We study the phase space of the quintom cosmologies for a class of exponential potentials. We combine normal forms expansions and the center manifold theory in order to describe the dynamics near equilibrium sets. Furthermore, we construct the unstable and center manifold of the massless scalar field cosmology motivated by the numerical results given in Lazkoz and Leon (Phys Lett B 638:303. arXiv:astro-ph/0602590, 2006). We study the role of the curvature on the dynamics. Several monotonic functions are defined on relevant invariant sets for the quintom cosmology. Finally, conservation laws of the cosmological field equations and algebraic solutions are determined by using the symmetry analysis and the singularity analysis.

This research is based on the study of a real database, in order to determine the factors of the High Cardiovascular Risk in the city of Santa Clara, in the Central Region of Cuba. Mathematical models of the high risk index, considering the characteristics of the population of the city are obtained. Four multivariate statistical techniques are applied to obtain the mathematical models: Linear Discriminant Analysis, Logistic Regression, Classification Trees and a Fuzzy Logic based model. Diversity measures are calculated for the base classifier. As a result, a set of classifiers are combined into a multiclassifier. This model is better than the others. The statistical package SPSS, Microsoft Excel and EFuzzy software were used to perform all the calculus.