Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems

In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem.Amer.Math. Soc. 2006, and generalized in Delshams and Huguet, Nonlinearity 2009, and provide explicit, concrete and easily verifiable conditions for the existence of diffusing orbits. The simplification of the hypotheses allows us to perform explicitly the computations along the proof, which contribute to present in an easily understandable way the geometric mechanism of diffusion. In particular, we fully describe the construction of the scattering map and the combination of two types of dynamics on a normally hyperbolic invariant manifold.

Refined asymptotics for the subcritical Keller-Segel system and related functional inequalities

We analyze the rate of convergence towards self-similarity for the subcritical Keller-Segel system in the radially symmetric two-dimensional case and in the corresponding one-dimensional case for logarithmic interaction. We measure convergence in Wasserstein distance. The rate of convergence towards self-similarity does not degenerate as we approach the critical case. As a byproduct, we obtain a proof of the logarithmic Hardy-Littlewood-Sobolev inequality in the one dimensional and radially symmetric two dimensional case based on optimal transport arguments. In addition we prove that the onedimensional equation is a contraction with respect to Fourier distance in the subcritical case.

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.

Rigid flat webs on the projective plane

This paper studies global webs on the projective plane with vanishing curvature. The study is based on an interplay of local and global arguments. The main local ingredient is a criterium for the regularity of the curvature at the neighborhood of a generic point of the discriminant. The main global ingredient, the Legendre transform, is an avatar of classical projective duality in the realm of differential equations. We show that the Legendre transform of what we call reduced convex foliations are webs with zero curvature, and we exhibit a countable infinity family of convex foliations which give rise to a family of webs with zero curvature not admitting non-trivial deformations with zero curvature.

Diseño y puesta en marcha de un laboratorio remoto de robótica

Este proyecto surge de la iniciativa de mejorar la calidad docente de las prácticas en la asignatura Robótica y Automatización Industrial impartida en la ETSE (Escola Tècnica Superior d’Enginyeria) de la UAB, mediante un sistema innovador. El objetivo es sustituir las actuales prácticas, basadas en la realización de simulaciones en entorno MATLAB para verificar las ecuaciones que gobiernan a los robots manipuladores, por un entorno de prácticas más atractivo consistente en un robot manipulador real, que podrá ser programado para la realización de tareas de PPO (Pick and Place Operation).

Women speaking across the Border: The impact of the Border and the conflict on women's health and roles

This research was commissioned by Derry Well Woman and carried out on its behalf by the Institute of Public Health in Ireland in association with the Institute for Conflict Research and Rethink.The research had two distinct aims:- to improve understanding of the impact of the border and of the conflict on both sidesof the border on women’s health- to improve understanding of women’s roles, particularly as they impact on mental health, in post conflict society.- The research was conducted with a view to its recommendations being used to inform the work of the Cross Border Women’  Health Network as well as other cross border health forums or organisations responsible for service planning and delivery.- The findings of this research are based on a series of 31 in-depth interviews and one focus group with women both north and south of the border and on one focus group and six interviews with women who were specifically consulted as service providers.

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.

Desenvolupament de codis numèrics per a la resolució de fluxos turbulents en ordinadors paral·lels emprant discretitzacions tipus symmetry-preserving

Projecte de recerca elaborat a partir d’una estada a la University of Groningen, Holanda, entre 2007 i 2009. La simulació directa de la turbulència (DNS) és una eina clau dins de la mecànica de fluids computacional. Per una banda permet conèixer millor la física de la turbulència i per l'altra els resultats obtinguts són claus per el desenvolupament dels models de turbulència. No obstant, el DNS no és una tècnica vàlida per a la gran majoria d'aplicacions industrials degut al elevats costos computacionals. Per tant, és necessari cert grau de modelització de la turbulència. En aquest context, s'han introduïts importants millores basades en la modelització del terme convectiu (no lineal) emprant symmetry-preserving regularizations. En tracta de modificar adequadament el terme convectiu a fi de reduir la producció d'escales més i més petites (vortex-stretching) tot mantenint tots els invariants de les equacions originals. Fins ara, aquest models s'han emprat amb èxit per nombres de Rayleigh (Ra) relativament elevats. En aquest punt, disposar de resultats DNS per a configuracions més complexes i nombres de Ra més elevats és clau. En aquest contexte, s'han dut a terme simulacions DNS en el supercomputador MareNostrum d'una Differentially Heated Cavity amb Ra=1e11 i Pr=0.71 durant el primer any dels dos que consta el projecte. A més a més, s'ha adaptat el codi a fi de poder simular el fluxe al voltant d'un cub sobre una pared amb Re=10000. Aquestes simulacions DNS són les més grans fetes fins ara per aquestes configuracions i la seva correcta modelització és un gran repte degut la complexitat dels fluxes. Aquestes noves simulacions DNS estan aportant nous coneixements a la física de la turbulència i aportant resultats indispensables per al progrés de les modelitzacións tipus symmetry-preserving regularization.

Estrategies per la inversió tridimensional de dades magnetotel.lúriques:

Projecte de recerca elaborat a partir d’una estada a la Dublin Institute for Advanced Studies, Irlanda, entre setembre i desembre del 2009.En els últims anys s’ha realitzat un important avanç en la modelització tridimensional en magnetotel•lúrica (MT) gracies a l'augment d’algorismes d’inversió tridimensional disponibles. Aquests codis utilitzen diferents formulacions del problema (diferències finites, elements finits o equacions integrals), diverses orientacions del sistema de coordenades i, o bé en el conveni de signe, més o menys, en la dependència temporal. Tanmateix, les impedàncies resultants per a tots els valors d'aquests codis han de ser les mateixes una vegada que es converteixen a un conveni de signe comú i al mateix sistema de coordenades. Per comparar els resultats dels diferents codis hem dissenyat models diferents de resistivitats amb estructures tridimensional incrustades en un subsòl homogeni. Un requisit fonamental d’aquests models és que generin impedàncies amb valors importants en els elements de la diagonal, que no són menyspreables. A diferència dels casos del modelització de dades magnetotel.lúriques unidimensionals i bidimensionals, pel al cas tridimensional aquests elements de les diagonals del tensor d'impedància porten informació sobre l'estructura de la resistivitat. Un dels models de terreny s'utilitza per comparar els diferents algoritmes que és la base per posterior inversió dels diferents codis. Aquesta comparació va ser seguida de la inversió per recuperar el conjunt de dades d'una estructura coneguda.

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.

Narrative Diagrammatik. Mit einer Modellanalyse: Die Diagrammatik des "Decameron"

Taking as a starting point the seeming inconsistency of late-medieval romances notoriously 'run wild' (verwildert), this article is concerned with the description of an abstract form of narrative coherence that is based on the notion of the diagrammatic. In a first section, this concept is illustrated in a simplified manner by an analysis of Boccaccio's Decameron based on two levels of spatial structure: that of the autograph Berlin manuscript (Codex Hamilton 90) and that of the recipient's mental visualisation of the relations between the frame and the tales of the work. It is argued that the connectivity of the work as a whole depends on the perception of those two spatial representations of the plot. A second section develops this concept in a more theoretical fashion, drawing on Charles Sanders Peirce's notion of diagrammatic reasoning as a way of perceiving relations through mental and material topological representations. Correspondingly, a view of narrative is proposed that does not depend on the traditional perspective of temporal sequence but emphasizes the spatial structure of literary narrative. It is argued that these conditions form the primary ontological mode of narrative, whereas the temporal development of a story is an aesthetic illusion that has been specifically stimulated by the narrative conventions of approximately the past three centuries and must thus be considered a secondary effect. To conclude, an interpretation in miniature of an aspect of Heinrich von Neustadt's Apollonius von Tyrland that seems to have 'run wild' is undertaken from a diagrammatic perspective.

Isolation and Identification of 9-methylgermacrene-B as the Putative Sex Pheromone of Lutzomyia cruzi (Mangabeira, 1938) (Diptera: Psychodidae)

Lutzomyia (Lutzomyia) cruzi has been named as a probable vector of Leishmania chagasi in Corumbá, Mato Grosso do Sul, Brazil. Taxonomically L. cruzi is closely related to the L. longipalpis species complex. Females of L. cruzi and L. longipalpis are morphologically indistinguishable and associated males must be examined carefully to confirm identifications. Chemical analysis hexane extracts of male L. cruzi has revealed the presence of a 9-methylgermacrene-B (C16), a homosesquiterpene (mw 218) previously shown to be the sex pheromone of one of the members of the L. longipalpis species complex.

Urgències neurovasculars a l’hospital universitari Vall D’HEBRON (2001-2008)

La malaltia cerebrovascular és una de les patologies més prevalents a Catalunya, motivant un gran nombre de consultes a urgències i una de les primeres causes de mortalitat i discapacitat en adults. L’objectiu d’aquest estudi descriptiu fou explorar les característiques dels pacients amb patologia neurovascular atesos a urgències de l’Hospital Vall d’Hebron entre 2001 i 2008 a través de diverses variables. En vuit anys, s’ha produit un canvi en el perfil d’aquests pacients, amb l’augment de la complexitat diagnòstico-terapèutica de l’atenció de l’ictus a urgències. Amb tot, observem una disminució de la necessitat d’ingrés, la mortalitat i l’estada mitja hospitalària.

Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation

This paper is concerned with the modeling and analysis of quantum dissipation phenomena in the Schrödinger picture. More precisely, we do investigate in detail a dissipative, nonlinear Schrödinger equation somehow accounting for quantum Fokker–Planck effects, and how it is drastically reduced to a simpler logarithmic equation via a nonlinear gauge transformation in such a way that the physics underlying both problems keeps unaltered. From a mathematical viewpoint, this allows for a more achievable analysis regarding the local wellposedness of the initial–boundary value problem. This simplification requires the performance of the polar (modulus–argument) decomposition of the wavefunction, which is rigorously attained (for the first time to the best of our knowledge) under quite reasonable assumptions.