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%\beamersetuncovermixins{\opaqueness<1>{25}}{\opaqueness<2->{15}}
\title{Folding vs Moments; \\Background studies}  
\author{\underline{Marcin Chrzaszcz}$^{1,2}$, Nicola Serra$^{1}$, Espen Bowen$^{1}$}
\date{\today} 

\begin{document}

{
\institute{$^1$ University of Zurich, $^2$ Institute of Nuclear Physics}
\setbeamertemplate{footline}{} 
\begin{frame}
\logo{
\vspace{2 mm}
\includegraphics[height=1cm,keepaspectratio]{images/uzh.jpg}~
\includegraphics[height=1cm,keepaspectratio]{images/ifj.png}}

  \titlepage
\end{frame}
}
\institute{UZH,IFJ} 

\section[Outline]{}
\begin{frame}
\tableofcontents
\end{frame}

\section{Reminder}
\begin{frame}\frametitle{Plan}
Method of moments:
\begin{enumerate}
\item On the last meeting I've showed the background moments in different $q^{2}$ bins and mass bins.
\item We did an update with smaller binning. 
\item Also we compared 
\item Many thanks to Tom for checking all my calculations.
\end{enumerate}
For today:
\begin{enumerate}
\item How this method behaves in terms of background?
\end{enumerate}

\end{frame}
\section{Fit Wars}
\begin{frame}\frametitle{Fit vs MM}
{~}
Not so long ago, in a building far away:\\{~}\\
A test was perform
\begin{itemize}
\item Simulated toys according to SM PDF. 
\item Fold fit, calculated the moments, compare the error on pull distribution.
\item See how the error changes with number of events.
\item Make pull plots for each case as Tom asked.
\end{itemize}



\end{frame}


\begin{frame}\frametitle{Obtained sensitivity I}
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.22]{plots_19/S4.png}
\column{2.5in}
\includegraphics[scale=0.22]{plots_19/S5.png}


\end{columns}
\begin{itemize}
\item Folding wins slightly over MM.
\end{itemize}


\end{frame}


\begin{frame}\frametitle{Obtained sensitivity II}
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.22]{plots_19/S7.png}
\column{2.5in}
\includegraphics[scale=0.22]{plots_19/S8.png}


\end{columns}
\begin{itemize}
\item Folding wins slightly over MM.
\end{itemize}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Scatter plots I}
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.22]{scater/scater_S4_400.png}
\column{2.5in}
\includegraphics[scale=0.22]{scater/scater_S4_600.png}


\end{columns}
\begin{itemize}
\item Highly correlated, everything in order.
\item Far more plots of this in the backups.
\end{itemize}

\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Scatter plots II }
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.22]{scater/scater_S4_800.png}
\column{2.5in}
\includegraphics[scale=0.22]{scater/scater_S4_1000.png}


\end{columns}
\begin{itemize}
\item Highly correlated, everything in order.
\item Far more plots of this in the backups.
\end{itemize}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull distributions I }
{~}

\begin{itemize}
\item For each point(n of events) we made a pull distribution.
\end{itemize}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.22]{plots_19/poolS4_950.png}
\column{2.5in}
\includegraphics[scale=0.22]{plots_19/poolS5_450.png}


\end{columns}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pool distributions II }
{~}
\begin{center}

\begin{columns}
\column{2.5in}
\begin{center}
\includegraphics[scale=0.16]{plots_19/PS4.png}\\
\includegraphics[scale=0.16]{plots_19/PS7.png}
\end{center}

\column{2.5in}
\begin{center}
\includegraphics[scale=0.16]{plots_19/PS5.png}\\
\includegraphics[scale=0.16]{plots_19/PS8.png}
\end{center}
\end{columns}
\end{center}

\end{frame}

\section{Background}

\begin{frame}\frametitle{Bck moments}
\begin{itemize}
\item Last time I showed the moments in the side-bands. \\
Today I prepared update with smaller $q^{2}$ binning:\\
$0.1, 0.98, 1.1, 2, 4, 6, 8, 11, 11.75, 12.5, 15, 17, 18$
\end{itemize}

\end{frame}
\begin{frame}\frametitle{Bck moments}
\only<1>
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\begin{center}
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\column{2.5in}
 \includegraphics[scale=0.16]{plots_folder/Q[0_1-0_98]_Fl1.png}\\
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  \includegraphics[scale=0.16]{plots_folder/Q[0_1-0_98]_Fl4.png}
\end{columns}
\end{center}
}



\end{frame}


\begin{frame}\frametitle{Bck moments}
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\begin{center}
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\end{columns}
\end{center}
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\end{frame}

\begin{frame}\frametitle{Bck moments}
\only<1>
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\begin{center}
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\end{columns}
\end{center}
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\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}\frametitle{Bck moments}
\only<1>
{
\begin{center}
\begin{columns}

\column{2.5in}
 \includegraphics[scale=0.16]{plots_folder/Q[1_1-2]_Fl1.png}\\
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  \includegraphics[scale=0.16]{plots_folder/Q[1_1-2]_Fl4.png}
\end{columns}
\end{center}
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\end{frame}


\begin{frame}\frametitle{Bck moments}
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\begin{center}
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\end{columns}
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\end{frame}

\begin{frame}\frametitle{Bck moments}
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\begin{center}
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    \includegraphics[scale=0.16]{plots_folder/Q[1_1-2]_S6c.png}\\

\end{columns}
\end{center}
}


\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}\frametitle{Bck moments}
\only<1>
{
\begin{center}
\begin{columns}

\column{2.5in}
 \includegraphics[scale=0.16]{plots_folder/Q[2-4]_Fl1.png}\\
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\end{columns}
\end{center}
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\end{frame}


\begin{frame}\frametitle{Bck moments}
\only<1>
{
\begin{center}
\begin{columns}

\column{2.5in}
 \includegraphics[scale=0.16]{plots_folder/Q[2-4]_S3.png}\\
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\end{columns}
\end{center}
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\end{frame}

\begin{frame}\frametitle{Bck moments}
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\begin{center}
\begin{columns}

\column{2.5in}
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    \includegraphics[scale=0.16]{plots_folder/Q[2-4]_S6c.png}\\

\end{columns}
\end{center}
}


\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}\frametitle{Bck moments}
\only<1>
{
\begin{center}
\begin{columns}

\column{2.5in}
 \includegraphics[scale=0.16]{plots_folder/Q[4-6]_Fl1.png}\\
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\end{columns}
\end{center}
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\end{frame}


\begin{frame}\frametitle{Bck moments}
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\begin{center}
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\column{2.5in}
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\end{columns}
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\end{frame}

\begin{frame}\frametitle{Bck moments}
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\begin{center}
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    \includegraphics[scale=0.16]{plots_folder/Q[4-6]_S6c.png}\\

\end{columns}
\end{center}
}


\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}\frametitle{Bck moments}
\only<1>
{
\begin{center}
\begin{columns}

\column{2.5in}
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\end{columns}
\end{center}
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\end{frame}


\begin{frame}\frametitle{Bck moments}
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\begin{center}
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\column{2.5in}
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\end{columns}
\end{center}
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\end{frame}

\begin{frame}\frametitle{Bck moments}
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\begin{center}
\begin{columns}

\column{2.5in}
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    \includegraphics[scale=0.16]{plots_folder/Q[6-8]_S6c.png}\\

\end{columns}
\end{center}
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\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}\frametitle{Bck moments}
\only<1>
{
\begin{center}
\begin{columns}

\column{2.5in}
 \includegraphics[scale=0.16]{plots_folder/Q[11_75-12_5]_Fl1.png}\\
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\end{columns}
\end{center}
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\end{frame}


\begin{frame}\frametitle{Bck moments}
\only<1>
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\begin{center}
\begin{columns}

\column{2.5in}
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\end{columns}
\end{center}
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\end{frame}

\begin{frame}\frametitle{Bck moments}
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\begin{center}
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\end{columns}
\end{center}
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\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}\frametitle{Bck moments}
\only<1>
{
\begin{center}
\begin{columns}

\column{2.5in}
 \includegraphics[scale=0.16]{plots_folder/Q[11-11_75]_Fl1.png}\\
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\end{frame}


\begin{frame}\frametitle{Bck moments}
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\end{frame}

\begin{frame}\frametitle{Bck moments}
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\end{columns}
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\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}\frametitle{Bck moments}
\only<1>
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\begin{center}
\begin{columns}

\column{2.5in}
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\end{frame}


\begin{frame}\frametitle{Bck moments}
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\end{frame}

\begin{frame}\frametitle{Bck moments}
\only<1>
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\begin{center}
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\column{2.5in}
 \includegraphics[scale=0.16]{plots_folder/Q[15-17]_S7.png}\\
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    \includegraphics[scale=0.16]{plots_folder/Q[15-17]_S6c.png}\\

\end{columns}
\end{center}
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\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}\frametitle{Bck moments}
\only<1>
{
\begin{center}
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\column{2.5in}
 \includegraphics[scale=0.16]{plots_folder/Q[17-19]_Fl1.png}\\
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\end{center}
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\end{frame}


\begin{frame}\frametitle{Bck moments}
\only<1>
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\column{2.5in}
 \includegraphics[scale=0.16]{plots_folder/Q[17-19]_S3.png}\\
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\end{frame}

\begin{frame}\frametitle{Bck moments}
\only<1>
{
\begin{center}
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\column{2.5in}
 \includegraphics[scale=0.16]{plots_folder/Q[17-19]_S7.png}\\
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\end{frame}
\section{Summary}
\begin{frame}\frametitle{Conclusions}
\begin{itemize}
\item Folding a bit better than Moments.
\item For robustness of the result we want to publish both methods
\begin{enumerate}
\item Folding is gives smaller errors
\item MM has is less sensitive to background.
\end{enumerate}
\item For sure we will look better in paper if we say both methods got the same.
\item Side-bands have some structure $\rightarrow$ could we missed some background?
\end{itemize}


\end{frame}



\begin{frame}\frametitle{To do}
\begin{itemize}
\item Explore the bck that we could missed.
\item We are making the situation more real life: add bck and swave pollution
\item Study then the errors.
\item Access the systematics from swave.
\item Do the unfolding.
\item Perform the stress test.
\end{itemize}


\end{frame}





\begin{frame}\frametitle{backup}


\Huge BACKUP
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Scatter plots I}
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{scater/scater_S4_250.png}\\
\includegraphics[scale=0.16]{scater/scater_S4_300.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{scater/scater_S4_350.png}\\
\includegraphics[scale=0.16]{scater/scater_S4_400.png}

\end{columns}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Scatter plots I}
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{scater/scater_S4_450.png}\\
\includegraphics[scale=0.16]{scater/scater_S4_500.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{scater/scater_S4_550.png}\\
\includegraphics[scale=0.16]{scater/scater_S4_600.png}

\end{columns}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Scatter plots I}
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{scater/scater_S4_650.png}\\
\includegraphics[scale=0.16]{scater/scater_S4_700.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{scater/scater_S4_750.png}\\
\includegraphics[scale=0.16]{scater/scater_S4_800.png}

\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Scatter plots I}
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{scater/scater_S4_850.png}\\
\includegraphics[scale=0.16]{scater/scater_S4_900.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{scater/scater_S4_950.png}\\
\includegraphics[scale=0.16]{scater/scater_S4_1000.png}

\end{columns}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Scatter plots I}
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{scater/scater_S5_250.png}\\
\includegraphics[scale=0.16]{scater/scater_S5_300.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{scater/scater_S5_350.png}\\
\includegraphics[scale=0.16]{scater/scater_S5_400.png}

\end{columns}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Scatter plots I}
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{scater/scater_S5_450.png}\\
\includegraphics[scale=0.16]{scater/scater_S5_500.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{scater/scater_S5_550.png}\\
\includegraphics[scale=0.16]{scater/scater_S5_600.png}

\end{columns}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Scatter plots I}
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{scater/scater_S5_650.png}\\
\includegraphics[scale=0.16]{scater/scater_S5_700.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{scater/scater_S5_750.png}\\
\includegraphics[scale=0.16]{scater/scater_S5_800.png}

\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Scatter plots I}
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{scater/scater_S5_850.png}\\
\includegraphics[scale=0.16]{scater/scater_S5_900.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{scater/scater_S5_950.png}\\
\includegraphics[scale=0.16]{scater/scater_S5_1000.png}

\end{columns}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Scatter plots I}
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{scater/scater_S7_250.png}\\
\includegraphics[scale=0.16]{scater/scater_S7_300.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{scater/scater_S7_350.png}\\
\includegraphics[scale=0.16]{scater/scater_S7_400.png}

\end{columns}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Scatter plots I}
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{scater/scater_S7_450.png}\\
\includegraphics[scale=0.16]{scater/scater_S7_500.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{scater/scater_S7_550.png}\\
\includegraphics[scale=0.16]{scater/scater_S7_600.png}

\end{columns}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Scatter plots I}
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{scater/scater_S7_650.png}\\
\includegraphics[scale=0.16]{scater/scater_S7_700.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{scater/scater_S7_750.png}\\
\includegraphics[scale=0.16]{scater/scater_S7_800.png}

\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Scatter plots I}
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{scater/scater_S7_850.png}\\
\includegraphics[scale=0.16]{scater/scater_S7_900.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{scater/scater_S7_950.png}\\
\includegraphics[scale=0.16]{scater/scater_S7_1000.png}

\end{columns}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Scatter plots I}
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{scater/scater_S8_250.png}\\
\includegraphics[scale=0.16]{scater/scater_S8_300.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{scater/scater_S8_350.png}\\
\includegraphics[scale=0.16]{scater/scater_S8_400.png}

\end{columns}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Scatter plots I}
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{scater/scater_S8_450.png}\\
\includegraphics[scale=0.16]{scater/scater_S8_500.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{scater/scater_S8_550.png}\\
\includegraphics[scale=0.16]{scater/scater_S8_600.png}

\end{columns}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Scatter plots I}
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{scater/scater_S8_650.png}\\
\includegraphics[scale=0.16]{scater/scater_S8_700.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{scater/scater_S8_750.png}\\
\includegraphics[scale=0.16]{scater/scater_S8_800.png}

\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Scatter plots I}
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{scater/scater_S8_850.png}\\
\includegraphics[scale=0.16]{scater/scater_S8_900.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{scater/scater_S8_950.png}\\
\includegraphics[scale=0.16]{scater/scater_S8_1000.png}

\end{columns}
\end{frame}









%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull distributions I }
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{plots_19/poolS4_250.png}\\
\includegraphics[scale=0.16]{plots_19/poolS4_300.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{plots_19/poolS4_350.png}\\
\includegraphics[scale=0.16]{plots_19/poolS4_400.png}

\end{columns}




\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull distributions I }
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{plots_19/poolS4_450.png}\\
\includegraphics[scale=0.16]{plots_19/poolS4_500.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{plots_19/poolS4_550.png}\\
\includegraphics[scale=0.16]{plots_19/poolS4_600.png}

\end{columns}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull distributions I }
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{plots_19/poolS4_650.png}\\
\includegraphics[scale=0.16]{plots_19/poolS4_700.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{plots_19/poolS4_750.png}\\
\includegraphics[scale=0.16]{plots_19/poolS4_800.png}

\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull distributions I }
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{plots_19/poolS4_850.png}\\
\includegraphics[scale=0.16]{plots_19/poolS4_900.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{plots_19/poolS4_950.png}\\
\includegraphics[scale=0.16]{plots_19/poolS4_1000.png}

\end{columns}



\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull distributions I }
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{plots_19/poolS5_450.png}\\
\includegraphics[scale=0.16]{plots_19/poolS5_500.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{plots_19/poolS5_550.png}\\
\includegraphics[scale=0.16]{plots_19/poolS5_600.png}

\end{columns}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull distributions I }
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{plots_19/poolS5_650.png}\\
\includegraphics[scale=0.16]{plots_19/poolS5_700.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{plots_19/poolS5_750.png}\\
\includegraphics[scale=0.16]{plots_19/poolS5_800.png}

\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull distributions I }
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{plots_19/poolS5_850.png}\\
\includegraphics[scale=0.16]{plots_19/poolS5_900.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{plots_19/poolS5_950.png}\\
\includegraphics[scale=0.16]{plots_19/poolS5_1000.png}

\end{columns}



\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull distributions I }
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{plots_19/poolS4F_250.png}\\
\includegraphics[scale=0.16]{plots_19/poolS4F_300.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{plots_19/poolS4F_350.png}\\
\includegraphics[scale=0.16]{plots_19/poolS4F_400.png}

\end{columns}




\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull distributions I }
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{plots_19/poolS4F_450.png}\\
\includegraphics[scale=0.16]{plots_19/poolS4F_500.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{plots_19/poolS4F_550.png}\\
\includegraphics[scale=0.16]{plots_19/poolS4F_600.png}

\end{columns}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull distributions I }
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{plots_19/poolS4F_650.png}\\
\includegraphics[scale=0.16]{plots_19/poolS4F_700.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{plots_19/poolS4F_750.png}\\
\includegraphics[scale=0.16]{plots_19/poolS4F_800.png}

\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull distributions I }
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{plots_19/poolS4F_850.png}\\
\includegraphics[scale=0.16]{plots_19/poolS4F_900.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{plots_19/poolS4F_950.png}\\
\includegraphics[scale=0.16]{plots_19/poolS4F_1000.png}

\end{columns}



\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull distributions I }
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{plots_19/poolS5F_450.png}\\
\includegraphics[scale=0.16]{plots_19/poolS5F_500.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{plots_19/poolS5F_550.png}\\
\includegraphics[scale=0.16]{plots_19/poolS5F_600.png}

\end{columns}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull distributions I }
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{plots_19/poolS5F_650.png}\\
\includegraphics[scale=0.16]{plots_19/poolS5F_700.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{plots_19/poolS5F_750.png}\\
\includegraphics[scale=0.16]{plots_19/poolS5F_800.png}

\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Pull distributions I }
{~}
\begin{columns}
\column{2.5in}

\includegraphics[scale=0.16]{plots_19/poolS5F_850.png}\\
\includegraphics[scale=0.16]{plots_19/poolS5F_900.png}\\
\column{2.5in}
\includegraphics[scale=0.16]{plots_19/poolS5F_950.png}\\
\includegraphics[scale=0.16]{plots_19/poolS5F_1000.png}

\end{columns}
\end{frame}




\end{document}