Thesis (Ph.D. (Statistics)) -- University of Limpopo, 2017 / Operations Research (OR) is a scientific method for developing quantitatively well-grounded recommendations for decision making. While it is true that it uses a variety of mathematical techniques, OR has a much broader scope. It is in fact a systematic approach to solving problems, which uses one or more analytical tools in the process of analysis. Over the years, OR has evolved through different stages. This study is motivated by new real-world challenges needed for efficiency and innovation in line with the aims and objectives of OR – the science of better, as classified by the OR Society of the United Kingdom. New real-world challenges are encountered on a daily basis from problems arising in the fields of water, energy, agriculture, mining, tourism, IT development, natural phenomena, transport, climate change, economic and other societal requirements. To counter all these challenges, new techniques ought to be developed. The growth of global markets and the resulting increase in competition have highlighted the need for OR techniques to be improved. These developments, among other reasons, are an indication that new techniques are needed to improve the day-to-day running of organisations, regardless of size, type and location. The principal aim of this study is to modify and develop new OR techniques that can be used to solve emerging problems encountered in the areas of linear programming, integer programming, mixed integer programming, network routing and travelling salesman problems. Distribution models, resource allocation models, travelling salesman problem, general linear mixed integer ii programming and other network problems that occur in real life, have been modelled mathematically in this thesis. Most of these models belong to the NP-hard (non-deterministic polynomial) class of difficult problems. In other words, these types of problems cannot be solved in polynomial time (P). No general purpose algorithm for these problems is known. The thesis is divided into two major areas namely: (1) network models and (2) resource allocation and distribution models. Under network models, five new techniques have been developed: the minimum weight algorithm for a non-directed network, maximum reliability route in both non-directed and directed acyclic network, minimum spanning tree with index less than two, routing through 0k0 specified nodes, and a new heuristic to the travelling salesman problem. Under the resource allocation and distribution models section, four new models have been developed, and these are: a unified approach to solve transportation and assignment problems, a transportation branch and bound algorithm for the generalised assignment problem, a new hybrid search method over the extreme points for solving a large-scale LP model with non-negative coefficients, and a heuristic for a mixed integer program using the characteristic equation approach. In most of the nine approaches developed in the thesis, efforts were done to compare the effectiveness of the new approaches to existing techniques. Improvements in the new techniques in solving problems were noted. However, it was difficult to compare some of the new techniques to the existing ones because computational packages of the new techniques need to be developed first. This aspect will be subject matter of future research on developing these techniques further. It was concluded with strong evidence, that development of new OR techniques is a must if we are to encounter the emerging problems faced by the world today. Key words: NP-hard problem, Network models, Reliability, Heuristic, Largescale LP, Characteristic equation, Algorithm.

This master thesis focuses on creating and processing a dataset, which contains semi-automatically processed images of vehicles licence plates. The main goal is to create videos and a set of tools, which are able to transform  input videos into a dataset used for traffic monitoring neural networks. Used programming language is Python, graphical library OpenCV and framework PyTorch for implementation of neural network.

This thesis discusses the technique of flow cytometry for multiplex analysis and its use in conjunction with imunochemical methods. As part of this work was carried out clinical studies dealing with secondary prevention of myocardial infarction and atherosclerosis in 186 pacientů. In this time represents myocardial infarction worldwide civilizational problem. A number of possible parameters for monitoring atherosclerosis in the world is still an unresolved issue. In the practical part of this work we performed an analysis using Luminex xMAP technology for new parameters (adiponectin, resistin, osteopontin) to predict atherosclerotic disease associated with myocardial infarcion. Also we wanted to see how these parameters are changed in patients after increasing the dose of therapeutic drugs.

This thesis deals with the characterization of electrochemical corrosion properties of magnesium alloys as promising materials for biomedical applications. The wrought alloys AZ31 and AZ61 were used and exposed to corrosive environments of Hanks solutions (SBF) to simulate environmental conditions in living organisms. For the evaluation of the surfaces was used scanning electron microscopy (SEM) with elemental analysis measured by energy-dispersive spectroscopy (EDS). Short-term (5 min) and long-term (72 h) corrosion tests were conducted in order to optimize the measurement methodology and obtain corrosion parameters - especially corrosion potential (Ekor), corrosion current density (ikor) and polarisation resistance (RP). To evaluation of the short-term tests were by potentiodynamic tests, namely the linear polarization (LP) test. Long-term tests were measured by electrochemical impedance spectroscopy (EIS). Effects of the composition of the alloys (AZ31 and AZ61), surface treatment (grinding and polishing) and the composition of the solution (SBF without Ca, Mg, and with Ca, Mg) were compared. Complex corrosion behaviour in time was characterized and corrosion mechanisms were discussed.

This thesis named Cosdensing steam turbine in combi-cycle deals with the calculation of thermal balancing scheme and the design of turbine. This double body steam turbine with combined HP-IP part and double-flow LP part does not have any additional samples of technological steam. LP part has two side outputs to the water-cooled condensers. There is a basic calculation of force effects on the LP part at operation. The thesis also includes a drawing of a longitudinal cut of LP part and its layout, including positron of the condensers.

The Drosophila Lipoprotein particles bear lipid-linked morphogens on their surface and are required for long-range signaling activity of Wingless and Hedgehog. They also bind a wide variety of gpi-linked proteins. Whether any of these proteins affect morphogen signaling is unknown. Here, I show that the gpi-linked heparan sulfate proteoglycan Dally is released from cell membranes and binds to lipoprotein particles both with and without its lipid anchor. Hedgehog signaling efficiency is reduced in Dally mutant discs, but can be rescued non-autonomously by expression of non-gpi-modified Dally. This Dally isoform colocalizes with Hedgehog, Patched and Lipophorin in endosomes and increases Hedgehog signaling efficiency without affecting Hedgehog distribution. These data show that Hedgehog signaling activity can be influenced by other Lipophorin-associated proteins, and suggest Lipoproteins provide a platform for regulation of morphogen signaling.

We consider a family of generalized Procrustes problems. In this class of problems, one aims at aligning a set of vectors to a given second set of vectors. The distance between both sets is measured in the q norm, and for the alignment, isometries with respect to the p norm are allowed. In contrast to the classical Procrustes problem with p = q = 2, we allow p and q to differ. We will see that it makes a difference whether the problem is real or cast over the complex field. Therefore, we discuss the solutions for p = 2 separately for these cases. We show that all the real cases can be solved efficiently. Most of the complex cases can up to now only be solved approximately in polynomial time, but we show the existence of polynomial time algorithms for q ∈ {2, 4, ∞}. Computational experiments illustrate the suggested algorithms.

We consider a family of generalized Procrustes problems. In this class of problems, one aims at aligning a set of vectors to a given second set of vectors. The distance between both sets is measured in the q norm, and for the alignment, isometries with respect to the p norm are allowed. In contrast to the classical Procrustes problem with p = q = 2, we allow p and q to differ. We will see that it makes a difference whether the problem is real or cast over the complex field. Therefore, we discuss the solutions for p = 2 separately for these cases. We show that all the real cases can be solved efficiently. Most of the complex cases can up to now only be solved approximately in polynomial time, but we show the existence of polynomial time algorithms for q ∈ {2, 4, ∞}. Computational experiments illustrate the suggested algorithms.:1. Introduction 2. The (lp, lq)-Procrustes problem 3. Optimization methods for the remaining cases with p not equal to 2 4. The one-dimensional complex optimization problems with p, q unequal to 2 5. Conclusions

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal. / L'étude présentée s'inscrit dans le cadre du phénomène de la vision résiduelle, c'est-à-dire les fonctions visuelles qui persistent après une lésion du cortex occipital. De façon plus précise, ces travaux portent sur la caractérisation des propriétés fonctionnelles des neurones du complexe LP-pulvinar suite à l'apparition d'une nouvelle voie rétinothalamique chez des chats ayant subi une ablation chronique du cortex visuel primaire. L'ablation totale ou partielle du cortex visuel primaire entraîne chez la plupart des espèces, une diminution ou perte des capacités visuelles dont la sévérité varie selon l'âge de l'animal et l'étendue de la lésion (Fendrich et al., 1992). Ces déficits sont généralement plus prononcés lorsque la lésion survient chez l'adulte plutôt que chez le jeune en développement. En effet, les animaux cérébrolésés en bas âge présentent un comportement visuel qualifié de quasi normal (Comwell et al., 1989). Chez le chat, une lésion du cortex visuel primaire entraîne l'apparition d'une nouvelle voie visuelle se projetant de la rétine vers la partie latérale du complexe LP-pulvinar (Payne et al., 1993). Le but de l'étude consiste à déterminer le carrelât physiologique de la compensation comportementale observée chez les animaux cérébrolésés au cours du développement et à l'âge adulte. L'hypothèse soulevée est que le maintien de l'intégrité visuelle observé chez les animaux cérébrolésés résulterait de la réorganisation des voies visuelles souscorticales et de façon plus précise, de l'apparition de la nouvelle voie rétine - LP-pulvinar. L'étude consistait à réaliser les ablations chirurgicales du cortex visuel chez des chats adultes et des chatons âgés de 7 à 30 jours. Après un délai suffisant pour permettre la réorganisation neuroanatomique, les animaux étaient anesthésiés et préparés pour les séances d'enregistrement électrophysiologique. Une microélectrode était descendue au LP-pulvinar afin d'enregistrer les réponses cellulaires lors de la présentation de différents stimuli visuels. A la fin de l'expérience, le cerveau était prélevé pour les vérifications neuroanatomiques et histo logiques. Les résultats obtenus ont permis de mettre en évidence des changements fonctionnels au niveau des neurones du LP-pulvinar chez les sujets cérébrolésés. Ces changements incluent notamment une modification dans l'organisation des champs récepteurs des cellules du LP-pulvinar. En effet, les cellules du LP-pulvinar des animaux lésés en bas âge présentent un haut niveau de linéarité spatiale et affichent un patron de décharge phasique. Ces nouvelles propriétés des neurones du LP-pulvinar semblent refléter la présence de la nouvelle voie rétino-thalamique qui serait de toute évidence d'origine W-phasique. Les résultats obtenus indiquent donc que le complexe LP-pulvinar participerait vraisemblablement au maintien du comportement visuo-moteur normal dans le phénomène de la vision résiduelle. L'étude présentée est importante, non seulement dans le contexte du rôle du complexe LP-pulvinar dans l'organisation des champs récepteurs chez l'animal cérébrolésé, mais aussi dans le contexte plus large de la plasticité neuronale.

Cette thèse présente quelques résultats de la théorie des probabilités quantiques et de l’analyse harmonique à valeurs operateurs. La thèse est composée des trois parties.Dans la première partie, on démontre la décomposition atomique des espaces de Hardy de martingales non commutatives. On identifie aussi les interpolés complexes et réels entre les versions conditionnelles des espaces de Hardy et BMO de martingales non commutatives.La seconde partie est consacrée à l’étude des espaces de Hardy à valeurs opérateursvia la méthode d’ondellettes. Cette approche est similaire à celle du cas des martingales non commutatives. On démontre que ces espaces de Hardy sont équivalents à ceux étudiés par Tao Mei. Par conséquent, on donne une base explicite complètement inconditionnelle pour l’espace de Hardy H1(R), muni d’une structure d’espace d’opérateurs naturelle. La troisième partie porte sur l’analyse harmonique sur le tore quantique. On établit les inégalités maximales pour diverses moyennes de sommation des séries de Fourier définies sur le tore quantique et obtient les théorèmes de convergence ponctuelle correspondant. En particulier, on obtient un analogue non commutative du théorème classique de Stein sur les moyennes de Bochner-Riesz. Ensuite, on démontre que les multiplicateurs de Fourier complètement bornés sur le tore quantique coïncident à ceux définis sur le tore classique. Finalement, on présente la théorie des espaces de Hardy et montre que ces espaces possèdent les propriétés des espaces de Hardy usuels. En particulier, on établit la dualité entre H1 et BMO. / This thesis presents some results in quantum probability and operator-valued harmonicanalysis. The main results obtained in the thesis are contained in the following three parts:In first part, we prove the atomic decomposition for the Hardy spaces h1 and H1 of noncommutative martingales. We also establish that interpolation results on the conditionedHardy spaces of noncommutative martingales. The second part is devoted to studying operator-valued Hardy spaces via Meyer’s wavelet method. It turns out that this way of approaching these spaces is parallel to that in the noncommutative martingale case. We also show that these Hardy spaces coincide with those introduced and studied by Tao Mei in [52]. As a consequence, we give an explicit completely unconditional base for Hardy spaces H1(R) equipped with a natural operator space structure. The third part deals with with harmonic analysis on quantum tori. We first establish the maximal inequalities for several means of Fourier series defined on quantum tori and obtain the corresponding pointwise convergence theorems. In particular, we prove the noncommutative analogue of the classical Stein theorem on Bochner-Riesz means. Then we prove that Lp completely bounded Fourier multipliers on quantum tori coincide with those on classical tori with equal cb-norms. Finally, we present the H1-BMO and Littlewood- Paley theories associated with the circular Poisson semigroup over quantum tori.