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

The degrees of freedom of the Lasso for general design matrix

In this paper, we investigate the degrees of freedom (\dof) of penalized $\ell_1$ minimization (also known as the Lasso) for linear regression models. We give a closed-form expression of the \dof of the Lasso response. Namely, we show that for any given Lasso regularization parameter $\lambda$ and any observed data $y$ belonging to a set of full (Lebesgue) measure, the cardinality of the support of a particular solution of the Lasso problem is an unbiased estimator of the degrees of freedom. This is achieved without the need of uniqueness of the Lasso solution. Thus, our result holds true for both the underdetermined and the overdetermined case, where the latter was originally studied in \cite{zou}. We also show, by providing a simple counterexample, that although the \dof theorem of \cite{zou} is correct, their proof contains a flaw since their divergence formula holds on a different set of a full measure than the one that they claim. An effective estimator of the number of degrees of freedom may have several applications including an objectively guided choice of the regularization parameter in the Lasso through the \sure framework. Our theoretical findings are illustrated through several numerical simulations.Comment: A short version appeared in SPARS'11, June 2011 Previously entitled "The degrees of freedom of penalized l1 minimization

A silicate disk in the heart of the Ant

We aim at getting high spatial resolution information on the dusty core of bipolar planetary nebulae to directly constrain the shaping process. Methods: We present observations of the dusty core of the extreme bipolar planetary nebula Menzel 3 (Mz 3, Hen 2-154, the Ant) taken with the mid-infrared interferometer MIDI/VLTI and the adaptive optics NACO/VLT. The core of Mz 3 is clearly resolved with MIDI in the interferometric mode, whereas it is unresolved from the Ks to the N bands with single dish 8.2 m observations on a scale ranging from 60 to 250 mas. A striking dependence of the dust core size with the PA angle of the baselines is observed, that is highly suggestive of an edge-on disk whose major axis is perpendicular to the axis of the bipolar lobes. The MIDI spectrum and the visibilities of Mz 3 exhibit a clear signature of amorphous silicate, in contrast to the signatures of crystalline silicates detected in binary post-AGB systems, suggesting that the disk might be relatively young. We used radiative-transfer Monte Carlo simulations of a passive disk to constrain its geometrical and physical parameters. Its inclination (74 degrees $\pm$ 3 degrees) and position angle (5 degrees $\pm$ 5 degrees) are in accordance with the values derived from the study of the lobes. The inner radius is 9$\pm$ 1 AU and the disk is relatively flat. The dust mass stored in the disk, estimated as 1 x 10-5Msun, represents only a small fraction of the dust mass found in the lobes and might be a kind of relic of an essentially polar ejection process

The expanding dusty bipolar nebula around the nova V1280 Sco

V1280 Sco is one of the slowest dust-forming nova ever historically observed. We performed multi-epoch high-spatial resolution observations of the circumstellar dusty environment of V1280 Sco to investigate the level of asymmetry of the ejecta We observed V1280 Sco in 2009, 2010 and 2011 using unprecedented high angular resolution techniques. We used the NACO/VLT adaptive optics system in the J, H and K bands, together with contemporaneous VISIR/VLT mid-IR imaging that resolved the dust envelope of V1280 Sco, and SINFONI/VLT observations secured in 2011. We report the discovery of a dusty hourglass-shaped bipolar nebula. The apparent size of the nebula increased from 0.30" x 0.17" in July 2009 to 0.64" x 0.42" in July 2011. The aspect ratio suggests that the source is seen at high inclination. The central source shines efficiently in the K band and represents more than 56+/-5% of the total flux in 2009, and 87+/-6% in 2011. A mean expansion rate of 0.39+/-0.03 mas per day is inferred from the VISIR observations in the direction of the major axis, which represents a projected upper limit. Assuming that the dust shell expands in that direction as fast as the low-excitation slow ejecta detected in spectroscopy, this yields a lower limit distance to V1280 Sco of 1kpc; however, the systematic errors remain large due to the complex shape and velocity field of the dusty ejecta. The dust seems to reside essentially in the polar caps and no infrared flux is detected in the equatorial regions in the latest dataset. This may imply that the mass-loss was dominantly polar

Dual Signaling System with an Extended-Tetrathiafulvalene–Phenanthroline Dyad Acting as an Electrooptical Cation Chemosensor

A tetrathiafulvalene donor has been annulated to 2,3-di(1H-2-pyrrolyl)quinoxaline affording a new chemosensor 1, which shows a unique optical selectivity and reactivity for the fluoride ion over other anions in CH2Cl2 leading to a colorimetric response. Electrochemical polymerization of 1 occurred in the presence of fluoride

A Fused Donor−Acceptor System Based on an Extended Tetrathiafulvalene and a Ruthenium Complex of Dipyridoquinoxaline

An application of the Horner−Wadsworth−Emmons reaction carried out on a ruthenium compound as the electrophilic precursor is described for the synthesis of fused donor−acceptor system 1 based on an extended tetrathiafulvalene and a ruthenium complex of dipyridoquinoxaline units

Adaptive estimation of an additive regression function from weakly dependent data

A $d$-dimensional nonparametric additive regression model with dependent observations is considered. Using the marginal integration technique and wavelets methodology, we develop a new adaptive estimator for a component of the additive regression function. Its asymptotic properties are investigated via the minimax approach under the $\mathbb{L}_2$ risk over Besov balls. We prove that it attains a sharp rate of convergence which turns to be the one obtained in the \iid case for the standard univariate regression estimation problem.Comment: Substantial improvement of the estimator and the main theore

Adaptive optics imaging of P Cygni in Halpha

We obtained Halpha diffraction limited data of the LBV star P Cyg using the ONERA Adaptive Optics (AO) facility BOA at the OHP 1.52m telescope on October 1997. Taking P Cyg and the reference star 59 Cyg AO long exposures we find that P Cyg clearly exhibits a large and diffuse intensity distribution compared to the 59 Cyg's point-like source. A deconvolution of P Cyg using 59 Cyg as the Point Spread Function was performed by means of the Richardson-Lucy algorithm. P Cyg clearly appears as an unresolved star surrounded by a clumped envelope. The reconstructed image of P Cyg is compared to similar spatial resolution maps obtained from radio aperture synthesis imaging. We put independent constraints on the physics of P Cyg which agree well with radio results. We discuss future possibilities to constrain the wind structure of P Cyg by using multi-resolution imaging, coronagraphy and long baseline interferometry to trace back its evolutionary status.Comment: 10 pages, 19 Encapsulated Postscript figure

Continuum limit of the nonlocal p-Laplacian evolution problem on random inhomogeneous graphs

International audienceIn this paper we study numerical approximations of the evolution problem for the nonlocal p-Laplacian operator with homogeneous Neumann boundary conditions on inhomogeneous random conver-gent graph sequences. More precisely, for networks on convergent inhomogeneous random graph sequences (generated first by deterministic and then random node sequences), we establish their continuum limits and provide rate of convergence of solutions for the discrete models to their continuum counterparts as the number of vertices grows. Our bounds reveals the role of the different parameters, and in particular that of p and the geometry/regularity of the data

A New Discrete Distribution: Properties, Characterizations, Modeling Real Count Data, Bayesian and Non-Bayesian Estimations

In this work, a new discrete distribution which includes the discrete Burr-Hatke distribution is defined and studied. Relevant statistical properties are derived. The probability mass function of the new distribution can be right skewed with different shapes, bimodal and uniformed . Also, the corresponding hazard rate function can be monotonically decreasing , upside down , monotonically increasing , upside down increasing , and upside down-constant-increasing . A numerical analysis for the mean, variance, skewness, kurtosis and the index of dispersion is presented. The new distribution could be useful in the modeling of under-dispersed or overdispersed count data. Certain characterizations of the new distribution are presented. These characterizations are based on the conditional expectation of a certain function of the random variable and in terms of the hazard rate function. Bayesian and non-Bayesian estimation methods are considered. Numerical simulations for comparing Bayesian and non-Bayesian estimation methods are performed. The new model is applied for modeling carious teeth data and counts of cysts of kidneys data