This is a notational question:
What does $\overset{\underset{\mathrm{\Delta }}{}}{=}$ denote in
$-0.5JDJ\overset{\underset{\mathrm{\Delta }}{}}{=} X^TX$ where $J=I-n^{-1}ee^T$ with $e$ being a vector of $1's$ and $D$ is a matrix of squared distances of the rows in $X$ i.e, $D_{ij}=||X_{i.}-X_{j.}||^2$