Kernel Inverse Regression for spatial random fields

In this paper, we propose a dimension reduction model for spatially dependent variables. Namely, we investigate an extension of the \emph{inverse regression} method under strong mixing condition. This method is based on estimation of the matrix of covariance of the expectation of the explanatory given the dependent variable, called the \emph{inverse regression}. Then, we study, under strong mixing condition, the weak and strong consistency of this estimate, using a kernel estimate of the \emph{inverse regression}. We provide the asymptotic behaviour of this estimate. A spatial predictor based on this dimension reduction approach is also proposed. This latter appears as an alternative to the spatial non-parametric predictor

The micronucleus assay as a biological dosimeter of in vivo ionising radiation exposure

Biological dosimetry, based on the analysis of micronuclei (MN) in the cytokinesis-block micronucleus (CBMN) assay can be used as an alternative method for scoring dicentric chromosomes in the field of radiation protection. Biological dosimetry or Biodosimetry, is mainly performed, in addition to physical dosimetry, with the aim of individual dose assessment. Many studies have shown that the number of radiation-induced MN is strongly correlated with dose and quality of radiation. The CBMN assay has become, in the last years, a thoroughly validated and standardised technique to evaluate in vivo radiation exposure of occupational, medical and accidentally exposed individuals. Compared to the gold standard, the dicentric assay, the CBMN assay has the important advantage of allowing economical, easy and quick analysis. The main disadvantage of the CBMN assay is related to the variable micronucleus ( MN) background frequency, by which only in vivo exposures in excess of 0.2-0.3 Gy X-rays can be detected. In the last years, several improvements have been achieved, with the ultimate goals (i) of further increasing the sensitivity of the CBMN assay for low-dose detection by combining the assay with a fluorescence in situ hybridisation centromere staining technique, (ii) of increasing the specificity of the test for radiation by scoring nucleoplasmic bridges in binucleated cells and (iii) of making the assay optimally suitable for rapid automated analysis of a large number of samples, viz. in case of a large-scale radiation accident. The development of a combined automated MN-centromere scoring procedure remains a challenge for the future, as it will allow systematic biomonitoring of radiation workers exposed to low-dose radiation

Saturation spaces for regularization methods in inverse problems

The aim of this article is to characterize the saturation spaces that appear in inverse problems. Such spaces are defined for a regularization method and the rate of convergence of the estimation part of the inverse problem depends on their definition. Here we prove that it is possible to define these spaces as regularity spaces, independent of the choice of the approximation method. Moreover, this intrinsec definition enables us to provide minimax rate of convergence under such assumptionsLinear inverse problems, regularization methods, structural econometrics

Viscous fingering of miscible slices

Viscous fingering of a miscible high viscosity slice of fluid displaced by a lower viscosity fluid is studied in porous media by direct numerical simulations of Darcy's law coupled to the evolution equation for the concentration of a solute controlling the viscosity of miscible solutions. In contrast with fingering between two semi-infinite regions, fingering of finite slices is a transient phenomenon due to the decrease in time of the viscosity ratio across the interface induced by fingering and dispersion processes. We show that fingering contributes transiently to the broadening of the peak in time by increasing its variance. A quantitative analysis of the asymptotic contribution of fingering to this variance is conducted as a function of the four relevant parameters of the problem i.e. the log-mobility ratio R, the length of the slice l, the Peclet number Pe and the ratio between transverse and axial dispersion coefficients $\epsilon$. Relevance of the results is discussed in relation with transport of viscous samples in chromatographic columns and propagation of contaminants in porous media.Comment: 10 pages, 13 figure

Deuterated molecules in DM Tau: DCO+, but no HDO

We report the detection of the J=2-1 line of DCO+ in the proto-planetary disk of DM Tau and re-analyze the spectrum covering the 465 GHz transition of HDO in this source, recently published by Ceccarelli et al. (2005). A modelling of the DCO+ line profile with the source parameters derived from high resolution HCO+ observations yields a DCO+/HCO+ abundance ratio of about 0.004, an order of magnitude smaller than that derived in the low mass cores. The re-analysis of the 465 GHz spectrum, using the proper continuum flux (0.5 Jy) and source systemic velocity (6.05 km/s), makes it clear that the absorption features attributed to HDO and C6H are almost certainly unrelated to these species. We show that the line-to-continuum ratio of an absorption line in front of a Keplerian disk can hardly exceed the ratio of the turbulent velocity to the projected rotation velocity at the disk edge, unless the line is optically very thick (tau > 10 000). This ratio is typically 0.1-0.3 in proto-planetary disks and is about 0.15 in DM Tau, much smaller than that for the alleged absorption features. We also show that the detection of H2D+ in DM Tau, previously reported by these authors, is only a 2-sigma detection when the proper velocity is adopted. So far, DCO+ is thus the only deuterated molecule clearly detected in proto-planetary disks