diff --git a/dynker.tex b/dynker.tex
index 4ea48e2..fff9bec 100644
--- a/dynker.tex
+++ b/dynker.tex
@@ -639,17 +639,17 @@ In the case of BSE2, the perturbative partitioning is simply
 	}
 	\begin{ruledtabular}
 		\begin{tabular}{|c|ccccccc|c|}
-			Singlets	&	BSE2	&	pBSE2	&	pBSE2(dTDA)	&	dBSE2	&	BSE2(TDA)	&	pBSE2(TDA)	&	dBSE2(TDA)	&	Exact	\\
+			Singlets			&	BSE2	&	pBSE2	&	pBSE2(dTDA)	&	dBSE2	&	BSE2(TDA)	&	pBSE2(TDA)	&	dBSE2(TDA)	&	Exact	\\
 			\hline
-			$\omega_1$	&	1.84903	&	1.90940	&	1.90950		&	1.90362	&	1.86299		&	1.92356		&	1.92359		&	1.92145	\\
-			$\omega_2$	&			&			&				&			&				&				&				&			\\
-			$\omega_3$	&			&			&				&	4.47124	&				&				&	4.47097		&	3.47880	\\
+			$\omega_1^{\updw}$	&	1.84903	&	1.90940	&	1.90950		&	1.90362	&	1.86299		&	1.92356		&	1.92359		&	1.92145	\\
+			$\omega_2^{\updw}$	&			&			&				&			&				&				&				&			\\
+			$\omega_3^{\updw}$	&			&			&				&	4.47124	&				&				&	4.47097		&	3.47880	\\
 			\hline
-			Triplets	&	BSE2	&	pBSE2	&	pBSE2(dTDA)	&	dBSE2	&	BSE2(TDA)	&	pBSE2(TDA)	&	dBSE2(TDA)	&	Exact	\\
+			Triplets			&	BSE2	&	pBSE2	&	pBSE2(dTDA)	&	dBSE2	&	BSE2(TDA)	&	pBSE2(TDA)	&	dBSE2(TDA)	&	Exact	\\
 			\hline
-			$\omega_1$	&	1.38912	&	1.44285	&	1.44304		&	1.42564	&	1.40765		&	1.46154		&	1.46155		&	1.47085	\\
-			$\omega_2$	&			&			&				&			&				&				&				&			\\
-			$\omega_3$	&			&			&				&	4.47797	&				&				&	4.47767		&			\\
+			$\omega_1^{\upup}$	&	1.38912	&	1.44285	&	1.44304		&	1.42564	&	1.40765		&	1.46154		&	1.46155		&	1.47085	\\
+			$\omega_2^{\upup}$	&			&			&				&			&				&				&				&			\\
+			$\omega_3^{\upup}$	&			&			&				&	4.47797	&				&				&	4.47767		&			\\
 		\end{tabular}
 	\end{ruledtabular}
 \end{table*}
@@ -720,9 +720,13 @@ For the double excitation, dBSE2 yields a slightly better energy, yet still in q
 %\end{gather}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Take-home messages}
+\section{Take-home message}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-What have we learned here? 
+The take-home message of the present paper is that dynamical kernels have much more to give that one would think.
+In more scientific terms, dynamical kernels can provide, thanks to their frequency-dependent nature, additional excitations that can be associated to higher-order excitations (such as the infamous double excitations).
+However, they sometimes give too much, and generate spurious excitations, \ie, excitation which does not corresponds to any physical excited state.
+The appearance of these factitious excitations is due to the approximate nature of the dynamical kernel.
+Moreover, because of the non-linear character of the linear response problem when one employs a dynamical kernel, it is computationally more involved to access these extra excitations.
 
 %%%%%%%%%%%%%%%%%%%%%%%%
 \acknowledgements{