With the deregulation of power industry and the market competition, low cost, reliable power supply, and secured system operations are major concerns of the advanced deregulation markets. Power system protection is important for service reliability and quality assurance. To reduce the outage duration and promptly restore power services, fault section estimate has to be done effectively and accurately with fault alarms. First, an operational strategy for secondary power system restoration using Modified Grey Relational Analysis (MGRA) is proposed. The Restoration Scheme (RS) can be divided into three steps involving fault section determination, recovering process, and voltage correction process. Three GRAs are incorporated to design the overall restoration scheme. The first GRA uses network switching status to identify the fault. The second GRA combines switching states and load levels for network recovery. The third GRA uses capacitor bank control to support bus voltages. For security operation of restoration scheme, an Equivalent Current Injection (ECI) based hybrid current-power Optimal Power Flow (OPF) model with Predictor-Corrector Interior Point Algorithm (PCIPA) is used to verify the proposed scheme by off-line analysis to confirm a secure overall network operation including load-power balance, power generation limits, voltage limits, and power flow limits. The proposed method can further decompose into two sub-problems. Computer simulations were conducted with an IEEE 30-bus power system to show the effectiveness of the proposed restoration scheme and the PCIPA technique is very accurate, robust, and efficient for the modified OPF solution.

La maladie osseuse est une complication sévère pour les patients atteints de mucoviscidose (Cystic Fibrosis, CF). Les fractures vertébrales et costales impactent les capacités pulmonaires et la clairance du mucus bronchique. La meilleure prise en charge des symptômes des patients CF a permis l’amélioration de leurs qualité et espérance de vie. Cependant malgré l’optimisation de facteurs impactant le métabolisme osseux aucune amélioration notable n’a été observée dans la fragilité osseuse. Plus de 80% des patients CF sont porteurs de la mutation F508del du gène CFTR (Cystic Fibrosis Transmembrane conductance Regulator) sur au moins un allèle. L’implication directe de la mutation F508del dans la maladie osseuse a été montrée, bien que son rôle dans le dysfonctionnement du métabolisme osseux reste encore à élucider. Notre travail a permis de mettre en évidence que la mutation F508del portée par les ostéoblastes humains est responsable d’une dérégulation importante de la voie de signalisation RANK/RANKL/OPG aboutissant à un ratio RANKL/OPG élevé, potentiateur de l’ostéoclastogénèse et de la résorption osseuse. Nous avons également mis en évidence que le contexte inflammatoire chronique de la pathologie pourrait exacerber la perte osseuse, les cellules CF étant plus sensibles à ces stimulations. Par ailleurs, nous avons montré que l’utilisation de molécules pharmaceutiques comme des correcteurs et potentiateurs de CFTR, actuellement utilisés en essais cliniques, permettent une normalisation au moins partielle des dérégulations observées des ostéoblastes CF, et apparaissent comme des nouvelles stratégies thérapeutiques. / Bone disease is a serious complication for patients with Cystic Fibrosis (CF). Rib and vertebral fractures worsen lung function and mucus clearance. Better care of CF patient’s symptoms enable an improvement in life quality and expectancy. Despite optimization of factors impacting bone metabolism no improvement was observed in bone loss of patients with CF. More than 80% CF patients carried the F508del mutation on the CFTR (Cystic Fibrosis Transmembrane Conductance Regulator) gene on at least one allele. The role of the F508del mutation in the dysfunction of bone metabolism is yet unclear, but its involvement has been already shown in clinical studies and mouse models.Our work shown that F508del mutation on human osteoblasts causes a dysregulation in the RANK/RANK-L/OPG signalling leading to a high RANK-L to OPG ratio that may improve osteoclastogenesis, and thus the bone résorption. We also show that chronic inflammatory status of CF patients could exacerbate bone loss because of a high sensitivity of osteoblasts with the F508del-CFTR mutation. In addition, we demonstrate that the use of drugs as CFTR correctors and potentiators cause an improvement of the dysregulation observed and seems to be a promising therapeutic strategy.

Stochastic differential equations (SDE’s) are used to describe systems which are influenced by randomness. Here, randomness is modelled as some external source interacting with the system, thus ensuring that the stochastic differential equation provides a more realistic mathematical model of the system under investigation than deterministic differential equations. The behaviour of the physical system can often be described by probability and thus understanding the theory of SDE’s requires the familiarity of advanced probability theory and stochastic processes. SDE’s have found applications in chemistry, physical and engineering sciences, microelectronics and economics. But recently, there has been an increase in the use of SDE’s in other areas like social sciences, computational biology and finance. In modern financial practice, asset prices are modelled by means of stochastic processes. Thus, continuous-time stochastic calculus plays a central role in financial modelling. The theory and application of interest rate modelling is one of the most important areas of modern finance. For example, SDE’s are used to price bonds and to explain the term structure of interest rates. Commonly used models include the Cox-Ingersoll-Ross model; the Hull-White model; and Heath-Jarrow-Morton model. Since there has been an expansion in the range and volume of interest rate related products being traded in the international financial markets in the past decade, it has become important for investment banks, other financial institutions, government and corporate treasury offices to require ever more accurate, objective and scientific forms for the pricing, hedging and general risk management of the resulting positions. Similar to ordinary differential equations, many SDE’s that appear in practical applications cannot be solved explicitly and therefore require the use of numerical methods. For example, to price an American put option, one requires the numerical solution of a free-boundary partial differential equation. There are various approaches to solving SDE’s numerically. Monte Carlo methods could be used whereby the physical system is simulated directly using a sequence of random numbers. Another method involves the discretisation of both the time and space variables. However, the most efficient and widely applicable approach to solving SDE’s involves the discretisation of the time variable only and thus generating approximate values of the sample paths at the discretisation times. This paper highlights some of the various numerical methods that can be used to solve stochastic differential equations. These numerical methods are based on the simulation of sample paths of time discrete approximations. It also highlights how these methods can be derived from the Taylor expansion of the SDE, thus providing opportunities to derive more advanced numerical schemes. / Dissertation (MSc (Mathematics of Finance))--University of Pretoria, 2007. / Mathematics and Applied Mathematics / MSc / unrestricted

Master of Science

Fires occur extensively across Zambia every year, a problem recognized as a major threat to biodiversity. Yet, basic tools for mapping at a spatial and temporal scale that provide useful information for understanding and managing this problem are not available. The objectives of this research were: to develop a method to map the spatio-temporal seasonal fire occurrence using satellite imagery, to develop a technique for estimating missing data in the satellite imagery considering the possibility of change in land cover over time, and to demonstrate applicability of these new tools by analyzing the fine-scale seasonal patterns of landscape fires in eastern Zambia. A new approach for mapping burned areas uses multitemporal image analysis with a fuzzy clustering algorithm to automatically select spectral-temporal signatures that are then used to classify the images to produce the desired spatio-temporal burned area information. Testing with Landsat data (30m resolution) in eastern Zambia showed accuracies in predicting burned areas above 92%. The approach is simple to implement, data driven, and can be automated, which can facilitate quicker production of burned area information. A profile-based approach for filling missing data uses multitemporal imagery and exploits the similarity in land cover temporal profiles and spatial relationships to reliably estimate missing data even in areas with significant changes. Testing with simulated missing data from an 8-image spectral index sequence showed highly correlated (R2 of 0.78-0.92) and precise estimates (deviations 4-7%) compared to actual values. The profile-based approach overcomes the common requirement of gap-filling methods that there is gradual or no change in land cover, and provides accurate gap-filling under conditions of both gradual and abrupt changes. The spatio-temporal progression of landscape burning was evaluated for the 2009 and 2012 fire seasons (June-November) using Landsat data. Results show widespread burning (~ 60%) with most fires occurring late (August-October) in the season. Fire occurrence and burn patch sizes decreased with increasing settlement density and landscape fragmentation reflecting human influences and fuel availability. Small fires (< 5ha) are predominant and were significantly under-detected (>50%) by a global dataset (MODIS Burned Area Product (500m resolution)), underscoring the critical need of higher geometric resolution imagery such as Landsat imagery for mapping such fine-scale fire activity. / Ph. D.

Yes / Type II congenitalLong QT syndrome (LQT2) is due to genetic mutations in hERG channel. Genetic or pharmacological factors could potentially affect hERG channel biogenesis and contributes to LQTS, for example, disease mutations G601S and T473P result in hERG trafficking deficiency [1,2]. Various rescue strategies for hERG dysfuction are being developed. Some correctors for CFTR channel have been reported to act indirectly on proteostasis pathways to promote folding and correction on hERG trafficking deficiency [3]. In this study, we tested the hypothesis that the CFTR corrector KM-11060 and the potentiator PG-01 may correct hERG mutation trafficking diseases. We use HEK293 cell line expressing a well-studied trafficking disease mutation G601S-hERG channel [4]. We treated cells with CFTR potentiator PG-01and corrector KM-11060, which function through different cellular mechanisms, and assessed whether correction occurred via immunoblotting. Whole cell proteins from HEK 293 cells expressing hERG channels were used for analysis [5]. Proteins were separated on 8% SDS-polyacrylamide electrophoresis gels for 1 hour, transferred onto PVDF membrane, and blocked for 1 h with 5% nonfat milk. The blots were incubated with the primary antibody (Santa Cruz Biotechnology) for 12-16 h at 4C temperature and then incubated with a donkey antigoat horseradish peroxidase-conjugated secondary antibody( Santa Cruz Biotechnology). Actin expression was used for loading controls. The blots were visualized using the ECL detection kit (Genshare).Results were deemed significantly different from controls by a one-way ANOVA (p < 0.05). Our results show that both KM-11060 (5, 10, 20uM) and PG-01(5, 15 uM) can correct G601S mutant alleles of hERG protein trafficking (Fig 1, 2). KM-11060 (20uM) but not PG-01(15 uM) enhance protein expression of wild type hERG channel (Fig 2). Further treatment on cells at low temperature with different drug concentration will be tested. Functional studies are also needed to test whether the drugs can correct the function of hERG mutation channel. These results could potentially provide novel insight into the correction mechanism of CFTR potentiator and also help to develop new treatment for LQT2.

Objectif : Récemment, un nouvel appareil issu de la technologie du Forsus™ et visant à corriger les malocclusions de classe III a été mis sur le marché et se popularise dans la pratique orthodontique : le Tandem Forsus Maxillary Corrector (TFMC). L’objectif de la présente étude est de mesurer les effets squelettiques, l’influence réelle sur la croissance, et les effets dento-alvéolaires du port du TFMC. Matériel et méthodes : 14 patients présentant une malocclusion de classe III (âge moyen de 9 ans 6 mois) traités par le même orthodontiste ont participé à cette étude prospective. Le groupe consiste en 10 garçons et 4 filles. Le Tandem Forsus Maxillary Corrector est porté de 12 à 14 heures par jour jusqu’à l’obtention d’une surcorrection du surplomb horizontal et une relation dentaire de classe I. Le traitement est généralement d’une durée de 8 à 9 mois. Des radiographies céphalométriques latérales prises avant (T1) et après (T2) le traitement ont été analysées afin de déterminer les changements dentaires et squelettiques. Les résultats ont été comparés à un groupe contrôle composé de 42 enfants provenant du Centre de croissance de l’Université de Montréal. Les radiographies ont été tracées et analysées de manière aveugle à l’aide du logiciel Dolphin Imaging (ver 11.0, Patterson Dental, Chatsworth, California). L’erreur sur la méthode a été évaluée avec la formule de Dahlberg, le coefficient de corrélation intra-classe et l’indice de Bland-Altman. L’effet du traitement a été évalué à l’aide du test t pour échantillons appariés. L’effet de la croissance pour le groupe contrôle a été calculé à l’aide d’un test t pour échantillons indépendants. Résultats : L’utilisation du TFMC produit un mouvement antérieur et une rotation antihoraire du maxillaire. De plus, il procline les incisives supérieures et rétrocline les incisives inférieures. Une rotation antihoraire du plan occlusal contribue aussi à la correction de la malocclusion de classe III. Par contre, le TFMC ne semble pas avoir pour effet de restreindre la croissance mandibulaire. Conclusion : La présente étude tend à démontrer que le port de l’appareil TFMC a un effet orthopédique et dento-alvéolaire significatif lors du traitement correctif des malocclusions modérées de classe III. / Aim: Recently, a new appliance used to correct class III malocclusions, equipped with the Forsus™ technology, has been marketed and is gaining popularity in orthodontic practice: the Tandem Forsus Maxillary Corrector (TFMC). The purpose of the present study is to measure the skeletal and dento-alveolar effects, and the true influence on growth of the TFMC. Materials and Methods: A prospective study was done with 14 growing children (mean age of 9 years 6 months) who had a class III malocclusion and were treated with the TFMC by the same orthodontist. The group consisted of 10 boys and 4 girls. The «Tandem Forsus Maxillary Corrector» was worn 12 to 14 hours a day until a positive overjet and a class I dental relationship was obtained. For each patient, lateral cephalograms taken before (T1) and after (T2) the treatment were analyzed to determine skeletal and dental changes resulting from treatment. These results were compared to a control group randomly selected from the Growth Center of the University of Montreal. The cephalograms were traced and analyzed with the software Dolphin Imaging (ver 11.0, Patterson Dental, Chatsworth, California). Consistency and repeatability of measurements was evaluated with the intraclass correlation, the Dahlberg formula and the Bland-Altman test. The effect of treatment was evaluated with a paired T-test. The effect of growth for the control group was calculated with an unpaired T-test. Results: Use of the TFMC results in an anterior movement and a counterclockwise rotation of the maxilla. The upper incisors proclined and the lower incisors retroclined. A counterclockwise rotation of the occlusal plane also contributed to the correction of the class III malocclusion. Furthermore, the TFMC does not seem to restrain mandibular growth. Conclusion: The TFMC appliance seems to have a significant orthopedic and dento-alveolar effect when correcting a moderate class III malocclusion.

La pathologie de la fibrose kystique (FK) est causée par des mutations dans le gène codant pour le canal CFTR. La mutation la plus commune est la délétion du résidu Phe508 (∆F508), qui entraîne un mauvais repliement et la dégradation de la protéine mutée. Ainsi, l’absence du CFTR cause un dysfonctionnement du transport ionique et liquidien qui altère le phénomène de clairance mucociliaire. Il en résulte une accumulation de mucus visqueux obstruant les voies aériennes favorisant une colonisation bactérienne, spécialement par P. aeruginosa, et une inflammation chronique. Ces phénomènes entraînent des lésions épithéliales et un remodelage des voies aériennes. Selon nos analyses ultrastructurales de poumons issus de patients FK au moment de la transplantation, certaines zones de l’épithélium FK montrait des signes de d’initiation des processus de réparation. Malgré cela, un dommage épithélial progressif est observé chez les patients FK et il apparaît évident que les processus de réparation sont insuffisants pour permettre le rétablissement de l’intégrité épithéliale. Le principal objectif de mon étude était d’étudier le rôle du CFTR dans les mécanismes de réparation de l’épithélium FK et de déterminer l’impact de la correction du CFTR sur la réparation épithéliale et ce, en condition aseptique et en présence d’infection. Mes travaux montrent que l’épithélium des voies aériennes FK présente un défaut de réparation, associé, du moins en partie, à l’absence d’un CFTR fonctionnel. De plus, nous avons démontré pour la première fois que l’application du correcteur du CFTR VRT-325 permettait, non seulement, la maturation du CFTR, mais également une amélioration de la capacité des monocouches de cellules des voies aériennes FK à se réparer. D’autre part, nous avons montré que la présence du filtrat bactérien de P. aeruginosa (PsaDM) altérait non seulement l’expression et la fonction du CFTR, mais également les processus de réparation épithéliale. Enfin, nos résultats montrent que l’infection affecte la maturation du CFTR induite par le VRT-325 et diminue les effets bénéfiques du VRT-325 sur la réparation épithéliale. Mes travaux permettent de mieux comprendre le rôle du CFTR dans les processus de réparation de l’épithélium FK et de proposer une nouvelle approche thérapeutique visant à promouvoir la régénération épithéliale chez les patients FK afin de tenter de stabiliser leur état, malgré l’effet délétère de la composante infectieuse. / The Cystic fibrosis (CF) pathology is caused by mutations of the gene coding for the CFTR channel. The most common mutation is the deletion of Phe508 (∆F508) causing protein misfolding and degradation. Thus, the absence of CFTR channel causes the dysfunction of ion and fluid transport that impairs mucociliary clearance resulting in mucus thickening and plugging in the airways. These conditions then favor P. aeruginosa bacterial colonisation and inflammation in the airways, which contribute to airway damage and remodeling. Ultrstructural analysis of bronchial sections of lungs collected from CF patients at the time of transplantation showed some area with signs of ongoing epithelial repair. However, a progressive epithelial damage is still observed in CF patients and it appears that the repair process is insufficient to restore epithelial integrity. The main objective of my work was to study the role of CFTR in the CF repair processes and to explore the impact of CFTR correction on epithelial repair under pathogen-free condition as well as in the presence of infectious products. Our study showed that CF airway epithelium exhibits a repair defect, associated, at least in part, to the absence of a functional CFTR channel. Furthermore, we demonstrated for the first time that CFTR rescue with the CFTR corrector VRT-325 significantly improved the wound-healing capacity of CF epithelial cell monolayers. Then, we showed that the presence of bacterial filtrate, more precisely P. aeruginosa diffusible material (PsaDM), not only alter CFTR function and expression, but also impaired epithelial repair processes. Finally, our results suggested that infection has a deleterious impact on CFTR rescue, and affected the beneficial effect on epithelial repair processes induced by VRT-325. My work allows to better understand the role of CFTR in the CF epithelial repair mechanisms and to propose new therapeutic strategies to promote epithelial regeneration in CF patients in attempt to stabilize their condition, despite the deleterious impact of infection.

La Fibrose kystique (FK), causée par des mutations du canal Cl- CFTR, entraîne une dysfonction de la sécrétion de Cl- et un débalancement dans la sécrétion des fluides. La diminution de la clairance mucociliaire qui s’en suit occasionne une accumulation du mucus. Cet environnement est alors favorable à l’installation d’infections et d’inflammation chroniques, responsables de lésions au niveau de l’épithélium respiratoire. Le vieillissement de la population FK, suite à la prise en charge plus appropriée de la maladie, est accompagné par l’émergence de pathologies associées, telles que le diabète. Celui-ci, ainsi que plusieurs autres facteurs comme l’infection à Pseudomonas aeruginosa, contribuent au déclin progressif de la fonction pulmonaire, principale cause de mortalité et de morbidité des patients FK. Le maintien de la fonction pulmonaire est dépendant notamment du transport ionique et liquidien régulant la clairance mucociliaire ainsi que de la réparation épithéliale nécessaire à la génération d’un épithélium fonctionnel en réponse aux agressions. Nous avons donc évalué l’impact de l’hyperglycémie et des exoproduits de P. aeruginosa sur ces deux mécanismes. Nos résultats ont tout d’abord montré qu’un niveau de glucose élevé diminue les courants Cl- CFTR et potassique et altère la réparation de l’épithélium bronchique FK et non FK. Nous avons aussi observé que l’hyperglycémie limite l’impact bénéfique de la correction de CFTR sur la réparation épithéliale. Dans un second temps, nous avons évalué l’impact de l’infection à Pseudomonas aeruginosa sur le CFTR, qui tient un rôle important dans la fonctionnalité de l’épithélium des voies aériennes non-FK. Nous avons noté que l’expression du CFTR ainsi que sa fonction sont réduites par l’exposition aux produits bactériens dans les cellules non-FK. De plus, ces exoproduits compromettent la maturation du CFTR muté par les correcteurs ainsi que leur bénéfice sur la réparation de l’épithélium FK. Finalement, nous avons testé différentes combinaisons de composés correcteurs et potentiateurs de CFTR afin de déterminer quelle stratégie serait la plus efficace afin de favoriser la réparation épithéliale bronchique FK malgré la présence d’infection. / Cystic fibrosis (CF), caused by mutations in the CFTR gene, is characterized by dysfunctional Cl- secretion and an imbalance in ion/fluid transport resulting in a decrease in mucociliary clearance. Accumulation of mucus then occurs and this favors bacterial infection in the airways. Chronic infection and inflammation is then responsible for progressive injuries to the lung epithelium. These mechanisms are associated with a decline in lung function, the main cause of morbidity and mortality in CF. The recent improvement in clinical care of patients with CF has led to an increase in median life expectancy, which allows the emergence of comorbidities, such as CF-related diabetes (CFRD). Because Pseudomonas aeruginosa infection and CFRD have been associated with decreased lung function, we investigated their impact on ion transports and epithelial repair, two main functions of airway epithelia. First, our results showed a reduction in Cl- secretion by CFTR and total K+ currents through CF and non-CF airway epithelial cells in hyperglycemic conditions. Moreover, our data indicated a decrease in wound closure rates of airway cell monolayers after exposure to high glucose. We also demonstrated an impairment of the beneficial effect of CFTR correctors on repair rates. The second part of our studies reveals a deleterious impact of Pseudomonas aeruginosa diffusible material (PsaDM) on CFTR expression and function in non-CF airways cells. Importantly, we showed, for the first time, that the presence of PsaDM altered the functional rescue of mutated CFTR by correctors and dampened their beneficial effect on CF wound repair. Finally, we tested several different combinations of corrector and potentiators in order to identify the most efficient compounds to improve the repair rates of CF monolayers despite the presence of PsaDM. Overall, our research demonstrated a deleterious impact of CFRD and PsaDM on ion transports and wound closure. Moreover, the new therapies with correctors may also be impacted by these two components.

On considère des méthodes de Galerkin stochastiques pour des systèmes hyperboliques faisant intervenir des données en entrée incertaines de lois de distribution connues paramétrées par des variables aléatoires. On s'intéresse à des problèmes où un choc apparaît presque sûrement en temps fini. Dans ce cas, la solution peut développer des discontinuités dans les domaines spatial et stochastique. On utilise un schéma de Volumes Finis pour la discrétisation spatiale et une projection de Galerkin basée sur une approximation polynomiale par morceaux pour la discrétisation stochastique. On propose un solveur de type Roe avec correcteur entropique pour le système de Galerkin, utilisant une technique originale pour approcher la valeur absolue de la matrice de Roe et une adaptation du correcteur entropique de Dubois et Mehlmann. La méthode proposée reste coûteuse car une discrétisation stochastique très fine est nécessaire pour représenter la solution au voisinage des discontinuités. Il est donc nécessaire de faire appel à des stratégies adaptatives. Comme les discontinuités sont localisées en espace et évoluent en temps, on propose des représentations stochastiques dépendant de l'espace et du temps. On formule cette méthodologie dans un contexte multi-résolution basé sur le concept d'arbres binaires pour décrire la discrétisation stochastique. Les étapes d'enrichissement et d'élagage adaptatifs sont réalisées en utilisant des critères d'analyse multi-résolution. Dans le cas multidimensionnel, une anisotropie de la procédure adaptative est proposée. La méthodologie est évaluée sur le système des équations d'Euler dans un tube à choc et sur l'équation de Burgers en une et deux dimensions stochastiques / This work is concerned with stochastic Galerkin methods for hyperbolic systems involving uncertain data with known distribution functions parametrized by random variables. We are interested in problems where a shock appears almost surely in finite time. In this case, the solution exhibits discontinuities in the spatial and in the stochastic domains. A Finite Volume scheme is used for the spatial discretization and a Galerkin projection based on piecewise poynomial approximation is used for the stochastic discretization. A Roe-type solver with an entropy correction is proposed for the Galerkin system, using an original technique to approximate the absolute value of the Roe matrix and an adaptation of the Dubois and Mehlman entropy corrector. Although this method deals with complex situations, it remains costly because a very fine stochastic discretization is needed to represent the solution in the vicinity of discontinuities. This fact calls for adaptive strategies. As discontinuities are localized in space and time, stochastic representations depending on space and time are proposed. This methodology is formulated in a multiresolution context based on the concept of binary trees for the stochastic discretization. The adaptive enrichment and coarsening steps are based on multiresolution analysis criteria. In the multidimensional case, an anisotropy of the adaptive procedure is proposed. The method is tested on the Euler equations in a shock tube and on the Burgers equation in one and two stochastic dimensions