Thesis (M.Com. (Economics))--North-West University, Vaal Triangle Campus, 2006.

Thesis (M.Com. (Economics))--North-West University, Vaal Triangle Campus, 2006.

The focus of this thesis is on numerical algorithms for efficient solution of QTL analysis problem in genetics. Firstly, we consider QTL mapping problems where a standard least-squares model is used for computing the model fit. We develop optimization methods for the local problems in a hybrid global-local optimization scheme for determining the optimal set of QTL locations. Here, the local problems have constant bound constraints and may be non-convex and/or flat in one or more directions. We propose an enhanced quasi-Newton method and also implement several schemes for constrained optimization. The algorithms are adopted to the QTL optimization problems. We show that it is possible to use the new schemes to solve problems with up to 6 QTLs efficiently and accurately, and that the work is reduced with up to two orders magnitude compared to using only global optimization. Secondly, we study numerical methods for QTL mapping where variance component estimation and a REML model is used. This results in a non-linear optimization problem for computing the model fit in each set of QTL locations. Here, we compare different optimization schemes and adopt them for the specifics of the problem. The results show that our version of the active set method is efficient and robust, which is not the case for methods used earlier. We also study the matrix operations performed inside the optimization loop, and develop more efficient algorithms for the REML computations. We develop a scheme for reducing the number of objective function evaluations, and we accelerate the computations of the derivatives of the log-likelihood by introducing an efficient scheme for computing the inverse of the variance-covariance matrix and other components of the derivatives of the log-likelihood.

It is well known that communication systems employing multiple transmit and multiple receive antennas provide high data rates along with increased reliability. Some of the design criteria of the space-time block codes (STBCs) for multiple input multiple output (MIMO)communication system are that these codes should attain large transmit diversity, high data-rate, low decoding-complexity, low decoding –delay and low peak-to-average power ratio (PAPR). STBCs based on real orthogonal designs (RODs) and complex orthogonal designs (CODs) achieve full transmit diversity and in addition, these codes are single-symbol maximum-likelihood (ML) decodable. It has been observed that the data-rate (in number of information symbols per channel use) of the square CODs falls exponentially with increase in number of antennas and it has led to the construction of rectangular CODs with high rate. We have constructed a class of maximal-rate CODs for n transmit antennas with rate if n is even and if n is odd. The novelty of the above construction is that they 2n+1 are constructed from square CODs. Though these codes have a high rate, this is achieved at the expense of large decoding delay especially when the number of antennas is 5or more. Moreover the rate also converges to half as the number of transmit antennas increases. We give a construction of rate-1/2 CODs with a substantial reduction in decoding delay when compared with the maximal- rate codes. Though there is a significant improvement in the rate of the codes mentioned above when compared with square CODs for the same number of antennas, the decoding delay of these codes is still considerably high. For certain applications, it is desirable to construct codes which are balanced with respect to both rate and decoding delay. To this end, we have constructed high rate and low decoding-delay RODs and CODs from Cayley-Dickson Algebra. Apart from the rate and decoding delay of orthogonal designs, peak-to-average power ratio (PAPR) of STBC is very important from implementation point of view. The standard constructions of square complex orthogonal designs contain a large number of zeros in the matrix result in gin high PAPR. We have given a construction for square complex orthogonal designs with lesser number of zero entries than the known constructions. When a + 1 is a power of 2, we get codes with no zero entries. Further more, we get complex orthogonal designs with no zero entry for any power of 2 antennas by introducing co- ordinate interleaved variables in the design matrix. These codes have significant advantage over the existing codes in term of PAPR. The only sacrifice that is made in the construction of these codes is that the signaling complexity (of these codes) is marginally greater than the existing codes (with zero entries) for some of the entries in the matrix consist of co-ordinate interleaved variables. Also a class of maximal-rate CODs (For mathematical equations pl see the pdf file)

Fatigue cracking is one of the most common distresses of asphalt pavements, whereas healing is a counter process to cracking which alleviates cracking damage and extends fatigue life of asphalt pavements. Most of existing methods to characterize fatigue cracking and healing are generally empirical or phenomenological in nature, which does not satisfy the need to develop mechanistic-based pavement design methods. The objective of this study is to characterize fatigue cracking and healing of asphalt mixtures using an energy-based mechanistic approach. A controlled-strain repeated direct tension (RDT) test is selected to generate both fatigue cracking and permanent deformation in an asphalt mixture specimen. Fatigue cracking is separated from permanent deformation from a mechanical viewpoint. The development of fatigue cracking is described by the evolution of the damage density and the increase of the average crack size with the increase of loading cycles. A creep and step-loading recovery (CSR) test is designed to measure the internal stress in the recovery phase of an asphalt mixture specimen. The internal stress and the strain measured in the recovery phase are used to conduct the mechanistic analysis of recovery and healing of the asphalt mixture specimen. Then healing is described using the decrease of the damage density and average crack size with time. Different types of asphalt mixtures produce distinctly different fatigue cracking and healing characteristics. The effect of mixture composition, temperature, and aging are evaluated using the approach above. The entire series of tests for fatigue, permanent deformation and healing can be completed in one day, with the healing part requiring only a matter of minutes. The methods proposed in this study characterize fatigue cracking and healing of asphalt mixtures using its essential cause and effect relationship.

The present work was initiated to investigate the surface- and interfacial phenomena for iron and slag/iron systems. The aim was to understand the mechanism of the effect of surface active elements on surface and interfacial properties. In the present work, the adsorption of oxygen and sulfur on iron surface as well as adatom surface movements were studied based on the ab initio method. BCC iron melting phenomena and sulfur diffusion in molten iron were investigated by Monte Carlo simulations. The impact of oxygen potential on interfacial mass transfer was carried out by X-ray sessile drop method. Firstly, the structural, electronic and magnetic properties as well as thermodynamic stability were studied by Density functional theory (DFT). The hollow site was found to be the most stable adsorption site both for oxygen and sulfur adsorbed on iron (100) surface, which is in agreement with the experiment. The relaxation geometries and difference charge density of the different adsorption systems were calculated to analyze the interaction and bonding properties between Fe and O/S. It can be found that the charge redistribution was related to the geometry relaxation. In addition, the sulfur coverage is considered from a quarter of one monolayer (1ML) to a full monolayer. It was found that the work function and its change Δφ increased with S coverage, in very good agreement with experiment. Due to a recent discussion regarding the influence of charge transfer on Δφ, it is shown in the present work that the increase in Δφ can be explained by the increasing surface dipole moment as a function of S coverage. S strongly interacts with the surface Fe layer and decreases the surface magnetic moment as the S coverage increases. Secondly, a two dimensional (2D) gas model based on density functional calculations combined with thermodynamics and statistical physics, was proposed to simulate the movement of the surface active elements, viz. oxygen and sulfur atoms on the Fe(100) surface. The average velocity of oxygen and sulfur atoms was found to be related to the vibration frequencies and energy barrier in the final expression developed. The calculated results were based on the density function and thermodynamics & statistical physics theories. In addition, this 2D gas model can be used to simulate and give an atomic view of the complex interfacial phenomena in the steelmaking refining process. A distance dependent atomistic Monte Carlo model was developed for studying the iron melting phenomenon as well as effect of sulfur on molten iron surface. The effect of boundary conditions on the melting process of an ensemble of bcc iron atoms has been investigated using a Lennard-Jones distance dependent pair potential. The stability of melting process was energetically and spatially analyzed under fixed wall and free surface conditions and the effects of short and long-range interactions were discussed. The role of boundary conditions was significantly reduced when long-range interactions were used in the simulation. This model was further developed for investigating the effect of sulfur on molten iron surface. A combination of fixed wall and free surface boundary condition was found to well-represent the molten bath configuration while considering the second nearest neighbor interactions. Calculations concerning the diffusion of sulfur on molten surface were carried out as a function of temperature and sulfur concentration. Our results show that sulfur atoms tended to diffuse away from the surface into the liquid bulk and the diffusion rate increased by increasing temperature. Finally, impact of oxygen potential on sulfur mass transfer at slag/metal interface, was carried out by X-ray sessile drop method. The movement of sulfur at the slag/metal interface was monitored in dynamic mode at temperature 1873 K under non-equilibrium conditions. The experiments were carried out with pure iron and CaO-SiO2-Al2O3-FeO slag (alumina saturated at the experimental temperature) contained in alumina crucibles with well-controlled partial pressures of oxygen and sulfur. As the partial pressure of oxygen increased, it was found that interfacial velocity as well as the oscillation amplitude increased. The thermo-physical and thermo-chemical properties of slag were also found to influence interfacial velocity. / QC 20101123

Actualment estem entrant a una nova era de la informació amb gran demanda de sistemes de comunicació sense fils. Nous serveis com dades i video requereixen transmissions fiables d'alta velocitat, fins i tot en escenaris d'alta mobilitat. A més a més, la dificultat d'assignar el limitat espectre radioelèctric juntament amb la necessitat d'incrementar el temps de vida de les bateries dels terminals mòbils, requereix el diseny de transceptors que usin la potència i l'ampla de banda disponibles de manera eficient. Les comunicacions multiportadora basades en OFDM són capaces de satisfer la majoria d'aquests requeriments. Però, entre altres reptes, reduir la sensibilitat a la amplificació no-lineal és un factor clau durant el diseny. En aquesta tesi doctoral s'analitza la sensibilitat dels sistemes multiportadora basats en OFDM a l'amplificació no-lineal i es consideren formes eficients per superar aquest problema. La tesi s'enfoca principalment al problema de reduir les fluctuacions de l'envolupant del senyal transmès. En aquest sentit es presenta també un estudi de les mètriques de l'envolupant del senyal, PAPR i CM. A més a més, basant-nos en l'anàlisis presentat es proposen noves tècniques per sistemes OFDM i MC-SS. Per MC-SS, també es tracta el diseny d'una tècnica de postprocessament en forma de detector multiusuari per canals no-lineals. / Actualmente estamos entrando en una nueva era de la información donde se da una gran demanda de sistemas de comunicación inalámbricos. Nuevos servicios como datos y vídeo requieren transmisiones fiables de alta velocidad, incluso en escenarios de alta movilidad. Además, la dificultad de asignar el limitado espectro radioeléctrico junto con la necesidad de incrementar el tiempo de vida de las baterías de los terminales móviles, requiere el diseño de transceptores que usen eficientemente la potencia y el ancho de banda disponibles. Las comunicaciones multiportadora basadas en OFDM son capaces de satisfacer la mayoría de dichos requerimientos. Sin embargo, entre otros retos, reducir su sensibilidad a la amplificación no-lineal es un factor clave durante el diseño. En esta tesis se analiza la sensibilidad de los sistemas multiportadora basados en OFDM a la amplificación no-lineal y se consideran formas eficientes para superar dicho problema. La tesis se enfoca principalmente al problema de reducir las fluctuaciones de la envolvente. En este sentido también se presenta un estudio de las métricas de la señal, PAPR y CM. Además, basándonos en el análisis presentado se proponen nuevas técnicas para OFDM y MC-SS. Para MC-SS, también se trata el diseño de un detector multiusuario para canales no-lineales. / We are now facing a new information age with high demand of wireless communication systems. New services such as data and video require achieving reliable high-speed transmissions even in high mobility scenarios. Moreover, the difficulty to allocate so many wireless communication systems in the limited frequency band in addition to the demand for long battery life requires designing spectrum and power efficient transceivers. Multicarrier communications based on OFDM are known to fulfill most of the requirements of such systems. However, among other challenges, reducing the sensitivity to nonlinear amplification has become a design key. In this thesis the sensitivity of OFDM-based multicarrier systems to nonlinear amplification is analyzed and efficient ways to overcome this problem are considered. The focus is mainly on the problem of reducing the envelope fluctuations. Therefore, a study of the signal metrics, namely PAPR and CM, is also presented. From the presented analysis, several new techniques for OFDM and MC-SS are proposed. For MC-SS, the design of a post-processing technique in the form of a multiuser detector for nonlinearly distorted MC-SS symbols is also addressed.

Aquesta tesi està dedicada al disseny i a l'anàlisi d'estructures de dades multidimensionals, és a dir, estructures de dades que serveixen per emmagatzemar registres $K$-dimensionals que solen representar-se com a punts en l'espai $[0,1]^K$. Aquestes estructures tenen aplicacions en diverses àrees de la informàtica com poden ser els sistemes d'informació geogràfica, la robòtica, el processament d'imatges, la world wide web, el data mining, entre d'altres. Les estructures de dades multidimensionals també es poden utilitzar com a indexos d'estructures de dades que emmagatzemen, possiblement en memòria externa, dades més complexes que els punts.Les estructures de dades multidimensionals han d'oferir la possibilitat de realitzar operacions d'inserció i esborrat de claus dinàmicament, a més de permetre realitzar cerques anomenades associatives. Exemples d'aquest tipus de cerques són les cerques per rangs ortogonals (quins punts cauen dintre d'un hiper-rectangle donat?) i les cerques del veí més proper (quin és el punt més proper a un punt donat?).Podem dividir les contribucions d'aquesta tesi en dues parts: La primera part està relacionada amb el disseny d'estructures de dades per a punts multidimensionals. Inclou el disseny d'arbres binaris $K$-dimensionals al·leatoritzats (Randomized $K$-d trees), el d'arbres quaternaris al·leatoritzats (Randomized quad trees) i el d'arbres multidimensionals amb punters de referència (Fingered multidimensional trees).La segona part analitza el comportament de les estructures de dades multidimensionals. En particular, s'analitza el cost mitjà de les cerques parcials en arbres $K$-dimensionals relaxats, i el de les cerques per rang en diverses estructures de dades multidimensionals. Respecte al disseny d'estructures de dades multidimensionals, proposem algorismes al·leatoritzats d'inserció i esborrat de registres per als arbres $K$-dimensionals i per als arbres quaternaris. Aquests algorismes produeixen arbres aleatoris, independentment de l'ordre d'inserció dels registres i desprès de qualsevol seqüència d'insercions i esborrats. De fet, el comportament esperat de les estructures produïdes mitjançant els algorismes al·leatoritzats és independent de la distribució de les dades d'entrada, tot i conservant la simplicitat i la flexibilitat dels arbres $K$-dimensionals i quaternaris estàndard. Introduïm també els arbres multidimensionals amb punters de referència. Això permet que les estructures multidimensionals puguin aprofitar l'anomenada localitat de referència en cerques associatives altament correlacionades.I respecte de l'anàlisi d'estructures de dades multidimensionals, primer analitzem el cost esperat de las cerques parcials en els arbres $K$-dimensionals relaxats. Seguidament utilitzem aquest resultat com a base per a l'anàlisi de les cerques per rangs ortogonals, juntament amb arguments combinatoris i geomètrics. D'aquesta manera obtenim un estimat asimptòtic precís del cost de les cerques per rangs ortogonals en els arbres $K$-dimensionals aleatoris. Finalment, mostrem que les tècniques utilitzades es poden estendre fàcilment a d'altres estructures de dades i per tant proporcionem una anàlisi exacta del cost mitjà de cerques per rang en estructures de dades com són els arbres $K$-dimensionals estàndard, els arbres quaternaris, els tries quaternaris i els tries $K$-dimensionals. / Esta tesis está dedicada al diseño y al análisis de estructuras de datos multidimensionales; es decir, estructuras de datos específicas para almacenar registros $K$-dimensionales que suelen representarse como puntos en el espacio $[0,1]^K$. Estas estructuras de datos tienen aplicaciones en diversas áreas de la informática como son: los sistemas de información geográfica, la robótica, el procesamiento de imágenes, la world wide web o data mining, entre otras.Las estructuras de datos multidimensionales suelen utilizarse también como índices de estructuras que almacenan, posiblemente en memoria externa, datos complejos.Las estructuras de datos multidimensionales deben ofrecer la posibilidad de realizar operaciones de inserción y borrado de llaves de manera dinámica, pero además deben permitir realizar búsquedas asociativas en los registros almacenados. Ejemplos de búsquedas asociativas son las búsquedas por rangos ortogonales (¿qué puntos de la estructura de datos están dentro de un hiper-rectángulo dado?) y las búsquedas del vecino más cercano (¿cuál es el punto de la estructura de datos más cercano a un punto dado?).Las contribuciones de esta tesis se dividen en dos partes:La primera parte está dedicada al diseño de estructuras de datos para puntos multidimensionales, que incluye el diseño de los árboles binarios $K$-dimensionales aleatorios (Randomized $K$-d trees), el de los árboles cuaternarios aleatorios (Randomized quad trees), y el de los árboles multidimensionales con punteros de referencia (Fingered multidimensional trees).La segunda parte contiene contribuciones al análisis del comportamiento de las estructuras de datos para puntos multidimensionales. En particular, damos el análisis del costo promedio de las búsquedas parciales en los árboles $K$-dimensionales relajados y el de las búsquedas por rango en varias estructuras de datos multidimensionales.Con respecto al diseño de estructuras de datos multidimensionales, proponemos algoritmos aleatorios de inserción y borrado de registros para los árboles $K$-dimensionales y los árboles cuaternarios que producen árboles aleatorios independientemente del orden de inserción de los registros y después de cualquier secuencia de inserciones y borrados intercalados. De hecho, con la aleatorización garantizamos un buen rendimiento esperado de las estructuras de datos resultantes, que es independiente de la distribución de los datos de entrada, conservando la flexibilidad y la simplicidad de los árboles $K$-dimensionales y de los árboles cuaternarios estándar. También proponemos los árboles multidimensionales con punteros de referencia, una técnica que permite que las estructuras de datos multidimensionales exploten la localidad de referencia en búsquedas asociativas que se presentan altamente correlacionadas.Con respecto al análisis de estructuras de datos multidimensionales, comenzamos dando un análisis preciso del costo esperado de las búsquedas parciales en los árboles $K$-dimensionales relajados. A continuación, utilizamos este resultado como base para el análisis de las búsquedas por rangos ortogonales, combinándolo con argumentos combinatorios y geométricos. Como resultado obtenemos un estimado asintótico preciso del costo de las búsquedas por rango en los árboles $K$-dimensionales relajados. Finalmente, mostramos que las técnicas utilizadas pueden extenderse fácilmente a otras estructuras de datos y por tanto proporcionamos un análisis preciso del costo promedio de búsquedas por rango en estructuras de datos como los árboles $K$-dimensionales estándar, los árboles cuaternarios, los tries cuaternarios y los tries $K$-dimensionales. / This thesis is about the design and analysis of point multidimensional data structures: data structures that store $K$-dimensional keys which we may abstract as points in $[0,1]^K$. These data structures are present in many applications of geographical information systems, image processing or robotics, among others. They are also frequently used as indexes of more complex data structures, possibly stored in external memory.Point multidimensional data structures must have capabilities such as insertion, deletion and (exact) search of items, but in addition they must support the so called {em associative queries}. Examples of these queries are orthogonal range queries (which are the items that fall inside a given hyper-rectangle?) and nearest neighbour queries (which is the closest item to some given point?).The contributions of this thesis are two-fold:Contributions to the design of point multidimensional data structures: the design of randomized $K$-d trees, the design of randomized quad trees and the design of fingered multidimensional search trees;Contributions to the analysis of the performance of point multidimensional data structures: the average-case analysis of partial match queries in relaxed $K$-d trees and the average-case analysis of orthogonal range queries in various multidimensional data structures.Concerning the design of randomized point multidimensional data structures, we propose randomized insertion and deletion algorithms for $K$-d trees and quad trees that produce random $K$-d trees and quad trees independently of the order in which items are inserted into them and after any sequence of interleaved insertions and deletions. The use of randomization provides expected performance guarantees, irrespective of any assumption on the data distribution, while retaining the simplicity and flexibility of standard $K$-d trees and quad trees.Also related to the design of point multidimensional data structures is the proposal of fingered multidimensional search trees, a new technique that enhances point multidimensional data structures to exploit locality of reference in associative queries.With regards to performance analysis, we start by giving a precise analysis of the cost of partial matches in randomized $K$-d trees. We use these results as a building block in our analysis of orthogonal range queries, together with combinatorial and geometric arguments and we provide a tight asymptotic estimate of the cost of orthogonal range search in randomized $K$-d trees. We finally show that the techniques used apply easily to other data structures, so we can provide an analysis of the average cost of orthogonal range search in other data structures such as standard $K$-d trees, quad trees, quad tries, and $K$-d tries.

The interest in the development of wireless high-speed data services is in response to the strong market demand for high-speed wireless Internet access. Current standards aim at delivering a peak data rate greater than 2Mbps on the forward link. Since data services and voice services are fundamentally different, new concepts were introduced in the design of the forward data channel. In addition, methods of evaluating the performance of a cellular CDMA system have to be revisited. This thesis proposes a method which can be used to find the forward link peak and average data rates, throughput and coverage of a cellular CDMA system which is capable of delivering high-speed wireless data. A summary of changes in design philosophy and recent advances in technologies which enable high-speed wireless data delivery are presented. The proposed method takes into account major aspects commonly found in the forward data channel and applies the generalized Shannon capacity formula for multi-element antenna (MEA) systems. The analysis focuses on the physical layer and is flexible enough to be adapted to various propagation environments, antenna configurations, multicode allocations, user distributions and cell site configurations. Sample numerical results for various multicode allocations are shown using a system model with two-tier interfering cells with one transmit antenna and two receive antennas operating under a frequency selective slow fading channel with propagation environment described by the Recommendation ITU-R M. 1225 indoor office, outdoor to indoor and pedestrian and vehicular test environments. Different transmit / receive antenna configurations and multicode allocations and their impact on the average data rate is also explored.

The interest in the development of wireless high-speed data services is in response to the strong market demand for high-speed wireless Internet access. Current standards aim at delivering a peak data rate greater than 2Mbps on the forward link. Since data services and voice services are fundamentally different, new concepts were introduced in the design of the forward data channel. In addition, methods of evaluating the performance of a cellular CDMA system have to be revisited. This thesis proposes a method which can be used to find the forward link peak and average data rates, throughput and coverage of a cellular CDMA system which is capable of delivering high-speed wireless data. A summary of changes in design philosophy and recent advances in technologies which enable high-speed wireless data delivery are presented. The proposed method takes into account major aspects commonly found in the forward data channel and applies the generalized Shannon capacity formula for multi-element antenna (MEA) systems. The analysis focuses on the physical layer and is flexible enough to be adapted to various propagation environments, antenna configurations, multicode allocations, user distributions and cell site configurations. Sample numerical results for various multicode allocations are shown using a system model with two-tier interfering cells with one transmit antenna and two receive antennas operating under a frequency selective slow fading channel with propagation environment described by the Recommendation ITU-R M. 1225 indoor office, outdoor to indoor and pedestrian and vehicular test environments. Different transmit / receive antenna configurations and multicode allocations and their impact on the average data rate is also explored.