Gravitational lens magnification by Abell 1689: Distortion of the background galaxy luminosity function

Gravitational lensing magnifies the luminosity of galaxies behind the lens. We use this effect to constrain the total mass in the cluster Abell 1689 by comparing the lensed luminosities of background galaxies with the luminosity function of an undistorted field. Since galaxies are assumed to be a random sampling of luminosity space, this method is not limited by clustering noise. We use photometric redshift information to estimate galaxy distance and intrinsic luminosity. Knowing the redshift distribution of the background population allows us to lift the mass/background degeneracy common to lensing analysis. In this paper we use 9 filters observed over 12 hours with the Calar Alto 3.5m telescope to determine the redshifts of 1000 galaxies in the field of Abell 1689. Using a complete sample of 151 background galaxies we measure the cluster mass profile. We find that the total projected mass interior to 0.25h^(-1)Mpc is (0.48 +/- 0.16) * 10^(15)h^(-1) solar masses, where our error budget includes uncertainties from the photometric redshift determination, the uncertainty in the off-set calibration and finite sampling. This result is in good agreement with that found by number count and shear-based methods and provides a new and independent method to determine cluster masses.Comment: 13 pages, 10 figures. Submitted to MNRAS (10/99); Replacement with 1 page extra text inc. new section, accepted by MNRA

A new fuzzy set merging technique using inclusion-based fuzzy clustering

This paper proposes a new method of merging parameterized fuzzy sets based on clustering in the parameters space, taking into account the degree of inclusion of each fuzzy set in the cluster prototypes. The merger method is applied to fuzzy rule base simplification by automatically replacing the fuzzy sets corresponding to a given cluster with that pertaining to cluster prototype. The feasibility and the performance of the proposed method are studied using an application in mobile robot navigation. The results indicate that the proposed merging and rule base simplification approach leads to good navigation performance in the application considered and to fuzzy models that are interpretable by experts. In this paper, we concentrate mainly on fuzzy systems with Gaussian membership functions, but the general approach can also be applied to other parameterized fuzzy sets

Inference in Additively Separable Models With a High-Dimensional Set of Conditioning Variables

This paper studies nonparametric series estimation and inference for the effect of a single variable of interest x on an outcome y in the presence of potentially high-dimensional conditioning variables z. The context is an additively separable model E[y|x, z] = g0(x) + h0(z). The model is high-dimensional in the sense that the series of approximating functions for h0(z) can have more terms than the sample size, thereby allowing z to have potentially very many measured characteristics. The model is required to be approximately sparse: h0(z) can be approximated using only a small subset of series terms whose identities are unknown. This paper proposes an estimation and inference method for g0(x) called Post-Nonparametric Double Selection which is a generalization of Post-Double Selection. Standard rates of convergence and asymptotic normality for the estimator are shown to hold uniformly over a large class of sparse data generating processes. A simulation study illustrates finite sample estimation properties of the proposed estimator and coverage properties of the corresponding confidence intervals. Finally, an empirical application to college admissions policy demonstrates the practical implementation of the proposed method

The link between career risk aversion and unemployment duration: Evidence of nonlinear and time-depending pattern

In this study, we investigate the nexus between career risk aversion and unemployment duration based on German survey data (GSOEP). Using a direct measurement of career risk aversion, we do not find a statistically significant linear effect from risk aversion on unemployment duration. However, we find significant effects when controlling for a non-linear or time varying correlation between risk aversion and unemployment duration. Our results show that risk aversion is important when deciding when to leave unemployment. This research takes into account the high complexity involved in how risk aversion enters an individual’s decision process during a job search.unemployment, risk aversion, duration model