A priori L∞L^{\infty}-estimates for degenerate complex Monge-Amp\`ere equations

We study families of complex Monge-Amp\`ere equations, focusing on the case where the cohomology classes degenerate to a non big class. We establish uniform a priori $L^{\infty}$-estimates for the normalized solutions, generalizing the recent work of S. Kolodziej and G. Tian. This has interesting consequences in the study of the K\"ahler-Ricci flow.Comment: 6 page

Plurisubharmonic functions with weak singularities

We study the complex Monge-Amp\`ere operator in bounded hyperconvex domains of \C^n. We introduce a scale of classes of weakly singular plurisubharmonic functions : these are functions of finite weighted Monge-Amp\`ere energy. They generalize the classes introduced by U.Cegrell, and give a stratification of the space of (almost) all unbounded plurisubharmonic functions. We give an interpretation of these classes in terms of the speed of decreasing of the Monge-Amp\`ere capacity of sublevel sets and solve associated complex Monge-Amp\`ere equations.Comment: 15 pages, dedicated to Christer Kiselman on the occasion of his retiremen

How does informational heterogeneity affect the quality of forecasts?

We investigate a toy model of inductive interacting agents aiming to forecast a continuous, exogenous random variable E. Private information on E is spread heterogeneously across agents. Herding turns out to be the preferred forecasting mechanism when heterogeneity is maximal. However in such conditions aggregating information efficiently is hard even in the presence of learning, as the herding ratio rises significantly above the efficient-market expectation of 1 and remarkably close to the empirically observed values. We also study how different parameters (interaction range, learning rate, cost of information and score memory) may affect this scenario and improve efficiency in the hard phase.Comment: 11 pages, 5 figures, updated version (to appear in Physica A

Ciclosporine et mycophénolate mofétil pour le traitement de la choriorétinopathie de type birdshot

Une cohorte de 211 patients a été examinée de manière standardisée chaque année entre 2002 et 2010 dans un centre de référence pour uvéites. L'efficacité de la ciclosporine et du mycophénolate a été comparée de manière rétrospective à un an de leur initiation, chez des patients présentant une forme active de la maladie, définie par la présence d'un oedème maculaire et/ou de vascularites rétiniennes angiographiques.Les critères d’analyse étaient les suivants : acuité visuelle, champ visuel, épaisseur maculaire centrale en OCT, cotation de l’oedème maculaire cystoïde et des vascularites sur l’angiographie à la fluorescéine. Le mode et la dose de corticothérapie associée, incluant le nombre d’injections de triamcinolone réalisées au cours de l’année ont également été considérés. Quarante-trois patients (17 hommes, 26 femmes, âge moyen 53.1 ans) remplissaient les critères d'inclusion, sans différence significative à l’initiation du traitement dans les proportions d’oedème maculaire (64.3% et 66.7%) et de vascularites (75% et 73.3%) dans les deux groupes. Vingt-huit patients ont été traités par ciclosporine (3 mg/kg/j) et quinze par mycophénolate (1,6 g/j). La ciclosporine était l'immunosuppresseur de choix entre 2002 et 2008, remplacé ensuite par le mycophénolate. Un traitement concomitant par prednisone orale avait été initié chez 100% des patients sous ciclosporine contre 33% des patients sous mycophénolate. À l’inverse, un plus grand nombre d'injections de triamcinolone a été comptabilisé dans le groupe mycophénolate vs. ciclosporine [1.4 vs. 0.9 par patient].Aucune différence significative d’efficacité n’a été retrouvée entre les deux groupes pour chacun des paramètres étudiés. Notre étude a en revanche mis en évidence une évolution des pratiques thérapeutiques, avec une modification du mode d’administration de la corticothérapie associée, parallèlement au remplacement de la ciclosporine par le mycophénolate mofétil

Clinical trial simulation to evaluate power to compare the antiviral effectiveness of two hepatitis C protease inhibitors using nonlinear mixed effect models: a viral kinetic approach.

International audienceBACKGROUND: Models of hepatitis C virus (HCV) kinetics are increasingly used to estimate and to compare in vivo drug's antiviral effectiveness of new potent anti-HCV agents. Viral kinetic parameters can be estimated using non-linear mixed effect models (NLMEM). Here we aimed to evaluate the performance of this approach to precisely estimate the parameters and to evaluate the type I errors and the power of the Wald test to compare the antiviral effectiveness between two treatment groups when data are sparse and/or a large proportion of viral load (VL) are below the limit of detection (BLD). METHODS: We performed a clinical trial simulation assuming two treatment groups with different levels of antiviral effectiveness. We evaluated the precision and the accuracy of parameter estimates obtained on 500 replication of this trial using the stochastic approximation expectation-approximation algorithm which appropriately handles BLD data. Next we evaluated the type I error and the power of the Wald test to assess a difference of antiviral effectiveness between the two groups. Standard error of the parameters and Wald test property were evaluated according to the number of patients, the number of samples per patient and the expected difference in antiviral effectiveness. RESULTS: NLMEM provided precise and accurate estimates for both the fixed effects and the inter-individual variance parameters even with sparse data and large proportion of BLD data. However Wald test with small number of patients and lack of information due to BLD resulted in an inflation of the type I error as compared to the results obtained when no limit of detection of VL was considered. The corrected power of the test was very high and largely outperformed what can be obtained with empirical comparison of the mean VL decline using Wilcoxon test. CONCLUSION: This simulation study shows the benefit of viral kinetic models analyzed with NLMEM over empirical approaches used in most clinical studies. When designing a viral kinetic study, our results indicate that the enrollment of a large number of patients is to be preferred to small population sample with frequent assessments of VL