Thirty years on … the social representation of AIDS among French teenagers

Teenagers, who are particularly concerned by the HIV virus, are targeted by plans of HIV prevention, as they are just beginning their sex lives. Since certain recent studies reveal that teenagers are not using HIV prevention methods, we analyse social representations of HIV/AIDS among a group of 100 French high school pupils, thirty years after it appeared and after the first studies of the social representation of AIDS. The results of a free associations test show that both girls and boys have the same social representation of AIDS. The results of a complementary questionnaire tend to show that this disease has become less frightening and less stigmatizing and that girls have a more preventive state of mind

On the propagation of an optical wave in a photorefractive medium

The aim of this paper is first to review the derivation of a model describing the propagation of an optical wave in a photorefractive medium and to present various mathematical results on this model: Cauchy problem, solitary waves

On approximate solutions of semilinear evolution equations

A general framework is presented to discuss the approximate solutions of an evolution equation in a Banach space, with a linear part generating a semigroup and a sufficiently smooth nonlinear part. A theorem is presented, allowing to infer from an approximate solution the existence of an exact solution. According to this theorem, the interval of existence of the exact solution and the distance of the latter from the approximate solution can be evaluated solving a one-dimensional "control" integral equation, where the unknown gives a bound on the previous distance as a function of time. For example, the control equation can be applied to the approximation methods based on the reduction of the evolution equation to finite-dimensional manifolds: among them, the Galerkin method is discussed in detail. To illustrate this framework, the nonlinear heat equation is considered. In this case the control equation is used to evaluate the error of the Galerkin approximation; depending on the initial datum, this approach either grants global existence of the solution or gives fairly accurate bounds on the blow up time.Comment: 33 pages, 10 figures. To appear in Rev. Math. Phys. (Shortened version; the proof of Prop. 3.4. has been simplified

On approximate solutions of semilinear evolution equations II. Generalizations, and applications to Navier-Stokes equations

In our previous paper [12] (Rev. Math. Phys. 16, 383-420 (2004)), a general framework was outlined to treat the approximate solutions of semilinear evolution equations; more precisely, a scheme was presented to infer from an approximate solution the existence (local or global in time) of an exact solution, and to estimate their distance. In the first half of the present work the abstract framework of \cite{uno} is extended, so as to be applicable to evolutionary PDEs whose nonlinearities contain derivatives in the space variables. In the second half of the paper this extended framework is applied to theincompressible Navier-Stokes equations, on a torus T^d of any dimension. In this way a number of results are obtained in the setting of the Sobolev spaces H^n(T^d), choosing the approximate solutions in a number of different ways. With the simplest choices we recover local existence of the exact solution for arbitrary data and external forces, as well as global existence for small data and forces. With the supplementary assumption of exponential decay in time for the forces, the same decay law is derived for the exact solution with small (zero mean) data and forces. The interval of existence for arbitrary data, the upper bounds on data and forces for global existence, and all estimates on the exponential decay of the exact solution are derived in a fully quantitative way (i.e., giving the values of all the necessary constants; this makes a difference with most of the previous literature). Nextly, the Galerkin approximate solutions are considered and precise, still quantitative estimates are derived for their H^n distance from the exact solution; these are global in time for small data and forces (with exponential time decay of the above distance, if the forces decay similarly).Comment: LaTeX, 84 pages. The final version published in Reviews in Mathematical Physic

On fractional Choquard equations

We investigate a class of nonlinear Schrodinger equations with a generalized Choquard nonlinearity and fractional diffusion. We obtain regularity, existence, nonexistence, symmetry as well as decays properties.Comment: revised version, 22 page

On the density-potential mapping in time-dependent density functional theory

The key questions of uniqueness and existence in time-dependent density functional theory are usually formulated only for potentials and densities that are analytic in time. Simple examples, standard in quantum mechanics, lead however to non-analyticities. We reformulate these questions in terms of a non-linear Schr\"odinger equation with a potential that depends non-locally on the wavefunction.Comment: 8 pages, 2 figure

Solitary wave dynamics in time-dependent potentials

We rigorously study the long time dynamics of solitary wave solutions of the nonlinear Schr\"odinger equation in {\it time-dependent} external potentials. To set the stage, we first establish the well-posedness of the Cauchy problem for a generalized nonautonomous nonlinear Schr\"odinger equation. We then show that in the {\it space-adiabatic} regime where the external potential varies slowly in space compared to the size of the soliton, the dynamics of the center of the soliton is described by Hamilton's equations, plus terms due to radiation damping. We finally remark on two physical applications of our analysis. The first is adiabatic transportation of solitons, and the second is Mathieu instability of trapped solitons due to time-periodic perturbations.Comment: 38 pages, some typos corrected, one reference added, one remark adde

Gene induction during differentiation of human monocytes into dendritic cells: an integrated study at the RNA and protein levels

Changes in gene expression occurring during differentiation of human monocytes into dendritic cells were studied at the RNA and protein levels. These studies showed the induction of several gene classes corresponding to various biological functions. These functions encompass antigen processing and presentation, cytoskeleton, cell signalling and signal transduction, but also an increase in mitochondrial function and in the protein synthesis machinery, including some, but not all, chaperones. These changes put in perspective the events occurring during this differentiation process. On a more technical point, it appears that the studies carried out at the RNA and protein levels are highly complementary.Comment: website publisher: http://www.springerlink.com/content/ha0d2c351qhjhjdm

Clusters of cytokines determine malaria severity in Plasmodium falciparum - Infected patients from endemic areas of central India

We investigated the role of interferon (IFN)- gamma , interleukin (IL)-1 beta , IL-2, IL-4, IL-5, IL-6, IL-10, IL-12, tumor necrosis factor (TNF)- alpha , and transforming growth factor (TGF)- beta in clinically well-defined groups of Plasmodium falciparum-infected patients manifesting mild malaria (MM), severe noncerebral malaria (SM), or cerebral malaria (CM) and in control subjects from Gondia, a malaria-endemic site in India, as well as in healthy subjects from non-malaria-endemic areas. Two-way coupled cluster analysis revealed 2 clusters of cytokines relevant to clinical subgroups of disease. The first cluster was composed of IFN- gamma , IL-2, IL-5, IL-6, and IL-12, the levels of which were significantly increased during infection but were predominant in patients with MM and allowed us to distinguish them from patients with SM or CM. The second cluster was composed of TGF- beta , TNF- alpha , IL-10, and IL-1 beta , the levels of which were highly correlated with each other in the different clinical groups of patients and significantly increased with disease severity, particularly in CM. Discriminant analyses allowed us to propose a minimal model. Levels of cytokines such as IL-5, IL-1 beta , IL-10, and IL-2 increase with infection. Levels of IL-12, IL-5, and IL-6 discriminate severe forms of malaria from MM. Finally, levels of IL-1 beta , IL-12, and IFN- gamma are relevant for the discrimination of CM from SM: high IL-1 beta levels are associated with CM, and high IL-12 and IFN- gamma levels are associated with S