  The purpose of this note is to extend the results on uniform smoothed
analysis of condition numbers from \cite{BuCuLo:07} to the case where the
perturbation follows a radially symmetric probability distribution. In
particular, we will show that the bounds derived in \cite{BuCuLo:07} still hold
in the case of distributions whose density has a singularity at the center of
the perturbation, which we call {\em adversarial}.
