On Az\'ema-Yor processes, their optimal properties and the Bachelier-drawdown equation

We study the class of Az\'ema-Yor processes defined from a general semimartingale with a continuous running maximum process. We show that they arise as unique strong solutions of the Bachelier stochastic differential equation which we prove is equivalent to the drawdown equation. Solutions of the latter have the drawdown property: they always stay above a given function of their past maximum. We then show that any process which satisfies the drawdown property is in fact an Az\'ema-Yor process. The proofs exploit group structure of the set of Az\'ema-Yor processes, indexed by functions, which we introduce. We investigate in detail Az\'ema-Yor martingales defined from a nonnegative local martingale converging to zero at infinity. We establish relations between average value at risk, drawdown function, Hardy-Littlewood transform and its inverse. In particular, we construct Az\'ema-Yor martingales with a given terminal law and this allows us to rediscover the Az\'ema-Yor solution to the Skorokhod embedding problem. Finally, we characterize Az\'ema-Yor martingales showing they are optimal relative to the concave ordering of terminal variables among martingales whose maximum dominates stochastically a given benchmark.Comment: Published in at http://dx.doi.org/10.1214/10-AOP614 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Analyzing cortical network dynamics with respect to different connectivity assumptions

ISBN : 978-2-9532965-0-1Current studies of cortical network dynamics are usually based on purely random wiring. Generally, these studies are focused on a local scale, where about 10 percent of all possible connections are realized. Neuronal connections in the cortex, however, show a more complex spatial pattern composed of local and long-range patchy connections. Here, we ask to what extent the assumption of such specific geometric traits influences the resulting dynamical behavior of network models. Analyzing the characteristic measures describing spiking neuronal networks (e.g., firing rate, coefficient of variation, correlation coefficient), we ascertain and compare the dynamical state spaces of different types of networks. To include long-range connections, we enlarge the spatial scale, resulting in a much sparser connectivity than what is usually assumed. Similar to previous studies, we can distinguish between different dynamical states (e.g., synchronous regular firing), depending on the external input rate and the numerical relation between excitatory and inhibitory synaptic weights. Yet, local couplings in such very sparsely connected networks seem to induce specific correlations and require another regularity measure than the coefficient of variation

Hyperfine excitation of N2_2H+^+ by H2_2: Toward a revision of N2_2H+^+ abundance in cold molecular clouds

The modelling of emission spectra of molecules seen in interstellar clouds requires the knowledge of collisional rate coefficients. Among the commonly observed species, N$_2$H$^+$ is of particular interest since it was shown to be a good probe of the physical conditions of cold molecular clouds. Thus, we have calculated hyperfine-structure resolved excitation rate coefficients of N$_2$H$^+$(X$^1\Sigma^+$) by H$_2(j=0)$, the most abundant collisional partner in the cold interstellar medium. The calculations are based on a new potential energy surface, obtained from highly correlated {\it ab initio} calculations. State-to-state rate coefficients between the first hyperfine levels were calculated, for temperatures ranging from 5 K to 70 K. By comparison with previously published N$_2$H$^+$-He rate coefficients, we found significant differences which cannot be reproduced by a simple scaling relationship. As a first application, we also performed radiative transfer calculations, for physical conditions typical of cold molecular clouds. We found that the simulated line intensities significantly increase when using the new H$_2$ rate coefficients, by comparison with the predictions based on the He rate coefficients. In particular, we revisited the modelling of the N$_2$H$^+$ emission in the LDN 183 core, using the new collisional data, and found that all three of the density, gas kinetic temperature and N$_2$H$^+$ abundance had to be revised

Tute de damas: poemas de Héléne Cadou, Nicole Laurent-Catrice, Francine Carón y Ariane Dreyfus

Antología de poemas de Héléne Cadou,Nicole Laurent-Catrice,Francine Carón y Ariane Dreyfus en edición bilingüe.230 págs

Short-term implantation effects of a DCPD-based calcium phosphate cement

International audienceCalcium phosphate cements can be handled in paste form and set in a wet medium after precipitation of calcium phosphate crystals in the implantation site. Depending on the products entering into the chemical reaction leading to the precipitation of calcium phosphates, different phases can be obtained with different mechanical properties, setting times and injectability. We tested a cement composed of a powder, containing-tricalcium phosphate (-TCP) and sodium pyrophosphate mixed with a solution of phosphoric and sulphuric acids. The cement set under a dicalcium phosphate dihydrate (DCPD)-based matrix containing-TCP particles. This was injected with a syringe into a defect drilled in rabbit condyles, the control being an identical defect left empty in the opposite condyle. The condyles were analysed histologically 2, 6 and 18 weeks after implantation. After injection into the bone defect the cement set and formed a porous calcium phosphate structure. Two different calcium phosphate phases with different solubility rates could be identified by scanning electron microscopy (SEM) observation. The less-soluble fragments could be degraded by cell phagocytosis in cell compartments of low pH or integrated in the newly formed bone matrix. The degradation rate of the material was relatively high but compatible with the ingrowth of bone trabeculae within the resorbing material. The ossification process was different from the creeping substitution occurring at the ceramic contact. Bone did not form directly at the cement surface following the differentiation of osteoblasts at the material surface. The trabeculae came to the material surface from the edges of the implantation site. Bone formation in the implantation site was significantly higher than in the control region during the first week of implantation. In conclusion, this material set in situ was well tolerated, inducing a mild foreign-body reaction, which did not impair its replacement by newly formed bone within a few weeks