Arithmetic geometry of toric varieties. Metrics, measures and heights

We show that the height of a toric variety with respect to a toric metrized line bundle can be expressed as the integral over a polytope of a certain adelic family of concave functions. To state and prove this result, we study the Arakelov geometry of toric varieties. In particular, we consider models over a discrete valuation ring, metrized line bundles, and their associated measures and heights. We show that these notions can be translated in terms of convex analysis, and are closely related to objects like polyhedral complexes, concave functions, real Monge-Amp\`ere measures, and Legendre-Fenchel duality. We also present a closed formula for the integral over a polytope of a function of one variable composed with a linear form. This allows us to compute the height of toric varieties with respect to some interesting metrics arising from polytopes. We also compute the height of toric projective curves with respect to the Fubini-Study metric, and of some toric bundles.Comment: Revised version, 230 pages, 3 figure

Social security and the search behaviour of workers approaching retirement

This paper explores the links between unemployment, retirement and their associated public insurance programs. It is a contribution to a growing body of literature focused on a better understanding of the labor behavior of advanced—age workers, which has gained importance as the pension crisis looms. The analysis combines the development of a new theoretical model and a detailed exploration of the empirical regularities using the Spanish Muestra Continua de Vidas Laborales (MCVL) dataset. The model is a extension of the standard search model, designed to reproduce the non—stationary environment faced by workers approaching retirement and to explore the interaction of unemployment benefits and retirement pensions. Via calibrated simulations we show that the basic empirical reemployment and retirement patterns can be rationalized as the optimal responses to both the labor market conditions and the institutional incentives. Generous Unemployment Benefits (for durations of up to two years) together with very significant early retirement penalties, make optimal to stay unemployed without searching for large groups of unemployed workers. This moral hazard problem can he substantially alleviated through institutional reform. Setting the early retirement penalties according to the age when the individual withdraws from the labor force (rather than when he/she claims the pension for the first time) seems particularly beneficial. It increases the labor supply, reduces the financial cost for the social security system and generate enough extra resources to compensate for the welfare loss of those unemployed directly hit by the reform.Unemployment search, job benefit, retirement

Introducción a la integración numérica de ecuaciones diferenciales algebraicas de índice 1

El objetivo de este trabajo es, tras introducir los conceptos y resultados básicos relacionados con las ecuaciones diferenciales algebraicas, el estudio de la integración numérica de las ecuaciones de índice 1 mediante métodos de tipo Rosenbrock. Se estudian con detalle las condiciones de orden de estos métodos, se han implementado métodos de Rosenbrock de órdenes 3 y 4, y se incluyen resultados numéricos obtenidos con dichos métodos cuando se integran las ecuaciones del péndulo y las de un amplificador con un transistor.Grado en Matemática

Android Malware Characterization using Metadata and Machine Learning Techniques

Android Malware has emerged as a consequence of the increasing popularity of smartphones and tablets. While most previous work focuses on inherent characteristics of Android apps to detect malware, this study analyses indirect features and meta-data to identify patterns in malware applications. Our experiments show that: (1) the permissions used by an application offer only moderate performance results; (2) other features publicly available at Android Markets are more relevant in detecting malware, such as the application developer and certificate issuer, and (3) compact and efficient classifiers can be constructed for the early detection of malware applications prior to code inspection or sandboxing.Comment: 4 figures, 2 tables and 8 page

A model problem concerning ionic transport in microstructured solid electrolytes

We consider ionic transport by diffusion and migration through microstructured solid electrolytes. The assumed constitutive relations for the constituent phases follow from convex energy and dissipation potentials which guarantee thermodynamic consistency. The effective response is determined by homogenizing the relevant field equations via the notion ofmulti-scale convergence. The resulting homogenized response involves several effective tensors, but they all require the solution of just one standard conductivity problem over the representative volume element. A multi-scale model for semicrystalline polymer electrolytes with spherulitic morphologies is derived by applying the theory to a specific class of two-dimensional microgeometries for which the effective response can be computed exactly. An enriched model accounting for a random dispersion of filler particles with interphases is also derived. In both cases, explicit expressions for the effective material parameters are provided. The models are used to explore the effect of crystallinity and filler content on the overall response. Predictions support recent experimental observations on doped poly-ethylene-oxide systems which suggest that the anisotropic crystalline phase can actually support faster ion transport than the amorphous phase along certain directions dictated by the morphology of the polymeric chains. Predictions also support the viewpoint that ceramic fillers improve ionic conductivity and cation transport number via interphasial effects.Facultad de IngenieríaDepartamento de Aeronáutic

A model problem concerning the ionic transport in microstructured solid electrolytes

We consider ionic transport by diffusion and migration through microstructured solid electrolytes. The effective response is determined by homogenizing the relevant field equations via the notion of multi-scale convergence. The theory is applied to semi-crystalline polymer electrolytes with spherulitic morphologies. Predictions support recent experimental observations on doped poly-ethylene-oxide (PEO) systems which suggest that the anisotropic crystalline phase can actually support faster ion transport than the amorphous phase along certain directions dictated by the morphology of the polymeric chains.Facultad de Ingenierí