Quaterninic Kähler manifolds, constrained instantons, and the magic square

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Of Eureka Moments and Magic Barometers: Freedom of Religion as the “First” Freedom in the Canadian Constitutional Context

"La liberté de religion, souvent reconnue comme étant la « première liberté » dans de nombreuses traditions juridiques, reflète également les différentes conceptions de la place de l'individu et de la communauté dans la société. Cet article examinera la liberté de religion dans le contexte constitutionnel canadien. Nous avons choisi d'étudier la liberté de religion dans trois vagues successives : avant l'entrée en vigueur de la Déclaration canadienne des droits, sous la Déclaration canadienne des droits; et enfin, après l'entrée en vigueur de la Charte canadienne des droits et libertés. De plus, l'accommodement ainsi que de la proportionnalité de la liberté de religion d'un individu sera également traité. Ainsi que nous le démontrerons, la liberté de religion a engendré un repositionnement de l'individu face aux intérêts de la communauté ainsi qu'une réinterprétation des justifications menant à la sauvegarde de ces croyances."

Non invasive classification system of scoliosis curve types using least-squares support vector machines

Objective To determine scoliosis curve types using non invasive surface acquisition, without prior knowledge from X-ray data. Methods Classification of scoliosis deformities according to curve type is used in the clinical management of scoliotic patients. In this work, we propose a robust system that can determine the scoliosis curve type from non invasive acquisition of the 3D back surface of the patients. The 3D image of the surface of the trunk is divided into patches and local geometric descriptors characterizing the back surface are computed from each patch and constitute the features. We reduce the dimensionality by using principal component analysis and retain 53 components using an overlap criterion combined with the total variance in the observed variables. In this work, a multi-class classifier is built with least-squares support vector machines (LS-SVM). The original LS-SVM formulation was modified by weighting the positive and negative samples differently and a new kernel was designed in order to achieve a robust classifier. The proposed system is validated using data from 165 patients with different scoliosis curve types. The results of our non invasive classification were compared with those obtained by an expert using X-ray images. Results The average rate of successful classification was computed using a leave-one-out cross-validation procedure. The overall accuracy of the system was 95%. As for the correct classification rates per class, we obtained 96%, 84% and 97% for the thoracic, double major and lumbar/thoracolumbar curve types, respectively. Conclusion This study shows that it is possible to find a relationship between the internal deformity and the back surface deformity in scoliosis with machine learning methods. The proposed system uses non invasive surface acquisition, which is safe for the patient as it involves no radiation. Also, the design of a specific kernel improved classification performance.