Die doel van hierdie verhandeling is om 'n algoritme vir kleinstekwadrate-benaderings te vind en om met behulp van die algoritme 'n rekenaarprogram te ontwikkel vir die minimering van die kleinstekwadrate- benadering en die passings van krommes deur gegewe eksperimentele data. Eerstens word die norm en die pseudo-inverse van matrikse sowel as Householder-transformasies bespreek, aangesien ons daarvan gebruik maak in die oplossing van ons probleem. In die lineere kleinstekwadrate-probleem word die koeffisiente matriks A ontbind in 'n produk van 'n ortogonale en 'n bo-driehoeksmatriks. Hierdie produk word dan gebruik om die pseudo-inverse van A te verkry. Die algoritme wat ontwikkel is vir die nie-lineere kleinstekwadrate- probleem is gebaseer op die Gauss-Newton-Marquardt-metode, waar met elke stap 'n lineere kleinstekwadrate-probleem opgelos word. Resultate wat met behulp van die algoritme verkry is, word ook vergelyk met die resultate van ander algoritmes. / Dissertation (MSc)--University of Pretoria, 1977. / gm2014 / Mathematics and Applied Mathematics / Unrestricted

Thesis (PhD (Logistics))--University of Stellenbosch, 2007. / In this dissertation original algorithms are introduced to solve separable resource allocation problems (RAPs) with increasing nonlinear functions in the objective function, and lower and upper bounds on each variable. Algorithms are introduced in three special cases. The first case arises when the objective function of the RAP consists of the sum of convex functions and all the variables for these functions range over the same interval. In the second case RAPs with the sum of convex functions in the objective function are considered, but the variables of these functions can range over different intervals. In the last special case RAPs with an objective function comprising the sum of convex and concave functions are considered. In this case the intervals of the variables can range over different values. In the first case two new algorithms, namely the fraction and the slope algorithm are presented to solve the RAPs adhering to the conditions of the case. Both these algorithms yield far better solution times than the existing branch and bound algorithm. A new heuristic and three new algorithms are presented to solve RAPs falling into the second case. The iso-bound heuristic yields, on average, good solutions relative to the optimal objective function value in faster times than exact algorithms. The three algorithms, namely the iso-bound algorithm, the branch and cut algorithm and the iso-bound branch and cut algorithm also yield considerably beter solution times than the existing branch and bound algorithm. It is shown that, on average, the iso-bound branch and cut algorithm yields the fastest solution times, followed by the iso-bound algorithm and then by die branch and cut algorithm. In the third case the necessary and sufficient conditions for optimality are considered. From this, the conclusion is drawn that search techniques for points complying with the necessary conditions will take too long relative to branch and bound techniques. Thus three new algorithms, namely the KL, SKL and IKL algorithms are introduced to solve RAPs falling into this case. These algorithms are generalisations of the branch and bound, branch and cut, and iso-bound algorithms respectively. The KL algorithm was then used as a benchmark. Only the IKL algorithm yields a considerable improvement on the KL algorithm.

Disputats, Göteborg : Chalmers Tekniska Högskola ; Göteborgs universitet, 2008. / Findes også på internet. Med litteraturhenvisninger.

Aquesta tesi presenta un nou mètode pel disseny invers de reflectors. Ens hem centrat en tres temes principals: l’ús de fonts de llum reals i complexes, la definició d’un algoritme ràpid pel càlcul de la il•luminació del reflector, i la definició d’un algoritme d’optimització per trobar més eficientment el reflector desitjat. Les fonts de llum estan representades per models near-field, que es comprimeixen amb un error molt petit, fins i tot per fonts de llum amb milions de raigs i objectes a il•luminar molt propers. Llavors proposem un mètode ràpid per obtenir la distribució de la il•luminació d’un reflector i la seva comparació amb la il•luminació desitjada, i que treballa completament en la GPU. Finalment, proposem un nou mètode d’optimització global que permet trobar la solució en menys passos que molts altres mètodes d’optimització clàssics, i alhora evitant mínims locals. / This thesis presents new methods for the inverse reflector design problem. We have focused on three main topics: the use of real and complex light sources, the definition of a fast lighting simulation algorithm to compute the reflector lighting, and the definition of an optimization algorithm to more efficiently find the desired reflector. The light sources are represented by near-field datasets, that are compressed with a low error, even with millions of rays and for very close objects. Then, we propose a fast method to obtain the outgoing light distribution of a reflector and the comparison with the desired one, working completely in the GPU. Finally, a new global optimization method is proposed to search the solution in less steps than most other classic optimization methods, also avoiding local minima.

The maintenance schedule of generators in power plants needs to match the electricity demand and needs to ensure the reliability of the power plant at a minimum cost of operation. In this study, a comparison is made between the modified generator maintenance scheduling model and the classic generator maintenance scheduling model using the reliability objective functions. Both models are applied to a 21-unit test system, and the results show that the modified generator maintenance scheduling model gives better and more reliable solutions than the regular generator maintenance scheduling model. The better results of the modified generator maintenance scheduling model are due the modified and additional constraints in the modified generator maintenance scheduling model. Due to the reliable results of the modified generator maintenance scheduling model, a robust model is formulated using the economic cost objective function. The model includes modified crew and maintenance window constraints, with some additional constraints such as the relationship constraints among the variables. To illustrate the robustness of the formulated GMS model, the maintenance of the Arnot power plant in South Africa is scheduled with open-loop and closed-loop controllers. Both controllers satisfy all the constraints but the closed-loop results are better than the open-loop results. AFRIKAANS : Die onderhoudskedule vir kragopwekkers (OSK) in kragstasies moet kan voorsien in die vraag na elektrisiteit en moet die betroubaarheid van die kragstasie teen ’n minimum operasiekoste verseker. In hierdie studie word die betroubaarheidsdoelwitfunksie gebruik om ’n gewysigde onderhoudskeduleringsmodel vir kragopwekkers te vergelyk met die konvensionele onderhoudskeduleringsmodel. Beide modelle word toegepas op 'n 21-eenheid-toetsstelsel, en die resultate toon dat die gewysigde model ’n beter en meer betroubare oplossing bied as die konvensionele model. Die beter resultate van die gewysigde model is die gevolg van die gewysigde en bykomende beperkings in die gewysigde model. As gevolg van die betroubare resultate van die gewysigde onderhoudskeduleringsmodel word die koste-ekonomie-doelwitfunksie gebruik om ’n robuuste model te formuleer. Die model sluit gewysigde bemanning- en onderhoudvensterbeperkings in, met ’n paar bykomende beperkings soos die verhoudingsbeperkings tussen die veranderlikes. Om die robuustheid van die geformuleerde OSK-model te illustreer word die instandhouding van die Arnot kragstasie in Suid-Afrika geskeduleer met oop- en geslotelus-beheerders. Beide beheerders voldoen aan al die beperkinge, maar die geslotelusresultate is beter as die ooplusresultate. / Dissertation (MSc)--University of Pretoria, 2011. / Electrical, Electronic and Computer Engineering / Unrestricted

Text in Afrikaans / Die doel van hierdie studie was om te bepaal tot watter mate ’n suiwer patroongebaseerde benadering tot woordafbreking bevredigende resultate lewer. Die masjienleertegnieke kunsmatige neurale netwerke, beslissingsbome en die TEX-algoritme is ondersoek aangesien dit met letterpatrone uit woordelyste afgerig kan word om lettergreep- en saamgesteldewoordverdeling te doen. ’n Leksikon van Afrikaanse woorde is uit ’n korpus van elektroniese teks genereer. Om lyste vir lettergreep- en saamgesteldewoordverdeling te kry, is woorde in die leksikon in lettergrepe verdeel en saamgestelde woorde is in hul samestellende dele verdeel. Uit elkeen van hierdie lyste van ±183 000 woorde is ±10 000 woorde as toetsdata gereserveer terwyl die res as afrigtingsdata gebruik is. ’n Rekursiewe algoritme is vir saamgesteldewoordverdeling ontwikkel. In hierdie algoritme word alle ooreenstemmende woorde uit ’n verwysingslys (die leksikon) onttrek deur stringpassing van die begin en einde van woorde af. Verdelingspunte word dan op grond van woordlengte uit die samestelling van begin- en eindwoorde bepaal. Die algoritme is uitgebrei deur die tekortkominge van hierdie basiese prosedure aan te spreek. Neurale netwerke en beslissingsbome is afgerig en variasies van beide tegnieke is ondersoek om die optimale modelle te kry. Patrone vir die TEX-algoritme is met die OPatGen-program gegenereer. Tydens toetsing het die TEX-algoritme die beste op beide lettergreep- en saamgesteldewoordverdeling presteer met 99,56% en 99,12% akkuraatheid, respektiewelik. Dit kan dus vir woordafbreking gebruik word met min risiko vir afbrekingsfoute in gedrukte teks. Die neurale netwerk met 98,82% en 98,42% akkuraatheid op lettergreep- en saamgesteldewoordverdeling, respektiewelik, is ook bruikbaar vir lettergreepverdeling, maar dis meer riskant. Ons het bevind dat beslissingsbome te riskant is om vir lettergreepverdeling en veral vir woordverdeling te gebruik, met 97,91% en 90,71% akkuraatheid, respektiewelik. ’n Gekombineerde algoritme is ontwerp waarin saamgesteldewoordverdeling eers met die TEXalgoritme gedoen word, waarna die resultate van lettergreepverdeling deur beide die TEXalgoritme en die neurale netwerk gekombineer word. Die algoritme het 1,3% minder foute as die TEX-algoritme gemaak. ’n Toets op gepubliseerde Afrikaanse teks het getoon dat die risiko vir woordafbrekingsfoute in teks met gemiddeld tien woorde per re¨el ±0,02% is. / The aim of this study was to determine the level of success achievable with a purely pattern based approach to hyphenation in Afrikaans. The machine learning techniques artificial neural networks, decision trees and the TEX algorithm were investigated since they can be trained with patterns of letters from word lists for syllabification and decompounding. A lexicon of Afrikaans words was extracted from a corpus of electronic text. To obtain lists for syllabification and decompounding, words in the lexicon were respectively syllabified and compound words were decomposed. From each list of ±183 000 words, ±10 000 words were reserved as testing data and the rest was used as training data. A recursive algorithm for decompounding was developed. In this algorithm all words corresponding with a reference list (the lexicon) are extracted by string fitting from beginning and end of words. Splitting points are then determined based on the length of reassembled words. The algorithm was expanded by addressing shortcomings of this basic procedure. Artificial neural networks and decision trees were trained and variations of both were examined to find optimal syllabification and decompounding models. Patterns for the TEX algorithm were generated by using the program OPatGen. Testing showed that the TEX algorithm performed best on both syllabification and decompounding tasks with 99,56% and 99,12% accuracy, respectively. It can therefore be used for hyphenation in Afrikaans with little risk of hyphenation errors in printed text. The performance of the artificial neural network was lower, but still acceptable, with 98,82% and 98,42% accuracy for syllabification and decompounding, respectively. The decision tree with accuracy of 97,91% on syllabification and 90,71% on decompounding was found to be too risky to use for either of the tasks A combined algorithm was developed where words are first decompounded by using the TEX algorithm before syllabifying them with both the TEX algoritm and the neural network and combining the results. This algoritm reduced the number of errors made by the TEX algorithm by 1,3% but missed more hyphens. Testing the algorithm on Afrikaans publications showed the risk for hyphenation errors to be ±0,02% for text assumed to have an average of ten words per line. / Decision Sciences / D. Phil. (Operational Research)

Las lipofuscinosis neuronal ceroidea (LNCs) constituyen uno de los grupos de enfermedades neurodegenerativas de herencia autosómica recesiva más frecuentes en la infancia. Presentan variabilidad en la edad de inicio y comparten amplio espectro fenotípico: epilepsia, déficit visual, deterioro motor y cognitivo progresivos con fallecimiento a edad precoz. Se han identificado ocho genes responsables de las diferentes formas clínicas en la edad pediátrica (CLN10/CTSD, CLN1/PPT1, CLN2/TPP1, CLN3, CLN5, CLN6, CLN7/MFSD8 y CLN8). El análisis mutacional permite asociar el defecto genético a cada una de las formas clínicas: congénita, LNCC (CLN10); infantil, LNCI (CLN1); infantil tardía, LNCIT (CLN2); juvenil, LNCJ (CLN3); variante infantil tardía finlandesa, vLNCITFin (CLN5); variante infantil tardía juvenil precoz, vLNCITJuv (CLN6); variante infantil tardía turca, vLNCITTur (CLN7) y variante infantil tardía epilepsia del norte con retraso mental, EPMR - variante infantil tardía (CLN8). Nos proponemos, a través de los estudios realizados en los pacientes españoles con LNC, profundizar en el conocimiento de los aspectos clínicos y moleculares de este grupo de enfermedades, determinar el espectro mutacional de los genes CLN1, CLN2, CLN3, CLN5 y CLN7 y establecer una adecuada correlación genotipo-fenotipo en la población pediátrica de nuestro país. Desde el año 1974-2011 se estudiaron 6 pacientes con LNCI (5 núcleos familiares). Desde el año 1979-2011 se estudiaron 12 pacientes con LNCIT (10 núcleos familiares). Desde el año 1975-2010 se estudiaron 24 pacientes con LNCJ, divididos en 2 grupos: variante (11 pacientes) con mutaciones en el gen CLN1 y clásico (13 pacientes) con mutaciones en el gen CLN3. Se describieron 3 pacientes con vLNCITFin y uno con vLNCITTur. Se creó una base de datos clínica con 50 ítems. Para el estudio estadístico se utilizó la prueba de Kaplan-Meier. Los pacientes con LNCI, iniciaron la enfermedad entre los 8-15 meses con retraso en el desarrollo motor y marcha inestable. La epilepsia puede aparecer en cualquier momento. La LNCI se caracteriza por un severo y progresivo curso clínico y en nuestra población, la mutación V181M en el gen CLN1 está asociada con el fenotipo más severo de la enfermedad. La LNCIT se inició entre los 18 meses y los 3.7 años con retraso del lenguaje y convulsiones febriles simples seguidas de epilepsia. El trastorno de aprendizaje y la ataxia ocurrieron a los 4 años. La regresión clínica se inició con una pérdida de las frases, seguido de pérdida de la deambulación. Todos los pacientes desarrollaron epilepsia mioclónica continua. La LNCIT presenta un curso clínico muy homogéneo y se demuestra heterogeneidad genética en nuestra población. La forma variante de LNCJ se inició con retraso / regresión del lenguaje y dificultades de aprendizaje mientras que la forma clásica se inició con déficit visual. La regresión clínica se inició con una pérdida de las frases seguida por una pérdida de la deambulación durante la adolescencia en el grupo variante y durante la edad adulta el grupo clásico. El curso clínico es más severo y progresivo en pacientes con mutaciones en el gen CLN1 que en el gen CLN3. La mutación V181L en el gen CLN1 fue identificada en homocigosis en 9 pacientes pertenecientes a 4 familias consanguíneas, no relacionadas, todas de etnia gitana. Se considera la posibilidad de realizar un diagnóstico precoz de LNCJ en base a la sintomatología inicial y la edad de inicio. El índice de progresión de la enfermedad orienta hacia los fenotipos causados por mutaciones en los genes CLN1 / CLN3 y el diagnóstico definitivo deberá confirmarse mediante el análisis mutacional de dichos genes. Se ha elaborado un protocolo diagnóstico que permite realizar estudios de correlación genotipo-fenotipo y amplía el espectro clínico-mutacional en la población española afectada de lipofuscinosis neuronal ceroidea. / Neuronal ceroid lipofuscinosis (NCLs) is one of the most common groups of progressive neurodegenerative diseases in childhood. Eight disease genes causing NCL in childhood have been identified: CLN10/CTSD, CLN1/PPT1, CLN2/TPP1, CLN3, CLN5, CLN6, CLN7/MFSD8, and CLN8. The main objective was to assess the natural history of the disease and to establish phenotype/genotype correlations in Spanish patients with NCL. Infantile neuronal ceroid lipofuscinosis (INCL) is caused by mutations in the CLN1/PPT gene. The age at disease onset in six Spanish patients with INCL ranged from 8 to 15 months. Delayed motor skills and ataxia were the initial symptoms. The V181M mutation in the CLN1 gene was found in homozygosis which is associated with the most severe INCL phenotype. Late infantile neuronal ceroid lipofuscinosis (LINCL) is caused by mutations in the CLN2. The clinical outcome in 12 Spanish patients reported the age at onset of clinical symptoms ranged from 18 months to 3.7 years, and they included delayed speech and simple febrile seizures followed by epilepsy. Clinical regression was initiated by loss of sentences followed by loss of walking ability. The clinical progression of LINCL was relatively homogeneous and genetic heterogeneity was demonstrated in the 10 families studied. Juvenile neuronal ceroid lipofuscinosis (JNCL) is usually caused by a 1.02-kb deletion in the CLN3 gene and mutations in the CLN1 gene may be associated with a variant form of JNCL (vJNCL). To assess the natural history of the disease, 24 Spanish patients with JNCL were studied. Patients were classified into the groups of vJNCL with mutations in the CLN1 gene (n= 11) and classic JNCL (cJNCL) with mutations in the CLN3 gene (n=13). Patients with vJNCL showed a more severe and progressive clinical course than those with cJNCL. The rate of disease progression may be useful to diagnose vJNCL or cJNCL, which should be confirmed by molecular studies in CLN1/CLN3 genes. Three unrelated patients with Finnish variant late infantile (CLN5) and another patient with Turkish variant late infantile (CLN7) were described. The diagnostic algorithm is a useful tool for the diagnosis of the patients with NCL and the correlation genotype-phenotype studies in Spain.

In this dissertation, generalized additive neural networks (GANNs) and multilayer perceptrons (MLPs) are studied and compared as prediction techniques. MLPs are the most widely used type of artificial neural network (ANN), but are considered black boxes with regard to interpretability. There is currently no simple a priori method to determine the number of hidden neurons in each of the hidden layers of ANNs. Guidelines exist that are either heuristic or based on simulations that are derived from limited experiments. A modified version of the neural network construction with cross–validation samples (N2C2S) algorithm is therefore implemented and utilized to construct good MLP models. This algorithm enables the comparison with GANN models. GANNs are a relatively new type of ANN, based on the generalized additive model. The architecture of a GANN is less complex compared to MLPs and results can be interpreted with a graphical method, called the partial residual plot. A GANN consists of an input layer where each of the input nodes has its own MLP with one hidden layer. Originally, GANNs were constructed by interpreting partial residual plots. This method is time consuming and subjective, which may lead to the creation of suboptimal models. Consequently, an automated construction algorithm for GANNs was created and implemented in the SAS R statistical language. This system was called AutoGANN and is used to create good GANN models. A number of experiments are conducted on five publicly available data sets to gain insight into the similarities and differences between GANN and MLP models. The data sets include regression and classification tasks. In–sample model selection with the SBC model selection criterion and out–of–sample model selection with the average validation error as model selection criterion are performed. The models created are compared in terms of predictive accuracy, model complexity, comprehensibility, ease of construction and utility. The results show that the choice of model is highly dependent on the problem, as no single model always outperforms the other in terms of predictive accuracy. GANNs may be suggested for problems where interpretability of the results is important. The time taken to construct good MLP models by the modified N2C2S algorithm may be shorter than the time to build good GANN models by the automated construction algorithm / Thesis (M.Sc. (Computer Science))--North-West University, Potchefstroom Campus, 2011.

In this dissertation, generalized additive neural networks (GANNs) and multilayer perceptrons (MLPs) are studied and compared as prediction techniques. MLPs are the most widely used type of artificial neural network (ANN), but are considered black boxes with regard to interpretability. There is currently no simple a priori method to determine the number of hidden neurons in each of the hidden layers of ANNs. Guidelines exist that are either heuristic or based on simulations that are derived from limited experiments. A modified version of the neural network construction with cross–validation samples (N2C2S) algorithm is therefore implemented and utilized to construct good MLP models. This algorithm enables the comparison with GANN models. GANNs are a relatively new type of ANN, based on the generalized additive model. The architecture of a GANN is less complex compared to MLPs and results can be interpreted with a graphical method, called the partial residual plot. A GANN consists of an input layer where each of the input nodes has its own MLP with one hidden layer. Originally, GANNs were constructed by interpreting partial residual plots. This method is time consuming and subjective, which may lead to the creation of suboptimal models. Consequently, an automated construction algorithm for GANNs was created and implemented in the SAS R statistical language. This system was called AutoGANN and is used to create good GANN models. A number of experiments are conducted on five publicly available data sets to gain insight into the similarities and differences between GANN and MLP models. The data sets include regression and classification tasks. In–sample model selection with the SBC model selection criterion and out–of–sample model selection with the average validation error as model selection criterion are performed. The models created are compared in terms of predictive accuracy, model complexity, comprehensibility, ease of construction and utility. The results show that the choice of model is highly dependent on the problem, as no single model always outperforms the other in terms of predictive accuracy. GANNs may be suggested for problems where interpretability of the results is important. The time taken to construct good MLP models by the modified N2C2S algorithm may be shorter than the time to build good GANN models by the automated construction algorithm / Thesis (M.Sc. (Computer Science))--North-West University, Potchefstroom Campus, 2011.

New approaches are needed to manage and analyze the enormous quantity of biological data generated by modern technologies. Existing solutions are often fragmented and uncoordinated and, thus, they require considerable bioinformatics skills from users. Three applications have been developed illustrating different strategies to help users without extensive IT knowledge to take maximum profit from their data. SNPator is an easy-to-use suite that integrates all the usual tools for genetic association studies: from initial quality control procedures to final statistical analysis. CHAVA is an interactive visual application for CNV calling from aCGH data. It presents data in a visual way that helps assessing the quality of the calling and assists in the process of optimization. Haplotype Association Pattern Analysis visually presents data from exhaustive genomic haplotype associations, so that users can recognize patterns of possible associations that cannot be detected by single-SNP tests. / Calen noves aproximacions per la gestió i anàlisi de les enormes quantitats de dades biològiques generades per les tecnologies modernes. Les solucions existents, sovint fragmentaries i descoordinades, requereixen elevats nivells de formació bioinformàtica. Hem desenvolupat tres aplicacions que il•lustren diferents estratègies per ajudar als usuaris no experts en informàtica a aprofitar al màxim les seves dades. SNPator és un paquet de fàcil us que integra les eines usades habitualment en estudis de associació genètica: des del control de qualitat fins les anàlisi estadístiques. CHAVA és una aplicació visual interactiva per a la determinació de CNVs a partir de dades aCGH. Presenta les dades visualment per ajudar a valorar la qualitat de les CNV predites i ajudar a optimitzar-la. Haplotype Pattern Analysis presenta dades d’anàlisi d’associació haplotípica de forma visual per tal que els usuaris puguin reconèixer patrons de associacions que no es possible detectar amb tests de SNPs individuals.