Minor changes to presentation

src/2025-03-28/presentation.tex

@@ -390,8 +390,8 @@ Homotopy Continuation Methods}
             \end{array}\right] \\
             G(\bm{x}) &= \left[
                 \begin{array}{c}
-                    x_1 - y_1\\
+                    x_1\\
-                    x_2 - y_2
+                    x_2
             \end{array}\right]\\
             H(\bm{x}, t) &= (1-t)G(\bm{x}) + tF(\bm{x})
         \end{align*}
@@ -485,6 +485,17 @@ func decode(y) {
 \begin{frame}[fragile]
     \frametitle{Simulation results}
 
+    \vspace*{-5mm}
+
+    \begin{itemize}
+        \item Simulation using the all-zeros codeword
+        \item Newton homotopy:
+            \begin{gather*}
+                G(\bm{x}) = F(x) - F(\bm{y}) \hspace{5mm} \Rightarrow
+                \hspace{5mm} H(\bm{x}) = F(\bm{x}) - (1 - t) F(\bm{y})
+            \end{gather*}
+    \end{itemize}
+
     \begin{figure}[H]
         \centering
 
@@ -503,17 +514,9 @@ func decode(y) {
                         legend pos= south west,
                         xmax=6
                     ]
-                    % \addplot+[scol0, densely dashed, mark=none, line
+
-                    % width=1pt, forget plot]
+                    \addplot+[scol0, densely dashed, mark=none, line
-                    %     table[col sep=comma, x=SNR, y=FER]
+                    width=1pt, forget plot]
-                    %         {\res/bch_31_26_hc.csv};
-                    % \addplot+[scol0, mark=none, line width=1pt]
-                    %     table[col sep=comma, x=SNR, y=BER]
-                    %         {\res/bch_31_26_hc.csv};
-                    % \addlegendentry{Homotopy continuation}
-                    %
-                    \addplot+[scol0, densely dashed, mark=none, line width=1pt,
-                    forget plot]
                     table[col sep=comma, x=SNR, y=FER]
                     {\res/bch_31_26_hc.csv};
                     \addplot+[scol0, mark=none, line width=1pt]
@@ -532,19 +535,8 @@ func decode(y) {
                     {\res/bch_31_26_proximal.csv};
                     \addlegendentry{Proximal decoding}
 
-                    % \addplot+[scol2, densely dashed, mark=none, line
-                    % width=1pt, forget plot]
-                    %     table[col sep=comma, x=SNR, y=FER]
-                    %         {\res/bch_31_26_ml.csv};
-                    % \addplot+[scol2, mark=none, line width=1pt]
-                    %     table[col sep=comma, x=SNR, y=BER]
-                    %         {\res/bch_31_26_ml.csv};
                     \addlegendentry{ML}
 
-                    % \addplot+[mark=none, line width=1pt]
-                    %     table[col sep=comma, x=SNR, y=DFR]
-                    %         {\res/bch_31_11.csv};
-                    % \addlegendentry{DFR}
                 \end{axis}
             \end{tikzpicture}
 
@@ -553,7 +545,7 @@ func decode(y) {
         \begin{subfigure}[c]{0.48\textwidth}
             \centering
 
-            \vspace*{-20mm}
+            \vspace*{-17mm}
 
             \begin{tabular}{rl|ccccc}
                 Parameter & Value \\ \hline
@@ -565,15 +557,10 @@ func decode(y) {
             \end{tabular}
 
             \bigskip
+            \smallskip
 
-            \begin{itemize}
+            (No comprehensive investigation into choice of parameters
-                \item Newton homotopy:
+            completed yet)
-                    \begin{align*}
-                        G(\bm{x}) &= F(x) - F(\bm{y}) \\
-                        H(\bm{x}) &= (1-t)G(\bm{x}) - tF(\bm{x})\\
-                        &= F(\bm{x}) - (1 - t) F(\bm{y})
-                    \end{align*}
-            \end{itemize}
         \end{subfigure}
     \end{figure}
 \end{frame}