Before revision:  In contrast, we show upper bounds of \tilde O(n^{3/2\tilde  ) and \tilde O( \sqrt{mn + n^{3/2}), respectively, where again the edge weights are between 1 and \tau.
After revision:  In contrast, we show upper bounds of \tilde O(n^{3/2\tilde ) and \tilde O( \sqrt{mn\tau + n^{3/2}), respectively, where again the edge weights are between 1 and \tau.