This dissertation deals with customised image analysis tools in cancer research. In the field of biomedical sciences, mathematical imaging has become crucial in order to account for advancements in technical equipment and data storage by sound mathematical methods that can process and analyse imaging data in an automated way. This thesis contributes to the development of such mathematically sound imaging models in four ways: (i) automated cell segmentation and tracking. In cancer drug development, time-lapse light microscopy experiments are conducted for performance validation. The aim is to monitor behaviour of cells in cultures that have previously been treated with chemotherapy drugs, since atypical duration and outcome of mitosis, the process of cell division, can be an indicator of successfully working drugs. As an imaging modality we focus on phase contrast microscopy, hence avoiding phototoxicity and influence on cell behaviour. As a drawback, the common halo- and shade-off effect impede image analysis. We present a novel workflow uniting both automated mitotic cell detection with the Hough transform and subsequent cell tracking by a tailor-made level-set method in order to obtain statistics on length of mitosis and cell fates. The proposed image analysis pipeline is deployed in a MATLAB software package called MitosisAnalyser. For the detection of mitotic cells we use the circular Hough transform. This concept is investigated further in the framework of image regularisation in the general context of imaging inverse problems, in which circular objects should be enhanced, (ii) exploiting sparsity of first-order derivatives in combination with the linear circular Hough transform operation. Furthermore, (iii) we present a new unified higher-order derivative-type regularisation functional enforcing sparsity of a vector field related to an image to be reconstructed using curl, divergence and shear operators. The model is able to interpolate between well-known regularisers such as total generalised variation and infimal convolution total variation. Finally, (iv) we demonstrate how we can learn sparsity promoting parametrised regularisers via quotient minimisation, which can be motivated by generalised Eigenproblems. Learning approaches have recently become very popular in the field of inverse problems. However, the majority aims at fitting models to favourable training data, whereas we incorporate knowledge about both fit and misfit data. We present results resembling behaviour of well-established derivative-based sparse regularisers, introduce novel families of non-derivative-based regularisers and extend this framework to classification problems.

Submitted by isabela.moljf@hotmail.com (isabela.moljf@hotmail.com) on 2016-08-15T14:53:56Z No. of bitstreams: 1 hugorolandojachohancco.pdf: 1087180 bytes, checksum: 30f544acc78e47c2892563f8ab257478 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-08-19T14:01:42Z (GMT) No. of bitstreams: 1 hugorolandojachohancco.pdf: 1087180 bytes, checksum: 30f544acc78e47c2892563f8ab257478 (MD5) / Made available in DSpace on 2016-08-19T14:01:42Z (GMT). No. of bitstreams: 1 hugorolandojachohancco.pdf: 1087180 bytes, checksum: 30f544acc78e47c2892563f8ab257478 (MD5) Previous issue date: 2016-07-18 / Consideramos os campos vetoriais C1 sobre uma variedade riemanniana compacta, sem bordo, de dimensão finita n, com n ≥3. Uma classe homoclínica de um campo vetorial é o fecho de conjunto de pontos homoclínicos transversais associados com uma órbita periódica hiperbólica. Neste trabalho, provamos que as classes homoclínicas para um conjunto residual de campos vetoriais C1 são conjuntos neutrais, mais ainda, a classe homoclínica é a intersecção dos fechos do conjunto estável e o conjunto instável. Como consequencia das propriedades do conjuntos neutrais, provamos as propriedades genéricas das classes homoclínicas. Assim, provamos que as classes homoclínicas de campos vetoriais C1-genérico X são conjuntos transitivos maximais, saturados e que dependem continuamente da órbita periódica. Também provamos que uma classe homoclínica de X não apresentam ciclos de X formados por classes homoclínicas de X. Além disso, uma classe homoclínica de X é isolado se, e somente se, é Ω-isolado. Mais ainda, é isolado, se a classe homoclínica é hiperbólica. Todas estas propriedades são bem conhecidos para campos vetoriais estruturalmente estáveis e Axioma A. / We consider the vector fields C1 on a compact Riemannian manifold, boundaryless of finite dimension n, with n ≥3. A homoclinic class of a vector field is the closure of the set transverse homoclinic point associated with a hyperbolic periodic orbit. In this work, we prove that the homoclinic classes for a residual set of vector fields C1, are neutral sets, moreover, the homoclinic class is the intersection of the closure the stable set and unstable set. As a consequence of the properties of the neutral sets, we prove the generic properties of homoclinic classes. Thus, we proved that in the homoclinic classes of generic C1 vector fields X are maximal transitive sets, saturated and depend continuously on the periodic orbit. We also proved that a homoclinic class X, does not exhibit cycles of X formed by homoclinic class of X. Furthermore, homoclinic class X is isolated if it only if it is Ω-isolated. But still, it is isolated, the homoclinic class is hyperbolic. All these properties are well known to structurally stable vector fields and Axiom A.

Cette thèse traite de la reconstruction d'hypersurfaces au sein de champs de normales en dimension quelconque et trouve des applications dans l’analyse des empreintes digitales (lignes dermiques), des images satellites météorologiques (lieux de turbulence) et astrophysiques (bras de galaxies) ainsi que dans l’analyse stratigraphique des images sismiques (horizons). Les méthodes développées s’appuient sur la minimisation d’une équation aux dérivées partielles non linéaire reliant une hypersurface au pendage déduit d’un champ de normales. Elles prennent en compte des contraintes diverses telles que des points de passages, des frontières, des bornes et des discontinuités. La contribution principale de la thèse réside dans l’introduction d’un changement d’espace du pendage qui permet de reconstruire aussi bien des hypersurfaces exprimées sous des formes implicites dans les repères de définition des champs de normales que des horizons sismiques de manière rapide et interactive. Deux schémas de reconstruction d’horizons sismiques unidimensionnels présentant une discontinuité d’amplitude et de lieu inconnus sont également proposés. / This thesis deals with the reconstruction of hypersurfaces from a finite-dimensional normal vector field. Application scopes can be found in the analysis of fingerprints (epidermal ridges), meteorological images (eddies and cyclones), astrophysical images (galaxy arms) and in the stratigraphic analysis of seismic images (horizons). The hypersurfaces are obtained by solving a non-linear partial derivative equation relied on the local dip deduced from a normal vector field. Several constraints such as boundaries, bounds, points belonging to the hypersurface or discontinuities can be considered.The major contribution of this thesis consists in a local dip transformation which allows to reconstruct implicit hypersurfaces as well as seismic horizons by a fast and interactive method. Two schemes dedicated to the reconstruction of discontinuous one-dimensional seismic horizons are also proposed when the discontinuity location and jump are unknown.

Quasi-hom-Lie algebras (qhl-algebras) were introduced by Larsson and Silvestrov (2004) as a generalisation of hom-Lie algebras, which are a deformation of Lie algebras. Lie algebras are defined by an operation called bracket, [·,·], and a three-term Jacobi identity. By the theorem from Hartwig, Larsson, and Silvestrov (2003), this bracket and the three-term Jacobi identity are deformed into a new bracket operation, <·,·>, and a six-term Jacobi identity, making it a quasi-hom-Lie algebra. Throughout this thesis we deform the Lie algebra sl2(F), where F is a field of characteristic 0. We examine the quasi-deformed relations and six-term Jacobi identities of the following polynomial algebras: F[t], F[t]/(t2), F[t]/(t3), F[t]/(t4), F[t]/(t5), F[t]/(tn), where n is a positive integer ≥2, and F[t]/((t-t0)3). Larsson and Silvestrov (2005) and Larsson, Sigurdsson, and Silvestrov (2008) have already examined some of these cases, which we repeat for the reader's convenience. We further investigate the following σ-twisted derivations, and how they act in the different cases of mentioned polynomial algebras: the ordinary differential operator, the shifted difference operator, the Jackson q-derivation operator, the continuous q-difference operator, the Eulerian operator, the divided difference operator, and the nilpotent imaginary derivative operator. We also introduce a new, general, σ-twisted derivation operator, which is σ(t) as a polynomial of degree k.

[pt] A visualização de campos vetoriais é uma componente essencial de numerosas aplicações, em particular na Visualização Científica. Porém, produzir representações de um fluxo nem sempre é uma tarefa simples, principalmente em se tratando de dados medidos, pois estes se apresentam corrompidos por ruídos. Esse trabalho apresenta uma técnica de visualização baseada em imagens auto-animadas, que expressa o movimento do fluxo à base de ilusões ópticas. A utilização de informações topológicas é proposta tanto como forma de melhorar o desempenho das técnicas existentes como na remoção de ruído, onde o conhecimento do usuário sobre o dado se torna peça fundamental no processo. / [en] Vector field visualization is an essential component of various applications, particularly in Scientific Visualization. However generating useful ow representation is not a simple task, especially when dealing with measured data which is corrupted by noise. This work presents a self-animating image visualization technique which conveys the ow movement based on optical illusions. The field s topological information is used to improve the performance of existing techniques and remove noise, where the user s knowledge of data is fundamental.

L'objectif de cette thèse est de décrire le comportement asymptotique des solutions à données petites du système de Vlasov-Maxwell. En particulier, on s'attachera à étudier tant le champ électromagnétique que le champ de Vlasov par des méthodes de champs de vecteurs, nous permettant ainsi d'éviter toute contrainte de support sur les données initiales. La structure isotrope du système de Vlasov-Maxwell est d'une importance capitale pour compenser le phénomène de résonance causé par les particules approchant la vitesse de propagation du champ électromagnétique. De ce fait, plusieurs parties de ce manuscrit sont dédiées à sa description. Ajoutons également que les méthodes de champs de vecteurs sont connues pour être robustes et s'adapter relativement bien à d'autres situations telles que l'étude des solutions de l'équation des ondes sur un espace-temps courbé. Cette souplesse nous a notamment permis, contrairement aux travaux précédents sur ce sujet, de considérer des plasmas avec des particules sans masse.Notre étude débute par le cas des grandes dimensions d ≥ 4 où les effets dispersifs sont plus importants et permettent ainsi d'obtenir de meilleurs taux de décroissance sur les solutions du système et leurs dérivées. Une nouvelle inégalité de décroissance pour les solutions d'une équation de transport relativiste constitue d'ailleurs un élément central de la démonstration. Afin d'établir un résultat analogue dans le cas où les particules sont sans masse, nous avons dû imposer que le champ de Vlasov s'annule initialement pour les petites vitesses puis nous avons ensuite montré que cette hypothèse était nécessaire. Dans un second temps, nous nous intéressons au cas tridimensionnel avec des particules sans masse, où une étude plus poussée de la structure des équations sera nécessaire afin d'obtenir les taux de décroissance optimaux pour les composantes isotropes du champ électromagnétique, les moyennes en vitesse de la fonction de distribution et leurs dérivées. Nous nous concentrons ensuite sur l'étude du comportement asymptotique des solutions à données petites du système de Vlasov-Maxwell massif en dimension 3. Des difficultés spécifiques nous forcent à modifier les champs de vecteurs utilisés précédemment pour l'équation de transport dans le but de compenser les pires termes d'erreurs des équations commutées. Enfin, on considère le même problème en se restreignant à l'étude des solutions à l'extérieur d'un cône de lumière. Les fortes propriétés de décroissance vérifiées par la moyenne en vitesse de la densité de particules dans cette région nous permettent d'affaiblir les hypothèses sur les données initiales et d'avoir une démonstration considérablement plus simple. / The purpose of this thesis is to study the asymptotic properties of the small data solutions of the Vlasov-Maxwell system using vector field methods for both the electromagnetic field and the particle density. No compact support asumption is required on the initial data. Instead, we make crucial use of the null structure of the equations in order to deal with a resonant phenomenon caused by the particles approaching the speed of propagation of the Maxwell equations. Due to the robustness of vector field methods and contrary to previous works on this topic, we also study plasmas with massless particles.We start by investigating the high dimensional cases d ≥ 4 where dispersive effects allow us to derive strong decay rate on the solutions of the system and their derivatives. For that purpose, we proved a new decay estimate for solutions to massive relativistic transport equations. In order to obtain an analogous result for massless particles, we required the velocity support of the distribution function to be initially bounded away from $0$ and we then proved that this assumption is actually necessary. The second part of this thesis is devoted to the three dimensional massless case, where a stronger understanding of the null structure of the Vlasov-Maxwell system is essential in order to derive the optimal decay rate of the null components of the electromagnetic field, the velocity average of the particle density and their derivatives. We then focus on the asymptotic behavior of the small data solutions of the massive Vlasov-Maxwell system in 3d. Specific problems force us to modify the vector fields used previously to study the Vlasov field in order to compensate the worst error terms in the commuted transport equations. Finally, still for the massive system in 3d, we restrict our study of the solutions to the exterior of a light cone. The strong decay properties satisfied by the velocity average of the particle density in such a region permit us to relax the hypothesis on the initial data and lead to a much simpler proof.

This dissertation develops the visual pursuit method for air-to-air tracking and rendezvous of unmanned aircraft systems. It also shows the development of vector-field and proportional-integral methods for controlling UAS flight in formation with other aircraft. The visual pursuit method is a nonlinear guidance method that uses vision-based line of sight angles as inputs to the algorithm that produces pitch rate, bank angle and airspeed commands for the autopilot to use in aircraft control. The method is shown to be convergent about the center of the camera image frame and to be stable in the sense of Lyapunov. In the lateral direction, the guidance method is optimized to balance the pursuit heading with respect to the prevailing wind and the location of the target on the image plane to improve tracking performance in high winds and reduce bank angle effort. In both simulation and flight experimentation, visual pursuit is shown to be effective in providing flight guidance in strong winds. Visual pursuit is also shown to be effective in guiding the seeker while performing aerial docking with a towed aerial drogue. Flight trials demonstrated the ability to guide to within a few meters of the drogue. Further research developed a method to improve docking performance by artificially increasing the length of the line of sight vector at close range to the target to prevent flight control saturation. This improvement to visual pursuit was shown to be an effective method for providing guidance during aerial docking simulations. An analysis of the visual pursuit method is provided using the method of adjoints to evaluate the effects of airspeed, closing velocity, system time constant, sensor delay and target motion on docking performance. A method for predicting docking accuracy is developed and shown to be useful for predicting docking performance for small and large unmanned aircraft systems.

No description available.

Ce travail de recherche s'intéresse à la commande sans capteur mécanique du moteur synchrone à aimants permanents (MSAP) à pôles saillants, particulièrement en basse vitesse, avec détection de la position initiale du rotor. Après une présentation des techniques et approches qui ont initié nos travaux, en terme d'estimation de la vitesse et/ou de la position, nous avons choisi celles qui présentent plus d'intérêt de point de vue stabilité, robustesse, précision et simplicité d'implémentation. La première approche est basée sur le Système Adaptatif avec Modèle de Référence (MRAS). Quant à la deuxième, elle est réalisée autour d'un observateur non-linéaire pour l'estimation de la position et de la vitesse du MSAP à pôles saillants. Les deux techniques d'observation de la vitesse sont associées à une commande par orientation du flux rotorique avec la technique MLI vectorielle. Pour détecter la position initiale du rotor, nous avons utilisé une nouvelle approche qui permet d'estimer cette position avec une incertitude de ±5° mécanique. Cette nouvelle approche est basée sur l'application de signaux tests aux bornes des phases statoriques du MSAP. Des résultats de simulation et expérimentaux sont présentés tout au long de ces travaux pour valider les études théoriques de la commande vectorielle sans capteur mécanique du MSAP. Enfin, nous avons étudié et analysé les performances de la commande tolérante aux défauts sans capteur mécanique du MSAP en présence de défaillances de types transistors à l'état-off. / This research focuses on the sensorless vector control of a salient pole permanent magnet synchronous motor (PMSM), particularly at low speed, with detection of the initial rotor position. In first step, an overview of the state of the art concerning the estimation of the rotor speed as well as the initial rotor position of PMSM is addressed. From such a study, we have adopted an interesting strategy based on the model reference adaptive system (MRAS). The second step in this research consists in studying the performances and the feasibility of a non-linear observer for closed-loop vector control of salient pole PMSM. The MRAS technique as well as the non-linear observer is associated to a vector control scheme based on the field oriented strategy with space vector pulse width modulation (SVPWM). To detect the initial rotor position, we have proposed a new approach which estimates the position with a resolution of ±5° mechanical degrees. This new approach is based on applying short voltage pulses to the stator winding of salient pole PMSM. Several simulation and experimental results are presented to confirm the theoretical studies of the sensorless vector control of the salient pole PMSM drive. Finally, we have analyzed the performances of the sensorless speed fault tolerant control (FTC) of salient pole PMSM under failures related to the voltage source inverter (open circuit fault). The experimental results obtained based on the proposed techniques using nonlinear and MRAS observers have been improved in term of the reliability and allow a continuous operation of the salient pole PMSM drive even when it is supplied with two inverter legs.

Abstract The dissertation considers a degree theory and the index of a critical point of demi-continuous, everywhere defined mappings of the monotone type. A topological degree is derived for mappings from a Banach space to its dual space. The mappings satisfy the condition (S+), and it is shown that the derived degree has the classical properties of a degree function. A formula for the calculation of the index of a critical point of a mapping A : X→X* satisfying the condition (S+) is derived without the separability of X and the boundedness of A. For the calculation of the index, we need an everywhere defined linear mapping A' : X→X* that approximates A in a certain set. As in the earlier results, A' is quasi-monotone, but our situation differs from the earlier results because A' does not have to be the Frechet or Gateaux derivative of A at the critical point. The theorem for the calculation of the index requires a construction of a compact operator T = (A' + Γ)-1Γ with the aid of linear mappings Γ : X→X and A'. In earlier results, Γ is compact, but here it need only be quasi-monotone. Two counter-examples show that certain assumptions are essential for the calculation of the index of a critical point.