G´en´etique Clinique dans le Service de P´ediatrie et de G´en´etique M´edicale du Centre National Hospitalier et Universitaire de Cotonou : Etat des Lieux et Perspectives

Il s’agissait d’une ´etude r´etrospective descriptive portant sur les patients rec¸us en consultation de g´en´etique m´edicale de Septembre 2004 `a Aoˆut 2007. Les patients b´en´eficiaient des examens dysmorphologique et physique, des bilans cytog´en´etiques et/ou mol´eculaires, des interventions th´erapeutiques et un suivi `a long terme. Les variables ´etudi´ees ´etaient les donn´ees sociod´emographiques et cliniques. Soixante et seize patients ont ´et´e rec¸us durant la p´eriode avec une pr´edominance masculine (57,89%). Les motifs de consultation ´etaient domin´es par le retard psychomoteur (38,15%), la dysmorphie faciale (30,26%) et les malformations (19,73%). Les principales malformations portaient sur les extr´emit´es et la face. Les pathologies confirm´ees comprenaient des aberrations chromosomiques (46,05%) avec une pr´edominance de la trisomie 21 et des maladies monog´eniques (7,89%). Le rendement de nos recherches pourrait ˆetre am´elior´e par l’acc`es `a la technique FISH. C’est une exp´erience quasi unique en Afrique de l’ouest et permet d’apporter des r´eponses aux personnes souffrant d’affections h´er´editaires.Mots Cl´es g´en´etique clinique ; retard psychomoteur ; dysmorphie ; malformation ; aberration chromosomique ; maladie monog´eniqu

A glimpse into the differential topology and geometry of optimal transport

This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former, uniqueness of the latter, and estimates for the dimension of its support, as well as the associated linear programming duality. It shows the answers to these questions concern the differential geometry and topology of the chosen transportation cost. It also establishes new connections --- some heuristic and others rigorous --- based on the properties of the cross-difference of this cost, and its Taylor expansion at the diagonal.Comment: 27 page

Stability of flows associated to gradient vector fields and convergence of iterated transport maps

In this paper we address the problem of stability of flows associated to a sequence of vector fields under minimal regularity requirements on the limit vector field, that is supposed to be a gradient. We apply this stability result to show the convergence of iterated compositions of optimal transport maps arising in the implicit time discretization (with respect to the Wasserstein distance) of nonlinear evolution equations of a diffusion type. Finally, we use these convergence results to study the gradient flow of a particular class of polyconvex functionals recently considered by Gangbo, Evans ans Savin. We solve some open problems raised in their paper and obtain existence and uniqueness of solutions under weaker regularity requirements and with no upper bound on the jacobian determinant of the initial datum

A reconstruction of the initial conditions of the Universe by optimal mass transportation

Reconstructing the density fluctuations in the early Universe that evolved into the distribution of galaxies we see today is a challenge of modern cosmology [ref.]. An accurate reconstruction would allow us to test cosmological models by simulating the evolution starting from the reconstructed state and comparing it to the observations. Several reconstruction techniques have been proposed [8 refs.], but they all suffer from lack of uniqueness because the velocities of galaxies are usually not known. Here we show that reconstruction can be reduced to a well-determined problem of optimisation, and present a specific algorithm that provides excellent agreement when tested against data from N-body simulations. By applying our algorithm to the new redshift surveys now under way [ref.], we will be able to recover reliably the properties of the primeval fluctuation field of the local Universe and to determine accurately the peculiar velocities (deviations from the Hubble expansion) and the true positions of many more galaxies than is feasible by any other method. A version of the paper with higher-quality figures is available at http://www.obs-nice.fr/etc7/nature.pdfComment: Latex, 4 pages, 3 figure

Multidimensional Conservation Laws: Overview, Problems, and Perspective

Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws. Some basic features and phenomena of multidimensional hyperbolic conservation laws are revealed, and some samples of multidimensional systems/models and related important problems are presented and analyzed with emphasis on the prototypes that have been solved or may be expected to be solved rigorously at least for some cases. In particular, multidimensional steady supersonic problems and transonic problems, shock reflection-diffraction problems, and related effective nonlinear approaches are analyzed. A theory of divergence-measure vector fields and related analytical frameworks for the analysis of entropy solutions are discussed.Comment: 43 pages, 3 figure

A user's guide to optimal transport

This text is an expanded version of the lectures given by the first author in the 2009 CIME summer school of Cetraro. It provides a quick and reasonably account of the classical theory of optimal mass transportation and of its more recent developments, including the metric theory of gradient flows, geometric and functional inequalities related to optimal transportation, the first and second order differential calculus in the Wasserstein space and the synthetic theory of metric measure spaces with Ricci curvature bounded from below

On Landau damping

Going beyond the linearized study has been a longstanding problem in the theory of Landau damping. In this paper we establish exponential Landau damping in analytic regularity. The damping phenomenon is reinterpreted in terms of transfer of regularity between kinetic and spatial variables, rather than exchanges of energy; phase mixing is the driving mechanism. The analysis involves new families of analytic norms, measuring regularity by comparison with solutions of the free transport equation; new functional inequalities; a control of nonlinear echoes; sharp scattering estimates; and a Newton approximation scheme. Our results hold for any potential no more singular than Coulomb or Newton interaction; the limit cases are included with specific technical effort. As a side result, the stability of homogeneous equilibria of the nonlinear Vlasov equation is established under sharp assumptions. We point out the strong analogy with the KAM theory, and discuss physical implications.Comment: News: (1) the main result now covers Coulomb and Newton potentials, and (2) some classes of Gevrey data; (3) as a corollary this implies new results of stability of homogeneous nonmonotone equilibria for the gravitational Vlasov-Poisson equatio

Implication des goitrigènes d’origine alimentaire dans le fonctionnement de la glande thyroïde : cas du manioc dans la production du H2O2

Le goitre endémique est principalement dû à la carence iodée. Le paradoxe selon lequel on retrouve le développement de goitre dans des régions sans déficience iodée a fait penser à d’autres facteurs alimentaires : le manioc. Le caractère goitrigène du manioc vient de ce qu’il contient deux glucosides cyanogéniques, la linamaroside et lotaustraloside dont l’hydrolyse libère du cyanure. Le cyanure est détoxifié en thiocyanate qui possède des propriétés goitrigènes évidentes. Les tranches de thyroïde de porc ont produit continuellement de H2O2, avec une brusque augmentation en présence de l’extrait du manioc. Ce saut de H2O2 peut être expliqué par un arrêt d’entrée de I- dans les thyrocytes provoquant ainsi une inhibition du symport Na+/I- par l’extrait. En conséquence l’accumulation des molécules de H2O2 non utilisées a été mise en évidence. Ces résultats, à l’étape actuelle, ne permettent pas d’envisager une action quelconque sur la NADPHoxydase et par conséquent sur le système générateur de H2O2Mots clés : Manioc, goitrigène, goitre, thyrocytes.Endemic goiter is mainly due to iodine deficiency. The paradox that we find the development of goiter in areas without iodine deficiency was thinking of other dietary factors: the cassava. The goitrogenic nature of cassava is that it contains two cyanogenic glucosides, the linamaroside and lotaustraloside whose hydrolysis releases cyanide. Cyanide is detoxified to thiocyanate which has goitrogenic properties obvious. Thyroid slices of pork produced continuously H2O2, with a sudden increase in the presence of the extract of cassava. This leap of H2O2 can be explained by a stop-entry of I- in thyrocytes causing an inhibition of symport Na+/I- by the extract. Therefore the accumulation of molecules of H2O2 used was not highlighted. These results, at this stage, do not consider any action on the NADPH oxidase and therefore on the H2O2-generating system.Keywords: Cassava, goitrogenic, goiter thyrocyte