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.

A general construction of internal sheaves in algebraic set theory

We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothen-dieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.

Rational first integrals in the Darboux theory of integrability in Cn

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Weighted limits in simplicial homotopy theory

We extend the theory of Quillen adjunctions by combining ideas of homotopical algebra and of enriched category theory. Our results describe how the formulas for homotopy colimits of Bousfield and Kan arise from general formulas describing the derived functor of the weighted colimit functor.

Job accessibility and employment probability

The objective of this paper is to estimate the impact of residential job accessibility on female employment probability in the metropolitan areas of Barcelona and Madrid. Following a “spatial mismatch” framework, we estimate a female employment probability equation where variables controlling for personal characteristics, residential segregation and employment potential on public transport network are included. Data used come from Microcensus 2001 of INE (National Institute of Statistics). The research focuses on the treatment of endogeneity problems and the measurement of accessibility variables. Our results show that low job accessibility in public transport negatively affects employment probability. The intensity of this effect tends to decrease with individual’s educational attainment. A higher degree of residential segregation also reduces job probability in a significant way..

Cooperative strategies for imperfect CSI scenarios based on distributed Alamouti

Les comunicacions cooperatives estan guanyant un gran interès en les comunicacions modernes degut a que permeten millorar la transmissió dʼinformació entre un emissor i un receptor utilitzant una sèrie de terminals situats entre ells. Aquest projecte és un estudi complet del sistemes cooperatius, analitzant el seu rendiment i comparant lʼús dʼun sol dʼaquests terminals amb lʼús del codi Alamouti, que utilitza dos terminals. Primer hi ha una introducció als sistemes cooperatius i a la teoria de la informació. Després hem estudiat un sistema cooperatiu amb la teoria de la informació com a base, en termes de probabilitat de fallada del sistema, i posteriorment lʼhem adaptat a un sistema cooperatiu real utilitzant una modulació QPSK, estudiant la seva probabilitat dʼerror de paquet. Finalment es proposen diversos protocols que permeten millorar el rendiment del sistema cooperatiu estudiat.

On the homotopy theory of spectral categories

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Migration and trade: Theory with an Application to the Eastern- Western European Integration

The remarkable increase in trade flows and in migratory flows of highly educated people are two important features of globalization of the last decades. This paper extends a two-country model of inter- and intraindustry trade to a rich environment featuring technological differences, skill differences and the possibility of international labor mobility. The model is used to explain the patterns of trade and migration as countries remove barriers to trade and to labor mobility. We parameterize the model to match the features of the Western and Eastern European members of the EU and analyze first the effects of the trade liberalization which occured between 1989 and 2004, and then the gains and losses from migration which are expected to occur if legal barriers to labor mobility are substantially reduced. The lower barriers to migration would result in significant migration of skilled workers from Eastern European countries. Interestingly, this would not only benefit the migrants and most Western European workers but, via trade, it would also benefit the workers remaining in Eastern Europe. Key Words: Skilled Migration, Gains from Variety, Real Wages, Eastern-Western Europe. JEL Codes: F12, F22, J61.

Jugant amb l'atzar i la probabilitat

Treball de recerca realitzat per un alumne d'ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit cientí­fic del Jovent l'any 2009. Quins científics van interessar-se per la probabilitat en els seus inicis?, quins altres van fer-la evolucionar? i quins conceptes coneixem i apliquem a l'actualitat? són preguntes que el treball teòric es proposa respondre. Pel que fa a la part pràctica del treball, el seu objectiu és el de crear un mecanisme capaç de generar nombres aleatoris a partir d'un taulell condicionat per paràmetres. El treball s'estructura en 4 blocs que aborden diversos camps de la probabilitat: la història de la probabilitat, els conceptes bàsics de la probabilitat, una introducció pràctica al mecanisme aleatori i el treball de camp. Els resultats finals rebel·len la possibilitat de generar nombres aleatoris a partir d'aparells senzills.

A well-posedness theory in measures for some kinetic models of collective motion

We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the behavior of large groups of animals, such as flocks of birds, swarms, or schools of fish. Our aim is to give a well-posedness theory for general models which possibly include a variety of effects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging effect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and self-propulsion effects, which take into account effects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models.

Lp theory for the multidimensional aggregation equation

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Aspects of Iwasawa theory over function fields

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A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics

To describe the collective behavior of large ensembles of neurons in neuronal network, a kinetic theory description was developed in [13, 12], where a macroscopic representation of the network dynamics was directly derived from the microscopic dynamics of individual neurons, which are modeled by conductance-based, linear, integrate-and-fire point neurons. A diffusion approximation then led to a nonlinear Fokker-Planck equation for the probability density function of neuronal membrane potentials and synaptic conductances. In this work, we propose a deterministic numerical scheme for a Fokker-Planck model of an excitatory-only network. Our numerical solver allows us to obtain the time evolution of probability distribution functions, and thus, the evolution of all possible macroscopic quantities that are given by suitable moments of the probability density function. We show that this deterministic scheme is capable of capturing the bistability of stationary states observed in Monte Carlo simulations. Moreover, the transient behavior of the firing rates computed from the Fokker-Planck equation is analyzed in this bistable situation, where a bifurcation scenario, of asynchronous convergence towards stationary states, periodic synchronous solutions or damped oscillatory convergence towards stationary states, can be uncovered by increasing the strength of the excitatory coupling. Finally, the computation of moments of the probability distribution allows us to validate the applicability of a moment closure assumption used in [13] to further simplify the kinetic theory.

Generic Nekhoroshev theory without small divisors

In this article, we present a new approach of Nekhoroshev theory for a generic unperturbed Hamiltonian which completely avoids small divisors problems. The proof is an extension of a method introduced by P. Lochak which combines averaging along periodic orbits with simultaneous Diophantine approximation and uses geometric arguments designed by the second author to handle generic integrable Hamiltonians. This method allows to deal with generic non-analytic Hamiltonians and to obtain new results of generic stability around linearly stable tori.

Conflict prevention and decentralized governance: some remarks about the state of the art in theory and practice

Is there a link between decentralized governance and conflict prevention? This article tries to answer the question by presenting the state of the art of the intersection of both concepts. Provided that social conflict is inevitable and given the appearance of new threats and types of violence, as well as new demands for security based on people (human security), our societies should focus on promoting peaceful changes. Through an extensive analysis of the existing literature and the study of several cases, this paper suggests that decentralized governance can contribute to these efforts by transforming conflicts, bringing about power-sharing and inclusion incentives of minority groups. Albeit the complexity of assessing its impact on conflict prevention, it can be contended that decentralized governance might have very positive effects on the reduction of causes that bring about conflicts due to its ability to foster the creation of war/violence preventors. More specifically, this paper argues that decentralization can have a positive impact on the so-called triggers and accelerators (short- and medium-term causes).