From 35ce3da68e51c95125faaa301957718f5097ea45 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Tue, 21 Nov 2023 17:38:18 +0100
Subject: Added subfigure captions in Fig. 1 at referee's recommendation.

---
 2-point.tex | 36 ++++++++++++++++++++++++++++++------
 1 file changed, 30 insertions(+), 6 deletions(-)

diff --git a/2-point.tex b/2-point.tex
index 6acc975..d5ef022 100644
--- a/2-point.tex
+++ b/2-point.tex
@@ -226,19 +226,43 @@ The gradient and Hessian at a stationary point are then
 where $\partial=\frac\partial{\partial\mathbf s}$ denotes the derivative with respect to $\mathbf s$.
 
 \begin{figure}
-  \includegraphics{figs/spectrum_saddle.pdf}
+  \begin{minipage}[t]{0.31\textwidth}
+    \centering
+    \includegraphics{figs/spectrum_saddle.pdf}\\
+    \footnotesize\textbf{extensive saddle}
+  \end{minipage}
   \hfill
-  \includegraphics{figs/spectrum_marginal.pdf}
+  \begin{minipage}[t]{0.31\textwidth}
+    \centering
+    \includegraphics{figs/spectrum_marginal.pdf}\\
+    \footnotesize\textbf{marginal minimum}
+  \end{minipage}
   \hfill
-  \includegraphics{figs/spectrum_minimum.pdf}\\
+  \begin{minipage}[t]{0.31\textwidth}
+    \centering
+    \includegraphics{figs/spectrum_minimum.pdf}\\
+    \footnotesize\textbf{stable minimum}
+  \end{minipage}
 
   \vspace{1em}
 
-  \includegraphics{figs/spectrum_saddle_2.pdf}
+  \begin{minipage}[t]{0.31\textwidth}
+    \centering
+    \includegraphics{figs/spectrum_saddle_2.pdf}\\
+    \footnotesize\textbf{oriented saddle}
+  \end{minipage}
   \hfill
-  \includegraphics{figs/spectrum_minimum_2.pdf}
+  \begin{minipage}[t]{0.31\textwidth}
+    \centering
+    \includegraphics{figs/spectrum_minimum_2.pdf}\\
+    \footnotesize\textbf{oriented minimum}
+  \end{minipage}
   \hfill
-  \includegraphics{figs/spectrum_saddle_3.pdf}
+  \begin{minipage}[t]{0.31\textwidth}
+    \centering
+    \includegraphics{figs/spectrum_saddle_3.pdf}\\
+    \footnotesize\textbf{oriented index-one saddle}
+  \end{minipage}
 
   \caption{
     Illustration of the interpretation of the stability $\mu$, which sets the
-- 
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