Smoothing under Diffeomorphic Constraints with Homeomorphic Splines

In this paper we introduce a new class of diffeomorphic smoothers based on general spline smoothing techniques and on the use of some tools that have been recently developed in the context of image warping to compute smooth diffeomorphisms. This diffeomorphic spline is defined as the solution of an ordinary differential equation governed by an appropriate time-dependent vector field. This solution has a closed form expression which can be computed using classical unconstrained spline smoothing techniques. This method does not require the use of quadratic or linear programming under inequality constraints and has therefore a low computational cost. In a one dimensional setting incorporating diffeomorphic constraints is equivalent to impose monotonicity. Thus, as an illustration, it is shown that such a monotone spline can be used to monotonize any unconstrained estimator of a regression function, and that this monotone smoother inherits the convergence properties of the unconstrained estimator. Some numerical experiments are proposed to illustrate its finite sample performances, and to compare them with another monotone estimator. We also provide a two-dimensional application on the computation of diffeomorphisms for landmark and image matching

Quantification and localization of the liquid zone of partially remelted M2 tool steel using X-ray microtomography and scanning electron microscopy

The authors warmly thank Luc Morhain and Marc Wary (Arts et Métiers ParisTech CER Metz) for their technical support.Thixoforming of steels poses challenges due to the high temperatures involved and the lack of understanding of thermomechanical behavior. The volume fractions of the liquid and solid phases in the semi-solid state are the most important parameters for such a form-ing process, as they affect the viscosity and hence the flow behavior of the material. Two-dimensional observations might not always be sufficient, as the size distribution and the connectivity of phases cannot be obtained from associated measurements, which can only be determined by three-dimensional (3-D) investigation. This paper presents the first application of high-energy X-ray microtomography to the microstructure of steel in the semi-solid state. The microstructure of M2 high-speed tool steel was studied in both as-received and heated-and-quenched states. From the reconstructed images, 3-D information could be obtained and was compared with scanning elec-tron microscopy and energy dispersive spectrometry observations. The volume fraction and the location of liquid phase in the semi-solid state were determined in particular, and the continuous solid skeleton was investigated

Isolated Splenic Metastasis from Colorectal Cancer: Report of a Case

The authors report a case of a patient with splenic metastasis with previous history of colorectal cancer. A 69-year-old woman underwent a left hemicolectomy for sigmoid colon cancer. The tumor was staged T3N0M0. Two years after the operation, there was an elevation of CEA and computed tomography (CT) scan revealed a mass in the spleen, considered as an isolated metastasis. The patient underwent splenectomy. Histological diagnosis confirmed a metastatic adenocarcinoma from colorectal carcinoma. Patient was alive without neoplasic recurrence 5 years after splenectomy. Generally, splenic metastasis is uncommon. However, with the case of colorectal cancers, metastasis to the spleen is particularly rare. As with splenic metastasis of all primary tumors, the literature recommends that the treatment, where possible, is surgical

Adaptive Covariance Estimation with model selection

We provide in this paper a fully adaptive penalized procedure to select a covariance among a collection of models observing i.i.d replications of the process at fixed observation points. For this we generalize previous results of Bigot and al. and propose to use a data driven penalty to obtain an oracle inequality for the estimator. We prove that this method is an extension to the matricial regression model of the work by Baraud

On the understanding of pulsations in the atmosphere of roAp stars: phase diversity and false nodes

Studies based on high-resolution spectroscopic data of rapidly oscillating Ap stars show a surprising diversity of pulsation behavior in the atmospheric layers, pointing, in particular, to the co-existence of running and standing waves. The correct interpretation of these data requires a careful modelling of pulsations in these magnetic stars. In light of this, in this work we present a theoretical analysis of pulsations in roAp stars, taking into account the direct influence of the magnetic field. We derive approximate analytical solutions for the displacement components parallel and perpendicular to the direction of the magnetic field, that are appropriate to the outermost layer. From these, we determine the expression for the theoretical radial velocity for an observer at a general position, and compute the corresponding pulsation amplitude and phase as function of height in the atmosphere. We show that the integral for the radial velocity has contributions from three different types of wave solutions, namely, running waves, evanescent waves, and standing waves of nearly constant amplitude. We then consider a number of case studies to illustrate the origin of the different pulsational behaviour that is found in the observations. Concerning pulsation amplitude, we find that it generally increases with atmospheric height. Pulsation phase, however, shows a diversity of behaviours, including phases that are constant, increasing, or decreasing with atmospheric height. Finally, we show that there are situations in which the pulsation amplitude goes through a zero, accompanied by a phase jumps of $\pi$, and argue that such behaviour does not correspond to a pulsation node in the outermost layers of the star, but rather to a visual effect, resulting from the observers inability to resolve the stellar surface.Comment: 21 pages, 25 figure

Simulations for single-dish intensity mapping experiments

HI intensity mapping is an emerging tool to probe dark energy. Observations of the redshifted HI signal will be contaminated by instrumental noise, atmospheric and Galactic foregrounds. The latter is expected to be four orders of magnitude brighter than the HI emission we wish to detect. We present a simulation of single-dish observations including an instrumental noise model with 1/f and white noise, and sky emission with a diffuse Galactic foreground and HI emission. We consider two foreground cleaning methods: spectral parametric fitting and principal component analysis. For a smooth frequency spectrum of the foreground and instrumental effects, we find that the parametric fitting method provides residuals that are still contaminated by foreground and 1/f noise, but the principal component analysis can remove this contamination down to the thermal noise level. This method is robust for a range of different models of foreground and noise, and so constitutes a promising way to recover the HI signal from the data. However, it induces a leakage of the cosmological signal into the subtracted foreground of around 5%. The efficiency of the component separation methods depends heavily on the smoothness of the frequency spectrum of the foreground and the 1/f noise. We find that as, long as the spectral variations over the band are slow compared to the channel width, the foreground cleaning method still works.Comment: 14 pages, 12 figures. Submitted to MNRA

Visibilities and bolometric corrections for stellar oscillation modes observed by Kepler

Kepler produces a large amount of data used for asteroseismological analyses, particularly of solar-like stars and red giants. The mode amplitudes observed in the Kepler spectral band have to be converted into bolometric amplitudes to be compared to models. We give a simple bolometric correction for the amplitudes of radial modes observed with Kepler, as well as the relative visibilities of non-radial modes. We numerically compute the bolometric correction c_{K-bol} and mode visibilities for different effective temperatures Teff within the range 4000-7500 K, using a similar approach to a recent one from the literature (Michel et al. 2009, A&A 495, 979). We derive a law for the correction to bolometric values: c_{K-bol} = 1 + a_1 (Teff-To) + a_2 (Teff-To)^2, with To = 5934 K, a_1 = 1.349e-4 K^{-1}, and a_2 = -3.120e-9 K^{-2} or, alternatively, as the power law c_{K-bol} = (Teff/To)^alpha with alpha = 0.80. We give tabulated values for the mode visibilities based on limb-darkening (LD), computed from ATLAS9 model atmospheres for Teff in [4000,7500] K, log g in [2.5,4.5], and [M/H] in [-1.0,+1.0]. We show that using LD profiles already integrated over the spectral band provides quick and good approximations for visibilities. We point out the limits of these classical visibility estimations.Comment: 5 pages, 4 figures, 1 table, minor language edition. Published in A&