Minor edits to cover letter

Cover_Letter/CoverLetter.tex

@@ -7,23 +7,23 @@
 \begin{document}
 
 \begin{letter}%
-{To the Editors of Journal of Physics: Condensed Matter (JPCM)}
+{To the Editors of the Journal of Physics: Condensed Matter (JPCM)}
 
 \opening{Dear Editors,}
 
 \justifying
 Following the recent invitation of Ania Wronski, please find enclosed our manuscript entitled \textit{``Perturbation Theory in the Complex Plane: Exceptional Points and Where to Find Them''}, which we would like you to consider as a Topical Review in \textit{J. Phys. Cond. Mat.}
 
-The present multidisciplinary review explores the non-Hermitian extension of computational quantum chemistry in the complex plane and its link with perturbation theory.
+This multidisciplinary review explores the non-Hermitian extension of computational quantum chemistry to the complex plane and its link with perturbation theory.
-In particular, we focus on its mathematical roots and its connection with physical phenomena such as quantum phase transitions and exceptional points in the complex plane.
+In particular, we focus on its mathematical roots and connections with physical phenomena such as quantum phase transitions and exceptional points in the complex plane.
-We begin by presenting the fundamental concepts behind non-Hermitian extensions of quantum chemistry into the complex plane, including the Hartree-Fock approximation and
+We begin by presenting the fundamental concepts behind non-Hermitian extensions of quantum chemistry into the complex plane, including the Hartree--Fock approximation and
-Rayleigh-Schr\"odinger perturbation theory. 
+Rayleigh--Schr\"odinger perturbation theory. 
-We then provide a comprehensive review of the various research that has been performed around the physics of complex singularities in perturbation theory, with a particular focus on M{\o}ller?Plesset theory.
+We then provide a comprehensive review of the various research that has been performed around the physics of complex singularities in perturbation theory, with a particular focus on M{\o}ller--Plesset theory.
-Finally, several resummation techniques that can be used to improve energy estimates for both convergent and divergent series (including Pad\'e and quadratic approximants) are discussed. 
+Finally, several resummation techniques are discussedthat can improve energy estimates for both convergent and divergent series, including Pad\'e and quadratic approximants.
 Throughout this review, we present illustrative and pedagogical examples based on the ubiquitous Hubbard dimer at half-filling, reinforcing the amazing versatility of this powerful simplistic model.
 
-Due to the genuine interdisciplinary nature of the present article and its pedological aspect, we believe that it will be of interest to a wide audience within the physics and chemistry communities.
+Due to the genuine interdisciplinary nature of the present article and its pedagogical aspect, we believe that it will be of interest to a wide audience within the physics and chemistry communities.
-We hope that the editors and the reviewers of JPCM will find this topical review enjoyable and educative.
+We hope that the editors and the reviewers of \textit{JPCM} will find this topical review enjoyable and educative.
 
 We suggest Paola Gori-Giorgi, Jeppe Olsen, So Hirata, Peter Knowles, and Kieron Burke as potential referees.
 We look forward to hearing from you soon.

Manuscript/EPAWTFT.tex

@@ -920,15 +920,6 @@ The Taylor expansion of the RMP energy can then be evaluated to obtain the $k$th
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % RADIUS OF CONVERGENCE PLOTS
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{figure}[htb]
-	\includegraphics[width=\linewidth]{fig5}
-	\caption{
-	Radius of convergence $r_c$ for the RMP ground state (red), the UMP ground state (blue), and the UMP excited state (orange) 
-    series as functions of the ratio $U/t$.
-	\label{fig:RadConv}}
-\end{figure}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
 The RMP series is convergent for $U = 3.5\,t$ with $\rc > 1$, as illustrated for the individual terms at each order
 of perturbation in Fig.~\ref{subfig:RMP_cvg}.
 In contrast, for $U = 4.5t$ one finds $\rc < 1$, and the RMP series becomes divergent.
@@ -940,6 +931,19 @@ outside this cylinder.
 In both cases, the EP connects the ground state with the doubly-excited state, and thus the convergence behaviour
 for the two states using the ground-state RHF orbitals is identical.
 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% RADIUS OF CONVERGENCE PLOTS
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{figure}[htb]
+	\includegraphics[width=\linewidth]{fig5}
+	\caption{
+	Radius of convergence $r_c$ for the RMP ground state (red), the UMP ground state (blue), and the UMP excited state (orange) 
+    series as functions of the ratio $U/t$.
+	\label{fig:RadConv}}
+\end{figure}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
 %%% FIG 3 %%%
 \begin{figure*}
 	\begin{subfigure}{0.32\textwidth}
@@ -1244,7 +1248,7 @@ states which share the symmetry of the ground state,\cite{Goodson_2004} and are
 		(\subref{subfig:rmp_cp}) Exact critical points with $t=0$ occur on the negative real $\lambda$ axis (dashed).
 		(\subref{subfig:rmp_cp_surf}) Modelling a finite basis using $t=0.1$ yields complex-conjugate EPs close to the
 		real axis, giving a sharp avoided crossing on the real axis (solid).
-		(\subref{subfig:rmp_ep_to_cp}) Convergence of the ground-state EP onto the real axis in the \trash{exact} limit $t \to 0$.
+		(\subref{subfig:rmp_ep_to_cp}) Convergence of the ground-state EP onto the real axis in the limit $t \to 0$.
 	\label{fig:RMP_cp}}
 \end{figure*}
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