Notes on Oscillator-Like Interactions of Various Spin Relativistic Particles

The equations for various spin particles with oscillator-like interactions are discussed in this talk. Contents: 1. Comment on "The Klein-Gordon Oscillator"; 2. The Dirac oscillator in quaternion form; 3. The Dirac-Dowker oscillator; 4. The Weinberg oscillator; 5. Note on the two-body Dirac oscillator.Comment: LaTeX file, 12 pp. Talk given at the Second Workshop "Osciladores Arm\'onicos". Cocoyoc, M\'exico, March 23-25, 1994. To be published in NASA Conference Proceedings. Preprint IFUNAM FT-94-44, EFUAZ-94-0

Automatic methods for predicting functionally important residues

Sequence analysis is often the first guide for the prediction of residues in a protein family that may have functional significance. A few methods have been proposed which use the division of protein families into subfamilies in the search for those positions that could have some functional significance for the whole family, but at the same time which exhibit the specificity of each subfamily (“Tree-determinant residues”). However, there are still many unsolved questions like the best division of a protein family into subfamilies, or the accurate detection of sequence variation patterns characteristic of different subfamilies. Here we present a systematic study in a significant number of protein families, testing the statistical meaning of the Tree-determinant residues predicted by three different methods that represent the range of available approaches. The first method takes as a starting point a phylogenetic representation of a protein family and, following the principle of Relative Entropy from Information Theory, automatically searches for the optimal division of the family int