Tree automorphisms and quasi-isometries of Thompson's group F

We prove that automorphisms of the infinite binary rooted tree T2 do not yield quasi-isometries of Thompson's group F, except for the map which reverses orientation on the unit interval, a natural outer automorphism of F. This map, together with the identity map, forms a subgroup of Aut(T2) consisting of 2-adic automorphisms, following standard terminology used in the study of branch groups. However, for more general p, we show that the analgous groups of p-adic tree automorphisms do not give rise to quasiisometries of F(p).

Anàlisi i disseny d'un reflector per banda W

Les ones passives mil·limètriques (30 a 300GHz) tenen la peculiaritat de propagar-se en medis com la boira o la roba, a diferència del rang visible o l’infraroig. D’aquesta peculiaritat, surt l’interès de reproduir imatges per diverses aplicacions (seguretat, vigilància, etc...). És per aquest motiu que es treballa en el disseny d’un reflector per aquest tipus d’aplicació, treballant a una de les finestres de propagació d’aquest rang, la de la banda W. Es dissenyen i analitzen tres tipus de reflector: parabòlic simètric, offset i Cassegrain. D’aquests, s’estudien les seves figures de mèrit i directivitats buscant que aquestes siguin el més elevades possibles per obtenir una bona resolució, així com l’escaneig de l’escena de la qual es vol obtenir una imatge, veient aquí els efectes de les aberracions més comunes.

The generator problem for Z-stable C*-algebras

The generator problem was posed by Kadison in 1967, and it remains open until today. We provide a solution for the class of C*-algebras absorbing the Jiang-Su algebra Z tensorially. More precisely, we show that every unital, separable, Z-stable C*-algebra A is singly generated, which means that there exists an element x є A that is not contained in any proper sub-C*- algebra of A. To give applications of our result, we observe that Z can be embedded into the reduced group C*-algebra of a discrete group that contains a non-cyclic, free subgroup. It follows that certain tensor products with reduced group C*-algebras are singly generated. In particular, C*r (F ∞) ⨂ C*r (F ∞) is singly generated.

Creació d'un programari per la transformació de dades

L'objectiu d'aquest TFC ha estat crear un programari que permeti transformacions ràpides de gran volums de dades. Cada procés de transformació hauria de dependre d'un conjunt de regles de transformació preestablertes per subconjunts de dades, de manera que el procés fos repetible i verificable per a poder garantir la qualitat dels processos de transformació; les regles de transformació s'haurien de poder especificar de manera fàcil i pràctica per a usuaris sense coneixements de programació; les transformacions possibles haurien de cobrir requeriments derivats de la neteja, la transformació i la formatació de dades en els nivells de taula, registre i camp, i per a cada subconjunt de dades i regles de transformació inicials, que constitueixen l'entrada, el programari hauria de retornar el corresponent subconjunt de dades transformades.

Ecological Footprint Inequality: A methodological review and some results

Scarcities of environmental services are no longer merely a remote hypothesis. Consequently, analysis of their inequalities between nations becomes of paramount importance for the achievement of sustainability in terms either of international policy, or of Universalist ethical principles of equity. This paper aims, on the one hand, at revising methodological aspects of the inequality measurement of certain environmental data and, on the other, at extending the scarce empirical evidence relating to the international distribution of Ecological Footprint (EF), by using a longer EF time series. Most of the techniques currently important in the literature are revised and then tested on EF data with interesting results. We look in depth at Lorenz dominance analyses and consider the underlying properties of different inequality indices. Those indices which fit best with environmental inequality measurements are CV2 and GE(2) because of their neutrality property, however a trade-off may occur when subgroup decompositions are performed. A weighting factor decomposition method is proposed in order to isolate weighting factor changes in inequality growth rates. Finally, the only non-ambiguous way of decomposing inequality by source is the natural decomposition of CV2, which additionally allows the interpretation of marginal term contributions. Empirically, this paper contributes to the environmental inequality measurement of EF: this inequality has been quite stable and its change over time is due to per capita vector changes rather than population changes. Almost the entirety of the EF inequality is explainable by differences in the means between the countries of the World Bank group. This finding suggests that international environmental agreements should be attempted on a regional basis in an attempt to achieve greater consensus between the parties involved. Additionally, source decomposition warns of the dangers of confining CO2 emissions reduction to crop-based energies because of the implications for basic needs satisfaction.

Ecological Footprint Inequality: A methodological review and some results

Scarcities of environmental services are no longer merely a remote hypothesis. Consequently, analysis of their inequalities between nations becomes of paramount importance for the achievement of sustainability in terms either of international policy, or of Universalist ethical principles of equity. This paper aims, on the one hand, at revising methodological aspects of the inequality measurement of certain environmental data and, on the other, at extending the scarce empirical evidence relating to the international distribution of Ecological Footprint (EF), by using a longer EF time series. Most of the techniques currently important in the literature are revised and then tested on EF data with interesting results. We look in depth at Lorenz dominance analyses and consider the underlying properties of different inequality indices. Those indices which fit best with environmental inequality measurements are CV2 and GE(2) because of their neutrality property, however a trade-off may occur when subgroup decompositions are performed. A weighting factor decomposition method is proposed in order to isolate weighting factor changes in inequality growth rates. Finally, the only non-ambiguous way of decomposing inequality by source is the natural decomposition of CV2, which additionally allows the interpretation of marginal term contributions. Empirically, this paper contributes to the environmental inequality measurement of EF: this inequality has been quite stable and its change over time is due to per capita vector changes rather than population changes. Almost the entirety of the EF inequality is explainable by differences in the means between the countries of the World Bank group. This finding suggests that international environmental agreements should be attempted on a regional basis in an attempt to achieve greater consensus between the parties involved. Additionally, source decomposition warns of the dangers of confining CO2 emissions reduction to crop-based energies because of the implications for basic needs satisfaction. Keywords: ecological footprint; ecological inequality measurement, inequality decomposition.

Effect of initial conditions on the speed of reaction-diffusion fronts

The effect of initial conditions on the speed of propagating fronts in reaction-diffusion equations is examined in the framework of the Hamilton-Jacobi theory. We study the transition between quenched and nonquenched fronts both analytically and numerically for parabolic and hyperbolic reaction diffusion. Nonhomogeneous media are also analyzed and the effect of algebraic initial conditions is also discussed

Biomechanical wall properties of human intracranial aneurysms resected following surgical clipping (IRRAs Project)

Background and purpose: Individual rupture risk assessment of intracranial aneurysms is a major issue in the clinical management of asymptomatic aneurysms. Aneurysm rupture occurs when wall tension exceeds the strength limit of the wall tissue. At present, aneurysmal wall mechanics are poorly understood and thus, risk assessment involving mechanical properties is inexistent. Aneurysm computational hemodynamics studies make the assumption of rigid walls, an arguable simplification. We therefore aim to assess mechanical properties of ruptured and unruptured intracranial aneurysms in order to provide the foundation for future patient-specific aneurysmal risk assessment. This work also challenges some of the currently held hypotheses in computational flow hemodynamics research. Methods: A specific conservation protocol was applied to aneurysmal tissues following clipping and resection in order to preserve their mechanical properties. Sixteen intracranial aneurysms (11 female, 5 male) underwent mechanical uniaxial stress tests under physiological conditions, temperature, and saline isotonic solution. These represented 11 unruptured and 5 ruptured aneurysms. Stress/strain curves were then obtained for each sample, and a fitting algorithm was applied following a 3-parameter (C(10), C(01), C(11)) Mooney-Rivlin hyperelastic model. Each aneurysm was classified according to its biomechanical properties and (un)rupture status.Results: Tissue testing demonstrated three main tissue classes: Soft, Rigid, and Intermediate. All unruptured aneurysms presented a more Rigid tissue than ruptured or pre-ruptured aneurysms within each gender subgroup. Wall thickness was not correlated to aneurysmal status (ruptured/unruptured). An Intermediate subgroup of unruptured aneurysms with softer tissue characteristic was identified and correlated with multiple documented risk factors of rupture. Conclusion: There is a significant modification in biomechanical properties between ruptured aneurysm, presenting a soft tissue and unruptured aneurysms, presenting a rigid material. This finding strongly supports the idea that a biomechanical risk factor based assessment should be utilized in the to improve the therapeutic decision making.

Políticas de dividendos y probabilidad de ruina

En este trabajo introducimos diversas clases de barreras del dividendo en la teoría modelo clásica de la ruina. Estudiamos la influencia de la estrategia de la barrera en probabilidad de la ruina. Un método basado en las ecuaciones de la renovación [Grandell (1991)], alternativa a la discusión diferenciada [Gerber (1975)], utilizado para conseguir las ecuaciones diferenciales parciales para resolver probabilidades de la supervivencia. Finalmente calculamos y comparamos las probabilidades de la supervivencia usando la barrera linear y parabólica del dividendo, con la ayuda de la simulación

Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Ground-state self-consistent calculation of quantum dots under magnetic fields: Addition spectrum

A density-functional self-consistent calculation of the ground-state electronic density of quantum dots under an arbitrary magnetic field is performed. We consider a parabolic lateral confining potential. The addition energy, E(N+1)-E(N), where N is the number of electrons, is compared with experimental data and the different contributions to the energy are analyzed. The Hamiltonian is modeled by a density functional, which includes the exchange and correlation interactions and the local formation of Landau levels for different equilibrium spin populations. We obtain an analytical expression for the critical density under which spontaneous polarization, induced by the exchange interaction, takes place.

Spin polarized neutron matter and magnetic susceptibility within the Brueckner-Hartree-Fock approximation

The Brueckner-Hartree-Fock formalism is applied to study spin polarized neutron matter properties. Results of the total energy per particle as a function of the spin polarization and density are presented for two modern realistic nucleon-nucleon interactions, Nijmegen II and Reid93. We find that the dependence of the energy on the spin polarization is practically parabolic in the full range of polarizations. The magnetic susceptibility of the system is computed. Our results show no indication of a ferromagnetic transition which becomes even more difficult as the density increases.

Subclass problem-dependent design for error-correcting output codes

A common way to model multiclass classification problems is by means of Error-Correcting Output Codes (ECOCs). Given a multiclass problem, the ECOC technique designs a code word for each class, where each position of the code identifies the membership of the class for a given binary problem. A classification decision is obtained by assigning the label of the class with the closest code. One of the main requirements of the ECOC design is that the base classifier is capable of splitting each subgroup of classes from each binary problem. However, we cannot guarantee that a linear classifier model convex regions. Furthermore, nonlinear classifiers also fail to manage some type of surfaces. In this paper, we present a novel strategy to model multiclass classification problems using subclass information in the ECOC framework. Complex problems are solved by splitting the original set of classes into subclasses and embedding the binary problems in a problem-dependent ECOC design. Experimental results show that the proposed splitting procedure yields a better performance when the class overlap or the distribution of the training objects conceal the decision boundaries for the base classifier. The results are even more significant when one has a sufficiently large training size.

Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Políticas de dividendos y probabilidad de ruina

En este trabajo introducimos diversas clases de barreras del dividendo en la teoría modelo clásica de la ruina. Estudiamos la influencia de la estrategia de la barrera en probabilidad de la ruina. Un método basado en las ecuaciones de la renovación [Grandell (1991)], alternativa a la discusión diferenciada [Gerber (1975)], utilizado para conseguir las ecuaciones diferenciales parciales para resolver probabilidades de la supervivencia. Finalmente calculamos y comparamos las probabilidades de la supervivencia usando la barrera linear y parabólica del dividendo, con la ayuda de la simulación