We consider spectral projectors associated to the Euclidean Laplacian on the two-dimensional torus, in the case where the spectral window is narrow. Bounds for their L2 to Lp operator norm are derived, extending the classical result of Sogge; a new question on the convolution kernel of the projector is introduced. The methods employed include $\ell^2$ decoupling, small cap decoupling and estimates of exponential sums.

This paper proposes a fairly general new point of view on the question of asymptotic stability of (topological) solitons. Our approach is based on the use of the distorted Fourier transform at the nonlinear level; it does not rely only on Strichartz or virial estimates and is therefore able to treat low-power nonlinearities (hence also nonlocalised solitons) and capture the global (in space and time) behaviour of solutions.

More specifically, we consider quadratic nonlinear Klein-Gordon equations with a regular and decaying potential in one space dimension. Additional assumptions are made so that the distorted Fourier transform of the solution vanishes at zero frequency. Assuming also that the associated Schrödinger operator has no negative eigenvalues, we obtain global-in-time bounds, including sharp pointwise decay and modified asymptotics, for small solutions.

These results have some direct applications to the asymptotic stability of (topological) solitons, as well as several other potential applications to a variety of related problems. For instance, we obtain full asymptotic stability of kinks with respect to odd perturbations for the double sine-Gordon problem (in an appropriate range of the deformation parameter). For the $\phi ^4$ problem, we obtain asymptotic stability for small odd solutions, provided the nonlinearity is projected on the continuous spectrum. Our results also go beyond these examples since our framework allows for the presence of a fully coherent phenomenon (a space-time resonance) at the level of quadratic interactions, which creates a degeneracy in distorted Fourier space. We devise a suitable framework that incorporates this and use multilinear harmonic analysis in the distorted setting to control all nonlinear interactions.

We investigate norms of spectral projectors on thin spherical shells for the Laplacian on tori. This is closely related to the boundedness of resolvents of the Laplacian and the boundedness of $L^{p}$ norms of eigenfunctions of the Laplacian. We formulate a conjecture and partially prove it.

Objectives: This study aims to analyze the key factors considered for the first application of the National Committee for the Evaluation of Medical Devices (CNEDiMTS) for achieving reimbursement through registration in the list of products and services qualifying for reimbursement (LPPR).

Methods: All the appraisals studied on medical devices (MD) for first inclusion in the LPPR during 2011 and 2012 were retrieved from the French National Authority for Health or Haute Autorité de santé (HAS) Web site. A list of relevant factors was analyzed for each included opinion, followed by univariate and multivariate analyses to highlight the key factors that impacted the expected benefit (EB) provided by HAS.

Results: A total of 151 appraisals were included in the study. Of them, 94 (62 percent) were granted with sufficient EB. The manufacturers were mostly from the United States (36 percent), while most of the applicants were from France (84 percent). After adjusting for other retrieved factors, it was observed that MDs complying with the technical standards, requests supported by opinion(s) from previous generation of MD, and the presence of recommendations or guidelines had more probability to obtain a sufficient EB. A lower probability was related to MDs supported by low-quality studies and with no specific health public benefit.

Conclusions: Our results confirmed that manufacturers seeking reimbursement should be aware of the expectations of the health authorities (level of evidence, technical standard, etc.) and foresee their plan of sending requests for funding so that they can provide evidence of good quality.

We study the local and global well-posedness of a full system of magnetohydrodynamic equations. The system is a coupling of the incompressible Navier—Stokes equations with the Maxwell equations through the Lorentz force and Ohm's law for the current. We show the local existence of mild solutions for arbitrarily large data in a space similar to the scale-invariant spaces classically used for Navier—Stokes. These solutions are global if the initial data are small enough. Our results not only simplify and unify the proofs for the space dimensions 2 and 3, but also refine those in [8]. The main simplification comes from an a prioriLt2 (Lx∞) estimate for solutions of the forced Navier—Stokes equations.

Though three-dimensional (3D) imaging gives deep insight into the inner structure of complex materials, the stereological analysis of 2D snapshots of material sections is still necessary for large-scale industrial applications for reasons related to time and cost constraints. In this paper, we propose an original framework to estimate the orientation distribution of generalized cylindrical structures from a single 2D section. Contrary to existing approaches, knowledge of the cylinder cross-section shape is not necessary. The only requirement is to know the area distribution of the cross-sections. The approach relies on minimization of a least squares criterion under linear equality and inequality constraints that can be solved with standard optimization solvers. It is evaluated on synthetic data, including simulated images, and is applied to experimental microscopy images of fibrous composite structures. The results show the relevance and capabilities of the approach though some limitations have been identified regarding sensitivity to deviations from the assumed model.

European Community regulations on chemicals promote alternative methods to test substances presenting potential risks for the environment. In the present work, cultured atrial cells isolated from oyster (Crassostrea gigas) were used as an experimental model to investigate the toxicity of tributyltin (TBT) after short-time exposure at concentrations representative of those that can be measured in seawater, marine sediments and/or bivalves bioaccumulating this pollutant. In vitro and in vivo assays produce values of the same order of magnitude for both animal/cell survival and heart/cardiomyocyte beating rate. The survival rate of whole animals decreased from 10-6 M TBT after 3 days. For cultured cells, the viability, evaluated using 3-(4, 5-dimethylthiazolyl-2)-2, 5-diphenyltetrazolium bromide (MTT) assay, significantly decreased after two days of treatment with 10-6 M TBT, and after six days with 10-10 M TBT. The percentage of apoptotic cells, quantified by flow cytometry and YO-PRO®-1 iodide, a nucleic acid stain that only permeates cells that are beginning to undergo apoptosis, increased significantly in these cases. Moreover, intracellular concentration of Ca++ had increased after 10 min of exposition to 10-6 M, and could be associated with apoptotic processes. As patch clamp experiments showed that Ca++ conductance was decreased, intracellular calcium increase could mainly be due to a release from internal stores. The decreases in beating rhythm could be explained by the decrease in adenosine triphosphate (ATP) production revealed by 31 P nuclear magnetic resonance (NMR) spectroscopy and confirmed by the increase of the KATP channel conductance. The related hyperpolarization and the disturbances of the energetic metabolism were clearly related to the loss of the atrial cell contractility and viability.

We propose an image-based framework to evaluate the uncertainty in the estimation of the volume fraction of specific microstructures based on the observation of a single section. These microstructures consist of cubes organized on a cubic mesh, such as monocrystalline nickel base superalloys. The framework is twofold: a model-based stereological analysis allows relating two-dimensional image observations to three-dimensional microstructure features, and a spatial statistical analysis allows computing approximate confidence bounds while assessing the representativeness of the image. The reliability of the method is assessed on synthetic models. Volume fraction estimation variances and approximate confidence intervals are computed on real superalloy images in the context of material characterization.

Retinoids (derivatives of vitamin A) are signalling molecules that play important roles in cell growth, differentiation and death. Retinoids act through two types of receptors – retinoic acid receptors (RARα, RARβ and RARγ) and retinoid X receptors (RXRα, RXRβ and RXRγ) – which themselves act as ligand-dependent transcription factors. Retinoids are of special interest in cancer research owing to their antiproliferative and cancer-preventative properties. They have been used successfully to cure acute promyelocytic leukaemia (APL) and can suppress carcinogenesis in a variety of tissue types (e.g. skin, lung, breast and oral cancers). Extensive research efforts have been dedicated to elucidating the molecular and cellular networks that are induced by retinoids, and this has recently yielded novel insights into how retinoids can both prevent and combat cancer.

1. Abdominal obesity is associated with numerous metabolic complications. Deep abdominal adipose tissue is critical in the association between the level of abdominal obesity and cardiovascular risk factors.

2. Adipose tissue localization was assessed by computed axial tomography (CAT), and its association with body density and anthropometric measurements was investigated in a sample of fifty-one obese women (percentage body fat 45·9 (SD 5·6)) aged 35·7 (SD 5·5) years. The CAT scans were performed at three levels: lower chest, abdomen and mid-thigh.

3. The total adipose tissue volume computed from these three scans was highly correlated with body fat mass (r 0·94, P < 0·001). The proportion of deep abdominal fat as measured by the ratio of deep: total adipose tissue areas at the abdominal level was not significantly correlated with body fat mass, but it was moderately associated with the ratio of waist: hip circumferences (WHR) (r 0·49, P < 0·001). The absolute amount of deep abdominal fat was, however, significantly correlated with body fat mass (r 0·72, P < 0·001).

4. The subscapular (r 0·38) and the abdominal (r 0·38) skinfolds were the only two skinfolds that were significantly associated with the proportion of deep abdominal fat (P < 0·01). These skinfolds were also those which showed the highest correlation with the absolute amount of deep abdominal fat (r 0·65, P < 0·001, for both skinfolds).

5. A three-site CAT-scan procedure can be used for the estimation of body fat mass in premenopausal obese women.

6. In these obese women, there was no significant association between total adiposity and the proportion of deep adipose tissue at the abdominal level.

7. In premenopausal obese women, the absolute amount of deep abdominal fat can be predicted from anthropometric measurements with more accuracy than the relative amount of deep abdominal fat.