Measuring efficiency with neural networks. An application to the public sector

In this note we propose the artificial neural networks for measuring efficiency as a complementary tool to the common techniques of the efficiency literature. In the application to the public sector we find that the neural network allows to conclude more robust results to rank decision-making units.DEA

Measurement in control and discrimination of entangled pairs under self-distortion

Quantum correlations and entanglement are fundamental resources for quantum information and quantum communication processes. Developments in these fields normally assume these resources stable and not susceptible of distortion. That is not always the case, Heisenberg interactions between qubits can produce distortion on entangled pairs generated for engineering purposes (e. g. for quantum computation or quantum cryptography). Experimental work shows how to produce entangled spin qubits in quantum dots and electron gases, so its identification and control are crucial for later applications. The presence of parasite magnetic fields modifies the expected properties and behavior for which the pair was intended. Quantum measurement and control help to discriminate the original state in order to correct it or, just to try of reconstruct it using some procedures which do not alter their quantum nature. Two different kinds of quantum entangled pairs driven by a Heisenberg Hamiltonian with an additional inhomogeneous magnetic field which becoming self-distorted, can be reconstructed without previous discrimination by adding an external magnetic field, with fidelity close to 1 (with respect to the original state, but without discrimination). After, each state can be more efficiently discriminated. The aim of this work is to show how combining both processes, first reconstruction without discrimination and after discrimination with adequate non-local measurements, it's possible a) improve the discrimination, and b) reprepare faithfully the original states. The complete process gives fidelities better than 0.9. In the meanwhile, some results about a class of equivalence for the required measurements were found. This property lets us select the adequate measurement in order to ease the repreparation after of discrimination, without loss of entanglement.Comment: 6 figure

A spectral-based numerical method for Kolmogorov equations in Hilbert spaces

We propose a numerical solution for the solution of the Fokker-Planck-Kolmogorov (FPK) equations associated with stochastic partial differential equations in Hilbert spaces. The method is based on the spectral decomposition of the Ornstein-Uhlenbeck semigroup associated to the Kolmogorov equation. This allows us to write the solution of the Kolmogorov equation as a deterministic version of the Wiener-Chaos Expansion. By using this expansion we reformulate the Kolmogorov equation as a infinite system of ordinary differential equations, and by truncation it we set a linear finite system of differential equations. The solution of such system allow us to build an approximation to the solution of the Kolmogorov equations. We test the numerical method with the Kolmogorov equations associated with a stochastic diffusion equation, a Fisher-KPP stochastic equation and a stochastic Burgers Eq. in dimension 1.Comment: 28 pages, 10 figure

On the uniqueness of the helicoid and Enneper’s surface in the Lorentz-Minkowski space R31

In this paper we deal with the uniqueness of the Lorentzian helicoid and Enneper’s surface among properly embedded maximal surfaces with lightlike boundary of mirror symmetry in the Lorentz-Minkowski space R3Ministerio de Ciencia y Tecnología MTM2004-00160Ministerio de Ciencia y Tecnología MTM2007-61775Junta de Andalucía P06-FQM-01642Junta de Andalucía FQM32

Harmonic mappings and conformal minimal immersions of Riemann surfaces into RN

We prove that for any open Riemann surface N, natural number N ≥ 3, non-constant harmonic map h:N→R N−2 and holomorphic 2-form H on N , there exists a weakly complete harmonic map X=(Xj)j=1,…,\scN:N→R\scN with Hopf differential H and (Xj)j=3,…,\scN=h. In particular, there exists a complete conformal minimal immersion Y=(Yj)j=1,…,\scN:N→R\scN such that (Yj)j=3,…,\scN=h . As some consequences of these results (1) there exist complete full non-decomposable minimal surfaces with arbitrary conformal structure and whose generalized Gauss map is non-degenerate and fails to intersect N hyperplanes of CP\scN−1 in general position. (2) There exist complete non-proper embedded minimal surfaces in R\scN, ∀\scN>3.Ministerio de Ciencia y Tecnología MTM2007-61775Ministerio de Ciencia y Tecnología MTM2007-64504Junta de Andalucía P09-FQM-508

Convergencia de la política impositiva en la Unión Europea: un análisis empírico

En este trabajo se analiza la convergencia de la política impositiva en la UE- 15 en el periodo 1965-2005 mediante un enfoque de series temporales. El principal objetivo es contrastar la convergencia de los principales componentes de los ingresos tributarios –renta y beneficios, contribuciones a la seguridad social, propiedad, impuestos generales sobre bienes y servicios, impuestos específicos sobre bienes y servicios- tomando como referencias Alemania, Reino Unido y la media europea. El análisis se realiza desde dos perspectivas complementarias: la presión fiscal y la estructura impositiva. Mediante contrastes de raíz unitaria y de estacionariedad con cambio estructural, y analizando la condición de beta convergencia, los resultados muestran poca evidencia de convergencia fiscal. La convergencia se presenta con similar intensidad con respecto a las tres referencias y en los años previos a la ruptura endógena que, en general, se sitúa a finales de los 80 y comienzos de los 90. Además, la convergencia se centra básicamente en la imposición sobre renta y beneficios y bienes y servicios. La evidencia empírica muestra por tanto que la autonomía de los países, sus estructuras económicas diferenciadas y las preferencias políticas sobre el grado de intervención pública prevalecen sobre la idea de igualdad fiscal en la UE.______________________________________________This paper examines the tax policy convergence in the EU-15 during the period 1965-2005 using a time series approach. The main purpose is to assess the convergence of the main components of tax revenue -income and profits, social security contributions, property, general taxes on goods and services, taxes on specific goods and services- taking as references Germany, the United Kingdom and the European average. The analysis is carried out from two complementary perspectives: the tax burden and the tax structure. Using unit roots and stationarity tests with a structural change, and also analyzing β-convergence, the results show little evidence of tax convergence. Convergence appears with similar intensity with respect to the three benchmarks, and in the years previous to the structural break which, in general, was situated endogenously at the end of the 1980s or at the beginning of the 1990s. Moreover, tax convergence is basically centred on income and profits, and goods and services taxation. The empirical evidence shows that the autonomy of the countries, their different economic structures and political preferences regarding the degree of public intervention, prevail over the idea of fiscal equalization in the EU

Complete minimal surfaces and harmonic functions

We prove that for any open Riemann surface N and any non constant harmonic function h : N → R, there exists a complete conformal minimal immersion X : N → R3 whose third coordinate function coincides with h. As a consequence, completeminimal surfaceswith arbitrary conformal structure andwhose Gauss map misses two points are constructed.Ministerio de Educación y Ciencia MTM2007-61775Ministerio de Educación y Ciencia MTM2007-64504Junta de Andalucía P06-FQM-01642