Re: Problem related to begin{case}
You probably already solved this long ago but I found that it works as long as you make sure
\usepackage{amsmath, amssymb}
\begin{equation}
\Psi _{ij} =
\begin{cases}
\frac{log\frac{P_{ij}}{P_{0}}}{log\frac{1}{p_{0}}}, & \mbox{if } P_{ij} \geqslant p^{*} \\
-\infty , & \mbox{otherwise}
\end{cases}
\end{equation}
Insert "&" in front of \mbox.
L