Social polarization: introducing distances between and within groups

The measurement of social polarization has received little attention from the literature. The only social polarization index that has been used to measure religious or ethnic polarization (the RQ index) has several shortcomings that are critically discussed in the paper. In particular, that index is not taking into account the existing distance between and within different groups. A couple of axiomatically characterized social polarization indices that overcome these limitations are presented. In the empirical section we show that the rankings of countries according to the levels of polarization change to a great extent when we replace the RQ index by the indices presented in this paper.

Experimental investigation of transient natural convection cooling of high prandtl number fluid with variable viscosity

Report for the scientific sojourn at the James Cook University, Australia, between June to December 2007. Free convection in enclosed spaces is found widely in natural and industrial systems. It is a topic of primary interest because in many systems it provides the largest resistance to the heat transfer in comparison with other heat transfer modes. In such systems the convection is driven by a density gradient within the fluid, which, usually, is produced by a temperature difference between the fluid and surrounding walls. In the oil industry, the oil, which has High Prandtl, usually is stored and transported in large tanks at temperatures high enough to keep its viscosity and, thus the pumping requirements, to a reasonable level. A temperature difference between the fluid and the walls of the container may give rise to the unsteady buoyancy force and hence the unsteady natural convection. In the initial period of cooling the natural convection regime dominates over the conduction contribution. As the oil cools down it typically becomes more viscous and this increase of viscosity inhibits the convection. At this point the oil viscosity becomes very large and unloading of the tank becomes very difficult. For this reason it is of primary interest to be able to predict the cooling rate of the oil. The general objective of this work is to develop and validate a simulation tool able to predict the cooling rates of high Prandtl fluid considering the variable viscosity effects.

Musical actions of dihedral groups

The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently music theorists have found an intriguing second way that the dihedral group of order 24 acts on the set of major and minor triads. We illustrate both geometrically and algebraically how these two actions are dual. Both actions and their duality have been used to analyze works of music as diverse as Hindemith and the Beatles.

Conjugacy in Thompson's groups

We give a unified solution the conjugacy problem in Thompson’s groups F, V , and T using strand diagrams, and we analyze the complexity of the resulting algorithms.

Mather invariants in groups of piecewise-linear homeomorphisms

We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [2] and Kassabov and Matucci in [5]. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows ua to easily recover centralizers and lends itself to generalization.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

On uniform conjugators in torsion-free hyperbolic groups

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Analyzing the effects of transient faults into applications

As computer chips implementation technologies evolve to obtain more performance, those computer chips are using smaller components, with bigger density of transistors and working with lower power voltages. All these factors turn the computer chips less robust and increase the probability of a transient fault. Transient faults may occur once and never more happen the same way in a computer system lifetime. There are distinct consequences when a transient fault occurs: the operating system might abort the execution if the change produced by the fault is detected by bad behavior of the application, but the biggest risk is that the fault produces an undetected data corruption that modifies the application final result without warnings (for example a bit flip in some crucial data). With the objective of researching transient faults in computer system’s processor registers and memory we have developed an extension of HP’s and AMD joint full system simulation environment, named COTSon. This extension allows the injection of faults that change a single bit in processor registers and memory of the simulated computer. The developed fault injection system makes it possible to: evaluate the effects of single bit flip transient faults in an application, analyze an application robustness against single bit flip transient faults and validate fault detection mechanism and strategies.

Structure theorems for subgroups of homeomorphism groups

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Bounding the residual finiteness of free groups

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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.

Higher arithmetic Chow groups

We give a new construction of higher arithmetic Chow groups for quasi-projective arithmetic varieties over a field. Our definition agrees with the higher arithmetic Chow groups defined by Goncharov for projective arithmetic varieties over a field. These groups are the analogue, in the Arakelov context, of the higher algebraic Chow groups defined by Bloch. The degree zero group agrees with the arithmetic Chow groups of Burgos. Our new construction is shown to be a contravariant functor and is endowed with a product structure, which is commutative and associative.

Twisted conjugacy in braid groups

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Diseño de filtros Bulk Acoustic Wave con topología en escalera de altas prestaciones

Degut als avenços als dispositius de telecomunicacions durant l’última dècada, els filtres integrats en aquests dispositius requereixen de millors prestacions, baix cost i, per sobre de tot, requereixen unes dimensions el més reduïdes possibles. Tot i que avui dia encara s’utilitzen el filtres SAW en aquests dispositius, cada cop més s’estan substituint pels filtres amb tecnologia BAW, ja que tenen millors prestacions. En l’actualitat la topologia BAW més extensa i utilitzada és la topologia en escala. En aquest projecte s’ha portat a terme un estudi en profunditat de les limitacions dels filtres en escala. A partir de les limitacions detectades s’ha presentat una nova estructura de disseny per aquest tipus de filtres que redueix les dimensions d’aquests i millora considerablement algunes de les limitacions de l’estructura convencional. Paral·lelament s’ha desenvolupat una metodologia sistemàtica pròpia pel disseny de la nova estructura.

Detecció i localització d'impactes a estructures aeroespacials

Projecte de recerca elaborat a partir d’una estada a la Universidad Politécnica de Madrid, Espanya, entre setembre i o desembre del 2007. Actualment la indústria aeroespacial i aeronàutica té com prioritat millorar la fiabilitat de las seves estructures a través del desenvolupament de nous sistemes per a la monitorització i detecció d’impactes. Hi ha diverses tècniques potencialment útils, i la seva aplicabilitat en una situació particular depèn críticament de la mida del defecte que permet l’estructura. Qualsevol defecte canviarà la resposta vibratòria de l’element estructural, així com el transitori de l’ona que es propaga per l’estructura elàstica. Correlacionar aquests canvis, que poden ser detectats experimentalment amb l’ocurrència del defecte, la seva localització i quantificació, és un problema molt complex. Aquest treball explora l’ús de l'Anàlisis de Components Principals (Principal Component Analysis - PCA-) basat en la formulació dels estadístics T2 i Q per tal de detectar i distingir els defectes a l'estructura, tot correlacionant els seus canvis a la resposta vibratòria. L’estructura utilitzada per l’estudi és l’ala d’una turbina d’un avió comercial. Aquesta ala s’excita en un extrem utilitzant un vibrador, i a la qual s'han adherit set sensors PZT a la superfície. S'aplica un senyal conegut i s'analitzen les respostes. Es construeix un model PCA utilitzant dades de l’estructura sense defecte. Per tal de provar el model, s'adhereix un tros d’alumini en quatre posicions diferents. Les dades dels assajos de l'estructura amb defecte es projecten sobre el model. Les components principals i les distàncies de Q-residual i T2-Hotelling s'utilitzaran per a l'anàlisi de les incidències. Q-residual indica com de bé s'adiu cadascuna de les mostres al model PCA, ja que és una mesura de la diferència, o residu, entre la mostra i la seva projecció sobre les components principals retingudes en el model. La distància T2-Hotelling és una mesura de la variació de cada mostra dins del model PCA, o el que vindria a ser el mateix, la distància al centre del model PCA.