Fitting theory to data in the presence of background uncertainties

When fitting theory to data in the presence of background uncertainties, the question of whether the spectral shape of the background happens to be similar to that of the theoretical model of physical interest has not generally been considered previously. These correlations in shape are considered in the present note and found to make important corrections to the calculations. The discussion is phrased in terms of $\chi^2$ fits, but the general considerations apply to any fits. Including these new correlations provides a more powerful test for confidence regions. Fake data studies, as used at present, may not be optimum.Comment: Example added; some conclusions change

Implications of Atmospheric Differential Refraction for Adaptive Optics Observations

Many adaptive optics systems operate by measuring the distortion of the wavefront in one wavelength range and performing the scientific observations in a second, different wavelength range. One common technique is to measure wavefront distortions at wavelengths <~1 micron while operating the science instrument at wavelengths >~1 micron. The index of refraction of air decreases sharply from shorter visible wavelengths to near-infrared wavelengths. Therefore, because the adaptive optics system is measuring the wavefront distortion in one wavelength range and the science observations are performed at a different wavelength range, residual image motion occurs and the maximum exposure time before smearing of the image can be significantly limited. We demonstrate the importance of atmospheric differential refraction, present calculations to predict the effect of atmospheric differential refraction, and finally discuss the implications of atmospheric differential refraction for several current and proposed observatories.Comment: PASP, accepted 15 January 200

Coarse homology theories

In this paper we develop an axiomatic approach to coarse homology theories. We prove a uniqueness result concerning coarse homology theories on the category of `coarse CW-complexes'. This uniqueness result is used to prove a version of the coarse Baum-Connes conjecture for such spaces.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-13.abs.htm

Warped cones and property A

We describe a construction (the `warped cone construction') which produces examples of coarse spaces with large groups of translations. We show that by this construction we can obtain many examples of coarse spaces which do not have property A or which are not uniformly embeddable into Hilbert space.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper4.abs.html Version 2: proof of theorem 1.10 correcte