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.

Evaluating the impact of public subsidies on a firm's performance: A quasi-experimental approach

Many regional governments in developed countries design programs to improve the competitiveness of local firms. In this paper, we evaluate the effectiveness of public programs whose aim is to enhance the performance of firms located in Catalonia (Spain). We compare the performance of publicly subsidised companies (treated) with that of similar, but unsubsidised companies (non-treated). We use the Propensity Score Matching (PSM) methodology to construct a control group which, with respect to its observable characteristics, is as similar as possible to the treated group, and that allows us to identify firms which retain the same propensity to receive public subsidies. Once a valid comparison group has been established, we compare the respective performance of each firm. As a result, we find that recipient firms, on average, change their business practices, improve their performance, and increase their value added as a direct result of public subsidy programs.

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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Connections between ∞-Poincaré inequality, quasi-convexity, and N1,∞

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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.

Twisted conjugacy in braid groups

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Educational innovation in large groups. Design of an experimental study implemented at the Polytechnic University of Madrid

The present paper shows de design of an experimental study conducted with large groups using educational innovation methodologies at the Polytechnic University of Madrid. Concretely, we have chosen the course titled "History and Politics of Sports" that belongs to the Physical Activity and Sport Science Degree. The selection of this course is because the syllabus is basically theoretical and there are four large groups of freshmen students who do not have previous experiences in a teaching-learning process based on educational innovation. It is hope that the results of this research can be extrapolated to other courses with similar characteristics.

How effective are policies to reduce gasoline consumption? evaluating a quasi-natural experiment in Spain

Using a panel of 48 provinces for four years we empirically analyze a series of temporary policies aimed at curbing fuel consumption implemented in Spain between March and June 2011. The first policy was a reduction in the speed limit in highways. The second policy was an increase in the biofuel content of fuels used in the transport sector. The third measure was a reduction of 5% in commuting and regional train fares that resulted in two major metropolitan areas reducing their overall fare for public transit. The results indicate that the speed limit reduction in highways reduced gasoline consumption by between 2% and 3%, while an increase in the biofuel content of gasoline increased this consumption. This last result is consistent with experimental evidence that indicates that mileage per liter falls with an increase in the biofuel content in gasolines. As for the reduction in transit fares, we do not find a significant effect for this policy. However, in specifications including the urban transit fare for the major cities in each province the estimated cross-price elasticity of the demand for gasoline -used as a proxy for car use- with respect to the price of transit is within the range reported in the literature. This is important since one of the main eficiency justification for subsidizing public transit rests on the positive value of this parameter and most of the estimates reported in the literature are quite dated.

Economic crisis and recovery: changes in second birth rates within occupational classes and educational groups

This study assesses the decline in second birth rates for men and women across different skill levels in transitional Russia. Changes within educational groups and occupational classes are observed over three distinct time periods: the Soviet era, economic crisis, and economic recovery. The most remarkable finding is the similarity in the extent second birth rates declined within educational groups and occupational classes during the economic crisis. Although further decline occurred in the recovery period, more variation emerged across groups.