Gravitation and the Local Symmetry Group of Spacetime

According to general relativity, the interaction of a matter field with gravitation requires the simultaneous introduction of a tetrad field, which is a field related to translations, and a spin connection, which is a field assuming values in the Lie algebra of the Lorentz group. These two fields, however, are not independent. By analyzing the constraint between them, it is concluded that the relevant local symmetry group behind general relativity is provided by the Lorentz group. Furthermore, it is shown that the minimal coupling prescription obtained from the Lorentz covariant derivative coincides exactly with the usual coupling prescription of general relativity. Instead of the tetrad, therefore, the spin connection is to be considered as the fundamental field representing gravitation.Comment: 8 pages, no figures. Some signs and references corrected; version to appear in Int. J. Theor. Phy

The whole mesh Deformation Model for 2D and 3D image segmentation

In this paper we present a novel approach for image segmentation using Active Nets and Active Volumes. Those solutions are based on the Deformable Models, with slight difference in the method for describing the shapes of interests - instead of using a contour or a surface they represented the segmented objects with a mesh structure, which allows to describe not only the surface of the objects but also to model their interiors. This is obtained by dividing the nodes of the mesh in two categories, namely internal and external ones, which will be responsible for two different tasks. In our new approach we propose to negate this separation and use only one type of nodes. Using that assumption we manage to significantly shorten the time of segmentation while maintaining its quality

Analysis domain model for shared virtual environments

The field of shared virtual environments, which also encompasses online games and social 3D environments, has a system landscape consisting of multiple solutions that share great functional overlap. However, there is little system interoperability between the different solutions. A shared virtual environment has an associated problem domain that is highly complex raising difficult challenges to the development process, starting with the architectural design of the underlying system. This paper has two main contributions. The first contribution is a broad domain analysis of shared virtual environments, which enables developers to have a better understanding of the whole rather than the part(s). The second contribution is a reference domain model for discussing and describing solutions - the Analysis Domain Model

Symplectic matrices with predetermined left eigenvalues

We prove that given four arbitrary quaternion numbers of norm 1 there always exists a $2\times 2$ symplectic matrix for which those numbers are left eigenvalues. The proof is constructive. An application to the LS category of Lie groups is given.Comment: 7 page