Classical horizontal inequity and reranking: an integrated approach

The last 20 years have seen a significant evolution in the literature on horizontal inequity (HI) and have generated two major and "rival" methodological strands, namely, classical HI and reranking. We propose in this paper a class of ethically flexible tools that integrate these two strands. This is achieved using a measure of inequality that merges the well-known Gini coefficient and Atkinson indices, and that allows a decomposition of the total redistributive effect of taxes and transfers in a vertical equity effect and a loss of redistribution due to either classical HI or reranking. An inequality-change approach and a money-metric cost-of-inequality approach are developed. The latter approach makes aggregate classical HI decomposable across groups. As in recent work, equals are identified through a nonparametric estimation of the joint density of gross and net incomes. An illustration using Canadian data from 1981 to 1994 shows a substantial, and increasing, robust erosion of redistribution attributable both to classical HI and to reranking, but does not reveal which of reranking or classical HI is more important since this requires a judgement that is fundamentally normative in nature.

Algebraic extensions in free groups

The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were given. We develop a theory of algebraic extensions for free groups, highlighting the analogies and differences with respect to the corresponding classical fieldt heoretic notions, and we discuss in detail the notion of algebraic closure. We apply that theory to the study and the computation of certain algebraic properties of subgroups (e.g. being malnormal, pure, inert or compressed, being closed in certain profinite topologies) and the corresponding closure operators. We also analyze the closure of a subgroup under the addition of solutions of certain sets of equations.

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.

Detection of moving groups among early type stars

Our procedure to detect moving groups in the solar neighbourhood (Chen et al., 1997) in the four-dimensional space of the stellar velocity components and age has been improved. The method, which takes advantadge of non-parametric estimators of density distribution to avoid any a priori knowledge of the kinematic properties of these stellar groups, now includes the effect of observational errors on the process to select moving group stars, uses a better estimation of the density distribution of the total sample and field stars, and classifies moving group stars using all the available information. It is applied here to an accurately selected sample of early-type stars with known radial velocities and Strömgren photometry. Astrometric data are taken from the HIPPARCOS catalogue (ESA, 1997), which results in an important decrease in the observational errors with respect to ground-based data, and ensures the uniformity of the observed data. Both the improvement of our method and the use of precise astrometric data have allowed us not only to confirm the existence of classical moving groups, but also to detect finer structures that in several cases can be related to kinematic properties of nearby open clusters or associations.

Introducing online teaching in Humanities: A case study about the acceptance of online activities by the academic staff of classical languages

The purpose of this paper is to show the perceptions of the academic staff of classical languages (ancient Greek and Latin) concerning use of online activities during their courses. The study was carried out in three countries: Greece (three major Universities), Spain (University of Barcelona) and the United States (University of California, Berkeley) with the participation of thirty-three academic instructors. Depending on the level of use and acceptance of the ICT and following G. Moore¿s classification, we separated the participating academics in three groups: the conservatives, the mainstream and the early adopters. The fact that the smallest group is the third clearly shows the necessity for teachers¿ preparation and training before introducing innovative projects in the classroom. Since the starting point for the application of innovation in the classroom is the teacher, policy makers should focus on helping them become conscious of changes in teaching methods and include their opinion during the design of innovative projects.

Introducing online teaching in Humanities: A case study about the acceptance of online activities by the academic staff of classical languages

The purpose of this paper is to show the perceptions of the academic staff of classical languages (ancient Greek and Latin) concerning use of online activities during their courses. The study was carried out in three countries: Greece (three major Universities), Spain (University of Barcelona) and the United States (University of California, Berkeley) with the participation of thirty-three academic instructors. Depending on the level of use and acceptance of the ICT and following G. Moore¿s classification, we separated the participating academics in three groups: the conservatives, the mainstream and the early adopters. The fact that the smallest group is the third clearly shows the necessity for teachers¿ preparation and training before introducing innovative projects in the classroom. Since the starting point for the application of innovation in the classroom is the teacher, policy makers should focus on helping them become conscious of changes in teaching methods and include their opinion during the design of innovative projects.

Polynomial-time complexity for instances of the endomorphism problem in free groups

We say the endomorphism problem is solvable for an element W in a free group F if it can be decided effectively whether, given U in F, there is an endomorphism Φ of F sending W to U. This work analyzes an approach due to C. Edmunds and improved by C. Sims. Here we prove that the approach provides an efficient algorithm for solving the endomorphism problem when W is a two- generator word. We show that when W is a two-generator word this algorithm solves the problem in time polynomial in the length of U. This result gives a polynomial-time algorithm for solving, in free groups, two-variable equations in which all the variables occur on one side of the equality and all the constants on the other side.

Distortion of surface groups in Cat (0) free-by-cyclic groups

Given a non-positively curved 2-complex with a circle-valued Morse function satisfying some extra combinatorial conditions, we describe how to locally isometrically embed this in a larger non- positively curved 2-complex with free-by-cyclic fundamental group. This embedding procedure is used to produce examples of CAT(0) free-by-cyclic groups that contain closed hyperbolic surface subgroups with polynomial distortion of arbitrary degree. We also produce examples of CAT(0) hyperbolic free-by-cyclic groups that contain closed hyperbolic surface subgroups that are exponentially distorted.

A proof that all Seifert 3-manifold groups and all virtual surface groups are conjugacy separable

We prove that the fundamental group of any Seifert 3-manifold is conjugacy separable. That is, conjugates may be distinguished infinite quotients or, equivalently, conjugacy classes are closed in the pro-finite topology.

The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils

We prove a general Zariski-van Kampen-Lefschetz type theorem for higher homotopy groups of generic and nongeneric pencils on singular open complex spaces.

Metrics on diagram groups and uniform embeddings in a Hilbert space

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

Pressure groups and experts in environmental regulation

We study a problem of adverse selection in the context of environmental regulation, where the firm may suffer from a certain degree of ignorance about its own type. In a framework like the construction of a certain infrastructure project, the presence of ignorance about its impact on the environment, can play an important role in the determination of the regulatory policy. First, an optimal contract is constructed for any exogenous level of ignorance. Second, the presence of potentially informed third-parties is studied from the perspective of the regulator, which allows us to analyze the impact on the efficiency of the contract, of the presence of environmentalists and of experts. Then, we obtain some insights on how the problem differs when the degree of ignorance is a choice variable for the firm. We finally use our results to derive policy implications concerning the existing envoronmental regulation, and the potential role of interested parties as information providers.

Pure braid subgroups of braided Thompson's groups

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

Endogenous population subgroups: the best population partition and optimal number of groups

The aim of this paper is to suggest a method to find endogenously the points that group the individuals of a given distribution in k clusters, where k is endogenously determined. These points are the cut-points. Thus, we need to determine a partition of the N individuals into a number k of groups, in such way that individuals in the same group are as alike as possible, but as distinct as possible from individuals in other groups. This method can be applied to endogenously identify k groups in income distributions: possible applications can be poverty