Fractional coloring of triangle-free planar graphs

We prove that every planar triangle-free graph on $n$ vertices has fractional chromatic number at most $3-\frac{1}{n+1/3}$

A unified approach to solve ill-posed inverse problems in econometrics

We consider the general issue of estimating a nonparametric function x from the inverse problem r = Tx given estimates of the function r and of the linear transform T. Two typical examples include the estimation of a probability density function fromdata contaminated by a noise whose distribution is unknown (blind deconvolution) and the nonparametric instrumental regression. We provide a unified framework based on Hilbert scales that synthesizes most of existing results in the econometric literature and also covers new relevant structural models. Results are given on the rate of convergence of the estimator of x as well as of its derivatives.inverse problem, Hilbert scale, deconvolution, instrumental variable, nonparametric regression

Iterative Regularization in Nonparametric Instrumental Regression

We consider the nonparametric regression model with an additive error that is correlated with the explanatory variables. We suppose the existence of instrumental variables that are considered in this model for the identification and the estimation of the regression function. The nonparametric estimation by instrumental variables is an illposed linear inverse problem with an unknown but estimable operator. We provide a new estimator of the regression function using an iterative regularization method (the Landweber-Fridman method). The optimal number of iterations and the convergence of the mean square error of the resulting estimator are derived under both mild and severe degrees of ill-posedness. A Monte-Carlo exercise shows the impact of some parameters on the estimator and concludes on the reasonable finite sample performance of the new estimator.Nonparametric estimation; Instrumental variable; Ill-posed inverse problem

Iterative regularization in nonparametric instrumental regression

We consider the nonparametric regression model with an additive error that is correlated with the explanatory variables. We suppose the existence of instrumental variables that are considered in this model for the identification and the estimation of the regression function. The nonparametric estimation by instrumental variables is an ill-posed linear inverse problem with an unknown but estimable operator. We provide a new estimator of the regression function using an iterative regularization method (the Landweber-Fridman method). The optimal number of iterations and the convergence of the mean square error of the resulting estimator are derived under both mild and severe degrees of ill-posedness. A Monte-Carlo exercise shows the impact of some parameters on the estimator and concludes on the reasonable finite sample performance of the new estimator.nonparametric estimation, instrumental variable, ill-posed inverse problem, iterative method, estimation by projection

First Resolved Dust Continuum Measurements of Individual Giant Molecular Clouds in the Andromeda Galaxy

© 2020 The American Astronomical Society.In our local Galactic neighborhood, molecular clouds are best studied using a combination of dust measurements, to determine robust masses, sizes, and internal structures of the clouds, and molecular-line observations to determine cloud kinematics and chemistry. We present here the first results of a program designed to extend such studies to nearby galaxies beyond the Magellanic Clouds. Utilizing the wideband upgrade of the Submillimeter Array (SMA) at 230 GHz, we have obtained the first continuum detections of the thermal dust emission on sub-GMC scales (∼15 pc) within the Andromeda galaxy (M31). These include the first resolved continuum detections of dust emission from individual giant molecular clouds (GMCs) beyond the Magellanic Clouds. Utilizing a powerful capability of the SMA, we simultaneously recorded CO(2-1) emission with identical (u, v) coverage, astrometry, and calibration, enabling the first measurements of the CO conversion factor, α CO(2-1), toward individual GMCs across an external galaxy. Our direct measurement yields an average CO-to-dust mass conversion factor of α' CO-dust = 0.042 ± 0.018 M o (K km s -1 pc 2) -1 for the J = 2-1 transition. This value does not appear to vary with galactocentric radius. Assuming a constant gas-to-dust ratio of 136, the resulting α CO = 5.7 ± 2.4 M o (K km s -1 pc 2) -1 for the 2-1 transition is in excellent agreement with that of GMCs in the Milky Way, given the uncertainties. Finally, using the same analysis techniques, we compare our results with observations of the local Orion molecular clouds, placed at the distance of M31 and simulated to appear as they would if observed by the SMA.Peer reviewedFinal Published versio

Instrumental Regression in Partially Linear Models

We consider the semiparametric regression Xtβ+φ(Z) where β and φ(·) are unknown slope coefficient vector and function, and where the variables (X,Z) are endogeneous. We propose necessary and sufficient conditions for the identification of the parameters in the presence of instrumental variables. We also focus on the estimation of β. An incorrect parameterization of φ may generally lead to an inconsistent estimator of β, whereas even consistent nonparametric estimators for φ imply a slow rate of convergence of the estimator of β. An additional complication is that the solution of the equation necessitates the inversion of a compact operator that has to be estimated nonparametrically. In general this inversion is not stable, thus the estimation of β is ill-posed. In this paper, a √n-consistent estimator for β is derived under mild assumptions. One of these assumptions is given by the so-called source condition that is explicitly interprated in the paper. Finally we show that the estimator achieves the semiparametric efficiency bound, even if the model is heteroscedastic. Monte Carlo simulations demonstrate the reasonable performance of the estimation procedure on finite samples.

Identification and estimation by penalization in nonparametric instrumental regression

The nonparametric estimation of a regression function x from conditional moment restrictions involving instrumental variables is considered. The rate of convergence of penalized estimators is studied in the case where x is not identified from the conditional moment restriction. We also study the gain of modifying the penalty in the estimation, considering for instance a Sobolev-type of penalty. We analyze the effect of this modification on the rate of convergence of the estimator and on the identification of the regression function x.instrumental variable, nonparametric estimation, ill-posed inverse problem, identification, penalized estimator, Tikhonov regularization, Sobolev norm