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.

Galois extension of CP-Graded ring extensions

In this paper, we investigate galois theory of CP-graded ring extensions. In particular, we generalize some galois results given in [1, 2] and, without restriction to nor graded fields nor torsion free of the grade groups, we show that some results of graded field extensions given in [3] hold.

Pure motives, mixed motives and extensions of motives associated to singular surfaces

We first recall the construction of the Chow motive modelling intersection cohomology of a proper surface X and study its fundamental properties. Using Voevodsky's category of effective geometrical motives, we then study the motive of the exceptional divisor D in a non-singular blow-up of X. If all geometric irreducible components of D are of genus zero, then Voevodsky's formalism allows us to construct certain one-extensions of Chow motives, as canonical subquotients of the motive with compact support of the smooth part of X. Specializing to Hilbert-Blumenthal surfaces, we recover a motivic interpretation of a recent construction of A. Caspar.

Orbit decidability and the conjugacy problem for some extensions of groups

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

Singling out individual inventors from patent data

An increasing number of studies have sprung up in recent years seeking to identify individual inventors from patent data. Different heuristics have been suggested to use their names and other information disclosed in patent documents in order to find out “who is who” in patents. This paper contributes to this literature by setting forth a methodology to identify them using patents applied to the European Patent Office (EPO hereafter). As in the large part of this literature, we basically follow a three-steps procedure: (1) the parsing stage, aimed at reducing the noise in the inventor’s name and other fields of the patent; (2) the matching stage, where name matching algorithms are used to group possible similar names; (3) the filtering stage, where additional information and different scoring schemes are used to filter out these potential same inventors. The paper includes some figures resulting of applying the algorithms to the set of European inventors applying to the EPO for a large period of time.

Patent policy, patent pools, and the accumulation of claims in sequential innovation

We present a dynamic model where the accumulation of patents generates an increasing number of claims on sequential innovation. We compare innovation activity under three regimes -patents, no-patents, and patent pools- and find that none of them can reach the first best. We find that the first best can be reached through a decentralized tax-subsidy mechanism, by which innovators receive a subsidy when they innovate, and are taxed with subsequent innovations. This finding implies that optimal transfers work in the exact opposite way as traditional patents. Finally, we consider patents of finite duration and determine the optimal patent length.

Deux extensions de Théorèmes de Hamburger (portant sur l'équation fonctionnelle de la fonction dzêta)

We propose two types of extensions to Hamburger’s theorems on the Dirichlet series with functional equation like the one of the Riemann zeta function, under weaker hypotheses. This builds upon the dictionary betweeen the moderate meromorphic functions with functional equation and the tempered distributions with extended S-support condition.

Generating functions for the numbers of Abelian extensions of a local field

The aim of this paper is to give an explicit formula for the num- bers of abelian extensions of a p-adic number field and to study the generating function of these numbers. More precisely, we give the number of abelian ex- tensions with given degree and ramification index, and the number of abelian extensions with given degree of any local field of characteristic zero. Moreover, we give a concrete expression of a generating function for these last numbers

Extensions of maps defined on many fibres

Let S be a fibred surface. We prove that the existence of morphisms from non countably many fibres to curves implies, up to base change, the existence of a rational map from S to another surface fibred over the same base reflecting the properties of the original morphisms. Under some conditions of unicity base change is not needed and one recovers exactly the initial maps.

Singling out individual inventors from patent data

An increasing number of studies in recent years have sought to identify individual inventors from patent data. A variety of heuristics have been proposed for using the names and other information disclosed in patent documents to establish who is who in patents. This paper contributes to this literature by describing a methodology for identifying inventors using patents applied to the European Patent Office, EPO hereafter. As in much of this literature, we basically follow a threestep procedure : 1- the parsing stage, aimed at reducing the noise in the inventor’s name and other fields of the patent; 2- the matching stage, where name matching algorithms are used to group similar names; and 3- the filtering stage, where additional information and various scoring schemes are used to filter out these similarlynamed inventors. The paper presents the results obtained by using the algorithms with the set of European inventors applying to the EPO over a long period of time.

Nonlinear principal and canonical directions from continuous extensions of multidimensional scaling

A continuous random variable is expanded as a sum of a sequence of uncorrelated random variables. These variables are principal dimensions in continuous scaling on a distance function, as an extension of classic scaling on a distance matrix. For a particular distance, these dimensions are principal components. Then some properties are studied and an inequality is obtained. Diagonal expansions are considered from the same continuous scaling point of view, by means of the chi-square distance. The geometric dimension of a bivariate distribution is defined and illustrated with copulas. It is shown that the dimension can have the power of continuum.

Mixed Hodge structures and vector bundles on the projective Plane I

We describe an equivalence of categories between the category of mixed Hodge structures and a category of vector bundles on the toric complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalises the notion of R-split mixed Hodge structure and compute extensions in the category of mixed Hodge structures in terms of extensions of the corresponding vector bundles. We also give a relative version of this correspondence and apply it to define stratifications of the bases of the variations of mixed Hodge structure.

Endogenous integration and welfare in complementary goods markets

This paper analyzes the strategic decision to integrate by firms that produce complementary products. Integration entails bundling pricing. We find out that integration is privately profitable for a high enough degree of product differentiation, that profits of the non-integrated firms decrease, and that consumer surplus need not necessarily increase when firms integrate despite the fact that prices diminish. Thus, integration of a system is welfare-improving for a high enough degree of product differentiation combined with a minimum demand advantage relative to the competing system. Overall, and from a number of extensions undertaken, we conclude that bundling need not be anti-competitive and that integration should be permitted only under some circumstances.

Research policy and endogenous growth

This paper studies the effects of different types of research policy on economic growth. We find that while tax incentives to private research, public funding of private projects, and basic research performed at public institutions have unambiguously positive effects on economic growth, performing applied research at public institutions could have negative growth effects. This is due to the large crowding out of private research caused by public R\&D when it competes with private firms in the "patent race". Concerning the effects of these policies on welfare, it is found that research policy can either improve or reduce consumer welfare depending on the characteristics of the policy and that an excessively high research subsidy will reduce it.

El Taller de traducción como metodología didáctica experimental en un marco epistemológico socioconstructivista y humanista

Aquest treball de recerca presenta les diferents fases d’un experiment pilot que vaig projectar i realitzar dins l’àmbit de l’ensenyament de la traducció a un context universitari. L’experiment va consistir en l’aplicació i observació d’una metodologia didàctica innovadora, amb una base epistemològica socioconstructivista i humanista, i en l’avaluació dels resultats obtinguts. Per l’experiment pilot vaig seleccionar com a marc teòric el model socioconstructivista del procés d’ensenyament i aprenentatge proposat per Williams i Burden (1997), que integra instàncies constructivistes, interaccionistes i humanistes. En aquest àmbit vaig elaborar una metodologia didàctica innovadora, el “Taller de Traducció”, modelat sobre el Constructivist Workshop proposat per Don Kiraly (2000: 62-64) al qual vaig aportar algunes modificacions per adequar-lo al context diferent d’ensenyament. El disseny experimental basat en la utilització d’un grup experimental i d’un de control, preveu el recurs a instruments de recollida de dades qualitatives i quantitatives. Les hipòtesis elaborades prospecten l’aparició de determinats efectes com a conseqüència de l’aplicació del tractament experimental (autonomia, motivació i presa de consciència) i, al mateix temps es basen en la pressuposició, sustentat sobre la literatura consultada, que els efectes prospectats milloren el procés d’ensenyament i aprenentatge. Per tant, vaig intentar, per una banda, verificar l’eficàcia del tractament relacionada amb l’aparició dels efectes prospectats i, per una altra, mesurar l’incidència d’aquests efectes sobre el procés d’ensenyament i aprenentatge. A més, vaig dur a terme l’observació i avaluació de la metodologia aplicada respecte la coherència amb les bases epistemològiques socioconstructivistes i a la funcionalitat dins el context universitari on es va aplicar. Totes les dades recollides confirmen la coherència i la funcionalitat de la metodologia aplicada, tant pel que fa a l’eficàcia relacionada amb l’aparició dels efectes prospectats a les hipòtesis elaborades i a la seva incidència sobre la millora del procés d’ensenyament i aprenentatge, tot i que es van detectar algunes fallides a l’experiment pilot que se solucionaran a l’experiment definitiu. Els resultats positius de l’experiment pilot han estat confirmades també per les dades d’altres dos experiments realitzats posteriorment amb altres grups d’estudiants de la mateixa assignatura. Tots els resultats recollits es faran servir per projectar l’experiment definitiu, aportant-hi les modificacions necessàries per eliminar les fallides evidenciades durant la fase d’aplicació de l’experiment pilot i de les seves extensions i seguiments, i serviran com a base per a la meva tesi doctoral a la qual voldria arribar a formular una proposta socioconstrucitivista i humanista integradora per a l’ensenyament de la traducció.