When ESDP confronts ENP: security sector reform as a bridge in the EU’s foreign policy

The European Neighbourhood Policy’s birth has taken place in parallel with the renewed momentum of the European Security and Defence Policy, which has launched 14 operations since 2003. Both policies’ instruments have converged in the neighbouring area covered by ENP: Georgia, in the East and the Palestinian Territories in the South. In both cases, the Security Sector Reform strategies have been the main focus for ESDP and an important objective for ENP. In this paper, two objectives are pursued: first, to assess the EU’s involvement in both cases in SSR terms; and second, to analyse whether the convergence of ESDP operations with a broader EU neighbourhood policy implies that the former has become an instrument for the a EU external action.

Labor productivity in Spain: 1977-2002

This study examines the evolution of labor productivity across Spanish regions during the period from 1977 to 2002. By applying the kernel technique, we estimate the effects of the Transition process on labor productivity and its main sources. We find that Spanish regions experienced a major convergence process in labor productivity and in human capital in the 1977-1993 period. We also pinpoint the existence of a transition co-movement between labor productivity and human capital. Conversely, the dynamics of investment in physical capital seem unrelated to the transition dynamics of labor productivity. The lack of co-evolution can be addressed as one of the causes of the current slowdown in productivity. Classification-JEL: J24, N34, N940, O18, O52, R10

Characterizations of Lojasiewicz inequalities and applications

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative characterizations of this type of inequalities for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In a metric context, we show that a generalized form of the Lojasiewicz inequality (hereby called the Kurdyka- Lojasiewicz inequality) relates to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by -∂f are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka- Lojasiewicz inequality is satisfied. Further characterizations in terms of talweg lines -a concept linked to the location of the less steepest points at the level sets of f- and integrability conditions are given. In the convex case these results are significantly reinforced, allowing in particular to establish the asymptotic equivalence of discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex C2 function in R2 is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka- Lojasiewicz inequality.

Inversión en infraestructuras, crecimiento y convergencia regional

This paper presents estimates of the contribution of infrastructure investment to the growth of output and employment in Spain and its regions and investigates the impact of this factor on the process of regional convergence in income per capita during the period 1965-2004.

Creation of a carrier-grade telco based on a voice over IP backbone

En aquesta memòria l'autor, fent servir un enfoc modern, redissenya i implementa la plataforma que una empresa de telecomunicacions del segle 21 necessita per poder donar serveis de telefonia i comunicacions als seus usuaris i clients. Al llarg d'aquesta exposició es condueix al lector des d'una fase inicial de disseny fins a la implementació i posada en producció del sistema final desenvolupat, centrant-nos en solucionar les necessitats actuals que això implica. Aquesta memòria cubreix el software, hardware i els processos de negoci associats al repte de fer realitat aquest objectiu, i presenta al lector les múltiples tecnologies emprades per aconseguir-ho, fent emfàsi en la convergència actual de xarxes cap al concepte de xarxes IP i basant-se en aquesta tendència i utilitzant aquesta tecnologia de veu sobre IP per donar forma a la plataforma que finalment, de forma pràctica, es posa en producció.

El problema de una sensibilización del campo de la moralidad en la filosofia trascendental de Kant

La problemática de la investigación se plantea en el contexto de la filosofía trascendental de Kant, en relación al modo en que es en general posible para nosotros representarnos el ámbito de la moralidad. Nuestra comprensión natural o preteórica del funcionamiento del lenguaje parece llevarnos a entender el significado de nuestras palabras en términos de la relación que se establece entre el signo lingüístico y el objeto: nuestros términos lingüísticos están en el lugar del objeto extralingüístico a que refieren y que constituye su significado. A nuestro modo de ver, la afirmación kantiana relativa a que todo nuestro conocimiento comienza con la experiencia, es decir, con aquello que procede de los sentidos, parece estar apuntando a esta intuición fundamental. Ahora bien, la cuestión que cabe plantearse es: de acuerdo con este modelo de significación, ¿cuál es el significado de nuestros términos morales? Si, con Kant, aceptamos que el concepto de deber moral exige el cumplimiento (u omisión) incondicionado de una acción y que, precisamente por las exigencias de universalidad y necesidad que le son inherentes, tal concepto es inderivable de la experiencia, cabe preguntarse cuál es el significado del concepto de deber en sentido moral (y, en general, de los términos morales) y de qué manera somos capaces de representárnoslo. Mi investigación ha pretendido esclarecer precisamente en qué sentido debe entenderse la afirmación kantiana de que en la reflexión sobre la corrección moral de nuestras acciones, para representarnos las exigencias de universalidad y necesidad que son propias del concepto de deber moral, nos servimos analógicamente del concepto de naturaleza, así como analizar la plausibilidad de la propuesta kantiana misma.

Condensation of polyhedric structures onto soap films

We study the existence of solutions to general measure-minimization problems over topological classes that are stable under localized Lipschitz homotopy, including the standard Plateau problem without the need for restrictive assumptions such as orientability or even rectifiability of surfaces. In case of problems over an open and bounded domain we establish the existence of a “minimal candidate”, obtained as the limit for the local Hausdorff convergence of a minimizing sequence for which the measure is lower-semicontinuous. Although we do not give a way to control the topological constraint when taking limit yet— except for some examples of topological classes preserving local separation or for periodic two-dimensional sets — we prove that this candidate is an Almgren-minimal set. Thus, using regularity results such as Jean Taylor’s theorem, this could be a way to find solutions to the above minimization problems under a generic setup in arbitrary dimension and codimension.

Climate change in the Atlantic Ocean since the 1940's and the effects on the global climate

En aquest projecte s’ha estudiat la relació entre els canvis en les temperatures superficials de l’Oceà Atlàntic i els canvis en la circulació atmosfèrica en el segle XX. Concretament s’han analitzat dos períodes de estudi: el primer des del 1940 al 1960 i el segon des del 1980 fins al 2000. S’ha posat especial interès en les anomalies en les temperatures superficials del mar en la regió tropical de l’Oceà Atlàntic i la possible interconnexió amb els canvis climàtics observats i predits. Per a la realització de l’estudi s’han dut a terme una sèrie d’experiments utilitzant el model climàtic elaborat a la universitat d’UCLA (UCLA‐AGCM model). Els resultats obtinguts han estat analitzats en forma de mapes i figures per a cada variable d’estudi. També s’ha fet una comparació entre els resultats obtinguts i altres trobats en altres treballs publicats sobre el mateix tema de recerca. Els resultats obtinguts són molt amplis i poden tenir diverses interpretacions. Tot i així algunes de les conclusions a les quals s’ha arribat són: les diferències més significatives per a les variables estudiades i trobades a partir dels resultats obtinguts del model per als dos períodes d’estudi són en els mesos d’hivern i a la zona dels tròpics; concretament a parts del nord de sud Amèrica i a parts del nord d’Àfrica. S’han trobat també canvis significatius en els patrons de precipitació sobre aquestes mateixes zones. També s’ha observant un moviment cap al nord de la zona d’interconvergència tropical i pot ser degut a l’anòmal gradient trobat a la zona equatorial en les temperatures superficial de l’Oceà. Tot i així per a una definitiva discussió i conclusions sobre els resultats dels experiments, seria necessari un estudi més ampli i profund.

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.

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Oscillations in a molecular structured cell population model

We consider a nonlinear cyclin content structured model of a cell population divided into proliferative and quiescent cells. We show, for particular values of the parameters, existence of solutions that do not depend on the cyclin content. We make numerical simulations for the general case obtaining, for some values of the parameters convergence to the steady state but also oscillations of the population for others.

A decision-making Fokker-Planck model in computational neuroscience

Minimal models for the explanation of decision-making in computational neuroscience are based on the analysis of the evolution for the average firing rates of two interacting neuron populations. While these models typically lead to multi-stable scenario for the basic derived dynamical systems, noise is an important feature of the model taking into account finite-size effects and robustness of the decisions. These stochastic dynamical systems can be analyzed by studying carefully their associated Fokker-Planck partial differential equation. In particular, we discuss the existence, positivity and uniqueness for the solution of the stationary equation, as well as for the time evolving problem. Moreover, we prove convergence of the solution to the the stationary state representing the probability distribution of finding the neuron families in each of the decision states characterized by their average firing rates. Finally, we propose a numerical scheme allowing for simulations performed on the Fokker-Planck equation which are in agreement with those obtained recently by a moment method applied to the stochastic differential system. Our approach leads to a more detailed analytical and numerical study of this decision-making model in computational neuroscience.

On rigid analytic uniformizations of Jacobians of Shimura curves

The main goal of this article is to give an explicit rigid analytic uniformization of the maximal toric quotient of the Jacobian of a Shimura curve over Q at a prime dividing exactly the level. This result can be viewed as complementary to the classical theorem of Cerednik and Drinfeld which provides rigid analytic uniformizations at primes dividing the discriminant. As a corollary, we offer a proof of a conjecture formulated by M. Greenberg in hispaper on Stark-Heegner points and quaternionic Shimura curves, thus making Greenberg's construction of local points on elliptic curves over Q unconditional.

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.