Statistical properties of subgroups of free groups

The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k-tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though equally natural point of view: we investigate the statistical properties of the same objects, but with respect to the so-called graph-based distribution, recently introduced by Bassino, Nicaud and Weil. Here, subgroups (and finite presentations) are determined by randomly chosen Stallings graphs whose number of vertices tends to infinity. Our results show that these two distributions behave quite differently from each other, shedding a new light on which properties of finitely generated subgroups can be considered frequent or rare. For example, we show that malnormal subgroups of a free group are negligible in the raph-based distribution, while they are exponentially generic in the word-based distribution. Quite surprisingly, a random finite presentation generically presents the trivial group in this new distribution, while in the classical one it is known to generically present an infinite hyperbolic group.

Is the Spanish Inheritance and Gift Tax incompatible with the free movement of workers and capital?: The reasoned opinion of the EU Commission IP/10/513

The aim of my speech is answering to the question if the Spanish Inheritance and Gift Tax is incompatible with the free movement of workers and capital. We are going to pay special attention to the European Commission’s request to Spain to change its Inheritance and Gift Tax provisions for Non-Residents or Assets held abroad. In order to answer to the question mentioned above five points will be explained. At first place I am going to describe the infrengement procedure established in the Article 258 that the EU Commission can follow when a Member State doesn’t comply with Community Law. At second place, we are going to explain what is the content of the EU Commission delivered on 5th of may 2010 regarding the spanish Inheritance and Gift Tax. Then, we will analise what establishes the Community Law regarding the freedom of workers and capital and how they are understood by the EU Court of Justice in similar cases. Finally, we are going to provide possible amendments that Spain could undertake.

Estudi de la configuració magnètica de l'experiment LTP (LISA Technology Package)

La Teoria de la Relativitat General preveu que quan un objecte massiu és sotmès a una certa acceleració en certes condicions ha d’emetre ones gravitacionals. Es tracta d’un tipus d’on altament energètica però que interacciona amb la matèria de manera molt feble i el seu punt d’emissió és força llunyà. Per la qual cosa la seva detecció és una tasca extraordinàriament complicada. Conseqüentment, la detecció d’aquestes ones es creu molt més factible utilitzant instruments situats a l’espai. Amb aquest objectiu, neis la missió LISA (Laser Interferometer Space Antenna). Es tracta aquesta d’una missió conjunta entre la NASA i l’ESA amb llançament previst per 2020-2025. Per reduir els riscs que comporta una primera utilització de tecnologia no testejada, unit a l’alt cost econòmic de la missió LISA. Aquesta missió contindrà instruments molt avançats: el LTP (LISA Technoplogy Package), desenvolupat per la Unió Europea, que provarà la tecnologia de LISA i el Drag Free flying system, que s’encarregarà de provar una sèrie de propulsors (thrusters) utilitzats per al control d’actitud i posició de satèl•lit amb precisió de nanòmetres. Particularment, el LTP, està composat per dues masses de prova separades per 35 centímetres, i d’un interferòmetre làser que mesura la variació de la distància relativa entre elles. D’aquesta manera, el LTP mesurarà les prestacions dels equips i les possibles interferències que afecten a la mesura. Entre les fonts de soroll es troben, entre d’altres, el vent i pressió de radiació solar, les càrregues electrostàtiques, el gradient tèrmic, les fluctuacions de voltatge o les forces internes. Una de les possibles causes de soroll és aquella que serà l’objecte d’estudi en aquest projecte de tesi doctoral: la presència dintre del LTP de camps magnètics, que exerceixen una força sobre les masses de prova, la seva estimació i el seu control, prenent en compte les caracterírstiques magnètiques de l’experiment i la dinàmica del satèl•lit.

A right to a national space of communication? : on Stateless nations, their right to a space of communication of their own

Hem establert les bases metodològiques i teòriques per investigar la pregunta “Tenen les nacions sense estat el dret de controlar el seu propi espai de comunicació?”. La investigació ajusta el concepte d’espai de comunicació a la teoria política, cercant els seus límits en els drets individuals i, des de la perspectiva del liberalisme 2, aportant la justificació del seu control en quant que plataforma que incideix en la conservació i supervivència d’una cultura nacional. El primer article i fase de la tesi és l’adaptació i definició del concepte espai de comunicació. Fins ara, la recerca ha proposat diferents models d’espai de comunicació entenent si es tracta d’una visió emfatitzant la distribució i la producció de material marcat amb els símbols de la identitat nacional de la societat emissora, o bé si emfatitza la idea d’un espai de circulació de fluxos comunicatiu ajustat a un territori tradicionalment vinculat a una identitat nacional o nació sense estat. Igualment, es distingeix la dimensió d’emissió –sortir del territori al món- i la de recepció –fluxos informatius rebuts des del món al territori, concretament, al ciutadà; el paper d’intervenció de les institucions democràtiques és diferent en una dimensió o una altra i, per tant, també són diferents els drets afectats i les teories o principis que neguen o justifiquen el control de l’espai de comunicació. També s’ha indagat en les teories sobre els efectes cognitius dels mitjans de comunicació per relacionar-los amb la construcció nacional com a cohesió simbòlica i cultural. Si bé els mitjans no poden fer canviar de pensament immediatament, sí que poden conformar a llarg termini una percepció nacional general. Una comunitat és imaginada, donada la distància física dels seus components, i la comunicació social és, juntament amb l’educació, el principal factor de construcció nacional, avui en dia.

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

Candidate quality in a Downsian Model with a continuous policy space

This paper characterizes a mixed strategy Nash equilibrium in a one-dimensional Downsian model of two-candidate elections with a continuous policy space, where candidates are office motivated and one candidate enjoys a non-policy advantage over the other candidate. We assume that voters have quadratic preferences over policies and that their ideal points are drawn from a uniform distribution over the unit interval. In our equilibrium the advantaged candidate chooses the expected median voter with probability one and the disadvantaged candidate uses a mixed strategy that is symmetric around it. We show that this equilibrium exists if the number of voters is large enough relative to the size of the advantage.

Industrial Location and Space: New Insights

This paper tries to resolve some of the main shortcomings in the empirical literature of location decisions for new plants, i.e. spatial effects and overdispersion. Spatial effects are omnipresent, being a source of overdispersion in the data as well as a factor shaping the functional relationship between the variables that explain a firm’s location decisions. Using Count Data models, empirical researchers have dealt with overdispersion and excess zeros by developments of the Poisson regression model. This study aims to take this a step further, by adopting Bayesian methods and models in order to tackle the excess of zeros, spatial and non-spatial overdispersion and spatial dependence simultaneously. Data for Catalonia is used and location determinants are analysed to that end. The results show that spatial effects are determinant. Additionally, overdispersion is descomposed into an unstructured iid effect and a spatially structured effect. Keywords: Bayesian Analysis, Spatial Models, Firm Location. JEL Classification: C11, C21, R30.

On Borel equivalence relations in generalized Baire space

"Vegeu el resum a l'inici del document del fitxer adjunt."

Aerotropolis: an aviation-linked space

This paper examines the conditions allowing the formation of aeropolitan areas as large industrial areas with a high concentration of commercial activities in the proximity of selected airports. We assume that firms deliver their production by plane and land competition takes place among service operators, firms and farmers. Service operators supply facilities that firms can absorb. Our framework identifies a unique land equilibrium characterized by the spatial sequence Airport - Industrial park - Rural area (A-I-R). Aerotropolis-type configurations are associated with the level of transport costs and the degree of intensity of facilities. Keywords: aerotropolis; facilities; bid-rent function. JEL Classification Numbers: L29; L90; R14.

New pre-dual space of Morrey space

In this paper we give new characterization of the classical Morrey space. Complementary global Morrey-type spaces are introduced. It is proved that for particular values of parameters these spaces give new pre-dual space of the classical Morrey space. We also show that our new pre-dual space of the Morrey space coincides with known pre-dual spaces.

Dynamical systems of type (m,n) and their C*-algebras

Given positive integers n and m, we consider dynamical systems in which n copies of a topological space is homeomorphic to m copies of that same space. The universal such system is shown to arise naturally from the study of a C*-algebra we denote by Om;n, which in turn is obtained as a quotient of the well known Leavitt C*-algebra Lm;n, a process meant to transform the generating set of partial isometries of Lm;n into a tame set. Describing Om;n as the crossed-product of the universal (m; n) -dynamical system by a partial action of the free group Fm+n, we show that Om;n is not exact when n and m are both greater than or equal to 2, but the corresponding reduced crossed-product, denoted Or m;n, is shown to be exact and non-nuclear. Still under the assumption that m; n &= 2, we prove that the partial action of Fm+n is topologically free and that Or m;n satisfies property (SP) (small projections). We also show that Or m;n admits no finite dimensional representations. The techniques developed to treat this system include several new results pertaining to the theory of Fell bundles over discrete groups.

A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations

We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued piecewise linear discontinuous finite element space, that are optimal with respect to the mesh size and the Lamé parameters. The pure displacement, the mixed and the traction free problems are discussed in detail. We present a convergence analysis of the proposed preconditioners and include numerical examples that validate the theory and assess the performance of the preconditioners.

On separation of a degenerate differential operator in Hilbert space

A coercive estimate for a solution of a degenerate second order di fferential equation is installed, and its applications to spectral problems for the corresponding dif ferential operator is demonstrated. The suffi cient conditions for existence of the solutions of one class of the nonlinear second order diff erential equations on the real axis are obtained.

Caracterización de materiales en banda W

Para medir los coeficientes de transmisión y reflexión, S21 y S11, de diferentes materiales o muestras planas, se usa un sistema de toma de medidas en espacio libre operando banda W (75 – 110 GHz). Usando estos parámetros, S21 y S11, podemos calcular la permitividad dieléctrica relativa compleja (Er ) y la permeabilidad magnética relativa compleja (μr) mediante un proceso llamado NRW (Nicolson-Ross-Weir). El sistema para medir consiste en dos antenas de bocina, una transmisora y otra receptora, dos espejos con los que obtenemos una onda plana para medir las propiedades del material y un ordenador o dispositivo que calcula los resultados. Este dispositivo requiere de calibración para la obtención de resultados óptimos. Dicho sistema se puede simular de manera ideal con un software llamado ADS (Assistance Design System) para el estudio y comparación de grosores, permitividades dieléctricas relativas y permeabilidades magnéticas relativas de los materiales en función de la frecuencia.

Free Technology Academy : a Joint Venture of Free Software and OER

The decision to publish educational materials openly and under free licenses brings up the challenge of doing it in a sustainable way. Some lessons can be learned from the business models for production, maintenance and distribution of Free and Open Source Software. The Free Technology Academy (FTA) has taken on these challenges and has implemented some of these models. We briefly review the FTA educational programme, methodologies and organisation, and see to which extent these models are proving successful in the case of the FTA.