Statistics for the Luria-Delbr\"uck distribution

The Luria-Delbr\"uck distribution is a classical model of mutations in cell kinetics. It is obtained as a limit when the probability of mutation tends to zero and the number of divisions to infinity. It can be interpreted as a compound Poisson distribution (for the number of mutations) of exponential mixtures (for the developing time of mutant clones) of geometric distributions (for the number of cells produced by a mutant clone in a given time). The probabilistic interpretation, and a rigourous proof of convergence in the general case, are deduced from classical results on Bellman-Harris branching processes. The two parameters of the Luria-Delbr\"uck distribution are the expected number of mutations, which is the parameter of interest, and the relative fitness of normal cells compared to mutants, which is the heavy tail exponent. Both can be simultaneously estimated by the maximum likehood method. However, the computation becomes numerically unstable as soon as the maximal value of the sample is large, which occurs frequently due to the heavy tail property. Based on the empirical generating function, robust estimators are proposed and their asymptotic variance is given. They are comparable in precision to maximum likelihood estimators, with a much broader range of calculability, a better numerical stability, and a negligible computing time

Parallel-in-Time Multi-Level Integration of the Shallow-Water Equations on the Rotating Sphere

The modeling of atmospheric processes in the context of weather and climate simulations is an important and computationally expensive challenge. The temporal integration of the underlying PDEs requires a very large number of time steps, even when the terms accounting for the propagation of fast atmospheric waves are treated implicitly. Therefore, the use of parallel-in-time integration schemes to reduce the time-to-solution is of increasing interest, particularly in the numerical weather forecasting field. We present a multi-level parallel-in-time integration method combining the Parallel Full Approximation Scheme in Space and Time (PFASST) with a spatial discretization based on Spherical Harmonics (SH). The iterative algorithm computes multiple time steps concurrently by interweaving parallel high-order fine corrections and serial corrections performed on a coarsened problem. To do that, we design a methodology relying on the spectral basis of the SH to coarsen and interpolate the problem in space. The methods are evaluated on the shallow-water equations on the sphere using a set of tests commonly used in the atmospheric flow community. We assess the convergence of PFASST-SH upon refinement in time. We also investigate the impact of the coarsening strategy on the accuracy of the scheme, and specifically on its ability to capture the high-frequency modes accumulating in the solution. Finally, we study the computational cost of PFASST-SH to demonstrate that our scheme resolves the main features of the solution multiple times faster than the serial schemes

Evidence, Mechanisms and Improved Understanding of Controlled Salinity Waterflooding Part 1 : Sandstones

Acknowledgements TOTAL are thanked for partial supporting Jackson through the TOTAL Chairs programme at Imperial College London, for supporting Vinogradov through the TOTAL Laboratory for Reservoir Physics at Imperial College London, and for granting permission to publish this work.Peer reviewedPostprin

Histoire de l'île Saint-Gildas et de son Pardon

National audienceL’île Saint-Gildas est à juste titre considérée comme un paisible paradis insulaire de vingt-cinq hectares où la nature maritime précieusement préservée côtoie à chaque pas les traces d’un riche et lointain passé, dominé par la figure tutélaire de saint Gildas : l’île (sur laquelle il n’a cependant jamais vécu), lui doit en effet non seulement son nom, mais également sa renommée, puisque le culte qui lui est rendu donne lieu annuellement à un Pardon aux chevaux fréquenté par un nombre très considérable de pèlerins.Après avoir pu découvrir les lieux le 14 juin 2010, lors de l’excursion annuelle de la Société d’Emulation, nous proposons aujourd’hui aux lecteurs de faire plus amplement connaissance avec leur histoire

L'adjuration à "Saint Yves de Vérité": persistance tardive d'une ordalie populaire bretonne

National audienceTelles étaient les mystérieuses formules bretonnes rituelles de « l'adjuration à saint Yves de Vérité », rite occulte des plus surprenants et expression superstitieuse de la confiance indéfectible que les Bretons placent en la puissance d'intercession de saint Yves : par ce rituel, une personne s'estimant gravement lésée dans un conflit et n'ayant pas réussi à obtenir gain de cause devant le tribunal des Hommes, instituait saint Yves juge suprême de son différend, remettant alors entre ses mains et sa vie, et celle de son adversaire . Cette adjuration exceptionnelle s'avérait ainsi des plus dangereuses, puisque la partie ayant tort devait mourir « de langueur » ou de « malemort » dans les neuf mois, châtiment terrible que la langue bretonne rend par une expression encore plus saisissante : « disec'han diwar e zreid » – littéralement : « se dessécher sur pieds ». Gare donc au plaideur téméraire ayant mal à propos sollicité saint Yves ! La sentence surnaturelle n'était pas toujours celle attendue, et le solliciteur pouvait périr de sa témérité