Traces of Sobolev functions on regular surfaces in infinite dimensions

In a Banach space $X$ endowed with a nondegenerate Gaussian measure, we consider Sobolev spaces of real functions defined in a sublevel set $O= \{x\in X:\;G(x) <0\}$ of a Sobolev nondegenerate function $G:X\mapsto \R$. We define the traces at $G^{-1}(0)$ of the elements of $W^{1,p}(O, \mu)$ for $p>1$, as elements of $L^1(G^{-1}(0), \rho)$ where $\rho$ is the surface measure of Feyel and de La Pradelle. The range of the trace operator is contained in $L^q(G^{-1}(0), \rho)$ for $1\leq q<p$ and even in $L^p(G^{-1}(0), \rho)$ under further assumptions. If $O$ is a suitable halfspace, the range is characterized as a sort of fractional Sobolev space at the boundary. An important consequence of the general theory is an integration by parts formula for Sobolev functions, which involves their traces at $G^{-1}(0)$

Transition between immune and disease states in a cellular automaton model of clonal immune response

In this paper we extend the Celada-Seiden (CS) model of the humoral immune response to include infectious virus and cytotoxic T lymphocytes (cellular response). The response of the system to virus involves a competition between the ability of the virus to kill the host cells and the host's ability to eliminate the virus. We find two basins of attraction in the dynamics of this system, one is identified with disease and the other with the immune state. There is also an oscillating state that exists on the border of these two stable states. Fluctuations in the population of virus or antibody can end the oscillation and drive the system into one of the stable states. The introduction of mechanisms of cross-regulation between the two responses can bias the system towards one of them. We also study a mean field model, based on coupled maps, to investigate virus-like infections. This simple model reproduces the attractors for average populations observed in the cellular automaton. All the dynamical behavior connected to spatial extension is lost, as is the oscillating feature. Thus the mean field approximation introduced with coupled maps destroys oscillations.Comment: 27 pages LaTeX + 7 Figures Postscrip

Alternative derivation of Krasnov's action for general relativity

Starting from Plebanski's action for general relativity with cosmological constant, we show that by integrating out all the auxiliary fields Krasnov's action immediately emerges. We also perform the Hamiltonian analysis of the latter and show that the constraints are those of the Ashtekar formalism.Comment: 4 page

Relato de una investigación en la acción : contextos de aprendizajes interculturales

En este artículo se presenta un reporte del proyecto de investigación “Estrategias educativas en contextos de aprendizajes interculturales" que fue presentado como Memoria Final del Programa de Postgrado “European Counsellor for Multicultural Affairs" (Asesor Europeo para Asuntos Multiculturales). La investigación que se relata, bajo el enfoque de la Investigación Acción fue realizada por un grupo de profesores: una investigadora externa de una universidad argentina, un profesor de interculturalidad y una profesora tutora de primaria. Este estudio se centró en indagar criterios y estrategias pedagógicas inclusivas con los objetivos de la posibilidad de mejorar las prácticas educativas y de promover el enriquecimiento de las mismas frente a una realidad educativa compleja y en creciente auge en Andalucía (España). Todo esto se enmarca en el desafío de una educación intercultural. El contexto educativo en el que se llevó a cabo fue en un colegio público español en el que más de la mitad del alumnado no poseía el español como lengua materna. La investigación básicamente se interesó en la intervención docente del “profesor de interculturalidad", en el marco del Plan para la Atención del Alumno Inmigrante dentro de las aulas de referencia, cuyos docentes (profesores tutores) aceptaron esta propuesta bajo la filosofía de la educación inclusiva.This article is a report of the research project, called “Educational Strategies for Intercultural Learning Contexts" that was, also, the final research report of “European Counsellor for Multicultural Affairs" postdegree course. The research we are going to present was an Action Research and was carried out by a group of professors, more exactly an external researcher from an Argentinian university and an interculturality teacher. Later on, a primary teacher who was a tutor, also, has join the group. The educational context of the research was a public Spanish school, in which, more than a half of the student body, did not have Spanish as their first language.Fil: Celada, Beatriz. Universidad Nacional del Comahu