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El texto completo de este trabajo no está disponible en el Repositorio Académico UPC por restricciones de la casa editorial donde ha sido publicado., This research proposes a prediction model that might help reducing the dropout rate of university students in Peru. For this, a three-phase predictive analysis model was designed which was combined with the stages proposed by the IBM SPSS Modeler methodology. Bayesian network techniques was compared with decision trees for their level of accuracy over other algorithms in an Educational Data Mining (EDM) scenario. Data were collected from 500 undergraduate students from a private university in Lima. The results indicate that Bayesian networks behave better than decision trees based on metrics of precision, accuracy, specificity, and error rate. Particularly, the accuracy of Bayesian networks reaches 67.10% while the accuracy for decision trees is 61.92% in the training sample for iteration with 8:2 rate. On the other hand, the variables athletic person (0.30%), own house (0.21%), and high school grades (0.13%) are the ones that contribute most to the prediction model for both Bayesian networks and decision trees.

Lifts of Frobenius on formal schemes X over the p-adic completion of the maximal unramified extension of the p-adic integers may be viewed as arithmetic analogues of vector fields on manifolds. In particular, vector fields on the tangent bundle of a manifold, appearing for instance in Hamiltonian mechanics, have as arithmetic analogues lifts of Frobenius on arithmetic jet spaces J^1(X) of schemes. In this thesis, we first consider the projective space P^m and prove that lifts of Frobenius do not exist on its arithmetic jet spaces J^n(P^m_R) for n, m >= 1. Exhibiting a contrast in the case n=m=1 between the arithmetic and geometric frameworks, we show on the other hand that the space of vector fields on the tangent bundle T(P^1_k) lifting vector fields on P^1_k, where k is an algebraically closed field, has dimension 6 over k. Nevertheless, "normalized" vector fields, which play a role in Hamiltonian mechanics, do not exist on T(P^1_k). We proceed to prove a stronger result for the case n=m=1, that there are no effective Cartier divisors on J^2(P^1) that are finite-to-one over J^1(P^1), and discover that an analogous result holds in geometry. As a final result, we prove the nonexistence of lifts of Frobenius on the first jet space of any smooth quadric hypersurface in projective space.