diff --git a/principal.tex b/principal.tex
index c1ffb78..d486b26 100644
--- a/principal.tex
+++ b/principal.tex
@@ -222,6 +222,10 @@
                         M}, \alpha)$.
         \end{block}
     }
+    \begin{itemize}
+        \item No shared nodes across networks
+        \item Agnostic of structure
+    \end{itemize}
 \end{frame}
 % \begin{frame}
 %     \frametitle{Parameter estimation}
@@ -269,12 +273,12 @@
     \end{align*}
 
     \onslide<3>{
-        We would like to use Expectation-Maximization (EM) algorithm~\parencite{dempsterMaximumLikelihoodIncomplete1977} but the law of $\mathbf{Z,W|Y},\theta^{(t-1)}$ is untractable due to dependence between rows and columns.}
+        We would like to use Expectation-Maximization (EM) algorithm~\parencite{dempsterMaximumLikelihoodIncomplete1977} but the law of $\mathbf{Z,W|Y},\theta^{(t-1)}$ is untractable due to dependence between row and column groups.}
 \end{frame}
 \begin{frame}{Parameter estimation}{Solution}
     By \emph{Variational EM}, as proposed
-    by~\cite{daudinMixtureModelRandom2008,
-        chabert-liddellLearningCommonStructures2024}.
+    by~\cite{daudinMixtureModelRandom2008} and adapted for joint simple networks
+    by~\cite{chabert-liddellLearningCommonStructures2024}.
     \begin{block}{Variational approximation of $\bm{Z,W|Y},\theta^{(t-1)}$}
         $\mathcal{R}_{Y^m,\tau}(Z^m, W^m) =
             \mathcal{R}^1_{Y^m,\tau}(Z^m)
@@ -294,15 +298,15 @@
 \end{frame}
 
 \begin{frame}{Selection criterion for $Q_1, Q_2$}
-    \cite{biernackiAssessingMixtureModel2000} introduced the Integrated Classification Likelihood (ICL).
+    \cite{biernackiAssessingMixtureModel2000} introduced the Integrated Classification Likelihood (ICL):
     \begin{align*}
         \text{ICL}(\bm{Y}, Q_1, Q_2) & = \mathbb{E} [\ell_c(\bm{Y,Z,W};\hat{\theta})] -\frac{1}{2}\text{pen}(Q_1, Q_2)                                          \\
                                      & = \ell(\mathbf{Y};\hat{\theta}) - \mathcal{H}(p(\mathbf{Z,W}|\mathbf{Y},\hat{\theta})) - \frac{1}{2}\text{pen}(Q_1, Q_2)
-    \end{align*} leads to low entropy clustering.
+    \end{align*} leads to low entropy clustering. Common in literature for SBM.
     \onslide<2->{
         \begin{align*}
-            \text{BIC-L}(\bm{Y}, Q_1, Q_2) & = \mathbb{E}_{\mathcal{R}_{\mathbf{Y},\hat{\tau}}} [\ell_c(\bm{Y,Z,W};\hat{\theta}^{\text{var}})] + \mathcal{H(\mathcal{R}_{\mathbf{Y},\hat{\tau}})} - \frac{1}{2}\text{pen}(Q_1, Q_2) \\
-                                           & = \mathcal{J(\mathcal{R}_{\mathbf{Y},\hat{\tau}}, \hat{\theta}^{\text{var}})} - \frac{1}{2}\text{pen}(Q_1, Q_2)
+            \text{BIC-L}(\bm{Y}, & Q_1, Q_2) = \mathbb{E}_{\mathcal{R}_{\mathbf{Y},\hat{\tau}}} [\ell_c(\bm{Y,Z,W};\hat{\theta}^{\text{var}})] + \mathcal{H(\mathcal{R}_{\mathbf{Y},\hat{\tau}})} - \frac{1}{2}\text{pen}(Q_1, Q_2)                   \\
+                                 & = \mathcal{J(\mathcal{R}_{\mathbf{Y},\hat{\tau}}, \hat{\theta}^{\text{var}})} - \frac{1}{2}\text{pen}(Q_1, Q_2) \textcolor{red}{\leq \log p(\mathbf{Y};\hat{\theta}^{\text{MV}})- \frac{1}{2}\text{pen}(Q_1, Q_2)} \\
         \end{align*}
         because we want fuzzier clustering.
     }