From f6cf5cb7dddef679ee40d4ce541632bb6b751c10 Mon Sep 17 00:00:00 2001
From: Youssef Kashef <youssef.kashef@gmail.com>
Date: Thu, 19 May 2022 14:51:26 +0200
Subject: [PATCH] fix layout of cdf figures in notes

---
 notes/04_density-transform/2_cdf.tex               | 8 ++++----
 notes/04_density-transform/3_density-transform.tex | 6 +++---
 2 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/notes/04_density-transform/2_cdf.tex b/notes/04_density-transform/2_cdf.tex
index dc0ccfd..24e097f 100644
--- a/notes/04_density-transform/2_cdf.tex
+++ b/notes/04_density-transform/2_cdf.tex
@@ -4,10 +4,10 @@ \subsection{The Inverse CDF technique}
 
 \only<1,2>{
 \begin{center}
-\begin{minipage}{0.45\textwidth}
+\begin{minipage}{\slidesonly{0.45}\notesonly{0.3}\textwidth}
 	\includegraphics[width=0.99\textwidth]{img/gauss_pdfcdf}
 \end{minipage}
-\begin{minipage}{0.45\textwidth}
+\begin{minipage}{\slidesonly{0.45}\notesonly{0.3}\textwidth}
 	\includegraphics[width=0.99\textwidth]{img/laplacian_pdfcdf}
 \end{minipage}
 \end{center}
@@ -21,10 +21,10 @@ \subsection{The Inverse CDF technique}
 
 \only<3>{
 \begin{center}
-\begin{minipage}{0.45\textwidth}
+\begin{minipage}{\slidesonly{0.45}\notesonly{0.3}\textwidth}
 	\includegraphics[width=0.99\textwidth]{img/gauss_cdfmarginals}
 \end{minipage}
-\begin{minipage}{0.45\textwidth}
+\begin{minipage}{\slidesonly{0.45}\notesonly{0.3}\textwidth}
 	\includegraphics[width=0.99\textwidth]{img/laplacian_cdfmarginals}
 \end{minipage}
 \end{center}
diff --git a/notes/04_density-transform/3_density-transform.tex b/notes/04_density-transform/3_density-transform.tex
index 8c9b5b2..6b1bbb3 100644
--- a/notes/04_density-transform/3_density-transform.tex
+++ b/notes/04_density-transform/3_density-transform.tex
@@ -23,7 +23,7 @@ \subsubsection{Setting}
 
 \pause
 
-and let $\vec g(\vec x) =\notesonly{ ( g_1(\vec x), g_2(\vec x))^\top =} ( g_1(x_1, x_2), g_2(x_1, x_2))^\top = (u_1, u_2)^\top = \vec u$ be a one-to-one mapping/transformation.
+and let $\vec g(\vec x) = ( g_1(x_1, x_2), g_2(x_1, x_2))^\top = (u_1, u_2)^\top = \vec u$ be a one-to-one mapping/transformation.
 
 \svspace{-3mm}
 
@@ -80,7 +80,7 @@ \subsubsection{Setting}
 =\int_{u(\Omega)} f(~\underbrace{\vec g^{-1}(\vec u)}_{= \vec x}~) \frac{1}{\left|\det \frac{\partial \vec{u}}{\partial \vec{x}} \right|} \mathbf{d}\vec{u},
 \end{equation}
 
-\notesonly{where $\vec g^{-1}(\vec u) = \vec x$ is the inverse mapping.}
+\notesonly{where $\vec g^{-1}(\vec u) = \vec x$ is the inverse mapping which we assume to exist and to be differentiable.}
 
 
 \end{frame}
@@ -248,7 +248,7 @@ \subsubsection{Mapping the vectors}
 - We use the same procedure on ${\color{red}\vec e_2}$:
 
 \begin{equation}
-u: {\color{red}\vec e_2} \mapsto 
+\vec g: {\color{red}\vec e_2} \mapsto 
 \rmat{
 \frac{\partial u_1}{\partial x_2} \Delta x_2\\[0.2cm]
 \frac{\partial u_2}{\partial x_2} \Delta x_2