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

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