoek die funksionaliteit, prestasie en implementering van die MPLS(multiprotokoletiketskakel)- meganismes om die verwagte pakketvertraging te minimeer. Ons bespreek 'n doeltreffende algoritme vir vloei-afwyking (EFDA) wat 'n klein hoeveelheid vloei toewys uit die versameling van roetes wat elke OT(oorsprong-teiken)- paar verbind aan die kortste pad wat die OT-paar koppel. Die vloei word toegewys sodanig dat die netwerk se gemiddelde pakketvertraging geminimeer word. Bellman se algoritme word gebruik om die kortste roetes tussen alle OT-pare te bepaal. Die tesis bespreek die probleem van die bepaling van roetes tussen 'n OT-paar en die toewysing van kapasiteite aan sulke roetes. Die EFDA-algoritme bepaal die globale minimum iteratief. Ons gebruik ook optimale vloeie vir die berekening van die optimale skakelkapasiteite in beide enkel- en multikoers netwerke. Die algoritme is toegepas op verskeie voorbeelde en op verskillende netwerkmodelle. Die skakelkapasiteite word aangewend om die prestasie van die EFDAalgoritme te evalueer en dit te vergelyk met die optimale oplossings verkry met verskillende aanvangstopologieë en tegnieke. Die resultate val binne klein koste-prestasie perke wat ook na aan die optimale oplossing lê.

International Telemetering Conference Proceedings / October 25-28, 1999 / Riviera Hotel and Convention Center, Las Vegas, Nevada / Gaussian Minimum Shift Keying (GMSK) is a form of Continuous Phase Modulation (CPM) whose spectral occupancy can be easily tailored to the available channel bandwidth by a suitable choice of signal parameters. The constant envelope of the GMSK signal enables it to corporate with saturated power amplifier without the spectral re-growth problem. This paper provides a quantitative synopsis of binary GMSK signals in terms of their bandwidth occupancy and coherent demodulation performance. A detailed account of how to demodulate such signals using the Viterbi Algorithm (VA) is given, along with analytical power spectral density (PSD) and computer simulated bit-error-rate (BER) results for various signal BT products. The effect of adjacent channel interference (ACI) is also quantified. Ideal synchronization for both symbol time and carrier phase is assumed.