  In this paper, we compare the virtual fundamental classes of the stacks of
$(g,\beta,\mu)$-stable ramified maps $\bar{\mathfrak U}_{g,\mu}(X,\beta)$ and
of $(g,\beta,\mu)$-log stable ramified maps $\bar{\mathfrak
U}^{\mathrm{log}}_{g,\mu}(X,\beta)$. For that we will see how they are
identified via virtual normalization and then apply Costello's push-forward
formula.
