A utilização da eletroestimulação muscular é uma estratégia utilizada para investigação da fadiga neuromuscular. Entretanto, esta técnica é pouco aplicada na musculatura extensora do cotovelo em função de limitações biomecâncias (atuação de músculos sinergistas), neurais (influência de reflexo neural) e fisiológicas (facilidade em atingir estados de potencialização pós-ativação e fadiga). Portanto, o objetivo deste estudo foi padronizar procedimentos para avaliação neuromuscular da musculatura extensora do cotovelo. Para isso, foram realizados três estudos que envolveram a adequação da técnica de eletroestimulação e um \"estudo principal\" para validar um novo protocolo de avaliação neuromuscular. Após resultados positivos em estudos complementares, a presente dissertação propôs a validação de um protocolo para análise neuromuscular com contrações submáximas para a musculatura extensora do cotovelo. Vinte participantes com idade de 25,1 ± 6,8 anos foram submetidos, em dias diferentes, a dois esforços, um a fim de promover fadiga central e fadiga periférica respectivamente. Antes e após os esforços envolvendo fadiga (periférica ou central) foram realizadas avaliações de fadiga neuromuscular para musculatura extensora do joelho (protocolo já validado) e musculatura extensora do cotovelo (protocolo proposto). Verificou-se que: (i.) o modelo de análise proposto não promove nenhum tipo de fadiga ou potencialização pós-ativação; (ii) a resposta de um pulso controle no início e no fim do modelo de análise proposto promovem respostas diferentes; (iii) o modelo proposto foi capaz de identificar redução da resposta neuromuscular; (iv) o esforço envolvendo fadiga central não promoveu fadiga central significante; (v) a utilização de um modelo matemático para investigação de fadiga neuromuscular (coeficientes resultantes de uma regressão linear) com os valores de estimulação em contrações submáximas foi sensível a fadiga mas não foi capaz de discriminar fadiga central e periférica. É possível concluir que o modelo de análise proposto para a musculatura extensora do cotovelo apresentou sensibilidade para verificar a fadiga neuromuscular. Entretanto, este não foi capaz de discriminar fadiga central e periférica. A utilização da regressão linear parece ser uma boa estratégia para diferenciar os dois modelos de fadiga e deve ser estudada com mais profundidade futuramente. / Muscular electrostimulation is a strategy used to investigate neuromuscular fatigue. However, this technique is poorly applied in the elbow extensor muscles due to the limitations of biomechanics (acting of synergistic muscles), neural (influence of neural reflex) and physiological (easiness to achieve post-activation and fatigue states of potentiation). Therefore, the purpose of this study was to standardize a neuromuscular evaluation strategy for the elbow extensor musculature. Thus, three complementary studies aimed at adjusting the electrostimulation technique and one \"main study\" to validate a new neuromuscular assessment protocol were realized. After positive results in complementary studies, the present dissertation proposed a protocol validation for neuromuscular analysis with submaximal contractions on the elbow extensor musculature. Twenty participants with 25.1 ± 6.8 years old performed, on different days, two efforts, one to promote central fatigue and peripheral fatigue respectively. Before and after the exercise involving fatigue (peripheral or central) there were realized neuromuscular fatigue evaluations for knee extensor muscles (protocol already validated) and elbow extensor musculature (protocol). The results indicate that: (i) the proposed analysis model does not promote any type of fatigue or post-activation potentiation; (ii) the response of a control pulse at the beginning and end of the proposed analysis model promotes different responses; (iii) the proposed model was able to identify reduction of neuromuscular response; (iv) the effort involving central fatigue did not promote significant central fatigue; (v) the use of a mathematical model to investigate neuromuscular fatigue (coefficients resulting from a linear regression) with the values of stimulation in submaximal contractions was sensitive after fatigue but was not able to discriminate central and peripheral fatigue. It is possible to conclude that the proposed analysis model for the elbow extensor musculature presented sensitivity to verify the neuromuscular fatigue. However, it was not able to discriminate central and peripheral fatigue. The use of linear regression seems to be a good strategy to differentiate the two models of fatigue and should be studied in more depth in the future.

Globally increasing levels of bandwidth and capacity requirements force the optical communications industry to produce new products that are faster, more powerful, and more efficient. In particular, optical-electronic-optical (O-E-O) conversions in Wavelength Division Multiplexing (WDM) mechanisms prevent higher data transfer speeds and create a serious bottleneck for optical communications. These O-E-O transitions are mostly encountered in the Wavelength converters of WDMs, and as a result, all-optical wavelength conversion methods have become extremely important. The main discussion in this thesis will concentrate on a specific all-optical wavelength conversion mechanism. In this mechanism, photonic crystal structures are integrated with moving MEMS/NEMS structures to create a state-of-the-art all-optical wavelength converter prototype. A wavelength conversion of 20% is achieved using this structure. Since the interaction of light with moving MEMS/NEMS structures plays an important role in the proposed wavelength conversion mechanism, modeling and simulation of electromagnetic waves becomes a very crucial step in the design process. Consequently, a subsection of this thesis will focus on a proposed enhancement to the finite-difference time-domain (FDTD) to model moving structures more efficiently and more realistically. This technique is named "Linear Dielectric Interpolation" and will be applied to more realistically and efficiently model the proposed photonic crystal MEMS/NEMS wavelength conversion mechanism.

El objetivo de esta tesis es desarrollar la interpolación de Birkhoff mediante polinomios lacunarios.En la interpolación algebraica de Birkhoff se determina un polinomio de grado menor que n, para ello se emplean n condiciones que fijan el valor del polinomio o sus derivadas. Los problemas clásicos de interpolación de Lagrange, Taylor, Hermite, Hermite-Sylvester y Abel-Gontcharov son casos particulares de interpolación algebraica de Birkhoff.Un espacio de polinomios lacunarios de dimensión n es el conjunto de los polinomios que pueden generarse por combinación lineal de n potencias distintas de grados, en general, no consecutivos. En particular, cuando tomamos potencias de grados 0,1,.,n-1, se obtiene el espacio de polinomios de grado menor que n, empleado en la interpolación algebraica clásica. En la interpolación algebraica clásica, el número de condiciones determina el espacio de interpolación. En contraste, en la interpolación mediante polinomios lacunarios las condiciones de interpolación determinan únicamente la dimensión del espacio de interpolación y pueden existir una infinidad de espacios sobre los que realizar la interpolación. Esto nos permite construir mejores estrategias de interpolación en ciertos casos, como la interpolación de funciones de gran crecimiento (interpolación de exponenciales y de ramas asintóticas).La aportación de la tesis consiste en la definición de un marco teórico adecuado para la interpolación de Birkhoff mediante polinomios lacunarios y en la extensión al nuevo marco de los principales elementos de la interpolación algebraica de Birkhoff. En concreto, se generaliza la condición de Pólya, se caracteriza la regularidad condicionada, se establecen condiciones suficientes de regularidad ordenada que extienden el teorema de Atkhison-Sharma, se extiende la descomposición normal y se establecen condiciones suficientes de singularidad en los casos indescomponibles.

In the thesis, the Wilcoxon approach to linear regression problems is combined with the fractal image compression to form a novel Wilcoxon fractal image compression. When the original image is corrupted by noise, we argue that the fractal image compression scheme should be insensitive to those outliers present in the corrupted image. This leads to the new concept of robust fractal image compression. The proposed Wilcoxon fractal image compression is the first attempt toward the design of robust fractal image compression. Four different numerical methods, i.e., steepest decent, line minimization based on quadratic interpolation, line minimization based on cubic interpolation, and least absolute deviation, will be proposed to solve the associated linear Wilcoxon regression problem. From the simulation results, it will be seen that, compared with the traditional fractal image compression, Wilcoxon fractal image compression has very good robustness against outliers caused by salt-and-pepper noise. However, it does not show great improvement of the robustness against outliers caused by Gaussian noise.

Thesis (MSc (Applied Mathematics))--Stellenbosch University, 2008. / A popular method for interpolating multidimensional scattered data is using radial basis functions. In this thesis we present the basic theory of radial basis function interpolation and also regard the solvability and stability of the method. Solving the interpolant directly has a high computational cost for large datasets, hence using numerical methods to approximate the interpolant is necessary. We consider some recent numerical algorithms. Software to implement radial basis function interpolation and to display the 3D interpolants obtained, is developed. We present results obtained from using our implementation for radial basis functions on GIS and 3D face data as well as an image warping application.

The Pick–Nevanlinna interpolation problem, in its fullest generality, is as follows: Given domains D1, D2 in complex Euclidean spaces, and a set f¹ zi; wiº : 1 i N g D1 D2, where zi are distinct and N 2 š+, N 2, find necessary and sufficient conditions for the existence of a holomorphic map F : D1 ! D2 such that F¹ziº = wi, 1 i N. When such a map F exists, we say that F is an interpolant of the data. Of course, this problem is intractable at the above level of generality. However, two special cases of the problem — which we shall study in this thesis — have been of lasting interest: Interpolation from the polydisc to the unit disc. This is the case D1 = „n and D2 = „, where „ denotes the open unit disc in the complex plane and n 2 š+. The problem itself originates with Georg Pick’s well-known theorem (independently discovered by Nevanlinna) for the case n = 1. Much later, Sarason gave another proof of Pick’s result using an operator-theoretic approach, which is very influential. Using this approach for n 2, Agler–McCarthy provided a solution to the problem with the restriction that the interpolant is in the Schur– Agler class. This is notable because, when n = 2, the latter result completely solves the problem for the case D1 = „2; D2 = „. However, Pick’s approach can also be effective for n 2. In this thesis, we give an alternative characterization for the existence of a 3-point interpolant based on Pick’s approach and involving the study of rational inner functions. Cole–Lewis–Wermer lifted Sarason’s approach to uniform algebras — leading to a char-acterization for the existence of an interpolant in terms of the positivity of a large, rather abstractly-defined family of N N matrices. McCullough later refined their result by identifying a smaller family of matrices. The second result of this thesis is in the same vein, namely: it provides a characterization of those data that admit a „n-to-„ interpolant in terms of the positivity of a family of N N matrices parametrized by a class of polynomials. Interpolation from the unit disc to the spectral unit ball. This is the case D1 = „ and D2 = n , where n denotes the set of all n n matrices with spectral radius less than 1. The interest in this arises from problems in Control Theory. Bercovici–Foias–Tannenbaum adapted Sarason’s methods to give a (somewhat hard-to-check) characterization for the existence of an interpolant under a very mild restriction. Later, Agler–Young established a relation between the interpolation problem in the spectral unit ball and that in the symmetrized polydisc — leading to a necessary condition for the existence of an interpolant. Bharali later provided a new inequivalent necessary condition for the existence of an interpolant for any n and N = 2. In this thesis, we shall present a necessary condition for the existence of an interpolant in the case when N = 3. This we shall achieve by adapting Pick’s approach and applying the aforementioned result of Bharali.

Le but de cette thèse est de construire une image couleur de haute qualité, contenant un faible niveau de bruit et d'aliasing, à partir d'une grande séquence (e.g. des centaines) d'images RAW prises avec un appareil photo grand public. C’est un problème complexe nécessitant d'effectuer à la volée du dématriçage, du débruitage et de la super-résolution. Les algorithmes existants produisent des images de haute qualité, mais le nombre d'images d'entrée est limité par des coûts de calcul et de mémoire importants. Dans cette thèse, nous proposons un algorithme de fusion d'images qui les traite séquentiellement de sorte que le coût mémoire ne dépend que de la taille de l'image de sortie. Après un pré-traitement, les images mosaïquées sont recalées en utilisant une méthode en deux étapes que nous introduisons. Ensuite, une image couleur est calculée par accumulation des données irrégulièrement échantillonnées en utilisant une régression à noyau classique. Enfin, le flou introduit est supprimé en appliquant l'inverse du filtre équivalent asymptotique correspondant (que nous introduisons). Nous évaluons la performance et la précision de chaque étape de notre algorithme sur des données synthétiques et réelles. Nous montrons que pour une grande séquence d'images, notre méthode augmente avec succès la résolution et le bruit résiduel diminue comme prévu. Nos résultats sont similaires à des méthodes plus lentes et plus gourmandes en mémoire. Comme la génération de données nécessite une méthode d'interpolation, nous étudions également les méthodes d'interpolation par polynôme trigonométrique et B-spline. Nous déduisons de cette étude de nouvelles méthodes d'interpolation affinées / The aim of this thesis is to build a high-quality color image, containing a low level of noise and aliasing, from a large sequence (e.g. hundreds or thousands) of RAW images taken with a consumer camera. This is a challenging issue requiring to perform on the fly demosaicking, denoising and super-resolution. Existing algorithms produce high-quality images but the number of input images is limited by severe computational and memory costs. In this thesis we propose an image fusion algorithm that processes the images sequentially so that the memory cost only depends on the size of the output image. After a preprocessing step, the mosaicked (or CFA) images are aligned in a common system of coordinates using a two-step registration method that we introduce. Then, a color image is computed by accumulation of the irregularly sampled data using classical kernel regression. Finally, the blur introduced is removed by applying the inverse of the corresponding asymptotic equivalent filter (that we introduce).We evaluate the performance and the accuracy of each step of our algorithm on synthetic and real data. We find that for a large sequence of RAW images, our method successfully performs super-resolution and the residual noise decreases as expected. We obtained results similar to those obtained by slower and memory greedy methods. As generating synthetic data requires an interpolation method, we also study in detail the trigonometric polynomial and B-spline interpolation methods. We derive from this study new fine-tuned interpolation methods

L'état du texte de l'auteur latin Properce fait l'objet de débat depuis plusieurs siècles déjà. Son état déterioré a laissé place à de nombreuses hypothèses sur sa transmission. Le présent mémoire vise à évaluer de façon macroscopique la validité de l'hypothèse voulant que dans l'archétype des manuscrits propertiens ou dans un antécédent de ce dernier, un interpolateur ait modifié les vers corrompus pour leur redonner une forme métriquement régulière. Pour ce faire, nous recensons l'état de la critique textuelle entourant Properce ainsi que l'état de la question en ce qui a trait à l'interpolation métrique plus précisément. Nous présentons ensuite un résumé des données pertinentes, relevées dans les tableaux de l'annexe, où nous trouvons d'un côté des erreurs métriques et de l'autre des corruptions identifiées unanimement par quatre éditeurs principaux du texte de Properce. Des observations sur les résultats sont par la suite présentées et soutenues par une comparaison avec la transmission du texte d'un autre auteur latin, Catulle. / The state of the text of the Latin author Propertius has been the subject of debate for several centuries now. Its deteriorated condition has given rise to numerous hypotheses about its transmission. This dissertation macroscopically evaluates the validity of the hypothesis which supposes that, in the archetype of the extant Propertius manuscripts or in an antecedent of it, an interpolator altered the corrupt verses to make them metrically regular again. To do so, the author surveys the state of textual criticism surrounding Propertius as well as the state of the question with respect to metrical interpolation specifically. She then presents a summary of the relevant data, found in the tables in the appendix, where are collected on the one hand metrical errors and on the other hand corruptions unanimously identified by four main editors of Propertius' text. Observations on the results are subsequently presented and supported by a comparison with the transmission of the text of another Latin author, Catullus.

L'analyse de la performance à l'état stationnaire dans de nombreux systèmes de files d'attente est complexe et les résultats sous forme explicite ne sont disponibles que dans des cas particuliers. Nous avons donc développé des approximations pour des critères de performance importants à l'état stationnaire tels que la longueur de la file d'attente, le temps d'attente et le temps de traitement total. Nous analysons d'abord la performance dans des cas à faible et fort trafic. Nous montrons ensuite comment développer une approximation basée sur une interpolation qui est valable pour n'importe quelle condition de trafic. Un avantage de l'approche proposée est qu'elle n'est pas dépendante d’un modèle particulier et donc elle peut être appliquée à d'autres modèles de files d'attente complexes. Nous appliquons cette technique pour trois modèles largement utilisés dans l'évaluation des performances des réseaux stochastiques : le modèle du supermarché, la file d'attente Discriminatory-Processor-Sharing (DPS) et la file d'attente Relative Priority (RP). Le modèle du supermarché est une file d'attente à plusieurs serveurs où lorsqu’un client arrive, deux serveurs sont choisis au hasard dans un ensemble de serveurs. La politique Join-the-Shortest-Queue (JSQ) est ensuite utilisée parmi les deux serveurs sélectionnés. DPS et RP sont deux files d'attente à plusieurs classes et à serveur unique mettant en œuvre des priorités relatives entre les clients des différentes classes. La discipline DPS sert tous les clients simultanément, tandis que RP sert un seul client à la fois de manière non-préemptive. Nous montrons que dans certains cas, l'interpolation est exacte. Nous utilisons ensuite cette approximation pour déduire comment la performance dépend des paramètres des modèles, et nous effectuons des expériences numériques illustrant la précision de l'interpolation dans un grand nombre de cas de figure / The analysis of the steady-state performance in many queuing systems is complex and closed-form results are available only in particular cases. We therefore set out to develop approximations for important performance measures in steady-state such as the queue length vector, waiting time and sojourn time. We first analyse the performance in a light-traffic and heavy-traffic regime. We then show how to develop an interpolation-based approximation that is valid for any load in the system. An advantage of the approach taken is that it is not model dependent and hence could potentially be applied to other complex queuing models. We apply this technique to three widely used models in the performance evaluation of stochastic networks: The supermarket model, the Discriminatory-Processor-Sharing (DPS) queue and the Relative Priority (RP) queue. The supermarket model is a multi-server queue where upon arrival of a customer two servers are selected at random from the available pool of servers. The Join-the-Shortest-Queue policy is then used in isolation with these two servers. DPS and RP are both single-server multi-class queues that implement relative priorities among customers of the various classes. The DPS discipline serves all customers simultaneously while RP serves one customer at a time in a non-preemptive way. We show that in some instances the interpolation approximation is exact. We then use the approximation to draw structural insights onto the performance of the system, and we carry out numerical experiments that illustrate that the interpolation approximation is accurate over a wide range of parameters

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