diff --git a/Manuscript/eDFT.tex b/Manuscript/eDFT.tex
index 2f05209..5411d9a 100644
--- a/Manuscript/eDFT.tex
+++ b/Manuscript/eDFT.tex
@@ -819,7 +819,7 @@ Note that, within the approximation of Eq.~\eqref{eq:min_with_HF_ener_fun}, the
 optimized with a non-local exchange potential rather than a
 density-functional local one, as expected from
 Eq.~\eqref{eq:var_ener_gokdft}. This procedure is actually general, \ie,
-applicable to not-necessarily spin polarized and real (higher-dimensional) systems. 
+applicable to not-necessarily spin-polarized and real (higher-dimensional) systems. 
 As readily seen from Eq.~\eqref{eq:eHF-dens_mat_func}, inserting the
 ensemble density matrix into the HF interaction energy functional
 introduces unphysical \textit{ghost-interaction} errors \cite{Gidopoulos_2002, Pastorczak_2014, Alam_2016, Alam_2017, Gould_2017}
@@ -834,9 +834,8 @@ as well as \textit{curvature}:\cite{Alam_2016,Alam_2017}
 \eeq
 The ensemble energy is of course expected to vary linearly with the ensemble
 weights [see Eq.~\eqref{eq:exact_GOK_ens_ener}].
-\manu{
 The explicit linear weight dependence of the ensemble Hx energy is actually restored when evaluating the individual energy
-levels on the basis of Eq.~\eqref{eq:exact_ind_ener_rdm}.}  
+levels on the basis of Eq.~\eqref{eq:exact_ind_ener_rdm}.
 
 Turning to the density-functional ensemble correlation energy, the
 following ensemble local-density approximation (eLDA) will be employed  
@@ -1031,9 +1030,9 @@ gaps, can be seen as more relevant in this context. \cite{Loos_2014a, Loos_2014b
 However, an obvious drawback of using finite uniform electron gases is
 that the resulting density-functional approximation for ensembles
 will inexorably depend on the number of electrons in the finite uniform electron gas (see below).
-Here, we propose to construct a weight-dependent eLDA for the
+Here, we propose to construct a weight-dependent LDA functional for the
 calculation of excited states in 1D systems by combining finite uniform electron gases with the
-usual infinite uniform electron gas. 
+usual infinite uniform electron gas paradigm.
 
 As a finite uniform electron gas, we consider the ringium model in which electrons move on a perfect ring (\ie, a circle) but interact \textit{through} the ring. \cite{Loos_2012, Loos_2013a, Loos_2014b}
 The most appealing feature of ringium regarding the development of
@@ -1209,9 +1208,9 @@ We use as basis functions the (orthonormal) orbitals of the one-electron system,
 \end{equation} 
 with $ \mu = 1,\ldots,\nBas$ and $\nBas = 30$ for all calculations.
 The convergence threshold $\tau = \max{ \abs{ \bF{\bw} \bGam{\bw}
-\bS - \bS \bGam{\bw} \bF{\bw}}}$ [see Eq.~\eqref{eq:commut_F_AO}] is set
-to $10^{-5}$. For comparison, regular HF and KS-DFT calculations 
-are performed with the same threshold.
+\bS - \bS \bGam{\bw} \bF{\bw}}}$ [see Eq.~\eqref{eq:commut_F_AO}] of the KS-DFT self-consistent calculation is set
+to $10^{-5}$. 
+%For comparison, regular HF and KS-DFT calculations are performed with the same threshold.
 In order to compute the various density-functional
 integrals that cannot be performed in closed form, 
 a 51-point Gauss-Legendre quadrature is employed.