Here's an excerpt from this paper:
I can't get access to the book the citation references. Does anyone know what this operator might be?
$\mathbf{p}$ is the joint pmf of two Bernoulli rvs:
\begin{equation*} \begin{bmatrix} p_{00} & p_{01}\\ p_{10} & p_{11} \end{bmatrix} \end{equation*}
The transformation labeled 5.4 is:
\begin{equation*} \frac{\Phi \cdot \mathbf{p} \cdot \Psi}{\lVert \Phi \cdot \mathbf{p} \cdot \Psi \rVert_1} \end{equation*} where $\Phi$ and $\Psi$ are defined as: \begin{equation*} \begin{bmatrix} 1 & 0\\ 0 & \phi \end{bmatrix} \end{equation*} and \begin{equation*} \begin{bmatrix} 1 & 0\\ 0 & \psi \end{bmatrix} \end{equation*}
So the transformation is just to rescale one of the marginals, then re-normalize the distribution.