Wavelet block thresholding for samples with random design: a minimax approach under the LpL^p risk

We consider the regression model with (known) random design. We investigate the minimax performances of an adaptive wavelet block thresholding estimator under the $\mathbb{L}^p$ risk with $p\ge 2$ over Besov balls. We prove that it is near optimal and that it achieves better rates of convergence than the conventional term-by-term estimators (hard, soft,...).Comment: Published at http://dx.doi.org/10.1214/07-EJS067 in the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Adapting to Unknown Smoothness by Aggregation of Thresholded Wavelet Estimators

We study the performances of an adaptive procedure based on a convex combination, with data-driven weights, of term-by-term thresholded wavelet estimators. For the bounded regression model, with random uniform design, and the nonparametric density model, we show that the resulting estimator is optimal in the minimax sense over all Besov balls under the $L^2$ risk, without any logarithm factor

On adaptive wavelet estimation of a class of weighted densities

We investigate the estimation of a weighted density taking the form $g=w(F)f$, where $f$ denotes an unknown density, $F$ the associated distribution function and $w$ is a known (non-negative) weight. Such a class encompasses many examples, including those arising in order statistics or when $g$ is related to the maximum or the minimum of $N$ (random or fixed) independent and identically distributed (\iid) random variables. We here construct a new adaptive non-parametric estimator for $g$ based on a plug-in approach and the wavelets methodology. For a wide class of models, we prove that it attains fast rates of convergence under the $\mathbb{L}_p$ risk with $p\ge 1$ (not only for $p = 2$ corresponding to the mean integrated squared error) over Besov balls. The theoretical findings are illustrated through several simulations

Block thresholding for wavelet-based estimation of function derivatives from a heteroscedastic multichannel convolution model

We observe $n$ heteroscedastic stochastic processes $\{Y_v(t)\}_{v}$, where for any $v\in\{1,\ldots,n\}$ and $t \in [0,1]$, $Y_v(t)$ is the convolution product of an unknown function $f$ and a known blurring function $g_v$ corrupted by Gaussian noise. Under an ordinary smoothness assumption on $g_1,\ldots,g_n$, our goal is to estimate the $d$-th derivatives (in weak sense) of $f$ from the observations. We propose an adaptive estimator based on wavelet block thresholding, namely the "BlockJS estimator". Taking the mean integrated squared error (MISE), our main theoretical result investigates the minimax rates over Besov smoothness spaces, and shows that our block estimator can achieve the optimal minimax rate, or is at least nearly-minimax in the least favorable situation. We also report a comprehensive suite of numerical simulations to support our theoretical findings. The practical performance of our block estimator compares very favorably to existing methods of the literature on a large set of test functions

VLTI/MIDI observations of 7 classical Be stars

We measured the mid-infrared extension of the gaseous disk surrounding seven Be stars in order to constrain the geometry of their circumstellar environments and to try to infer physical parameters characterizing these disks. We used the VLTI/MIDI instrument with baselines up to 130 m to obtain an angular resolution of about 15 mas in the N band and compared our results with previous K band measurements obtained with the VLTI/AMBER instrument and/or the CHARA interferometer. We obtained one calibrated visibility measurement for each of the four stars, p Car, zeta Tau, kappa CMa, and alpha Col, two for delta Cen and beta CMi, and three for alpha Ara. Almost all targets remain unresolved even with the largest VLTI baseline of 130m, evidence that their circumstellar disk extension is less than 10 mas. The only exception is alpha Ara, which is clearly resolved and well-fitted by an elliptical envelope with a major axis a=5.8+-0.8mas and an axis ratio a/b=2.4+-1 at 8 microns. This extension is similar to the size and flattening measured with the VLTI/AMBER instrument in the K band at 2 microns. The size of the circumstellar envelopes for these classical Be stars does not seem to vary strongly on the observed wavelength between 8 and 12microns. Moreover, the size and shape of Alpha Ara's disk is almost identical at 2, 8, and 12microns

Optical interferometry and adaptive optics of bright transients

Bright optical transients (i.e. transients typically visible with the naked eye) are populated mainly by novae eruptions plus a few supernovae (among which the SN1987a event). One bright nova happen every two years, either in the North ot in the South hemisphere. It occurs that current interferometers have matching sensitivities, with typically visible or infrared limiting magnitude in the range 5--7. The temporal development of the fireball, followed by a dust formation phase or the appearance of many coronal lines can be sudied with the Very Large Telescope Interferometer. The detailed geometry of the first phases of novae in outburst remains virtually unexplored. This paper summarizes the work which has been done to date using the VLTI.Comment: Hot-wiring the transien Universe 3, Santa Fe : United States (2013

Fabrication of Metal-Insulator-Metal assemblies for spintronic devices using self-assembled monolayers

New, efficient and reproducible methods for the fabrication of Metal-Insulator-Metal (MIM) junctions for applications in spintronic devices have been developed. The junctions consisted of a gold substrate as bottom contact, p-terphenyl-based self-assembled monolayers (SAMs) as insulator layer, and thin ferromagnetic metal films (nickel) as top contact. Both pristine and electron irradiated (denoted by the prefix CL-) SAMs of [1,1’:4’,1”-terphenyl]-4,4”-dimethanethiol (TPDMT), (4’-(pyridin-4-yl)biphenyl-4-yl)alkanethiol (PPPn, n = 1,3) and perfluoroterphenyl-substituted alkanethiols (FTPn, n = 2,3) on Au(111) were used as test systems. All molecules were found to form well-ordered, high quality SAMs, a prerequisite for the fabrication of SAM-based MIM devices. In addition, the influence of the SAMs’ molecular architecture on its transport properties has been investigated. In particular, we have studied the effect of the small alkane linker (between the head group and the p-terphenyl backbone) found in all the molecules used in this work. The alkane linker was found act as an insulator, allowing us to decouple of the aromatic core’s electronic system from the substrate. We then studied the effects of electron irradiation on PPPn/Au and FTPn/Au SAMs. Both SAMs were modified with electrons. In particular, the charge transport properties of the FTPn/Au surface could be fine-tuned simply by controlling the irradiation dose. Finally, nickel was deposited on all SAMs to test their usefulness as dielectric layers in MIM devices. Whereas nickel was found, by XPS and NEXAFS spectroscopy, to penetrate into and through the SAMs of TPDMT, CL-TPDMT, PPP1 and CL-PPP1 on Au(111), a single layer of palladium chloride, deposited from solution on either TPDMT/Au or CL-PPPn/Au, promoted the nucleation and growth of nickel thin films on top of the respective SAMs via alloying of nickel with palladium. Furthermore, reaction of nickel with the perfluorinated FTPn SAMs yielded a new class of organometallic thin films in which nickel was found to reside mainly at the top. Irradiation of the FTPn monolayers with electrons gave us precise control over the work function of the CL-FPTn/Au surfaces (a crucial parameter for the fabrication of nanoelectronic devices) while favouring the nucleation and growth of top ferromagnetic contacts. The penetration of nickel into and through CL-FTPn/Au SAMs was found to decrease by as much as 30 % at high irradiation doses (> 30 mC/cm2) making FTPn systems attractive as dielectric layers for nano junctions

Spectro-interferometric observations of interacting massive stars with VEGA/CHARA

We obtained spectro-interferometric observations in the visible of $\beta$ Lyrae and $\upsilon$ Sgr using the instrument VEGA of the CHARA interferometric array. For $\beta$ Lyrae, the dispersed fringe visibilities and differential phases were obtained in spectral regions containing the H$\alpha$ and HeI 6678 lines and the H$\beta$ and HeI 4921 lines. Whereas the source is unresolved in the continuum, the source of the emission lines is resolved and the photocenter of the bulk of the H$\alpha$ emission exhibits offsets correlated with the orbital phase. For $\upsilon$ Sgr, both the continuum and H$\alpha$ sources are resolved, but no clear binary signal is detected. The differential phase shift across the line reveals that the bulk of the H$\alpha$ emission is clearly offset from the primary