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

A contribution to the knowledge of the skin albuminose cells of Torpedo ocellata Raf [Riv.Istochim.norm.pat. 8 411-416, 1962]

Glandular cells, other than the mucous cells, have been described in the skin of various groups of fish (Teleosts, Ganoids, Selachii) and they have been called 'albuminose' by various authors. The authors propose to study the albuminose cells in the skin of Torpedo ocellata Raf. from a histochemical point of view. The albuminose cells have a complex morphological structure and a correspondingly complicated histochemical make-up. One must treat them as an example of cell with secretions of a particular type, which must and will be better incorporated when more is known of characteristics existent in other species