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

Contribución a la caracterización químico-mineralógica de los esquistos del "Complejo de Ordes"

[Resumen] Se presentan los datos qUlmlcos y mineralógicos de 77 muestras de rocas esquistosas de la "Unidad Betanzos-Arzúa", perteneciente al "Complejo de Ordes" , con objeto de analizar la variabilidad existente y discutir las posibilidades de sectorización de los distintos tipos de rocas en función de parámetros de composición.[Abstract] This paper presents the chemical and mineralogical composi tion of 77 samples of schi ts belonging to the "Unit of Betanzos-Arzua" , included in the "Ordenes Complex" . Tqe data were used to make an analysis the variability in the composi tion of the rocks and a subdivision of the " Unidad " based on the rock characteristics was intented

Independent Component Analysis to Detect Clustered Microcalcification Breast Cancers

The presence of clustered microcalcifications is one of the earliest signs in breast cancer detection. Although there exist many studies broaching this problem, most of them are nonreproducible due to the use of proprietary image datasets. We use a known subset of the currently largest publicly available mammography database, the Digital Database for Screening Mammography (DDSM), to develop a computer-aided detection system that outperforms the current reproducible studies on the same mammogram set. This proposal is mainly based on the use of extracted image features obtained by independent component analysis, but we also study the inclusion of the patient's age as a nonimage feature which requires no human expertise. Our system achieves an average of 2.55 false positives per image at a sensitivity of 81.8% and 4.45 at a sensitivity of 91.8% in diagnosing the BCRP_CALC_1 subset of DDSM