published_or_final_version / abstract / Mathematics / Doctoral / Doctor of Philosophy

Infection by Campylobacter is the most notified gastrointestinal disease in New Zealand. Reliable recovery and identification of campylobacters is challenging. Improved and validated methods are needed to increase the power of subtyping and epidemiological studies to trace the sources and transmission routes of Campylobacter. An enrichment-PCR method for the isolation and detection of C. jejuni and C. coli was developed and sensitivity levels determined in 13 environmental matrices, including animal faeces, food and water. Less than ten cells per sample of either C. jejuni or C. coli could be detected, except for rabbit faeces where the minimum number of cells detected per sample was greater than ten cells for C. coli (range 3-32 cells). The sensitivity of the method was comparable to that determined for the conventional methods in the same matrices. Application of the method to retail chicken carcasses (n =204) determined a prevalence of 27.5% C. jejuni and 1% C. coli. River water assays (n = 293) found 55.3% of samples to contain C. jejuni and 4.1% C. coli. Furthermore, the enrichment-PCR assay was shown to identify up to three subtypes in individual water samples. It was proposed that the identification of non-dominant subtypes carried by a chicken carcass may aid the identification of subtypes implicated in human cases of campylobacteriosis. An average of twenty-three C. jejuni isolates from each of ten retail chicken carcass were subtyped by PFGE using the two restriction enzymes SmaI and KpnI. Fifteen subtypes, in total, were identified from the ten carcasses. One subtype was identified on three carcasses. Five carcasses carried a single subtype, three carcasses carried two subtypes each and two carcasses carried three subtypes each. Some of the subtypes carried by an individual carcass were shown to be clonally related raising the question of in vivo recombination events during host passage. Comparison of C. jejuni subtypes from chickens with those isolated from human clinical cases revealed three of the fifteen subtypes correlated with those from human cases. None of the minority subtypes were identified in human case isolate data, suggesting that the lack of identification of non-dominant subtypes from chicken carcasses may not hinder the investigation of campylobacteriosis outbreaks.

No description available.

No description available.

No description available.

Cette thèse traite de l'étude de méthodes de diagonalisation conjointe de matrices complexes, en vue de la séparation de sources, que ce soit dans le domaine des télécommunications numériques ou de la radioastronomie. Après avoir présenté les motivations qui ont poussé cette étude, nous faisons un bref état de l'art dans le domaine. Le problème de la diagonalisation conjointe, ainsi que celui de la séparation de source sont rappelés, et un lien entre ces deux sujets est établi. Par la suite, plusieurs algorithmes itératifs sont développés. Dans un premier temps, des méthodes utilisant une mise à jour de la matrice de séparation, de type gradient, sont présentées. Elles sont basées sur des approximations judicieuses du critère considéré. Afin d'améliorer la vitesse de convergence, une méthode utilisant un calcul du pas optimal est présentée, et plusieurs variantes de ce calcul, basées sur les approximations faites précédemment, sont développées. Deux autres approches sont ensuite introduites. La première détermine la matrice de séparation de manière analytique, en calculant algébriquement les termes composant la matrice de mise à jour par paire à partir d'un système d'équations linéaire. La deuxième estime récursivement la matrice de mélange, en se basant sur une méthode de moindres carrés alternés. Afin d'améliorer la vitesse de convergence, une recherche de pas d'adaptation linéaire est proposée. Ces méthodes sont alors validées sur un problème de diagonalisation conjointe classique. Puis les algorithmes sont appliqués à la séparation de sources de signaux de télécommunication numérique, en utilisant des statistiques d'ordre deux ou supérieur. Des comparaisons sont également effectuées avec des méthodes standards. La deuxième application concerne l'élimination des interférences terrestres à partir de l'estimation de l'espace associé, afin d'observer au mieux des sources cosmiques, issues de données de station LOFAR. / This thesis deals with the study of joint diagonalization of complex matrices methods for source separation, wether in the field of numerical telecommunications and radioastronomy. After having introduced the motivations that drove this study, we present a brief state-of-the-art in the field. The joint diagonalization and source separation problems are reminded, and a link between these two themes is established. Thereafter, several iterative algorithms are developed. First, methods using a gradient-like update of the separation matrix are introduced. They are based on wise approximations of the considered criterion. In order to improve the convergence speed, a method using a computation of an optimal step size is presented, and variations around this computation, based on the previously introduced approximations are done. Two other approaches are then introduced. The first one analytically determines the separation matrix, by algebraically computing the terms composing the update matrix pairwise from a linear equation system. The second one recursively estimates the mixing matrix, based on an alternating least squares method. In order to enhance the convergence speed, a seek of an enhanced line search algorithm is proposed. These methods are then validated on a classical joint diagonalization problem. Aterwards, these algorithms are applied to the source separation of numerical communication signals, while using second or higher order statistics. Comparisons are also made with well-known methods. The second application relates to elimination of rterrestrial interferences from the estimation of the associated space in order to observe at best cosmic sources from LOFAR station data.

No description available.

Determining the intrinsic dimension of a hyperspectral image is an important step in the spectral unmixing process, since under- or over- estimation of this number may lead to incorrect unmixing for unsupervised methods. In this thesis we introduce a new method for determining the intrinsic dimension, using recent advances in Random Matrix Theory (RMT). This method is not sensitive to non-i.i.d. and correlated noise, and it is entirely unsupervised and free from any user-determined parameters. The new RMT method is mathematically derived, and robustness tests are run on synthetic data to determine how the results are a ected by: image size; noise levels; noise variability; noise approximation; spectral characteristics of the endmembers, etc. Success rates are determined for many di erent synthetic images, and the method is compared to two principal state of the art methods, Noise Subspace Projection (NSP) and HySime. All three methods are then tested on twelve real hyperspectral images, including images acquired by satellite, airborne and land-based sensors. When images that were acquired by di erent sensors over the same spatial area are evaluated, RMT gives consistent results, showing the robustness of this method to sensor characterisics.

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in ful lment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2014 / Matrix models, and their associated integrals, are encoded with a rich structure, especially when studied in the large N limit. In our project we study the dynamics of a Gaussian ensemble of m complex matrices or 2m hermitian matrices for d = 0 and d = 1 systems. We rst investigate the two hermitian matrix model parameterized in \matrix valued polar coordinates", and study the integral and the quantum mechanics of this system. In the Hamiltonian picture, the full Laplacian is derived, and in the process, the radial part of the Jacobian is identi ed. Loop variables which depend only on the eigenvalues of the radial matrix turn out to form a closed subsector of the theory. Using collective eld theory methods and a density description, this Jacobian is independently veri ed. For potentials that depend only on the eigenvalues of the radial matrix, the system is shown to be equivalent to a system of non-interacting (2+1)-dimensional \radial fermions" in a harmonic potential. The matrix integral of the single complex matrix system, (d = 0 system), is studied in the large N semi-classical approximation. The solutions of the stationary condition are investigated on the complex plane, and the eigenvalue density function is obtained for both the single and symmetrically extended intervals of the complex plane. The single complex matrix model is then generalized to a Gaussian ensemble of m complex matrices or 2m hermitian matrices. Similarly, for this generalized ensemble of matrices, we study both the integral of the system and the Hamiltonian of the system. A closed sector of the system is again identi ed consisting of loop variables that only depend on the eigenvalues of a matrix that has a natural interpretation as that of a radial matrix. This closed subsector possess an enhanced U(N)m+1 symmetry. Using the Schwinger-Dyson equations which close on this radial sector we derive the Jacobian of the change of variables to this radial sector. The integral of the system of m complex matrices is evaluated in the large N semi-classical approximation in a density description, where we observe the emergence of a new logarithmic term when m 2. The solutions of the stationary condition of the system are investigated on the complex plane, and the eigenvalue density functions for m 2 are obtained in the large N limit. The \fermionic description" of the Gaussian ensemble of m complex matrices in radially invariant potentials is developed resulting in a sum of non-interacting Hamiltonians in (2m + 1)-dimensions with an induced singular term, that acts on radially anti-symmetric wavefunctions. In the last chapter of our work, the Hamiltonian of the system of m complex matrices is formulated in the collective eld theory formalism. In this density description we will study the large N background and obtain the eigenvalue density function.

Lau Yuk Hong. / Bibliography: leaves 63-64 / Thesis (M.Ph.)--Chinese University of Hong Kong, 1984