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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Narrating urban entrepreneurship: a matter of imagineering?

The battle between cities with regard to their creative possibilities has evolved into a process of multiplying ever-new images and variegated stories of urban attractiveness and success. Engineering “cool” images and “hot” stories about one’s city is now a central endeavor in the narratives of urban policy-making that center more and more on the idea of the entrepreneurial city. The making of an entrepreneurial image is enacted through various narrative genres that lie somewhere between place making and place marketing, between branding and boosting, between restoration and revanchism, between iconic architecture and mega-spectacle. This “imagineering” is not only part of the way cities try to (re)present themselves as entrepreneurial to various audiences through a real “image inflation” (Zukin, 2008, p. xii) but is 1 Forthcoming in: B. Lange,.A. Kalandides, B. Stoeber, I. Wellmann (Hrsg.) (2009): Governance der Kreativwirtschaft. Diagnosen und Handlungsoptionen. Transcript-Verlag, Bielefeld. 2 also inscribed in the various ways urban creativity and entrepreneurship can be studied, researched and imagined. In this chapter we aim to differentiate the political narratives of the entrepreneurial city as we emphasize the need to understand the politics of narration and make a plea for critical reflexivity in our forms of researching and theorizing. We will thus try to investigate how the politics of narration is intertwined with the narration of political concepts and will argue that the narrating of urban entrepreneurship can raise very different images and discourses of city life beyond those that are currently engineered. We will distinguish between a grand narrative, a counter-narrative, and an assemblage of more ambivalent little narratives, which we call prosaic narration. While the distinction between these three types might be seen as a bit too simple and “straight”, we believe that by juxtaposing these different forms of narration and alternating between them, we can help problematize the engineering of the city as entrepreneurial and imagine alternative views both of city life and of what is understood as its creativity.

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.

Generic optimality conditions for semi-algebraic convex programs

We consider linear optimization over a nonempty convex semi-algebraic feasible region F. Semidefinite programming is an example. If F is compact, then for almost every linear objective there is a unique optimal solution, lying on a unique \active" manifold, around which F is \partly smooth", and the second-order sufficient conditions hold. Perturbing the objective results in smooth variation of the optimal solution. The active manifold consists, locally, of these perturbed optimal solutions; it is independent of the representation of F, and is eventually identified by a variety of iterative algorithms such as proximal and projected gradient schemes. These results extend to unbounded sets F.

Identificación de variedades de vitis vinifera procedentes de diferentes regiones del mundo mediante tècnica de biologia molecular de los microsatéllites

El objetivo de este estudio se centró en analizar una colección privada de germoplasma de Vitis vinifera L., de 338 cultivares procedentes de 24 países, para caracterizarlas creando una base de datos, utilizando 11 marcadores microsatélites o SSR (Simple Sequence Repeat). Como resultado se encontraron que algunas de las muestras analizadas presentaron un perfil idéntico de SSR, indicando que se trata de una sinonimia (la misma variedad pero con diferente nombre). Se detectaron 293 perfiles únicos. Adicionalmente, 15 pares de variedades presentaron diferencias en un solo locus y otros 7 grupos difieren en 2 loci, lo cual indicaría la alta proximidad genética entre esas variedades, sin llegar a ser la misma. El germoplasma analizado cuenta con una compleja biodiversidad varietal que se debe preservar. El estudio se realizó programando para el primer año la revisión bibliográfica detallada, recolección de las hojas y el inicio de la puesta a punto de la metodología, en el segundo año se completa la puesta a punto de la metodología, se trituran las hojas y se realiza la extraccinón del ADN. El tercer año se emplea para amplificar los fragmentos de ADN por medio de la PCR (reacción en cadena de la polimerasa), obtener la longitud de los fragmentos con un secuenciador ABI PRISM 310, valorar resultados y realizar repeticiones. El último año se analizan los resultados obtenidos, se realizan repeticiones pertinentes y se comienza la redacción de artículos científicos.

A simple model of aggregate pension expenditure

This paper develops a simple model that can be used to analyze the long-term sustainability of the contributive pension system and the steady-state response of pension expenditure to changes in some key demographic and economic variables, in the characteristics of the average pensioner and in the parameters that describe how pensions are calculated in Spain as a function of workers' Social Security contribution histories.

An algorithm for semi-infinite polynomial optimization

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Twisted conjugacy in braid groups

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