Thesis (M. Sc.)--University of Canterbury, 2008. / Typescript (photocopy). Includes bibliographical references (p. [58]). Also available via the World Wide Web.

Discontinuous dynamical system defined by impulsive autonomous differential equation is a field that has actually been considered rarely. Also, the properties of such systems have not been discussed thoroughly in the course of mathematical researches so far. This thesis comprises two parts, elaborated with a number of examples. In the first part, some results of the previous studies on the classical dynamical system are exposed. In the second part, the definition of discontinuous dynamical system defined by impulsive autonomous differential equation is formulated, and its properties are investigated, in the view of the known results of the studies on the classical dynamical system and impulsive differential equations.

Thesis (M. Sc.)--Dept. of Mathematics and Statistics, Concordia University, 1996. / "May 1996." Includes bibliographical references. Available also on the Internet.

We discuss Lojasiewicz's beautiful proof of the division theorem for smooth functions. The standard proofs are based on the Weierstrass preparation theorem for analytic functions and use techniques from the theory of partial differential equations. Lojasiewicz's approach is more geometric and syn¬thetic. In the appendices appear new proofs of results which are required for the theorem. / Dissertation (MSc (Mathematics))--University of Pretoria, 2006. / Mathematics and Applied Mathematics / unrestricted

Smoothness is a hallmark of healthy movement and has the potential to be used as a marker of recovery in rehabilitation settings. While much past research has focused on shoulder and elbow movements (reaching), little is known about movements of the wrist despite its importance in everyday life and its impairment in many neurological and biomechanical disorders. Our current lack of knowledge regarding wrist movement prevents us from improving current models, diagnosis, and treatment of wrist disorders. In particular, while movement smoothness is a well-known characteristic of reaching movements and may potentially be used to diagnose and monitor recovery from neurological impairments, little is known about the smoothness of wrist rotations. Therefore, because the smoothness of wrist rotations has not been characterized, it cannot be used as a marker for diagnosis and evaluation. This study examines the smoothness of wrist rotations in comparison to the known baseline of reaching movements. Subjects were asked to perform wrist and reaching movements under a variety of conditions, including different speed and direction. To measure movement smoothness, this study used an established metric of speed profile number of maxima and presents a novel method for characterizing smoothness by fitting a minimum-jerk trajectory to real movement data.The results show that 1) wrist rotations are significantly less smooth than reaching movements (p≤0.0016), 2) smoothness decreases significantly as speed decreases (p<0.0001), and 3) wrist movements exhibit a pattern of smoothness that varies significantly between targets and outbound/inbound movement directions (p<0.0001). Potential causes for results 1 and 3 are presented and tested by simulation or reference to prior studies, because these findings were previously unknown. The decrease in smoothness with speed (result 2) has been found in prior studies of smoothness in reaching and finger movements. The reasoning behind the first result is explored by testing whether the difference in smoothness between wrist and reaching movements was due to differences in mechanical, muscular, neural, or protocol-related properties. The reasoning behind the third result is explored by testing whether the difference in wrist direction was due to anisotropy in musculoskeletal dynamics or anisotropy in movement duration. The simulations show that the wrist’s bandwidth is greater than that of the arm, and that there is nonvoluntary power in the bandwidth of the wrist that would be low-pass filtered in reaching movements, indicating that at least some of the difference in smoothness between wrist and reaching movements is due to differences in mechanical properties. Differences in muscular, neural, or protocol-related properties (signal-dependent noise, proprioceptive acuity, and the speed requirements of the task, respectively) do not appear to be the cause of the difference in smoothness between wrist and reaching movements. Differences in wrist smoothness between movement directions appears to be related to differences in movement duration between directions.

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Les objectifs de cette thèse sont la validation d’une méthodologie de détermination de la température de surface (LST) et de l’émissivité de surface (LES) à partir des radiances hyperspectrales du capteur IASI à bord du satellite METOP. Il s’agit de montrer la possibilité d’extraire ces deux paramètres d’un signal hyperspectral IRT télédétecté dans une approche physique. Le domaine spectral d'étude s'étend de 750 à 1250 cm-1 (8 à 13,3 μm) et la résolution spectrale est de l'ordre du 0,25 cm-1, inscrivant ainsi ce travail dans le giron de la radiométrie à très haute résolution spectrale infrarouge. Après une étude des méthodes de séparation existantes, la méthode SpSm (Spectral Smothness), est validée. Une étude de sensibilité aux erreurs aux bruits atmosphérique et instrumental est menée. La méthode SpSm est appliquée aux données IASI en conditions réelles pour l’année 2008 dans une zone spatiale couvrant l’Europe et le Nord d’ Afrique. Les résultats sont validés d’une part avec les produits MODIS et SEVIRI, et d’autre part avec les paramètres température et émissivité obtenus à partir des radiances SEVIRI et l’algorithme TISI. / This thesis focuses on the validation of a methodology for determining the surface temperature (LST) and surface emissivity (LES) from hyperspectral radiances from the IASI sensor on board of the European satellite METOP. We show that it is possible to extract these two parameters from a remotely sensed TIR signal using a physical approach. The spectral range under study extends from 750 to 1250 cm-1 (8 to 13.3 μm) and the spectral resolution is 0.25 cm-1, placing this work in the context of very high spectral resolution infrared radiometry. After studying the existing methods of separation, the SpSm method (Spectral Smothness), is validated. A study of sensitivity to atmospheric and instrumental noise is conducted. The SpSm method is applied to the IASI data in real conditions in 2008 in a spatial area that covers Europeand North Africa. The results are validated on one hand with the MODIS and SEVIRI products, and on the otherhand with temperatures and emissivities obtained from the SEVIRI radiances and the TISI algorithm.

Neste trabalho, primeiramente, exploramos certos módulos de suavidade e K - funcionais definidos na esfera unitária m - dimensional e suas propriedades, dando prioridade a suas equivalências assintóticas e comparação com o erro de melhor aproximação. Uma das principais referências utilizadas foi (DAI; XU, 2010). Posteriormente, consideramos um módulo de suavidade e um K-funcional em espaços mais gerais, os espaços compactos 2-homogêneos, classe de espaços esta que contém a classe das esferas. A relação entre estes objetos e o raio de aproximação do operador translação (translação esférica, no contexto esférico) foi estudada. As principais referências foram (PLATONOV, 2009) e (PLATONOV, 1997). / In this work, we firstly explored certain moduli of smoothness and K - functionals defined on the m-dimensional unit sphere and their properties, mainly their asymptotic equivalence and relation to the best approximation error. The main reference is (DAI; XU, 2010). Later we consider a moduli of smoothness and a K-functional on a general setting, namely two-point homogeneous spaces, which has the unit spheres as one of its classes. Relations between those tools and the rate of approximation of the shiffting operator were studied. The main references here were (PLATONOV, 2009) and (PLATONOV, 1997).

The task of automatically segmenting 3-D surfaces representing object boundaries is important in quantitative analysis of volumetric images, which plays a vital role in numerous biomedical applications. For the diagnosis and management of disease, segmentation of images of organs and tissues is a crucial step for the quantification of medical images. Segmentation finds the boundaries or, limited to the 3-D case, the surfaces, that separate regions, tissues or areas of an image, and it is essential that these boundaries approximate the true boundary, typically by human experts, as closely as possible. Recently, graph-based methods with a global optimization property have been studied and used for various applications. Sepecifically, the state-of-the-art graph search (optimal surface segmentation) method has been successfully used for various such biomedical applications. Despite their widespread use for image segmentation, real world medical image segmentation problems often pose difficult challenges, wherein graph based segmentation methods in its purest form may not be able to perform the segmentation task successfully. This doctoral work has a twofold objective. 1)To identify medical image segmentation problems which are difficult to solve using existing graph based method and develop novel methods by employing graph search as a building block to improve segmentation accuracy and efficiency. 2) To develop a novel multiple surface segmentation strategy using deep learning which is more computationally efficient and generic than the exisiting graph based methods, while eliminating the need for human expert intervention as required in the current surface segmentation methods. This developed method is possibly the first of its kind where the method does not require and human expert designed operations. To accomplish the objectives of this thesis work, a comprehensive framework of graph based and deep learning methods is proposed to achieve the goal by successfully fulfilling the follwoing three aims. First, an efficient, automated and accurate graph based method is developed to segment surfaces which have steep change in surface profiles and abrupt distance changes between two adjacent surfaces. The developed method is applied and validated on intra-retinal layer segmentation of Spectral Domain Optical Coherence Tomograph (SD-OCT) images of eye with Glaucoma, Age Related Macular Degneration and Pigment Epithelium Detachment. Second, a globally optimal graph based method is developed to attain subvoxel and super resolution accuracy for multiple surface segmentation problem while imposing convex constraints. The developed method was applied to layer segmentation of SD-OCT images of normal eye and vessel walls in Intravascular Ultrasound (IVUS) images. Third, a deep learning based multiple surface segmentation is developed which is more generic, computaionally effieient and eliminates the requirement of human expert interventions (like transformation designs, feature extrraction, parameter tuning, constraint modelling etc.) required by existing surface segmentation methods in varying capacities. The developed method was applied to SD-OCT images of normal and diseased eyes, to validate the superior segmentaion performance, computation efficieny and the generic nature of the framework, compared to the state-of-the-art graph search method.