Strong isomorphism reductions in complexity theory

We give the first systematic study of strong isomorphism reductions, a notion of reduction more appropriate than polynomial time reduction when, for example, comparing the computational complexity of the isomorphim problem for different classes of structures. We show that the partial ordering of its degrees is quite rich. We analyze its relationship to a further type of reduction between classes of structures based on purely comparing for every n the number of nonisomorphic structures of cardinality at most n in both classes. Furthermore, in a more general setting we address the question of the existence of a maximal element in the partial ordering of the degrees.

Vintage capital growth theory: three breakthroughs

Vintage capital growth models have been at the heart of growth theory in the 60s. This research line collapsed in the late 60s with the so-called embodiment controversy and the technical sophisitication of the vintage models. This paper analyzes the astonishing revival of this literature in the 90s. In particular, it outlines three methodological breakthroughs explaining this resurgence: a growth accounting revolution, taking advantage of the availability of new time series, an optimal control revolution allowing to safely study vintage capital optimal growth models, and a vintage human capital revolution, along with the rise of economic demography, accounting for the vintage structure of human capital similarly to physical capital age structuring. The related literature is surveyed.

An axiomatic justification of mediation in bankruptcy problems.

This paper provides a natural way of reaching an agreement between two prominent proposals in a bankruptcy problem. Particularly, using the fact that such problems can be faced from two different points of views, awards and losses, we justify the average of any pair of dual bankruptcy rules through the definition a double recursive process. Finally, by considering three posible sets of equity principles that a particular society may agree on, we retrieve the average of old and well known bankruptcy rules, the Constrained Equal Awards and the Constrained Equal Losses rules, Piniles’ rule and its dual rule, and the Constrained Egalitarian rule and its dual rule. Keywords: Bankruptcy problems, Midpoint, Bounds, Duality, Recursivity. JEL classification: C71, D63, D71.

A way to play bankruptcy problems.

The commitment among agents has always been a difficult task, especially when they have to decide how to distribute the available amount of a scarce resource among all. On the one hand, there are a multiplicity of possible ways for assigning the available amount; and, on the other hand, each agent is going to propose that distribution which provides her the highest possible award. In this paper, with the purpose of making this agreement easier, firstly we use two different sets of basic properties, called Commonly Accepted Equity Principles, to delimit what agents can propose as reasonable allocations. Secondly, we extend the results obtained by Chun (1989) and Herrero (2003), obtaining new characterizations of old and well known bankruptcy rules. Finally, using the fact that bankruptcy problems can be analyzed from awards and losses, we define a mechanism which provides a new justification of the convex combinations of bankruptcy rules. Keywords: Bankruptcy problems, Unanimous Concessions procedure, Diminishing Claims mechanism, Piniles’ rule, Constrained Egalitarian rule. JEL classification: C71, D63, D71.

On Lundh's percolation diffusion

A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable configurations are generated with positive probability Lundh calls this percolation diffusion. An integral condition for percolation diffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.

On Lundh's percolation diffusion

A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable con gurations are generated with positive probability Lundh calls this percolation di usion. An integral condition for percolation di ffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.

Temperament in Bach’s Well-tempered clavier: a historical survey and a new evaluation according to dissonance theory

After a historical survey of temperament in Bach’s Well-Tempered Clavier by Johann Sebastian Bach, an analysis of the work has been made by applying a number of historical good temperaments as well as some recent proposals. The results obtained show that the global dissonance for all preludes and fugues in major keys can be minimized using the Kirnberger II temperament. The method of analysis used for this research is based on the mathematical theories of sensory dissonance, which have been developed by authors such as Hermann Ludwig Ferdinand von Helmholtz, Harry Partch, Reinier Plomp, Willem J. M. Levelt and William A. Sethares

Law and the practise of principle in diverse societies

Projecte de recerca elaborat a partir d’una estada a la London School of Economics and Political Science, United Kingdom, entre 2007 i 2009. L’objecte principal del projecte ha estat analitzar les implicacions jurídico-polítiques i institucionals d’una teoria de la justícia i la igualtat liberals aplicada a societats multiculturals amb un marcat predomini de la diversitat cultural. L’anàlisi desenvolupa una línia d'investigació interdisciplinar - entre el dret i la teoria política - iniciada en una tesis doctoral sobre multiculturalisme i drets de les minories culturals (UPF, 2000) que va culminar en la publicació de Group Rights as Human Rights (Springer, 2006). La recerca adopta com a punt de partida les conclusions de l'esmentada obra, en especial, la rellevància del reconeixement de drets col•lectius; tanmateix, el tipus de qüestions plantejades, l’enfoc i la metodologia emprades són substancialment diferents. En concret, s'adrecen preguntes específiques sobre el model i aspiracions del constitucionalisme democràtic i el paper del dret en contextos multiculturals. També s’atorga un pes central a la dimensió institucional dels models de gestió de la diversitat que s’analitzen, prioritzant un enfocament comparatiu a partir de l’estudi de controvèrsies concretes. L’objectiu és superar algunes limitacions importants de la literatura actual, com ara la tendència a examinar en abstracte la compatibilitat de determinades demandes amb el constitucionalisme democràtic, sense abordar el funcionament d'estratègies de gestió de la diversitat cultural emprades en contextos concrets. Els treballs producte d'aquest projecte articulen les línies bàsiques d’un model pluralista, basat en principis més que en regles, que desafia els plantejaments dominants actualment. Aquest model es caracteritza pel compromís amb la legitimitat i igualtat comparatives, rebutjant el paternalisme i les visions liberals típiques sobre el paper de la regulació. La presumpció de l’“standing” moral dels grups identitaris és fonamental per tal de considerar-los interlocutors vàlids amb interessos genuïns. També s’argumenta que la integració social en contextos multiculturals no depèn tant de l’eliminació del conflicte sinó, sobre tot, d’una gestió eficient que eviti abusos de poder sistemàtics. El model defensa el rol del dret en la institucionalització del diàleg intercultural, però admet que el diàleg no necessàriament condueix a l’acord o a una estructura reguladora coherent i uniforme. Les aspiracions del ordre jurídic pluralista són més modestes: afavorir la negociació i resolució en cada conflicte, malgrat la persistència de la fragmentació i la provisionalitat dels acords. La manca d'un marc regulador comú esdevé una virtut en la mesura que permet la interacció de diferents subordres; una interacció governada per una multiplicitat de regles no necessàriament harmòniques. Els avantatges i problemes d’aquest model s'analitzen a partir de l'anàlisi de l’estructura fragmentària de l'ordre jurídic internacional i del règim Europeu de drets humans.

A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations

We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued piecewise linear discontinuous finite element space, that are optimal with respect to the mesh size and the Lamé parameters. The pure displacement, the mixed and the traction free problems are discussed in detail. We present a convergence analysis of the proposed preconditioners and include numerical examples that validate the theory and assess the performance of the preconditioners.

A Proportional Approach to Bankruptcy Problems with a guaranteed minimum

In a distribution problem, and specfii cally in bankruptcy issues, the Proportional (P) and the Egalitarian (EA) divisions are two of the most popular ways to resolve the conflict. The Constrained Equal Awards rule (CEA) is introduced in bankruptcy literature to ensure that no agent receives more than her claim, a problem that can arise when using the egalitarian division. We propose an alternative modi cation, by using a convex combination of P and EA. The recursive application of this new rule finishes at the CEA rule. Our solution concept ensures a minimum amount to each agent, and distributes the remaining estate in a proportional way. Keywords: Bankruptcy problems, Proportional rule, Equal Awards, Convex combination of rules, Lorenz dominance. JEL classi fication: C71, D63, D71.

Solidarity and uniform rules in bankruptcy problems

The idea of ensuring a guarantee (a minimum amount of the resources) to each agent has recently acquired great relevance, in both social and politi- cal terms. Furthermore, the notion of Solidarity has been treated frequently in redistribution problems to establish that any increment of the resources should be equally distributed taking into account some relevant characteris- tics. In this paper, we combine these two general concepts, guarantee and solidarity, to characterize the uniform rules in bankruptcy problems (Con- strained Equal Awards and Constrained Equal Losses rules). Keywords: Constrained Equal Awards, Constrained Equal Losses, Lower bounds, Bankruptcy problems, Solidarity. JEL classification: C71, D63, D71.

A New Approach for Bounding Awards in Bankruptcy Problems

The solution for the ‘Contested Garment Problem’, proposed in the Babylonic Talmud, suggests that each agent should receive at least some part of the resources whenever the demand overcomes the available amount. In this context, we propose a new method to define lower bounds on awards, an idea that has underlied the theoretical analysis of bankruptcy problems from its beginning (O’Neill, 1982) to present day (Dominguez and Thomson, 2006). Specifically, starting from the fact that a society establishes its own set of ‘Commonly Accepted Equity Principles’, our proposal ensures to each agent the smallest amount she gets according to all the admissible rules. As in general this new bound will not exhaust the estate, we analyze its recursive application for different sets of equity principles. Keywords: Bankruptcy problems, Bankruptcy rules, Lower bounds, Recursive process