\begin{align}
&(1 + \partial_t)x^A_i(t) = \sum_j J_{ij}\phi^A_j(t) \nonumber \\
&+ \frac{k}{p}\int_{-\infty}^t dt' e^{-({t-t'})/{p}} \left[\frac{1}{N}\sum_j \phi^A_j(t)\phi^A_j(t') \right] \phi^A_i(t'),
	\label{eq:highd2replicaA} \\
&(1 + \partial_t) x^B_i(t) =  \sum_j J_{ij}\phi_j^B(t) \nonumber\\
&+ \frac{k}{p} \int_{0}^\infty dt' e^{-t'/p} \left[\frac{1}{N}\sum_j \phi^A_j(-t')\phi^B_j(t) \right] \phi^A_i(-t').
	\label{eq:highd2replicaB}
\end{align}
