AIMS To estimate the impact of school fruit tuck shops on children's consumption of fruit and sweet and savoury snacks. DESIGN Cluster randomised effectiveness trial with school as the unit of randomisation. SETTING 43 primary schools in deprived areas in south Wales and south-west England with a range of school food policies. INTERVENTION Schools operated fruit tuck shops throughout one ...

We prove that there are no restrictions on the spatial topology of asymptotically flat solutions of the vacuum Einstein equations in (n + 1)-dimensions. We do this by gluing a solution of the vacuum constraint equations on an arbitrary compact manifold Σn to an asymptotically Euclidean solution of the constraints on Rn. This is a special case of a more general gluing construction for nondegener...