On Neumann Type Problems for nonlocal Equations set in a half Space

International audienceWe study Neumann type boundary value problems for nonlocal equations related to Lévy processes. Since these equations are nonlocal, Neumann type problems can be obtained in many ways, depending on the kind of reflection we impose on the outside jumps. To focus on the new phenomenas and ideas, we consider different models of reflection and rather general non-symmetric Lévy measures, but only simple linear equations in half-space domains. We derive the Neumann/reflection problems through a truncation procedure on the Lévy measure, and then we develop a viscosity solution theory which includes comparison, existence, and some regularity results. For problems involving fractional Laplacian type operators like e.g.$(-\Delta)^{\alpha/2}$, we prove that solutions of all our nonlocal Neumann problems converge as alpha goes to 2 to the solution of a classical Neumann problem. The reflection models we consider include cases where the underlying Lévy processes are reflected, projected, and/or censored upon exiting the domain

Mathematical Modeling of Transport and Degradation of Feedstuffs in the Small Intestine

We describe a mathematical modeling of the digestion in the small intestine. The main interest of our work is to consider, at the same time, different aspects of the digestion i.e. the transport of the bolus all along the intestine, feedstuffs degradation according to the enzymes and local physical conditions, and nutrients absorption. A system of coupled ordinary differential equations is used to model these phenomena. The major unknowns of this system are the position of the bolus and its composition. This system of equations is solved numerically. We present different numerical computations for the degradation, absorption and transport of the bolus with acceptable accuracy with experimental data. The main feature and interest of this model are its generality. Even if we are at an early stage of development, our approach can be adapted to treat any kind of feedstuffs in any non-ruminant animal to predict the composition and velocity of bolus in the small intestine

Continuous dependence results for Non-linear Neumann type boundary value problems

We obtain estimates on the continuous dependence on the coefficient for second order non-linear degenerate Neumann type boundary value problems. Our results extend previous work of Cockburn et.al., Jakobsen-Karlsen, and Gripenberg to problems with more general boundary conditions and domains. A new feature here is that we account for the dependence on the boundary conditions. As one application of our continuous dependence results, we derive for the first time the rate of convergence for the vanishing viscosity method for such problems. We also derive new explicit continuous dependence on the coefficients results for problems involving Bellman-Isaacs equations and certain quasilinear equation

Effect of fixed orthodontic appliances on salivary microbial parameters at 6 months:a controlled observational study

Objective: The aim of this study was to assess the microbial changes in children with fixed orthodontic appliances compared with a control group of children without orthodontic treatment. Material and Methods: Ninety-five children, aged between 12 and 16 years, participated in this study. Forty-eight subjects were fitted with fixed orthodontic appliances and forty-seven were free of any such appliances. The follow-up was 6 months for all children. The association between orthodontic appliances and high levels of Streptococcus mutans and Lactobacillus spp was assessed with logistic regression models, taking age, sex, pH and buffer capacity into account. Results: Differences at baseline between the two groups were not statistically significant. We found that wearing a fixed orthodontic appliance was associated with high levels of Streptococcus mutans and Lactobacillus spp (adjusted OR: 6.65, 95% CI [1.98-22.37]; 9.49, 95% CI [2.57-35.07], respectively), independently of other variables. Conclusion: The originality of the present epidemiological study was to evaluate the evolution of salivary microbial parameters in a population of children with fixed orthodontic appliances. Our results show an increase of Streptococcus mutans and Lactobacillus spp values during the follow-up. The whole dental workforce should be aware that preventive measures are of paramount importance during orthodontic treatment

Contribution a l'etude de quelques problemes en elasticite tridimensionnelle

SIGLECNRS T Bordereau / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

A Simple Proof of Convergence for an Approximation Scheme for Computing Motions by Mean Curvature

International audienceWe prove the convergence of an approximation scheme recently proposed by Bence, Merriman and Osher for computing motions of hypersurfaces by Mean Curvature. Our proof is based on viscosity solutions methods

CONTINUOUS DEPENDENCE RESULTS FOR NON-LINEAR NEUMANN TYPE BOUNDARY VALUE PROBLEMS

Abstract. We obtain estimates on the continuous dependence on the coefficient for second order non-linear degenerate Neumann type boundary value problems. Our results extend previous work of Cockburn et.al., Jakobsen-Karlsen, and Gripenberg to problems with more general boundary conditions and domains. A new feature here is that we account for the dependence on the boundary conditions. As one application of our continuous dependence results, we derive for the first time the rate of convergence for the vanishing viscosity method for such problems. We also derive new explicit continuous dependence on the coefficients results for problems involving Bellman-Isaacs equations and certain quasilinear equation. hal-00294479, version 1- 9 Jul 2008 1

Spike detection for calcium activity

We present in this paper a global methodology for the spike detection in a biological context of fluorescence recording of GnRh-neurons calcium activity. For this purpose we first propose a simple stochastic model that could mimic experimental time series by considering an autoregressive AR(1) process with a linear trend and specific innovations involving spiking times. Estimators of parameters with asymptotic normality are established and used to set up a statistical test on estimated innovations in order to detect spikes. We compare several procedures and illustrate on biological data the performance of our procedure