Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Biased quantitative measurement of interval ordered homothetic preferences

We represent interval ordered homothetic preferences with a quantitative homothetic utility function and a multiplicative bias. When preferences are weakly ordered (i.e. when indifference is transitive), such a bias equals 1. When indifference is intransitive, the biasing factor is a positive function smaller than 1 and measures a threshold of indifference. We show that the bias is constant if and only if preferences are semiordered, and we identify conditions ensuring a linear utility function. We illustrate our approach with indifference sets on a two dimensional commodity space.

The complexity of random ordered structures

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

Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates

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

Monte Carlo Study of the Growth of L12 ordered domains in fcc A3B binary alloys

A Monte Carlo study of the late time growth of L12-ordered domains in a fcc A3B binary alloy is presented. The energy of the alloy has been modeled by a nearest-neighbor interaction Ising Hamiltonian. The system exhibits a fourfold degenerated ground state and two kinds of interfaces separating ordered domains: flat and curved antiphase boundaries. Two different dynamics are used in the simulations: the standard atom-atom exchange mechanism and the more realistic vacancy-atom exchange mechanism. The results obtained by both methods are compared. In particular we study the time evolution of the excess energy, the structure factor and the mean distance between walls. In the case of atom-atom exchange mechanism anisotropic growth has been found: two characteristic lengths are needed in order to describe the evolution. Contrarily, with the vacancyatom exchange mechanism scaling with a single length holds. Results are contrasted with existing experiments in Cu3Au and theories for anisotropic growth.

Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates

Let $Q$ be a suitable real function on $C$. An $n$-Fekete set corresponding to $Q$ is a subset ${Z_{n1}},\dotsb, Z_{nn}}$ of $C$ which maximizes the expression $\Pi^n_i_{sets are, in a sense, maximally spread out with respect to the equilibrium measure. In general, our results apply only to a part of the Fekete set, which is at a certain distance away from the boundary of the droplet. However, for the potential $Q=|Z|^2$ we obtain results which hold globally, and we conjecture that such global results are true for a wide range of potentials.

On the Connectivity of the Julia sets of meromorphic functions

We prove that every transcendental meromorphic map $f$ with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions, whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton's method for entire maps are simply connected, which solves a well-known open question.

Multiscaling and information content of natural color images

Naive scale invariance is not a true property of natural images. Natural monochrome images possess a much richer geometrical structure, which is particularly well described in terms of multiscaling relations. This means that the pixels of a given image can be decomposed into sets, the fractal components of the image, with well-defined scaling exponents [Turiel and Parga, Neural Comput. 12, 763 (2000)]. Here it is shown that hyperspectral representations of natural scenes also exhibit multiscaling properties, observing the same kind of behavior. A precise measure of the informational relevance of the fractal components is also given, and it is shown that there are important differences between the intrinsically redundant red-green-blue system and the decorrelated one defined in Ruderman, Cronin, and Chiao [J. Opt. Soc. Am. A 15, 2036 (1998)].

On the trace of an endofunctor of a small category

The trace of a square matrix can be defined by a universal property which, appropriately generalized yields the concept of "trace of an endofunctor of a small category". We review the basic definitions of this general concept and give a new construction, the "pretrace category", which allows us to obtain the trace of an endofunctor of a small category as the set of connected components of its pretrace. We show that this pretrace construction determines a finite-product preserving endofunctor of the category of small categories, and we deduce from this that the trace inherits any finite-product algebraic structure that the original category may have. We apply our results to several examples from Representation Theory obtaining a new (indirect) proof of the fact that two finite dimensional linear representations of a finite group are isomorphic if and only if they have the same character.

A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.

Policy evaluation and uncertainty about the effects of oil prices on economic activity

This paper addresses the issue of policy evaluation in a context in which policymakers are uncertain about the effects of oil prices on economic performance. I consider models of the economy inspired by Solow (1980), Blanchard and Gali (2007), Kim and Loungani (1992) and Hamilton (1983, 2005), which incorporate different assumptions on the channels through which oil prices have an impact on economic activity. I first study the characteristics of the model space and I analyze the likelihood of the different specifications. I show that the existence of plausible alternative representations of the economy forces the policymaker to face the problem of model uncertainty. Then, I use the Bayesian approach proposed by Brock, Durlauf and West (2003, 2007) and the minimax approach developed by Hansen and Sargent (2008) to integrate this form of uncertainty into policy evaluation. I find that, in the environment under analysis, the standard Taylor rule is outperformed under a number of criteria by alternative simple rules in which policymakers introduce persistence in the policy instrument and respond to changes in the real price of oil.

La legislación como condicionante en la creatividad: perspectiva de género y estereotipos

Entre los varios tópicos que rodean al ámbito publicitario, aquellos relacionados con el tratamiento de género, específicamente al femenino, a través de las representaciones de roles y estereotipos en las que, además, el cuerpo tiene especial relevancia, han determinado que la publicidad sea considerada como uno de los factores que refuerzan y fomentan la discriminación hacia las mujeres. Dentro de los límites que el marco regulador establece para la libertad de expresión y por iniciativas propias del sistema publicitario a través del autocontrol, en las estrategias creativas y en quienes las producen, se han iniciado procesos, llamados a repensar las identidades femeninas y masculinas, pese a ello, existen efluvios que demuestran que el sexismo continua presente en las sociedades en las que la publicidad se desenvuelve, por tanto le dan cabida a ésta y otras formas de comunicación y de procesos y comportamientos sociales

An assessment of gene prediction accuracy in large DNA sequences

One of the first useful products from the human genome will be a set of predicted genes. Besides its intrinsic scientific interest, the accuracy and completeness of this data set is of considerable importance for human health and medicine. Though progress has been made on computational gene identification in terms of both methods and accuracy evaluation measures, most of the sequence sets in which the programs are tested are short genomic sequences, and there is concern that these accuracy measures may not extrapolate well to larger, more challenging data sets. Given the absence of experimentally verified large genomic data sets, we constructed a semiartificial test set comprising a number of short single-gene genomic sequences with randomly generated intergenic regions. This test set, which should still present an easier problem than real human genomic sequence, mimics the approximately 200kb long BACs being sequenced. In our experiments with these longer genomic sequences, the accuracy of GENSCAN, one of the most accurate ab initio gene prediction programs, dropped significantly, although its sensitivity remained high. Conversely, the accuracy of similarity-based programs, such as GENEWISE, PROCRUSTES, and BLASTX was not affected significantly by the presence of random intergenic sequence, but depended on the strength of the similarity to the protein homolog. As expected, the accuracy dropped if the models were built using more distant homologs, and we were able to quantitatively estimate this decline. However, the specificities of these techniques are still rather good even when the similarity is weak, which is a desirable characteristic for driving expensive follow-up experiments. Our experiments suggest that though gene prediction will improve with every new protein that is discovered and through improvements in the current set of tools, we still have a long way to go before we can decipher the precise exonic structure of every gene in the human genome using purely computational methodology.

Incorporating features of distribution and progression for automatic Makam classification

Automatic classification of makams from symbolic data is a rarely studied topic. In this paper, first a review of an n-gram based approach is presented using various representations of the symbolic data. While a high degree of precision can be obtained, confusion happens mainly for makams using (almost) the same scale and pitch hierarchy but differ in overall melodic progression, seyir. To further improve the system, first n-gram based classification is tested for various sections of the piece to take into account a feature of the seyir that melodic progression starts in a certain region of the scale. In a second test, a hierarchical classification structure is designed which uses n-grams and seyir features in different levels to further improve the system.