Maladie de Lyme, syndrome autistique et traitement antibiotique : une réflexion à partir d'un cas

International audienceFollowing an overview of the definition of autism and Lyme disease, a clinical case will be presented of a young subject (aged 14 years and a half) diagnosed with autism, and characterized by a typical development in the first year of life, followed by a general deterioration of abilities shortly after diagnosis of the onset of Lyme disease. The subject presented positive reactivity for Mycoplasma Pneumoniae. According to recent studies, misdiagnosis of initial symptoms of Lyme disease and delayed treatment can lead to persistent interactive coinfections in the organism which may result in chronic pathologies. Thus, a link could exist between a chronic infectionwith Mycoplasma Pneumoniae and an atypical symptomology similar to autism. So the hypothesis proposed is that there may be a correlation between Lyme disease and autism and that long-term antibiotic therapy may be an effective treatment. Following a clinical presentation of the history of this young patient, the evolution of the subject's symptomology and behavior during one year of antibiotic therapy will be described.A la suite d'un rappel de la définition de l'autisme infantile et de la maladie de Lyme, un cas clinique sera développé. Il s'agit d'un jeune patient avec autisme âgé de 14 ans et demi, caractérisé par un développement initial typique pendant sa première année puis par une dégradation générale de ses aptitudes peu après avoir été atteint de la maladie de Lyme. A la suite d'une présentation sous la forme d'une vignette clinique, nous aborderons l'évolution de la symptomatologie et du comportement de ce jeune pendant un an d'antibiothérapie. Cette présentation de cas permettra finalement d'interroger la définition de l'autisme, son étiologie et la validité du diagnostic établi initialement pour ce patient

Matrix representations for toric parametrizations

In this paper we show that a surface in P^3 parametrized over a 2-dimensional toric variety T can be represented by a matrix of linear syzygies if the base points are finite in number and form locally a complete intersection. This constitutes a direct generalization of the corresponding result over P^2 established in [BJ03] and [BC05]. Exploiting the sparse structure of the parametrization, we obtain significantly smaller matrices than in the homogeneous case and the method becomes applicable to parametrizations for which it previously failed. We also treat the important case T = P^1 x P^1 in detail and give numerous examples.Comment: 20 page

Implicitization of rational maps

Motivated by the interest in computing explicit formulas for resultants and discriminants initiated by B\'ezout, Cayley and Sylvester in the eighteenth and nineteenth centuries, and emphasized in the latest years due to the increase of computing power, we focus on the implicitization of hypersurfaces in several contexts. Our approach is based on the use of linear syzygies by means of approximation complexes, following [Bus\'e Jouanolou 03], where they develop the theory for a rational map $f:P^{n-1}\dashrightarrow P^n$. Approximation complexes were first introduced by Herzog, Simis and Vasconcelos in [Herzog Simis Vasconcelos 82] almost 30 years ago. The main obstruction for this approximation complex-based method comes from the bad behavior of the base locus of $f$. Thus, it is natural to try different compatifications of $A^{n-1}$, that are better suited to the map $f$, in order to avoid unwanted base points. With this purpose, in this thesis we study toric compactifications $T$ for $A^{n-1}$. We provide resolutions $Z.$ for $Sym_I(A)$, such that $\det((Z.)_\nu)$ gives a multiple of the implicit equation, for a graded strand $\nu\gg 0$. Precisely, we give specific bounds $\nu$ on all these settings which depend on the regularity of \SIA. Starting from the homogeneous structure of the Cox ring of a toric variety, graded by the divisor class group of $T$, we give a general definition of Castelnuovo-Mumford regularity for a polynomial ring $R$ over a commutative ring $k$, graded by a finitely generated abelian group $G$, in terms of the support of some local cohomology modules. As in the standard case, for a $G$-graded $R$-module $M$ and an homogeneous ideal $B$ of $R$, we relate the support of $H_B^i(M)$ with the support of $Tor_j^R(M,k)$.Comment: PhD. Thesis of the author, from Universit\'e de Paris VI and Univesidad de Buenos Aires. Advisors: Marc Chardin and Alicia Dickenstein. Defended the 29th september 2010. 163 pages 15 figure

MS

thesisThe gilsonite and ozokerite deposits of the Unita Basin, Utah, were investigated geochemically. Soil samples were collected along traverses across productive veins in several areas. These soil samples were analysed for gilsonite and ozokerite. The gilsonite and ozokerite content of the soil samples was related to vein proximity. The veins investigated were the Cowboy vein, the Chepetta lode, the Carbon lode, the Rainbow vein, the Pariette vein, and the Soldier Summit ozokerite deposit. Three laboratory procedures were developed to separate gilsonite from the soil samples. All were based on the difference in specific gravity between gilsonite, which has a specific gravity of 1.04, and soil fraction, which has a specific gravity of about 2.0 - 2.6. In one procedure tetrabromoethane in benzene was the heavy liquid medium. In the other procedure carbon tetrachloride was the heavy liquid medium. In each of these procedures, the gilsonite was floated. In the third procedure, the gilsonite was separated from the soil by panning. In each procedure the gilsonite fraction was weighed, and the gilsonite content of each sample was expressed as parts gilsonite per million parts of sample by weight. The precision of the procedures was determined by replicate analyses. The standard deviation of the derived result in the calculation for PPM gilsonite is +-16.6%. Geochemical anomalies were recognized in each instance. Background values ranged from 200 PPM to 1,000 PPM. Anomalies ranged from 2,910 PPM to 264,000 PPM, and the contrast raged from 16 t0 545. In addition to geochemical anomalies disclosed over each vein, several anomalies at a distance from known veins were observed. These anomalies may reflect covered veins. Gilsonite content and dispersion halos surrounding the veins are due to weathering and erosion of gilsonite veins