A construction for modified generalized Hadamard matrices using QGH matrices

Let G be a group of order mu and U a normal subgroup of G of order u. Let G/U = {U_1, U_2,･･･, U_m} be the set of cosets of U in G. We say a matrix H = [h_] order k with entries from G is a quasi-generalized Hadamard matrix with respect to the cosets G/U if Σ_ h_ h^_ = λ_ U_1 + ･･･ + λ_ U_m (∃λ_, ･･･ , ∃λ_ ∊ Z) for any i≠j. On the other hand, in our previous article we defined a modified generalized Hadamard matrix GH (s,u,λ) over a group G, from which a TD_λ(uλ, u) admitting G as a semiregular automorphism group is obtained. In this article, we present a method for combining quasi-generalized Hadamard matrices and semiregular relative difference sets to produce modified generalized Hadamard matrices

Exploitation de la phase en imagerie acoustique audible et ultrasonore

L’imagerie à partir d’ondes acoustiques permet de répondre à plusieurs besoins. D’une part, les ondes ultrasonores sont utilisées pour effectuer des échographies dans le domaine médical, mais aussi pour inspecter et suivre la santé de structures. D’autre part, en utilisant les ondes sonores, il est possible de localiser, caractériser, et évaluer l’intensité de diverses sources de bruits. Étant alimentées par des applications et visées différentes, les techniques d’imagerie proposées et utilisées dans les dernières décennies pour ces deux domaines se distinguent. Étant donné les bases communes à l’imagerie sonore et ultrasonore, il serait pertinent de faire bénéficier chaque domaine des avancées en traitement de signal de l’autre domaine. Ce projet de thèse suggère donc une revue des techniques d’imagerie des deux domaines d’imagerie afin d’identifier les outils et techniques d’imagerie prometteuses à adapter et tester sur l’autre domaine d’imagerie. Afin de tester et valider différentes approches d’imagerie, deux types de sources étendues ont été considérées dans le domaine de l’audible. Numériquement, des pistons et plaques simplement supportées bafflées ont été considérés. Pour la validation expérimentale, les cartographies obtenues à l’aide de différents algorithmes ont été comparées avec une mesure de référence obtenue par déflectométrie optique. Dans le domaine ultrasonore, un appareil de calibration (phantom CIRS Model 040GSE) a permis de comparer les résolutions et contrastes obtenus à l’aide de différents algorithmes. Il est montré que l’utilisation de la cohérence de phase dans le domaine de l’audible aide à la reconstruction de sources étendues. En effet, les formulations proposées sont basées sur une réduction du domaine d’imagerie à partir de la cohérence de phase. Cette réduction aide au conditionnement du problème et se traduit par une solution moins sensible au bruit. Aussi, contrairement aux techniques de formation de voies dans le domaine temporel, les algorithmes proposés permettent de reconstruire l’amplitude du champ vibratoire transitoire (vitesse/accélération normale) de sources étendues cohérentes. De plus, les cartographies obtenues présentent moins d’artefacts d’imagerie que les techniques de référence. En imagerie médicale par ultrasons, les résultats montrent que lorsque couplé avec une nouvelle métrique de cohérence de phase, l’algorithme Excitelet développé dans le formalisme de la Generalized Cross Correlation (répandue en imagerie acoustique) résulte en de meilleures résolutions et contrastes que l’algorithme de référence. Par ailleurs, l’utilisation de la métrique de cohérence de phase et du filtre fréquentiel proposé résulte en une diminution des artefacts d’imagerie. Enfin, étant flexible et grandement parallélisable, le formalisme d’imagerie proposé s’avère utile pour le suivi d’outils médicaux en anesthésie régionale guidée par ultrasons.Abstract : Imaging using acoustical waves can meet several needs. On the one hand, ultrasonic waves are used to perform ultrasound scans in the medical field, but also to inspect and monitor the health of structures. On the other hand, by using sound waves, it is possible to locate, characterize, and evaluate the intensity of various noise sources. Being driven by different applications and aims, the imaging techniques proposed and used in the last decades for these two fields differ. Given the common bases of sound and ultrasound imaging, it would be relevantto make each field benefit from the signal processing advances of the other field. This thesis project therefore suggests to firstly review the imaging techniques of the two imaging domains in order to identify promising imaging tools and techniques, and secondly adapt and use those concepts for the other imaging field. In order to test and validate different imaging approaches, two types of extended sources were considered in the audible domain. Numerically, baffled simply supported plates and pistons were considered. Experimentally, the maps obtained using different algorithms were compared with reference measurements obtained by optical deflectometry. In the ultrasonic field, a phantom (CIRS Model 040GSE) was used to compare the resolutions and contrasts obtained using different algorithms. It is shown that the use of phase coherence in acoustic imaging helps for the reconstruction of extended sources. Indeed, the proposed formulations are based on a reduction of the imaging domain using phase coherence. This reduction improves the conditioning of the problem and results in a less sensitive to noise solution. Also, contrary to delay and sum techniques, the proposed algorithm allows the reconstruction of the amplitude of the transient vibration field (normal acceleration) of the structure under consideration. In addition, the resulting images present fewer artifacts than the reference techniques. In medical ultrasound imaging, the results show that when coupled with a new phase coherence metric, the Excitelet algorithm developed in the formalism of Generalized Cross Correlation (widely used in acoustic imaging) results in better resolutions and contrasts than the reference algorithm. In addition, the use of the proposed phase coherence metrics and frequency filter results in a reduction of imaging artifacts. Finally, being flexible and highly parallelizable, the proposed imaging formalism shows potential for the monitoring of medical tools in ultrasound-guided regional anesthesia

Longitudinal clinical covariates influence on CD4+ cell count after seroconversion.

Doctoral Degree. University of KwaZulu-Natal, Durban.The Acquired Immunodeficiency Syndrome (AIDS) pandemic is a global challenge. The human immunodeficiency virus (HIV) is notoriously known for weakening the immune system and opening channels for opportunistic infections. The Cluster of Difference 4 (CD4+) cells are mainly killed by the HIV and hence used as a health indicator for HIV infected patients. In the past, the CD4+ count diagnostics were very expensive and therefore beyond the reach of many in resource-limited settings. Accordingly, the CD4+ count’s clinical covariates were the potential diagnostic tools. From a different angle, it is essential to examine a trail of the clinical covariates effecting the CD4+ cell response. That is, inasmuch as the immune system regulates the CD4+ count fluctuations in reaction to the viral invasion, the body’s other complex functional systems are bound to adjust too. However, little is known about the corresponding adaptive behavioural patterns of the clinical covariates influence on the CD4+ cell count. The investigation in this study was carried out on data obtained from the Centre for the Programme of AIDS research in South Africa (CAPRISA), where initially, HIV negative patients were enrolled into different cohorts, for different objectives. These HIV negative patients were then followed up in their respective cohort studies. As soon as a patient seroconverted in any of the cohort studies, the patient was then enrolled again, into a new cohort of HIV positive patients only. The follow-up on the seroconvertants involved a simultaneous recording of repeated measurements of the CD4+ count and 46 clinical covariates. An extensive exploratory analysis was consequently performed with three variable reduction methods for high-dimensional longitudinal data to identify the strongest clinical covariates. The sparse partial least squares approach proved to be the most appropriate and a robust technique to adopt. It identified 18 strongest clinical covariates which were subsequently used to fit other sophisticated statistical models including the longitudinal multilevel models for assessing inter-individual variation in the CD4+ count due to each clinical covariate. Generalised additive mixed models were then used to gain insight into the CD4+ count trends and possible adaptive optimal set-points of the clinical covariates. To single out break-points in the change of linear relationships between the CD4+ count and the covariates, segmented regression models were employed. In getting to grips with the understanding of the highly complex and intertwined relationships between the CD4+ count, clinical covariates and the time lagged effects during the HIV disease progression, a Structural Equation Model (SEM) was constructed and fitted. The results showed that sodium consistently changed its effects at 132mEq/L and 140 mEq/L across all the post HIV infection phases. Generally, the covariate influence on the CD4+ count varied with infection phase and widely between individuals during the anti-retroviral therapy (ART). We conlude that there is evidence of covariate set-point adaptive behaviour to positively influence the CD4+ cell count during the HIV disease progression