Partial version 01
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figs/Poster.png
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figs/bul.png
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figs/bulandhex.png
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figs/chemin-rythm1.png
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figs/chemin-rythm2.png
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figs/eulers-tonnetz.png
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figs/foam2D-disordered.png
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figs/foam2D-grain-boundaries.png
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figs/foam2D-honeycomb.png
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figs/hex.png
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figs/lauriesfoam.png
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figs/speaker.png
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figs/visual-prog.png
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277
presentation.tex
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@ -26,7 +26,7 @@
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\defaultfontfeatures{Scale=MatchLowercase}
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\defaultfontfeatures{Scale=MatchLowercase}
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\setromanfont[Mapping=tex−text]{Linux Libertine O}
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\setromanfont[Mapping=tex−text]{Linux Libertine O}
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\setsansfont [Mapping=tex−text]{Ubuntu}
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\setsansfont [Mapping=tex−text]{Ubuntu}
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\setmonofont [Mapping=tex−text]{Ubuntu Mono}
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\setmonofont [Mapping=tex−text]{Inconsolata}
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|
|
||||||
\newcommand{\ircam}{Ircam}
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\newcommand{\ircam}{Ircam}
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||||||
\newcommand{\lps}{Lps}
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\newcommand{\lps}{Lps}
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||||||
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@ -34,8 +34,10 @@
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||||||
\newcommand{\mlys}{Modalys}
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\newcommand{\mlys}{Modalys}
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||||||
\newcommand{\om}{OpenMusic}
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\newcommand{\om}{OpenMusic}
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||||||
\newcommand{\mpri}{Mpri}
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\newcommand{\mpri}{Mpri}
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||||||
|
|
||||||
\newcommand{\todo}{\fbox{\texttt{todo}}}
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\newcommand{\todo}{\fbox{\texttt{todo}}}
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||||||
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\newcommand{\sonif}[2]{%
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||||||
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\parbox{2ex}{\includegraphics[height=2ex]{figs/speaker}}%
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||||||
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\hspace{.5em}\emph{#2}}
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||||||
|
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||||||
\hyphenation{con-cen-trent}
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\hyphenation{con-cen-trent}
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||||||
\AtBeginSection[]{
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\AtBeginSection[]{
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||||||
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@ -43,14 +45,16 @@
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||||||
}
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}
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||||||
|
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||||||
\begin{document}
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\begin{document}
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\title{De la sonification à la « musification » de systèmes complexes}
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\title{De la sonification à la « musification »\\de systèmes complexes}
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\author{Martin Potier}
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\subtitle{Présentation de stage}
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\author{Martin Potier\\
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||||||
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{\scriptsize MPRI, Université Paris Diderot}}
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\date{6 septembre 2012}
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\date{6 septembre 2012}
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\institute{{\scriptsize Stage encadré par :}\\
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\institute{
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{\small\textbf{Moreno Andreatta} et \textbf{Jean-Louis Giavitto}}\\
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{\small\textbf{Moreno Andreatta} et \textbf{Jean-Louis Giavitto}}\\
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Institut de Recherche et Coordination Acoustique/Musique, CNRS \and
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Équipe Représentation Musicales, Institut de Recherche et Coordination Acoustique/Musique, CNRS \and
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||||||
{\small\textbf{Wiebke Drenckhan}}\\
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{\small\textbf{Wiebke Drenckhan}}\\
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||||||
Laboratoire de Physique des Solides, CNRS}
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Laboratoire de Physique des Solides, Université Paris Sud, CNRS}
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||||||
|
|
||||||
% Each presentation will last 30 minutes (20 minutes of presentation + 10
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% Each presentation will last 30 minutes (20 minutes of presentation + 10
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||||||
% minutes of questions). A video-projector will be available.
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% minutes of questions). A video-projector will be available.
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||||||
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@ -64,16 +68,36 @@ Laboratoire de Physique des Solides, CNRS}
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||||||
\section{Motivations}
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\section{Motivations}
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% Trouver des lois d'un système complexe sans connaissance a priori
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% Trouver des lois d'un système complexe sans connaissance a priori
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\begin{frame}{Comprendre l'évolution d'une mousse liquide}
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\begin{frame}{Comprendre l'évolution d'une mousse liquide}
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% video
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Vidéo
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||||||
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% movie
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||||||
\end{frame}
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\end{frame}
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||||||
|
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||||||
\begin{frame}{Comprendre l'évolution d'une mousse liquide (suite)}
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\begin{frame}{Comprendre l'évolution d'une mousse liquide (suite)}
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||||||
% video
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\begin{columns}
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||||||
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\column{.3\textwidth}
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||||||
|
\includegraphics[width=\textwidth]{figs/foam2D-honeycomb}
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||||||
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\column{.3\textwidth}
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||||||
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\includegraphics[width=\textwidth]{figs/foam2D-grain-boundaries}
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||||||
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\column{.3\textwidth}
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||||||
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\includegraphics[width=\textwidth]{figs/foam2D-disordered}
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||||||
|
\end{columns}
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||||||
|
|
||||||
|
\pause
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||||||
|
\begin{center}
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||||||
|
\includegraphics[width=.6\textwidth]{figs/lauriesfoam}
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||||||
|
|
||||||
|
10 ans pour obtenir le modèle
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||||||
|
\end{center}
|
||||||
\end{frame}
|
\end{frame}
|
||||||
|
|
||||||
\section{De la sonification\ldots}
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\section{De la sonification\ldots}
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||||||
\begin{frame}{Un domaine nouveau}
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\begin{frame}{Un domaine nouveau}
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||||||
\centering
|
\begin{quote}
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||||||
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« Sonification is the transformation of data relations into perceived
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relations in an acoustic signal for the purposes of facilitating
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communication or interpretation. »\hfill\textbf{Kramer~1999}
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||||||
|
\end{quote}
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||||||
|
\begin{center}
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||||||
\usebeamercolor{frametitle}
|
\usebeamercolor{frametitle}
|
||||||
\begin{tikzpicture}[align=center, every node/.style={fg,auto}]
|
\begin{tikzpicture}[align=center, every node/.style={fg,auto}]
|
||||||
\node (phystate) {État local du système};
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\node (phystate) {État local du système};
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||||||
|
@ -81,7 +105,7 @@ Laboratoire de Physique des Solides, CNRS}
|
||||||
\node (sonrel) [right=of phystate] {Relations sonores\\(analogiques)};
|
\node (sonrel) [right=of phystate] {Relations sonores\\(analogiques)};
|
||||||
\node (sonobs) [below=of sonrel] {Objets sonores};
|
\node (sonobs) [below=of sonrel] {Objets sonores};
|
||||||
\node (qb) at (barycentric cs:phyobs=1,sonobs=1)
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\node (qb) at (barycentric cs:phyobs=1,sonobs=1)
|
||||||
[black,yshift=-1cm,font=\scriptsize] {mappings\\sonification/musification};
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[black,yshift=-1cm,font=\scriptsize] {mappings\\sonification};
|
||||||
|
|
||||||
\draw[thick,->, dotted] (phyobs) -- (phystate);
|
\draw[thick,->, dotted] (phyobs) -- (phystate);
|
||||||
\draw[black,thick,->] (phyobs) |- (qb) -| (sonobs);
|
\draw[black,thick,->] (phyobs) |- (qb) -| (sonobs);
|
||||||
|
@ -89,14 +113,32 @@ Laboratoire de Physique des Solides, CNRS}
|
||||||
to node [swap,text width=21mm] {perception (IHM)} (sonrel);
|
to node [swap,text width=21mm] {perception (IHM)} (sonrel);
|
||||||
\draw[black,thick,->,dotted] (sonrel) to node [swap] {?} (phystate);
|
\draw[black,thick,->,dotted] (sonrel) to node [swap] {?} (phystate);
|
||||||
\end{tikzpicture}
|
\end{tikzpicture}
|
||||||
|
\end{center}
|
||||||
\end{frame}
|
\end{frame}
|
||||||
|
|
||||||
\begin{frame}{M$_1$ : synthèse modale, timbre et ordre}
|
\begin{frame}{\sonif{sound/M1}{M$_1$ : synthèse modale, timbre et ordre (30 s)}}
|
||||||
|
Utilise Modalys (outil de l'IRCAM) pour la synthèse de timbre
|
||||||
|
|
||||||
|
\begin{tabular}{|l|l|}
|
||||||
|
Nombre de voisines & $\rightarrow$ Fréquence \\
|
||||||
|
Nombre de voisines & $\rightarrow$ Fréquence \\
|
||||||
|
Nombre de voisines & $\rightarrow$ Fréquence \\
|
||||||
|
\end{tabular}
|
||||||
|
|
||||||
|
Modalys simule 900 oscillateurs (un par bulle).
|
||||||
|
|
||||||
|
On peut entendre les configurations spatiales :
|
||||||
|
\begin{description}
|
||||||
|
\item[Ordre] $\rightarrow$ fréquence pure ;
|
||||||
|
\item[Grain boundaries] $\rightarrow$ battement (deux fréquences proches) ;
|
||||||
|
\item[Désordre] $\rightarrow$ bruit non caractéristique.
|
||||||
|
\end{description}
|
||||||
\end{frame}
|
\end{frame}
|
||||||
|
|
||||||
\section{\ldots à la musification}
|
\section{\ldots à la musification}
|
||||||
\begin{frame}{Enrichir la sonification}
|
\begin{frame}{Enrichir la sonification}
|
||||||
\centering
|
\begin{columns}
|
||||||
|
\column{.7\textwidth}
|
||||||
\usebeamercolor{frametitle}
|
\usebeamercolor{frametitle}
|
||||||
\pgfdeclarelayer{background}
|
\pgfdeclarelayer{background}
|
||||||
\pgfsetlayers{background,main}
|
\pgfsetlayers{background,main}
|
||||||
|
@ -125,29 +167,228 @@ Laboratoire de Physique des Solides, CNRS}
|
||||||
fit=(phystate) (sonrel) (sonobs) (phyobs) (qb)] {};
|
fit=(phystate) (sonrel) (sonobs) (phyobs) (qb)] {};
|
||||||
\end{pgfonlayer}
|
\end{pgfonlayer}
|
||||||
\end{tikzpicture}
|
\end{tikzpicture}
|
||||||
%+ de parametre
|
|
||||||
%+ de multi-échelle
|
\column{.3\textwidth}
|
||||||
|
\begin{itemize}
|
||||||
|
\item plus de paramètres
|
||||||
|
\item plus de multi-échelle
|
||||||
|
\end{itemize}
|
||||||
|
\end{columns}
|
||||||
\end{frame}
|
\end{frame}
|
||||||
|
|
||||||
\begin{frame}{M$_2$ : un mapping rythmique}
|
\begin{frame}{\sonif{sound/M2}{M$_2$ : un mapping rythmique (24 s)}}
|
||||||
|
|
||||||
|
\begin{columns}
|
||||||
|
\column{.5\textwidth}
|
||||||
|
\includegraphics[width=\textwidth]{figs/chemin-rythm1}
|
||||||
|
\column{.5\textwidth}
|
||||||
|
\includegraphics[width=\textwidth]{figs/chemin-rythm2}
|
||||||
|
\end{columns}
|
||||||
|
|
||||||
\end{frame}
|
\end{frame}
|
||||||
|
|
||||||
\begin{frame}{Des Tonnetz aux graphes de Cayley}
|
\begin{frame}{Des Tonnetz aux graphes de Cayley}
|
||||||
|
\begin{columns}[c]
|
||||||
|
\column{.4\textwidth}
|
||||||
|
\includegraphics[width=\textwidth]{figs/eulers-tonnetz}
|
||||||
|
|
||||||
|
\column{.05\textwidth}
|
||||||
|
$$ \rightarrow $$
|
||||||
|
|
||||||
|
\column{.4\textwidth}
|
||||||
|
\begin{tikzpicture}
|
||||||
|
[note/.style={draw,black,circle,inner sep=.5mm,minimum size=8mm},
|
||||||
|
label distance=-1mm,label position=below left,
|
||||||
|
double distance=.5mm, scale=.5, transform shape]
|
||||||
|
\node[note,double] (C) {Do };
|
||||||
|
\node[note,left=of C] (F) {Fa };
|
||||||
|
\node[note,right=of C] (G) {Sol };
|
||||||
|
\node[note,right=of G] (D) {Ré };
|
||||||
|
|
||||||
|
\node[note,above=of F] (A) {La };
|
||||||
|
\node[note,right=of A] (E) {Mi };
|
||||||
|
\node[note,right=of E] (B) {Si };
|
||||||
|
\node[note,right=of B] (Fd) { Fa\#};
|
||||||
|
|
||||||
|
\node[note,above=of A] (Cd) { Do\#};
|
||||||
|
\node[note,right=of Cd] (Gd) {Sol\#};
|
||||||
|
\node[note,right=of Gd] (Dd) { Ré\#};
|
||||||
|
\node[note,right=of Dd] (Ad) { La\#};
|
||||||
|
|
||||||
|
\draw (F) -- (C) -- node[above,midway] {+7} (G) -- (D);
|
||||||
|
\draw (A) -- (E) -- (B) -- (Fd);
|
||||||
|
\draw (Cd) -- (Gd) -- (Dd) -- (Ad);
|
||||||
|
|
||||||
|
\draw (F) -- (A) -- (Cd);
|
||||||
|
\draw (C) -- node[right,midway] {+4} (E) -- (Gd);
|
||||||
|
\draw (G) -- (B) -- (Dd);
|
||||||
|
\draw (D) -- (Fd) -- (Ad);
|
||||||
|
|
||||||
|
\draw[dashed] (Cd.north) -- +(0cm ,6mm );
|
||||||
|
\draw[dashed] (Gd.north) -- +(0cm ,6mm );
|
||||||
|
\draw[dashed] (Dd.north) -- +(0cm ,6mm );
|
||||||
|
\draw[dashed] (Ad.north) -- +(0cm ,6mm );
|
||||||
|
\draw[dashed] (F.south) -- +(0cm ,-6mm);
|
||||||
|
\draw[dashed] (C.south) -- +(0cm ,-6mm);
|
||||||
|
\draw[dashed] (G.south) -- +(0cm ,-6mm);
|
||||||
|
\draw[dashed] (D.south) -- +(0cm ,-6mm);
|
||||||
|
\draw[dashed] (F.west) -- +(-6mm,0cm );
|
||||||
|
\draw[dashed] (A.west) -- +(-6mm,0cm );
|
||||||
|
\draw[dashed] (Cd.west) -- +(-6mm,0cm );
|
||||||
|
\draw[dashed] (Ad.east) -- +(6mm ,0cm );
|
||||||
|
\draw[dashed] (Fd.east) -- +(6mm ,0cm );
|
||||||
|
\draw[dashed] (D.east) -- +(6mm ,0cm );
|
||||||
|
\end{tikzpicture}
|
||||||
|
\end{columns}
|
||||||
|
|
||||||
|
\medskip
|
||||||
|
Présentation du groupe $\mathbb{Z}_{12}$ :
|
||||||
|
$$ g_{4,7} = < \mathbf{4}, \mathbf{7}\ |\ 3.\mathbf{4} + 0.\mathbf{7} = 0,\quad0.\mathbf{4} +
|
||||||
|
12.\mathbf{7} = 0,\quad\mathbf{4} + \mathbf{7} = \mathbf{7} + \mathbf{4} > $$
|
||||||
\end{frame}
|
\end{frame}
|
||||||
|
|
||||||
\begin{frame}{Des Tonnetz aux graphes de Cayley (suite)}
|
\begin{frame}{Des Tonnetz aux graphes de Cayley (suite)}
|
||||||
|
\begin{center}
|
||||||
|
\begin{tikzpicture}
|
||||||
|
[note/.style={draw,black,circle,inner sep=2mm},
|
||||||
|
hex/.style={},
|
||||||
|
label distance=-1mm,label position=below left,
|
||||||
|
double distance=.5mm,xscale=.60\textwidth/9.2cm,
|
||||||
|
yscale=.50\textwidth/9.2cm]
|
||||||
|
\begin{scope}[opacity=.5]
|
||||||
|
\node[note] (F) at (-1cm,0cm) {};
|
||||||
|
\node[note,double] (C) at ( 1cm,0cm) {};
|
||||||
|
\node[note] (G) at ( 3cm,0cm) {};
|
||||||
|
\node[note] (D) at ( 5cm,0cm) {};
|
||||||
|
|
||||||
|
\node[note] (A) at ( 0cm,2cm) {};
|
||||||
|
\node[note] (E) at ( 2cm,2cm) {};
|
||||||
|
\node[note] (B) at ( 4cm,2cm) {};
|
||||||
|
\node[note] (Fd) at ( 6cm,2cm) {};
|
||||||
|
|
||||||
|
\node[note] (Cd) at ( 1cm,4cm) {};
|
||||||
|
\node[note] (Gd) at ( 3cm,4cm) {};
|
||||||
|
\node[note] (Dd) at ( 5cm,4cm) {};
|
||||||
|
\node[note] (Ad) at ( 7cm,4cm) {};
|
||||||
|
|
||||||
|
\draw (F) -- (C) -- (G) -- (D);
|
||||||
|
\draw (A) -- (E) -- (B) -- (Fd);
|
||||||
|
\draw (Cd) -- (Gd) -- (Dd) -- (Ad);
|
||||||
|
|
||||||
|
\draw (F) -- (A) -- (Cd);
|
||||||
|
\draw (C) -- (E) -- (Gd);
|
||||||
|
\draw (G) -- (B) -- (Dd);
|
||||||
|
\draw (D) -- (Fd) -- (Ad);
|
||||||
|
\draw (Cd) -- (E) -- (G);
|
||||||
|
\draw (Gd) -- (B) -- (D);
|
||||||
|
\draw (Dd) -- (Fd);
|
||||||
|
\draw (A) -- (C);
|
||||||
|
|
||||||
|
\node (1u) at (barycentric cs:A=1,Cd=1,E=1) {};
|
||||||
|
\node (2u) at (barycentric cs:Gd=1,B=1,E=1) {};
|
||||||
|
\node (3u) at (barycentric cs:B=1,Dd=1,Fd=1) {};
|
||||||
|
\node (4u) at (barycentric cs:F=1,A=1,C=1) {};
|
||||||
|
\node (5u) at (barycentric cs:E=1,G=1,C=1) {};
|
||||||
|
\node (6u) at (barycentric cs:B=1,G=1,D=1) {};
|
||||||
|
\node (1d) at (barycentric cs:Cd=1,Gd=1,E=1) {};
|
||||||
|
\node (2d) at (barycentric cs:Dd=1,Gd=1,B=1) {};
|
||||||
|
\node (3d) at (barycentric cs:Dd=1,Ad=1,Fd=1) {};
|
||||||
|
\node (4d) at (barycentric cs:A=1,E=1,C=1) {};
|
||||||
|
\node (5d) at (barycentric cs:G=1,E=1,B=1) {};
|
||||||
|
\node (6d) at (barycentric cs:D=1,Fd=1,B=1) {};
|
||||||
|
|
||||||
|
\draw[dashed] (Cd.north) -- +(0cm ,6mm );
|
||||||
|
\draw[dashed] (Gd.north) -- +(0cm ,6mm );
|
||||||
|
\draw[dashed] (Dd.north) -- +(0cm ,6mm );
|
||||||
|
\draw[dashed] (Ad.north) -- +(0cm ,6mm );
|
||||||
|
\draw[dashed] (F.south) -- +(0cm ,-6mm);
|
||||||
|
\draw[dashed] (C.south) -- +(0cm ,-6mm);
|
||||||
|
\draw[dashed] (G.south) -- +(0cm ,-6mm);
|
||||||
|
\draw[dashed] (D.south) -- +(0cm ,-6mm);
|
||||||
|
\draw[dashed] (F.west) -- +(-6mm,0cm );
|
||||||
|
\draw[dashed] (A.west) -- +(-6mm,0cm );
|
||||||
|
\draw[dashed] (Cd.west) -- +(-6mm,0cm );
|
||||||
|
\draw[dashed] (Ad.east) -- +(6mm ,0cm );
|
||||||
|
\draw[dashed] (Fd.east) -- +(6mm ,0cm );
|
||||||
|
\draw[dashed] (D.east) -- +(6mm ,0cm );
|
||||||
|
\end{scope}
|
||||||
|
|
||||||
|
\draw[hex] (1u.center) -- (1d.center) -- (2u.center)
|
||||||
|
-- (2d.center) -- (3u.center) -- (3d.center);
|
||||||
|
\draw[hex] (4u.center) -- (4d.center) -- (5u.center)
|
||||||
|
-- (5d.center) -- (6u.center) -- (6d.center);
|
||||||
|
\draw[hex] (1u.center) -- (4d.center);
|
||||||
|
\draw[hex] (2u.center) -- (5d.center);
|
||||||
|
\draw[hex] (3u.center) -- (6d.center);
|
||||||
|
\draw[hex,dashed] (1d.center) -- +(0, 1.5cm);
|
||||||
|
\draw[hex,dashed] (2d.center) -- +(0, 1.5cm);
|
||||||
|
\draw[hex,dashed] (3d.center) -- +(0, 1.5cm);
|
||||||
|
\draw[hex,dashed] (4u.center) -- +(0,-1.5cm);
|
||||||
|
\draw[hex,dashed] (5u.center) -- +(0,-1.5cm);
|
||||||
|
\draw[hex,dashed] (6u.center) -- +(0,-1.5cm);
|
||||||
|
|
||||||
|
\draw[hex,dashed] (1u.center) -- +(150:1.0cm);
|
||||||
|
\draw[hex,dashed] (4u.center) -- +(150:1.0cm);
|
||||||
|
\draw[hex,dashed] (3d.center) -- +(-30:1.0cm);
|
||||||
|
\draw[hex,dashed] (6d.center) -- +(-30:1.0cm);
|
||||||
|
\end{tikzpicture}
|
||||||
|
\end{center}
|
||||||
\end{frame}
|
\end{frame}
|
||||||
|
|
||||||
\begin{frame}{M$_3$ : un mapping musical simple}
|
\begin{frame}{\sonif{sounds/M3}{M$_3$ : un mapping intervallique (45 s)}}
|
||||||
|
\begin{columns}
|
||||||
|
\column{.2\textwidth}
|
||||||
|
\begin{tikzpicture}[rotate=30,scale=.5,
|
||||||
|
hex/.style={regular polygon, regular polygon sides=6, draw, inner sep=.5cm,
|
||||||
|
transform shape, text width=0}]
|
||||||
|
\node[hex,gray] (5) at ( 30:1.41cm) {}; %5
|
||||||
|
\node[hex,gray] (6) at ( 90:1.41cm) {}; %6
|
||||||
|
\node[hex,gray] (1) at (150:1.41cm) {}; %1
|
||||||
|
\node[hex,gray] (2) at (210:1.41cm) {}; %2
|
||||||
|
\node[hex,gray] (3) at (270:1.41cm) {}; %3
|
||||||
|
\node[hex,gray] (4) at (330:1.41cm) {}; %4
|
||||||
|
\node[hex,thick] (h) at (0,0) {};
|
||||||
|
|
||||||
|
\foreach \i in {1,...,6} {
|
||||||
|
\draw[gray,->,dashed] (h.center) -- (\i) node[gray] {\i} ;}
|
||||||
|
\end{tikzpicture}
|
||||||
|
|
||||||
|
\column{.6\textwidth}
|
||||||
|
\includegraphics[width=\textwidth]{figs/bulandhex}
|
||||||
|
\end{columns}
|
||||||
|
|
||||||
|
\medskip
|
||||||
|
\begin{columns}
|
||||||
|
\column{.3\textwidth}
|
||||||
|
\includegraphics[width=\textwidth]{figs/hex}
|
||||||
|
\column{.3\textwidth}
|
||||||
|
\includegraphics[width=\textwidth]{figs/bul}
|
||||||
|
\end{columns}
|
||||||
|
|
||||||
|
\medskip
|
||||||
|
\begin{center}
|
||||||
|
\end{center}
|
||||||
\end{frame}
|
\end{frame}
|
||||||
|
|
||||||
\begin{frame}{M$_4$ : un mapping musical étendu}
|
\begin{frame}{\sonif{sounds/M4}{M$_4$ : un mapping intervallique et rythmique (56 s)}}
|
||||||
|
Association de M$_2$ et de M$_3$
|
||||||
\end{frame}
|
\end{frame}
|
||||||
|
|
||||||
\section{Bilan et perspectives}
|
\section{Bilan et perspectives}
|
||||||
\begin{frame}{Bilan}
|
\begin{frame}{Bilan}
|
||||||
|
Ce qui a été fait :
|
||||||
|
\begin{itemize}
|
||||||
|
\item Musify
|
||||||
|
\end{itemize}
|
||||||
|
|
||||||
|
Résultats préliminaires encourageants
|
||||||
\end{frame}
|
\end{frame}
|
||||||
|
|
||||||
\begin{frame}{Perspectives}
|
\begin{frame}{Perspectives}
|
||||||
|
Ce qui est prévu :
|
||||||
|
\begin{itemize}
|
||||||
|
\item \texttt{gnusic} (en référence à gnuplot)
|
||||||
|
\item exploration assisté des mappings
|
||||||
|
\end{itemize}
|
||||||
\end{frame}
|
\end{frame}
|
||||||
\end{document}
|
\end{document}
|
||||||
|
|