Gap probabilities for the cardinal sine

We study the zero set of random analytic functions generated by a sum of the cardinal sine functions which form an orthogonal basis for the Paley-Wiener space. As a model case, we consider real-valued Gaussian coefficients. It is shown that the asymptotic probability that there is no zero in a bounded interval decays exponentially as a function of the length.

Measuring sustained superior performance at the firm level

This paper proposes a two-dimensional Strategic Performance Measure (SPM) to evaluate the achievement of sustained superior performance. This proposal builds primarily on the fact that, under the strategic management perspective, a firm's prevalent objective is the pursuit of sustained superior performance. Three basic conceptual dimensions stem from this objective: relativity, sign dependence, and dynamism. These are the foundations of the SPM, which carries out a separate evaluation of the attained superior performance and of its sustainability over time. In contrast to existing measures of performance, the SPM provides: (i) a dynamic approach by considering the progress or regress in performance over time, and (ii) a cardinal measurement of performance differences and its changes over time. The paper also proposes an axiomatic framework that a measure of strategic performance should comply with to be theoretically and managerially sound. Finally, an empirical illustration of the Spanish banking sector during 1987-1999 is herein provided by discussing some relevant cases.

The orthogonal subcategory problem in homotopy theory

It is known that, in a locally presentable category, localization exists with respect to every set of morphisms, while the statement that localization with respect to every (possibly proper) class of morphisms exists in locally presentable categories is equivalent to a large-cardinal axiom from set theory. One proves similarly, on one hand, that homotopy localization exists with respect to sets of maps in every cofibrantly generated, left proper, simplicial model category M whose underlying category is locally presentable. On the other hand, as we show in this article, the existence of localization with respect to possibly proper classes of maps in a model category M satisfying the above assumptions is implied by a large-cardinal axiom called Vopënka's principle, although we do not know if the reverse implication holds. We also show that, under the same assumptions on M, every endofunctor of M that is idempotent up to homotopy is equivalent to localization with respect to some class S of maps, and if Vopënka's principle holds then S can be chosen to be a set. There are examples showing that the latter need not be true if M is not cofibrantly generated. The above assumptions on M are satisfied by simplicial sets and symmetric spectra over simplicial sets, among many other model categories.

Epireflections and supercompact cardinals

We prove that, under suitable assumptions on a category C, the existence of supercompact cardinals implies that every absolute epireflective class of objects of C is a small-orthogonality class. More precisely, if L is a localization functor on an accessible category C such that the unit morphism X→LX is an extremal epimorphism for all X, and the class of L-local objects is defined by an absolute formula with parameters, then the existence of a supercompact cardinal above the cardinalities of the parameters implies that L is a localization with respect to some set of morphisms.

Estudi neurofisiològic del control executiu de l'atenció en l'esquizofrènia

Report for the scientific sojourn carried out at the Departament de Psicologia de la Universitat de les Illes Balears, Spain, from May until July 2006. Abnormalities in executive functions, including set shifting ability, represent a cardinal feature in schizophrenia. This ability to adapt behavior to changing environmental events or contingencies requires a mechanism for switching attention between learned stimulus-response associations, or task-sets. This project aimed at gaining further knowledge on the brain mechanisms related to the executive control of attention in schizophrenia during the performace of a task switching paradigm. Furthermore, a secondary goal was to further examine the interrelationships between endogenous and exogenous control processes in task set switching.

Preference intensities and risk aversion in school choice: a laboratory experiment

We experimentally investigate in the laboratory two prominent mechanisms that are employed in school choice programs to assign students to public schools. We study how individual behavior is influenced by preference intensities and risk aversion. Our main results show that (a) the Gale-Shapley mechanism is more robust to changes in cardinal preferences than the Boston mechanism independently of whether individuals can submit a complete or only a restricted ranking of the schools and (b) subjects with a higher degree of risk aversion are more likely to play "safer" strategies under the Gale-Shapley but not under the Boston mechanism. Both results have important implications for the efficiency and the stability of the mechanisms.

J2EE Tienda Virtual

Aquest treball de final de carrera exposa totes les etapes que intervenen en el desenvolupament d'una aplicació empresarial mostrant les virtuts que ens facilita l'arquitectura J2EE.

Measuring sustained superior performance at the firm level

This paper proposes a two-dimensional Strategic Performance Measure (SPM) to evaluate the achievement of sustained superior performance. This proposal builds primarily on the fact that, under the strategic management perspective, a firm's prevalent objective is the pursuit of sustained superior performance. Three basicconceptual dimensions stem from this objective: relativity, sign dependence, and dynamism. These are the foundations of the SPM, which carries out a separate evaluation of the attained superior performance and of its sustainability over time. In contrast to existing measures of performance, the SPM provides: (i) a dynamic approach by considering the progress or regress in performance over time, and (ii) a cardinal measurement of performance differences and its changes over time. The paper also proposes an axiomatic framework that ameasure of strategic performance should comply with to be theoretically and managerially sound. Finally, anempirical illustration of the Spanish banking sector during 1987-1999 is herein provided by discussing some relevant case

Criptosistema ElGammal mediante curvas hiperelípticas

En este trabajo se ha realizado un estudio de las curvas hiperelípticas, y más concretamente, de su variedad jacobiana. Se han implementado una serie de operaciones matemáticas sobre elementos de la variedad jacobiana (Divisores), como la suma, el doblado o el cálculo del divisor mitad, así como el cálculo del cardinal de la jacobiana. Una vez realizada esta parte se ja implementado, haciendo uso de estas operaciones, una variante del criptosistema ElGammal mediante curvas hiperelípticas, así como la firma diital del mismo.

Atac al problema del logaritme discret mitjançant l'algorisme de Pohlig-Hellman

En els darrers anys, l'ús de les corbes el·líptiques en criptografia basada en el problema del logaritme discret s'ha anat incrementant, degut al fet que garanteixen la mateixa seguretat emprant claus més petites. Tot i això, per tal que una corba el·líptica sigui criptogràficament útil, cal que el seu cardinal satisfaci certes propietats, altrament existeixen atacs que resolen el problema del logaritme discret. En aquest treball de final de carrera s'ha implementat l'atac de Pohlig-Hellman en el grup multiplicatiu d'un cos finit i sobre el grup de punts d'una corba el·líptica.

Determinació del subgrup de 7-Sylow d'una corba el·líptica

La criptografia de corbes el·líptiques ha despertat un interés molt gran degut a que garanteix la mateixa seguretat amb longituds de claus molt més petites.Tot i això, queden problemes oberts com el de trobar el cardinal d'una corba el·líptica sobre un cos finit, que és un problema computacionalment difícil. En aquest treball estudiem i implementem un algoritme per determinar el subgrup de 7-Sylow d'una corba el·líptica. El coneixement d'aquest subgrup ens dóna informació parcial del cardinal de la corba, concretament, la potència del factor 7 que té el cardinal. Així, si aquesta potència fos molt gran, la corba s'hauria de descartar per a usos criptogràfics basats en el problema del logaritme discret.

Trisecció de divisors sobre corbes hiperel·líptiques de gènere 2

La criptografia amb corbes el·liptiques i hiperel·líptiques ha adquirit un gran interès en els últims anys. Per a determinar si una corba és bona criptogràficament és necessari, en el cas d'una corba el·liptica trobar el cardinal del grup de punts i, en el cas d'una corba hiperel·líptica trobar el cardinal de la varietat jacobiana. En aquest treball donem mètodes per trobar els trisecats d'un divisor d'una corba de gènere 2. Això ens permetrà determinar el subgrup de 3-Sylow i trobar la major potencia de 3 que divideix al cardinal de la seva Jacobiana, obtenin així informació sobre aquest cardinal.

The HP-filter in cross-country comparisons

Many empirical studies of business cycles have followed the practise ofapplying the Hodrick-Prescott filter for cross-country comparisons. Thestandard procedure is to set the weight \lambda, which determines the'smoothness' of the trend equal to 1600. We show that if this value isused for against common wisdom about business cycles. As an example, weshow that the long recession occurred inSpain between 1975 and 1985 goesunnotoced by the HP filter. We propose a method for adjusting \lambda byreinterpreting the HP-filter as the solution to a constrained minimizationproblem. We argue that the common practice of fixing \lambda across countriesamounts to chankging the constraints on trend variability across countries.Our proposed method is easy to apply, retains all the virtues of thestandard HP-filter and when applied to Spanish data the results are inthe line with economic historian's view. Applying the method to a numberof OECD countries we find that, with the exception of Spain, Italy andJapan, the standard choice of \lambda=1600 is sensible.

Determinacy and Weakly Ramsey sets in Banach spaces

We give a sufficient condition for a set of block subspaces in an infinite-dimensional Banach space to be weakly Ramsey. Using this condition we prove that in the Levy-collapse of a Mahlo cardinal, every projective set is weakly Ramsey. This, together with a construction of W. H. Woodin, is used to show that the Axiom of Projective Determinacy implies that every projective set is weakly Ramsey. In the case of co we prove similar results for a stronger Ramsey property. And for hereditarily indecomposable spaces we show that the Axiom of Determinacy plus the Axiom of Dependent Choices imply that every set is weakly Ramsey. These results are the generalizations to the class of projective sets of some theorems from W. T. Gowers, and our paper "Weakly Ramsey sets in Banach spaces."

Conocimiento, vida y virtud moral

Macintyre ha dividido su última obra Dependent Rational Animals en dos partes. Enla primera analiza las habilidades que los animales racionales tienen en común con losirracionales, mientras que en la segunda parte expone el concepto de 'autonomía moral'. El artículo expone las ideas del último libro de MacIntyre relacionándolas con sus trabajos anteriores. El artículo fue presentado en las jornadas sobre 'El pensamiento filosófico-moral de Alasdair Machtyre' que se realizaron el pasado año en Madrid organizadas por Facultad de CC. Jundicas y de la Administración, de la Universidad San Pablo-CEU.