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changeset 70:4e3e078f5338

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remove trailing whitespace, retab
author Markus Kaiser <markus.kaiser@in.tum.de>
date Fri, 14 Dec 2012 22:42:15 +0100
parents 276d1908df24
children b06e34b08f9b
files bayesian_networks/beamerthemeLEA2.sty bayesian_networks/presentation.tex planarity/beamerthemeLEA2.sty planarity/presentation.tex theme/LEA_beamer/beamerthemeLEA2.sty theme/LEA_beamer/example.tex theme/LEA_paper/example.tex theme/LEA_paper/seminararbeit.tex
diffstat 8 files changed, 248 insertions(+), 251 deletions(-) [+]
line wrap: on
line diff
--- a/bayesian_networks/beamerthemeLEA2.sty	Thu Dec 13 19:36:52 2012 +0100
+++ b/bayesian_networks/beamerthemeLEA2.sty	Fri Dec 14 22:42:15 2012 +0100
@@ -38,16 +38,16 @@
 \logo{\pgfuseimage{uni}}
 
 \defbeamertemplate*{footline}{infolines theme}{%
-	\hspace*{2ex}\raisebox{1.5ex}[-1.5ex]{%
-	\tiny\insertframenumber{}/\inserttotalframenumber \hspace{5mm} \insertnavigation{0.8\paperwidth}}%
+    \hspace*{2ex}\raisebox{1.5ex}[-1.5ex]{%
+    \tiny\insertframenumber{}/\inserttotalframenumber \hspace{5mm} \insertnavigation{0.8\paperwidth}}%
 }
 
 \setbeamertemplate{frametitle}{
-	\begin{beamercolorbox}[wd=80mm,leftskip=0mm]{frametitle}
-		\usebeamerfont*{frametitle}
-		\insertframetitle\hfill\parbox{10mm}{\vspace{-2mm}\insertlogo}\hspace{-2mm}
-	\end{beamercolorbox}
-	\vspace{-3mm}\textcolor{tumblue}{\noindent\rule{\textwidth}{0.4px}}
+    \begin{beamercolorbox}[wd=80mm,leftskip=0mm]{frametitle}
+        \usebeamerfont*{frametitle}
+        \insertframetitle\hfill\parbox{10mm}{\vspace{-2mm}\insertlogo}\hspace{-2mm}
+    \end{beamercolorbox}
+    \vspace{-3mm}\textcolor{tumblue}{\noindent\rule{\textwidth}{0.4px}}
 }
 % hier kein Logo
 \setbeamertemplate{sidebar right}{\vfill\vskip2pt\llap{\usebeamertemplate***{navigation symbols}\hskip1mm}\vskip2pt}
--- a/bayesian_networks/presentation.tex	Thu Dec 13 19:36:52 2012 +0100
+++ b/bayesian_networks/presentation.tex	Fri Dec 14 22:42:15 2012 +0100
@@ -33,9 +33,9 @@
 \newcommand{\inter}   {\cap}                % Schnittmenge
 \newcommand{\union}   {\cup}                % Vereinigung
 \newcommand{\Oh}      {\mathcal{O}}         % O-Notation (Landau-Symbole)
-\newcommand{\mycite}[1]{\textcolor{tumgreen}{[#1]}} 
+\newcommand{\mycite}[1]{\textcolor{tumgreen}{[#1]}}
 
-\newenvironment{changemargin}[2]{% 
+\newenvironment{changemargin}[2]{%
     \begin{list}{}{%
             \setlength{\topsep}{0pt}%
             \setlength{\leftmargin}{#1}%
@@ -56,14 +56,14 @@
     minimum width=6em, minimum height=2.5em,
 node distance=10em, inner sep = 0]
 \tikzstyle{selected net node} = [net node, fill=tumred!20]
-\def \netvspace {8em}						
+\def \netvspace {8em}
 \tikzstyle{net cpt} = [draw, thick, fill = tumgreen!20,
     font=\scriptsize, node distance=3em,
 inner sep = 2pt]
 
 \title{Bayesnetze}
 \subtitle{Seminar ``Kognitive Robotik''}
-\author{\href{mailto:markus.kaiser@in.tum.de}{Markus Kaiser}} 
+\author{\href{mailto:markus.kaiser@in.tum.de}{Markus Kaiser}}
 %\date{\today}
 \date{12-12-12}
 \institute{Technische Universität München}
@@ -75,9 +75,9 @@
 %  \end{frame}
 %}
 %\AtBeginSection[]{
-%	\begin{frame}[plain]
-%		\begin{center} \LARGE\insertsectionhead \end{center} 	
-%	\end{frame}
+%   \begin{frame}[plain]
+%       \begin{center} \LARGE\insertsectionhead \end{center}
+%   \end{frame}
 %}
 
 \begin{document}
@@ -107,22 +107,20 @@
                         \item Vorgeschichte
                         \item Symptome
                         \item Testergebnisse
-                    \end{itemize}		
+                    \end{itemize}
                 \end{column}
                 \begin{column}{.10\textwidth}
-                    \begin{figure}
-                        \begin{tikzpicture}[auto]
-                            \useasboundingbox (0, 0.5) rectangle (1, -0.5);
-                            \draw[->, >=latex, line width=.35em, black!75] (0,0) -- (1,0);
-                        \end{tikzpicture}
-                    \end{figure}
+                    \begin{tikzpicture}[auto]
+                        \useasboundingbox (0, 0.5) rectangle (1, -0.5);
+                        \draw[->, >=latex, line width=.35em, black!75] (0,0) -- (1,0);
+                    \end{tikzpicture}
                 \end{column}
                 \begin{column}{.35\textwidth}
                     \begin{itemize}
                         \item Diagnose
                         \item Therapie
-                    \end{itemize}		
-                \end{column}				
+                    \end{itemize}
+                \end{column}
             \end{columns}
         \end{center}
     \end{example}
@@ -204,30 +202,30 @@
         Ich habe einen Nachmittag lang Zeit. Ich könnte \alert{Lebensmittel kaufen}, \alert{Sport machen} oder \alert{Lernen}. Ich habe genug Zeit für alle drei. Da ich ein sehr unentschlossener Mensch bin \alert{würfle} ich mittags mit einem \alert{W20}.
     \end{example}
 
-    \vspace{2em}	
+    \vspace{2em}
 
     \begin{center}
         \begin{tikzpicture}
-            \node [net node] (sport) {Sport};	
+            \node [net node] (sport) {Sport};
             \node [net cpt] [below of = sport]
             {\begin{tabu}{c}
-                $\Pr[S]$ \\ 	\tabucline{-} 
-                $0.4$ \\ 
+                $\Pr[S]$ \\     \tabucline{-}
+                $0.4$ \\
             \end{tabu}};
 
             \node [net node] (kaufen) [left of = sport] {Kaufen};
             \node [net cpt] [below of = kaufen]
             {\begin{tabu}{c}
-                $\Pr[K]$ \\ 	\tabucline{-} 
-                $0.5$ \\ 
+                $\Pr[K]$ \\     \tabucline{-}
+                $0.5$ \\
             \end{tabu}};
 
             \node [net node] (lernen) [right of = sport] {Lernen};
             \node [net cpt] [below of = lernen]
             {\begin{tabu}{c}
-                $\Pr[L]$ \\ 	\tabucline{-} 
-                $0.2$ \\ 
-            \end{tabu}};	
+                $\Pr[L]$ \\     \tabucline{-}
+                $0.2$ \\
+            \end{tabu}};
         \end{tikzpicture}
     \end{center}
 \end{frame}
@@ -237,30 +235,30 @@
 
     \begin{center}
         \begin{tikzpicture}
-            \node [net node] (sport) {Sport};	
+            \node [net node] (sport) {Sport};
             \node [net cpt] [below of = sport]
             {\begin{tabu}{c}
-                $\Pr[S]$ \\ 	\tabucline{-} 
-                $0.4$ \\ 
+                $\Pr[S]$ \\     \tabucline{-}
+                $0.4$ \\
             \end{tabu}};
 
             \node [net node] (kaufen) [left of = sport] {Kaufen};
             \node [net cpt] [below of = kaufen]
             {\begin{tabu}{c}
-                $\Pr[K]$ \\ 	\tabucline{-} 
-                $0.5$ \\ 
+                $\Pr[K]$ \\     \tabucline{-}
+                $0.5$ \\
             \end{tabu}};
 
             \node [net node] (lernen) [right of = sport] {Lernen};
             \node [net cpt] [below of = lernen]
             {\begin{tabu}{c}
-                $\Pr[L]$ \\ 	\tabucline{-} 
-                $0.2$ \\ 
-            \end{tabu}};	
+                $\Pr[L]$ \\     \tabucline{-}
+                $0.2$ \\
+            \end{tabu}};
         \end{tikzpicture}
-    \end{center}	
+    \end{center}
 
-    \vspace{1em}	
+    \vspace{1em}
     \only<1>{
         Wie groß ist die Wahrscheinlichkeit,
         \vspace{1em}
@@ -284,15 +282,15 @@
                 \hline
                 K & S & L & $\Pr$ & K & S & L & $\Pr$ \\
                 \tabucline[1.2pt]{-}
-                F & F & F & 0.24 & T & F & F & 0.24 \\  
-                \hline 
+                F & F & F & 0.24 & T & F & F & 0.24 \\
+                \hline
                 F & F & T & 0.06 & T & T & T & 0.06 \\
-                \hline 
-                F & T & F & 0.16 & T & T & T & 0.16 \\ 
-                \hline 
-                F & T & T & 0.04 & T & T & T & 0.04 \\ 
-                \hline 
-            \end{tabu} 
+                \hline
+                F & T & F & 0.16 & T & T & T & 0.16 \\
+                \hline
+                F & T & T & 0.04 & T & T & T & 0.04 \\
+                \hline
+            \end{tabu}
         \end{center}
     }
 \end{frame}
@@ -306,8 +304,8 @@
     \end{example}
 
     \vspace{1em}
+    Probleme:
 
-    Probleme:
     \begin{itemize}
         \item $\Pr[R, S] \neq \Pr[R] \cdot \Pr[S]$
         \item Alle Sätze brauchen \alert{Unabhängigkeit}
@@ -338,19 +336,19 @@
 
     \begin{tikzpicture}
         \node [net node] (sport) {Sport};
-        \node [net node] (kaufen) [left of = sport] {Kaufen};				
+        \node [net node] (kaufen) [left of = sport] {Kaufen};
         \node [net node] (lernen) [right of = sport] {Lernen};
 
         \node [net node] (gewissen) at ($0.5*(sport.center) + 0.5*(lernen.center) - (0,\netvspace)$) {Gewissen};
         \node [net node] (regen) at ($0.5*(sport.center) + 0.5*(kaufen.center) + (0,\netvspace)$) {Regen};
 
         \node<2,3> [selected net node] (sport) {Sport};
-        \node<2> [selected net node] (kaufen) [left of = sport] {Kaufen};				
+        \node<2> [selected net node] (kaufen) [left of = sport] {Kaufen};
         \node<3> [selected net node] (lernen) [right of = sport] {Lernen};
 
         \node<3> [selected net node] (gewissen) at ($0.5*(sport.center) + 0.5*(lernen.center) - (0,\netvspace)$) {Gewissen};
-        \node<2,4> [selected net node] (regen) at ($0.5*(sport.center) + 0.5*(kaufen.center) + (0,\netvspace)$) {Regen};	
-        \node<4> [selected net node] (gewissen) at ($0.5*(sport.center) + 0.5*(lernen.center) - (0,\netvspace)$) {Gewissen};				
+        \node<2,4> [selected net node] (regen) at ($0.5*(sport.center) + 0.5*(kaufen.center) + (0,\netvspace)$) {Regen};
+        \node<4> [selected net node] (gewissen) at ($0.5*(sport.center) + 0.5*(lernen.center) - (0,\netvspace)$) {Gewissen};
 
         \foreach \src/\dest in {regen/kaufen, regen/sport,
         sport/gewissen, lernen/gewissen}
@@ -374,15 +372,15 @@
         \end{enumerate}
     \end{definition}
 
-    \vfill	
+    \vfill
 
     \uncover<2-5> {
         \begin{center}
             \begin{tikzpicture}
                 \tikzstyle {dag node} = [circular node, font=\normalfont, inner sep = 2pt,
-                node distance = 4em]	
+                node distance = 4em]
                 \tikzstyle {bad dag node} = [dag node, fill=tumred!20]
-                \tikzstyle {good dag node} = [dag node, fill=tumgreen!20]		
+                \tikzstyle {good dag node} = [dag node, fill=tumgreen!20]
 
                 \def \xdist {4em}
                 \def \ydist {3em}
@@ -440,11 +438,11 @@
 
     \begin{tikzpicture}
         \node [net node] (sport) {Sport};
-        \node [net node] (kaufen) [left of = sport] {Kaufen};				
+        \node [net node] (kaufen) [left of = sport] {Kaufen};
         \node [net node] (lernen) [right of = sport] {Lernen};
 
         \node [net node] (gewissen) at ($0.5*(sport.center) + 0.5*(lernen.center) - (0,\netvspace)$) {Gewissen};
-        \node [net node] (regen) at ($0.5*(sport.center) + 0.5*(kaufen.center) + (0,\netvspace)$) {Regen};		
+        \node [net node] (regen) at ($0.5*(sport.center) + 0.5*(kaufen.center) + (0,\netvspace)$) {Regen};
 
         \foreach \src/\dest in {regen/kaufen, regen/sport,
         sport/gewissen, lernen/gewissen}
@@ -453,38 +451,38 @@
         \only<2> {
             \node [net cpt] at ($(regen.center)-(5em,0)$)
             {\begin{tabu}{c}
-                $\Pr[R]$ \\ 	\tabucline{-} 
-                $0.1$ \\ 
-            \end{tabu}};	
+                $\Pr[R]$ \\     \tabucline{-}
+                $0.1$ \\
+            \end{tabu}};
 
             \node [net cpt] at ($(lernen.center)+(0,3em)$)
             {\begin{tabu}{c}
-                $\Pr[L]$ \\ 	\tabucline{-} 
-                $0.2$ \\ 
+                $\Pr[L]$ \\     \tabucline{-}
+                $0.2$ \\
             \end{tabu}};
 
             \node [net cpt] at ($(kaufen.center)-(0,3em)$)
             {\begin{tabu}{c|c}
-                R & $\Pr[K]$ \\ 	\tabucline{-}
-                F & $0.5$ \\ 
+                R & $\Pr[K]$ \\     \tabucline{-}
+                F & $0.5$ \\
                 T & $0.25$ \\
-            \end{tabu}};		
+            \end{tabu}};
 
             \node [net cpt] at ($(sport.center)-(2em,3em)$)
             {\begin{tabu}{c|c}
-                R & $\Pr[S]$ \\ 	\tabucline{-}
-                F & $0.4$ \\ 
+                R & $\Pr[S]$ \\     \tabucline{-}
+                F & $0.4$ \\
                 T & $0.2$ \\
-            \end{tabu}};			
+            \end{tabu}};
 
             \node [net cpt] at ($(gewissen.center)+(7em,1.1em)$)
             {\begin{tabu}{cc|c}
-                S & L & $\Pr[G]$ \\ 	\tabucline{-}
-                F & F & $0.8$ \\ 
+                S & L & $\Pr[G]$ \\     \tabucline{-}
+                F & F & $0.8$ \\
                 F & T & $0.25$ \\
                 T & F & $0.5$ \\
                 T & T & $0.1$ \\
-            \end{tabu}};			
+            \end{tabu}};
         }
     \end{tikzpicture}
 \end{frame}
@@ -494,7 +492,7 @@
 
     \begin{theorem}[Gemeinsame Verteilung]
         Für einen Eintrag $\Pr[x_1,\ldots,x_n]$ in der gemeinsamen Verteilung eines Bayesnetzes gilt
-        $$\Pr[x_1,\ldots,x_n] = \prod_{i=1}^n \Pr[x_i \mid \mathsf{parents}(X_i)]$$	
+        $$\Pr[x_1,\ldots,x_n] = \prod_{i=1}^n \Pr[x_i \mid \mathsf{parents}(X_i)]$$
     \end{theorem}
 
     Was ist die Wahrscheinlichkeit, dass ich ein \alert{schlechtes Gewissen} bei \alert{schönem Wetter} habe, obwohl ich \alert{Sport gemacht} habe nachdem ich \alert{einkaufen} war?
@@ -508,7 +506,7 @@
 \begin{frame}[t]
     \frametitle{Konstruktion}
     \begin{block}{}
-        Wie konstruiert man zu einer Domäne ein möglichst \alert{kompaktes}, \alert{lokal strukturiertes} und \alert{natürliches} Netz?	
+        Wie konstruiert man zu einer Domäne ein möglichst \alert{kompaktes}, \alert{lokal strukturiertes} und \alert{natürliches} Netz?
     \end{block}
 
     \begin{itemize}
@@ -525,7 +523,7 @@
                 \item Direkte Einflüsse
                 \item Kleine Einflüsse ignorieren
             \end{itemize}
-            \vspace{.2em}		
+            \vspace{.2em}
         \item \alert{Kausale Reihenfolge} abbilden
     \end{itemize}
 \end{frame}
@@ -551,11 +549,11 @@
                     \hline
                     E & G & $\Pr[B]$ & $\Pr[\neg B]$ & E & G & $\Pr[B]$ & $\Pr[\neg B]$ \\
                     \tabucline[1.2pt]{-}
-                    F & F & 0 & 1 & T & F & 0.4 & \alert{0.6} \\  
-                    \hline 
+                    F & F & 0 & 1 & T & F & 0.4 & \alert{0.6} \\
+                    \hline
                     F & T & 0.8 & \alert{0.2} & T & T & 0.88 & 0.12 \\
-                    \hline 
-                \end{tabu} 
+                    \hline
+                \end{tabu}
             \end{center}
         \end{example}
     }
@@ -589,20 +587,20 @@
         \path [edge] (\src) -- (\dest);
 
         \node [net cpt] at ($(schlafen.center)-(-3em,2.2em)$)
-        {$V \sim GV(0,100)$};	
+        {$V \sim GV(0,100)$};
 
         \node [net cpt] at ($(mensa.center)-(1em,3em)$)
         {\begin{tabu}{c}
-            $\Pr[M]$ \\ 	\tabucline{-} 
-            $0.4$ \\ 
-        \end{tabu}};	
+            $\Pr[M]$ \\     \tabucline{-}
+            $0.4$ \\
+        \end{tabu}};
 
         \node [net cpt] at ($(schlange.center)-(5em,3em)$)
         {\begin{tabu}{c|c}
-            M & $S$ \\ 	\tabucline{-}
-            F & $S \sim N(\mu_t(v),\sigma_t)$ \\ 
+            M & $S$ \\  \tabucline{-}
+            F & $S \sim N(\mu_t(v),\sigma_t)$ \\
             T & $S \sim N(\mu_f(v),\sigma_f)$ \\
-        \end{tabu}};	
+        \end{tabu}};
 
         \node [net cpt] at ($(hotdog.center)-(-1em,2.2em)$)
         {$\Pr[h \mid S = s] = \Phi(\frac{-s + \mu}{\sigma})$};
@@ -613,8 +611,8 @@
                     xshift=.225\textwidth,yshift=-6em,width=0.55\textwidth,
                     colormap={tum}{color(0cm)=(tumblue); color(1cm)=(yellow);
                     color(2cm)=(tumorange); color(3cm)=(tumred)}]
-                    \addplot3[surf,domain=0:40,domain y=0:100] 
-                    {0.6 * exp(-0.5*((x-(30-0.25*y))/\sdiv)^2 )/(2.5*\sdiv) + 
+                    \addplot3[surf,domain=0:40,domain y=0:100]
+                    {0.6 * exp(-0.5*((x-(30-0.25*y))/\sdiv)^2 )/(2.5*\sdiv) +
                     0.4 * exp(-0.5*((x-(15-0.1*y))/\sdiv)^2 )/(2.5*\sdiv)};
                 \end{axis}
 
@@ -643,14 +641,14 @@
 \begin{frame}
     \frametitle{Inferenz durch Aufzählen}
 
-    \only<1>{	
+    \only<1>{%
         \begin{example}[Bekämpfung des schlechten Gewissens]
             Wenn ich ein \alert{schlechtes Gewissen} habe werde ich unglücklich. Unglück kann man bekämpfen, indem man sich mit einem \alert{Film} ablenkt oder passend zur Jahreszeit Schokolade aus dem \alert{Adventskalender} isst.\\
             Zur Vereinfachung soll der Einfluss des Regens nun \alert{nicht mehr} beachtet werden.
         \end{example}
     }
 
-    \only<2>{
+    \only<2>{%
         \begin{center}
             \begin{tikzpicture}
                 \node [net node] (sport) {Sport};
@@ -667,40 +665,40 @@
 
                 \node [net cpt] at ($(lernen.center)+(6em,0)$)
                 {\begin{tabu}{c}
-                    $\Pr[L]$ \\ 	\tabucline{-} 
-                    $0.2$ \\ 
+                    $\Pr[L]$ \\     \tabucline{-}
+                    $0.2$ \\
                 \end{tabu}};
 
                 \node [net cpt] at ($(film.center)-(7em,0)$)
                 {\begin{tabu}{c|c}
-                    G & $\Pr[M]$ \\ 	\tabucline{-}
-                    F & $0.4$ \\ 
+                    G & $\Pr[M]$ \\     \tabucline{-}
+                    F & $0.4$ \\
                     T & $0.75$ \\
-                \end{tabu}};	
+                \end{tabu}};
 
                 \node [net cpt] at ($(advent.center)+(7em,0)$)
                 {\begin{tabu}{c|c}
-                    G & $\Pr[A]$ \\ 	\tabucline{-}
-                    F & $0.6$ \\ 
+                    G & $\Pr[A]$ \\     \tabucline{-}
+                    F & $0.6$ \\
                     T & $0.9$ \\
-                \end{tabu}};					
+                \end{tabu}};
 
                 \node [net cpt] at ($(sport.center)-(6em,0)$)
                 {\begin{tabu}{c}
-                    $\Pr[S]$ \\ 	\tabucline{-} 
-                    $0.4$ \\ 
-                \end{tabu}};				
+                    $\Pr[S]$ \\     \tabucline{-}
+                    $0.4$ \\
+                \end{tabu}};
 
                 \node [net cpt] at ($(gewissen.center)+(7em,0)$)
                 {\begin{tabu}{cc|c}
-                    S & L & $\Pr[G]$ \\ 	\tabucline{-}
-                    F & F & $0.8$ \\ 
+                    S & L & $\Pr[G]$ \\     \tabucline{-}
+                    F & F & $0.8$ \\
                     F & T & $0.25$ \\
                     T & F & $0.5$ \\
                     T & T & $0.1$ \\
                 \end{tabu}};
-            \end{tikzpicture}	
-        \end{center}	
+            \end{tikzpicture}
+        \end{center}
     }
 \end{frame}
 
@@ -730,7 +728,7 @@
         \tikzstyle{edge from parent} = [edge]
 
         \tikzstyle{level 2} = [sibling distance = 14em]
-        \tikzstyle{level 3} = [sibling distance = 7em]	
+        \tikzstyle{level 3} = [sibling distance = 7em]
 
 
         \node[op] {}
@@ -749,7 +747,7 @@
                         }
                         edge from parent
                         node[left] {$\Pr[M \mid g]$}
-                    }	
+                    }
                     edge from parent
                     node[left] {$\Pr[g \mid \neg S, l]$}
                 }
@@ -764,10 +762,10 @@
                         }
                         edge from parent
                         node[left] {$\Pr[M \mid \neg g]$}
-                    }	
+                    }
                     edge from parent
                     node[right] {$\Pr[\neg g \mid \neg S, l]$}
-                }            
+                }
                 edge from parent
                 node[above left] {$\Pr[l]$}
             }
@@ -784,7 +782,7 @@
                         }
                         edge from parent
                         node[left] {$\Pr[M \mid g]$}
-                    }	
+                    }
                     edge from parent
                     node[left] {$\Pr[g \mid \neg S, \neg l]$}
                 }
@@ -799,16 +797,16 @@
                         }
                         edge from parent
                         node[left] {$\Pr[M \mid \neg g]$}
-                    }	
+                    }
                     edge from parent
                     node[right] {$\Pr[\neg g \mid \neg S, \neg l]$}
-                }            
+                }
                 edge from parent
                 node[above right] {$\Pr[\neg l]$}
-            }    		
+            }
             edge from parent
             node[left] {$\Pr[\neg S]$}
-        };	
+        };
     \end{tikzpicture}
 \end{frame}
 
@@ -854,8 +852,8 @@
         \item haben eine kompakte Darstellung
         \item benötigen \alert{Expertenwissen}
         \item modellieren \alert{Kausalitätszusammenhänge}
-        \item sparen Speicher				
+        \item sparen Speicher
         \item erlauben Interferenz
-    \end{itemize}  
+    \end{itemize}
 \end{frame}
 \end{document}
--- a/planarity/beamerthemeLEA2.sty	Thu Dec 13 19:36:52 2012 +0100
+++ b/planarity/beamerthemeLEA2.sty	Fri Dec 14 22:42:15 2012 +0100
@@ -38,16 +38,16 @@
 \logo{\pgfuseimage{uni}}
 
 \defbeamertemplate*{footline}{infolines theme}{%
-	%\hspace*{2ex}\raisebox{1.5ex}[-1.5ex]{%
-	%\tiny\insertframenumber{}/\inserttotalframenumber \hspace{5mm} \insertnavigation{0.8\paperwidth}}%
+    %\hspace*{2ex}\raisebox{1.5ex}[-1.5ex]{%
+    %\tiny\insertframenumber{}/\inserttotalframenumber \hspace{5mm} \insertnavigation{0.8\paperwidth}}%
 }
 
 \setbeamertemplate{frametitle}{
-	\begin{beamercolorbox}[wd=80mm,leftskip=0mm]{frametitle}
-		\usebeamerfont*{frametitle}
-		\insertframetitle\hfill\parbox{10mm}{\vspace{-2mm}\insertlogo}\hspace{-2mm}
-	\end{beamercolorbox}
-	\vspace{-3mm}\textcolor{tumblue}{\noindent\rule{\textwidth}{0.4px}}
+    \begin{beamercolorbox}[wd=80mm,leftskip=0mm]{frametitle}
+        \usebeamerfont*{frametitle}
+        \insertframetitle\hfill\parbox{10mm}{\vspace{-2mm}\insertlogo}\hspace{-2mm}
+    \end{beamercolorbox}
+    \vspace{-3mm}\textcolor{tumblue}{\noindent\rule{\textwidth}{0.4px}}
 }
 % hier kein Logo
 \setbeamertemplate{sidebar right}{\vfill\vskip2pt\llap{\usebeamertemplate***{navigation symbols}\hskip1mm}\vskip2pt}
--- a/planarity/presentation.tex	Thu Dec 13 19:36:52 2012 +0100
+++ b/planarity/presentation.tex	Fri Dec 14 22:42:15 2012 +0100
@@ -27,9 +27,9 @@
 \newcommand{\inter}   {\cap}                % Schnittmenge
 \newcommand{\union}   {\cup}                % Vereinigung
 \newcommand{\Oh}      {\mathcal{O}}         % O-Notation (Landau-Symbole)
-\newcommand{\mycite}[1]{\textcolor{tumgreen}{[#1]}} 
+\newcommand{\mycite}[1]{\textcolor{tumgreen}{[#1]}}
 
-\newenvironment{changemargin}[2]{% 
+\newenvironment{changemargin}[2]{%
     \begin{list}{}{%
             \setlength{\topsep}{0pt}%
             \setlength{\leftmargin}{#1}%
@@ -58,7 +58,7 @@
 
 \title{Testen eines Graphen auf Planarität}
 \subtitle{Proseminar ``Graph Drawing''}
-\author{\href{mailto:markus.kaiser@in.tum.de}{Markus Kaiser}} 
+\author{\href{mailto:markus.kaiser@in.tum.de}{Markus Kaiser}}
 %\date{\today}
 \date{2012-05-22}
 \institute{Technische Universität München}
@@ -70,9 +70,9 @@
 %  \end{frame}
 %}
 %\AtBeginSection[]{
-%	\begin{frame}[plain]
-%		\begin{center} \LARGE\insertsectionhead \end{center} 	
-%	\end{frame}
+%   \begin{frame}[plain]
+%       \begin{center} \LARGE\insertsectionhead \end{center}
+%   \end{frame}
 %}
 
 \begin{document}
@@ -128,7 +128,7 @@
                     \foreach \source/ \dest in {a/b, a/c, c/d, b/d,
                         b/e, e/f,
                     f/g, f/h, h/i, g/i, h/k}
-                    \path[edge] (\source) -- (\dest);        
+                    \path[edge] (\source) -- (\dest);
                     \path[edge] (g) .. controls (3, 5.5) .. (k);
 
                     \foreach \vertex / \fr in {e/2,
@@ -139,18 +139,18 @@
                     }
                     \path<\fr> node[selected vertex] at (\vertex) {};
 
-                    \begin{pgfonlayer}{background}        
+                    \begin{pgfonlayer}{background}
                         \foreach \source / \dest / \fr in {
                             f/g/3, f/h/3, h/i/3, g/i/3, h/k/3,
                             a/b/4, b/e/4, e/f/4,
                             a/b/5, b/d/5, c/d/5, c/a/5
                         }
-                        \path<\fr>[selected edge] (\source) -- (\dest);     
+                        \path<\fr>[selected edge] (\source) -- (\dest);
                         \path<3>[selected edge] (g) .. controls (3, 5.5) .. (k);
 
                         \fill<6>[red!50] (a.center) -- (b.center) -- (d.center) -- (c.center);
-                        \draw<6> (1, 0.75) node {f};            
-                    \end{pgfonlayer}   
+                        \draw<6> (1, 0.75) node {f};
+                    \end{pgfonlayer}
                 \end{tikzpicture}
             \end{figure}
             \vspace{1em}
@@ -161,7 +161,7 @@
 \begin{frame}
     \frametitle{Planarität}
     \begin{itemize}
-        \item \alert{offene Jordankurve}	
+        \item \alert{offene Jordankurve}
             \vspace{0.2em}
             \begin{figure}
                 \begin{tikzpicture}
@@ -170,7 +170,7 @@
                     \draw (4,0) .. controls (5,1) .. (6,0.3) .. controls (7,0.5) .. (7,1);
                     \draw (6,0.3) .. controls (8,-0.5) and (3,0) .. (6,0.3);
                 \end{tikzpicture}
-            \end{figure}		
+            \end{figure}
             \vspace{1em}
 
         \item<2-> Eine \alert{Zeichnung} ordnet in $\R^2$ jedem Knoten Koordinaten und jeder Kante eine offene Jordankurve zu
@@ -204,7 +204,7 @@
                 h/i, h/j, h/k,
                 i/j, i/k,
             j/k}
-            \path[edge] (\source) -- (\dest);   
+            \path[edge] (\source) -- (\dest);
 
             \node at (1,0) {$K_{3,3}$};
             \node at (4.814,0) {$K_5$};
@@ -232,7 +232,7 @@
                 \item<5> nicht planar wenn $|E| > 3|V| - 6$
             \end{itemize}
         \end{column}
-        \begin{column}{.4\textwidth}	
+        \begin{column}{.4\textwidth}
             \begin{figure}
                 \begin{tikzpicture}[auto]
                     \useasboundingbox (-1, -1) rectangle (7,7);
@@ -249,11 +249,11 @@
 
                     \foreach \pos/\name in {{(0,4)/f}, {(2,4)/g}, {(3,5)/h},{(2,6)/i},
                     {(0,6)/j}}
-                    \node<2>[vertex, fill=red!25] (\name) at \pos {};        
+                    \node<2>[vertex, fill=red!25] (\name) at \pos {};
 
                     \foreach \source/ \dest in {a/b, a/c, c/d, b/d,
                     a/e, e/d, f/g, g/h, h/i, h/j, g/i}
-                    \path<2>[edge] (\source) -- (\dest); 
+                    \path<2>[edge] (\source) -- (\dest);
 
                     \foreach \pos/\name in {{(0,0)/a}, {(0,1.5)/b}, {(2,0)/c},{(2,1.5)/d}}
                     \node<3,5>[vertex] (\name) at \pos {};
@@ -262,12 +262,12 @@
                     {(1,6.5)/k}}
                     \node<3,5>[vertex, fill=red!25] (\name) at \pos {};
 
-                    \node<3,5>[vertex, fill=green!25] (e) at (-1,2.5) {};                
+                    \node<3,5>[vertex, fill=green!25] (e) at (-1,2.5) {};
 
                     \foreach \source/ \dest in {a/b, a/c, c/d, b/d,
                         b/e, e/f,
                     f/g, f/h, h/i, g/i, h/k}
-                    \path<3,5>[edge] (\source) -- (\dest);        
+                    \path<3,5>[edge] (\source) -- (\dest);
                     \path<3,5>[edge] (g) .. controls (3, 5.5) .. (k);
 
                     \foreach \pos/\name in {{(0,3)/a}, {(0,5)/b}, {(2,3)/c},{(2,5)/d}}
@@ -276,7 +276,7 @@
 
                     \foreach \source/ \dest in {a/b, a/c, c/d, b/d,
                     a/e, e/d}
-                    \path<4>[edge] (\source) -- (\dest); 	
+                    \path<4>[edge] (\source) -- (\dest);
                 \end{tikzpicture}
             \end{figure}
             \vspace{1em}
@@ -286,7 +286,7 @@
 
 \begin{frame}
     \frametitle{Algorithmen}
-    \begin{itemize}	
+    \begin{itemize}
         \item \alert{Knotenbasiert}
             \begin{itemize}
                 \item Ein Graph bleibt planar wenn man einzelne Knoten entfernt
@@ -352,11 +352,11 @@
 
                     \foreach \source/ \dest in {a/b, b/c, c/d, c/e, e/f, e/g,
                     b/h, h/i, i/j, i/k}
-                    \path[tree edge] (\source) -- (\dest);        
+                    \path[tree edge] (\source) -- (\dest);
 
                     \foreach \source/\dest/\ctrl in {{f/b/(2.5, 9.2)}, {g/c/(0.5,5)}, {d/a/(-2,2)},
                     {j/b/(4.5, 3)}, {k/b/(6,3)}}
-                    \path[back edge] (\source) .. controls \ctrl .. (\dest);         
+                    \path[back edge] (\source) .. controls \ctrl .. (\dest);
                 \end{tikzpicture}
             \end{figure}
             \vspace{1em}
@@ -386,19 +386,19 @@
             \foreach \source/ \dest in {a/b, b/c, c/d, d/e, e/f, e/g,
                 e/h, h/i, i/j, j/k,
             h/l, l/m, m/n}
-            \path<2->[tree edge] (\source) -- (\dest);        
+            \path<2->[tree edge] (\source) -- (\dest);
 
             \foreach \source/ \dest in {f/b, k/c, k/i, j/a, g/d, m/e, n/l, n/a}
-            \path<1>[edge] (\source) -- (\dest);      
+            \path<1>[edge] (\source) -- (\dest);
 
             \foreach \source/ \dest in {f/b, k/c, k/i, j/a, g/d, m/e, n/l, n/a}
-            \path<2>[back edge] (\source) -- (\dest); 
+            \path<2>[back edge] (\source) -- (\dest);
 
             \foreach \source/ \dest in {f/b, m/e, n/a}
-            \path<3>[left edge] (\source) -- (\dest);     
+            \path<3>[left edge] (\source) -- (\dest);
 
             \foreach \source/ \dest in {k/c, k/i, j/a, g/d, n/l}
-            \path<3>[right edge] (\source) -- (\dest); 
+            \path<3>[right edge] (\source) -- (\dest);
 
             \draw<2> (0,0) node {DFS};
             \draw<3> (0,0) node {LR-Zerlegung};
@@ -419,14 +419,14 @@
     \begin{center}
         \begin{figure}
             \begin{tikzpicture}[auto]
-                \useasboundingbox (-2, 0.5) rectangle (7, 5);	
+                \useasboundingbox (-2, 0.5) rectangle (7, 5);
 
                 \draw[edge] (0,0.5) -- (0,3);
                 \draw[edge] (-1.5,4) -- (0,3) node[midway, above] {};
                 \draw[edge] (1.5,4) -- (0,3) node[midway, above] {};
 
                 \draw[left edge, rounded corners] (-1.5,4) .. controls (-0.5,1) .. (0,1);
-                \draw[right edge] (1.5,4) .. controls (0.5,2) .. (0,2);    
+                \draw[right edge] (1.5,4) .. controls (0.5,2) .. (0,2);
 
 
                 \draw[edge] (4.5,0.5) -- (4.5,3);
@@ -434,10 +434,10 @@
                 \draw[edge] (6,4) -- (4.5,3) node[midway, above] {};
 
                 \draw[right edge, rounded corners] (3,4) .. controls (8.5,6) and (5.5,1) .. (4.5,1);
-                \draw[right edge] (6,4) .. controls (5,2) .. (4.5,2);   
+                \draw[right edge] (6,4) .. controls (5,2) .. (4.5,2);
             \end{tikzpicture}
         \end{figure}
-    \end{center}	
+    \end{center}
 \end{frame}
 
 \begin{frame}
@@ -454,24 +454,24 @@
     \begin{center}
         \begin{figure}
             \begin{tikzpicture}[auto, scale=0.5]
-                \useasboundingbox (-4, 2) rectangle (4, 9);	
+                \useasboundingbox (-4, 2) rectangle (4, 9);
 
                 \node[small vertex] (u) at (0,3) {};
                 \node[small vertex] (v) at (0,6) {$v$};
-                \node[small vertex] (w) at (-2,8) {};	
+                \node[small vertex] (w) at (-2,8) {};
                 \node[small vertex] (x) at (2,8) {};
 
                 \path[edge] (u) -- (v);
                 \path[edge, ->] (v) -- (w) node[midway, below] {$e_1$};
-                \path[edge, ->] (v) -- (x) node[midway, below] {$e_2$};	
+                \path[edge, ->] (v) -- (x) node[midway, below] {$e_2$};
                 \path[edge] (0,2) -- (u);
 
                 \draw[left edge] (w) .. controls (-2, 5) .. (u);
                 \draw[right edge] (x) .. controls (2, 5) .. (u);
                 \draw[back edge] (w) .. controls (-3, 5) .. (0,2);
-                \draw[back edge] (x) .. controls (3, 5) .. (0,2);	
+                \draw[back edge] (x) .. controls (3, 5) .. (0,2);
             \end{tikzpicture}
-        \end{figure}		
+        \end{figure}
     \end{center}
 \end{frame}
 
@@ -482,7 +482,7 @@
         Ein Graph ist genau dann planar, wenn er eine \alert{LR-Zerlegung} zulässt.
     \end{theorem}
 
-    \vspace{2em}	
+    \vspace{2em}
 
     \begin{itemize}
         \item Planare Zeichnung $\rightarrow$ LR-Zerlegung intuitiv
@@ -510,14 +510,14 @@
     \begin{center}
         \begin{figure}
             \begin{tikzpicture}[auto]
-                \useasboundingbox (-2, 0.5) rectangle (7, 5);	
+                \useasboundingbox (-2, 0.5) rectangle (7, 5);
 
                 \draw[edge] (0,1) -- (0,3);
                 \draw[edge] (-1.5,4) -- (0,3) node[midway, above] {$e_1$};
                 \draw[edge] (1.5,4) -- (0,3) node[midway, above] {$e_2$};
 
                 \draw[back edge, rounded corners] (-1.5,4) .. controls (4,6) and (1,1) .. (0,1);
-                \draw[back edge] (1.5,4) .. controls (0.5,2) .. (0,2);    
+                \draw[back edge] (1.5,4) .. controls (0.5,2) .. (0,2);
 
 
                 \draw[edge] (4.5,1) -- (4.5,3);
@@ -525,29 +525,29 @@
                 \draw[edge] (6,4) -- (4.5,3) node[midway, above] {$e_2$};
 
                 \draw[back edge, rounded corners] (3,4) .. controls (8.5,6) and (5.5,1) .. (4.5,1);
-                \draw[back edge] (6,4) .. controls (5,2) .. (4.5,2);   
-                \draw[back edge] (6,4) .. controls (5.5,2) .. (4.5,1);   
+                \draw[back edge] (6,4) .. controls (5,2) .. (4.5,2);
+                \draw[back edge] (6,4) .. controls (5.5,2) .. (4.5,1);
             \end{tikzpicture}
         \end{figure}
     \end{center}
 \end{frame}
 
 \begin{frame}
-    \frametitle{Verschachtelung}		
+    \frametitle{Verschachtelung}
     \begin{columns}[T]
         \begin{column}{.5\textwidth}
             \begin{figure}
                 \begin{tikzpicture}[auto, scale=0.5]
-                    \useasboundingbox (-5, 0) rectangle (5, 8);	
+                    \useasboundingbox (-5, 0) rectangle (5, 8);
 
                     \node[vertex] (u) at (0,0) {$u$};
                     \node[vertex] (v) at (0,3) {$v$};
                     \node[small vertex] (w) at (-4,3) {};
                     \node[small vertex] (x) at (-3,6) {};
-                    \node[small vertex] (y) at (-1,8) {};		
-                    \node[small vertex] (a) at (1,8) {};	
-                    \node[small vertex] (b) at (3,6) {};	
-                    \node[small vertex] (c) at (4,3) {};			
+                    \node[small vertex] (y) at (-1,8) {};
+                    \node[small vertex] (a) at (1,8) {};
+                    \node[small vertex] (b) at (3,6) {};
+                    \node[small vertex] (c) at (4,3) {};
 
                     \path[edge, ->] (u) -- (v);
                     \path[left edge] (v) -- (w) node[near end, below, black] {$e_l^L$};
@@ -563,12 +563,12 @@
         \begin{column}{.5\textwidth}
             \begin{figure}
                 \begin{tikzpicture}[auto, scale=0.5]
-                    \useasboundingbox (-5, 0) rectangle (5, 8);	
+                    \useasboundingbox (-5, 0) rectangle (5, 8);
 
                     \node[vertex] (u) at (0,0) {$u$};
                     \node[vertex] (v) at (0,3) {$v$};
                     \node[small vertex] (w) at (-3,6) {};
-                    \node[small vertex] (x) at (3,6) {};	
+                    \node[small vertex] (x) at (3,6) {};
 
                     \path[edge, ->] (u) -- (v);
                     \path[left edge] (v) -- (w) node[near end, below, black] {$e^L$};
@@ -576,14 +576,14 @@
 
                     \draw[edge] (w) -- (-4,7);
                     \draw[left edge] (-4,7) .. controls(-4, 3.5) .. (v);
-                    \draw[left edge] (-4,7) .. controls(-3, 3.5) .. (v);	
-                    \draw[right edge] (-4,7) .. controls(-2, 7) .. (v);	
+                    \draw[left edge] (-4,7) .. controls(-3, 3.5) .. (v);
+                    \draw[right edge] (-4,7) .. controls(-2, 7) .. (v);
 
                     \draw[edge] (x) -- (4,7);
-                    \draw[right edge] (4,7) .. controls(4, 3.5) .. (v);	
-                    \draw[left edge] (4,7) .. controls(2, 7) .. (v);	
+                    \draw[right edge] (4,7) .. controls(4, 3.5) .. (v);
+                    \draw[left edge] (4,7) .. controls(2, 7) .. (v);
                 \end{tikzpicture}
-            \end{figure}		
+            \end{figure}
         \end{column}
     \end{columns}
 \end{frame}
@@ -630,7 +630,7 @@
     \frametitle{Algorithmus}
 
     \begin{itemize}
-        \item Testen auf Planarität entspricht Testen auf \alert{LR-Zerlegung}	
+        \item Testen auf Planarität entspricht Testen auf \alert{LR-Zerlegung}
         \item \alert{LR-Zerlegung} stellt Randbedingungen
             \vspace{2em}
         \item Welche Bedingungen gibt es?
@@ -649,11 +649,11 @@
         \begin{column}{.33\textwidth}
             \begin{figure}
                 \begin{tikzpicture}[auto, scale=0.5]
-                    \useasboundingbox (-4, 0) rectangle (4, 9);	
+                    \useasboundingbox (-4, 0) rectangle (4, 9);
 
                     \node[small vertex] (u) at (0,3) {};
                     \node[small vertex] (v) at (0,6) {$v$};
-                    \node[small vertex] (w) at (-2,8) {$w_1$};	
+                    \node[small vertex] (w) at (-2,8) {$w_1$};
 
                     \path[edge] (u) -- (v);
                     \path[edge, ->] (v) -- (w);
@@ -665,50 +665,50 @@
 
                     \draw[right edge] (2, 8) .. controls (2, 4) .. (0,2);
                 \end{tikzpicture}
-            \end{figure}				
+            \end{figure}
         \end{column}
         \begin{column}{.33\textwidth}
             \begin{figure}
                 \begin{tikzpicture}[auto, scale=0.5]
-                    \useasboundingbox (-4, 0) rectangle (4, 9);	
+                    \useasboundingbox (-4, 0) rectangle (4, 9);
 
                     \node[small vertex] (u) at (0,3) {};
                     \node[small vertex] (v) at (0,6) {$v$};
-                    \node[small vertex] (w) at (-2,8) {$w_1$};	
+                    \node[small vertex] (w) at (-2,8) {$w_1$};
                     \node[small vertex] (x) at (2,8) {$w_2$};
 
                     \path[edge] (u) -- (v);
                     \path[edge, ->] (v) -- (w);
-                    \path[edge, ->] (v) -- (x);	
+                    \path[edge, ->] (v) -- (x);
                     \draw[edge] (0,0) -- (u);
 
                     \draw[left edge] (w) .. controls (-2, 5) .. (u);
                     \draw[right edge] (x) .. controls (2, 5) .. (u);
                     \draw[back edge] (w) .. controls (-3, 5) .. (-1,1);
-                    \draw[back edge] (x) .. controls (3, 5) .. (1,1);	
+                    \draw[back edge] (x) .. controls (3, 5) .. (1,1);
                 \end{tikzpicture}
-            \end{figure}	
+            \end{figure}
         \end{column}
         \begin{column}{.33\textwidth}
             \begin{figure}
                 \begin{tikzpicture}[auto, scale=0.5]
-                    \useasboundingbox (-4, 0) rectangle (4, 9);	
+                    \useasboundingbox (-4, 0) rectangle (4, 9);
 
                     \node[small vertex] (u) at (0,3) {$v_2$};
                     \node[small vertex] (v) at (0,5) {$v_1$};
-                    \node[small vertex] (w) at (0,7) {$x$};	
+                    \node[small vertex] (w) at (0,7) {$x$};
                     \node[small vertex] (x) at (0,9) {};
 
                     \path[edge] (u) -- (v);
                     \path[edge] (v) -- (w);
-                    \path[edge] (w) -- (x);	
+                    \path[edge] (w) -- (x);
                     \draw[edge] (0,0) -- (u);
 
                     \draw[right edge] (x) .. controls (3, 7) .. (u);
                     \draw[right edge] (x) .. controls (1.5, 7) .. (v);
-                    \draw[back edge] (w) .. controls (-2, 5) .. (0,1);	
+                    \draw[back edge] (w) .. controls (-2, 5) .. (0,1);
                 \end{tikzpicture}
-            \end{figure}	
+            \end{figure}
         \end{column}
     \end{columns}
 \end{frame}
@@ -723,7 +723,7 @@
         \end{itemize}
     \end{block}
 
-    \alert{$C(b)$} bezeichnet Knoten auf dem Zyklus, der durch $b$ geschlossen wird.	
+    \alert{$C(b)$} bezeichnet Knoten auf dem Zyklus, der durch $b$ geschlossen wird.
 \end{frame}
 
 \begin{frame}
@@ -752,13 +752,13 @@
             \foreach \source/ \dest in {a/b, b/c, c/d, d/e, e/f, e/g,
                 e/h, h/i, i/j, j/k,
             h/l, l/m, m/n}
-            \path<1>[tree edge] (\source) -- (\dest);        
+            \path<1>[tree edge] (\source) -- (\dest);
 
             \foreach \source/ \dest in {f/b, m/e, n/a}
-            \path<1>[left edge] (\source) -- (\dest);     
+            \path<1>[left edge] (\source) -- (\dest);
 
             \foreach \source/ \dest in {k/c, k/i, j/a, g/d, n/l}
-            \path<1>[right edge] (\source) -- (\dest); 
+            \path<1>[right edge] (\source) -- (\dest);
 
             \begin{pgfonlayer}{background}
                 \foreach \pos/\name/\ctn in {{(0,1)/a/1},{(0,2)/b/2},{(1,3)/c/3},{(0.75,4)/d/4},{(-0.5,4.5)/e/5},
@@ -770,11 +770,11 @@
                 \foreach \source/ \dest in {a/b, b/c, c/d, d/e, e/f, e/g,
                     e/h, h/i, i/j, j/k,
                 h/l, l/m, m/n}
-                \path<2->[tree edge, opacity=0.35] (\source) -- (\dest);        
+                \path<2->[tree edge, opacity=0.35] (\source) -- (\dest);
 
                 \foreach \source/ \dest / \name in {f/b, m/e, n/a}
                 \path<2->[left edge, opacity=0.35] (\source) -- (\dest)
-                node[midway, anchor=center] (\source\dest) {};     
+                node[midway, anchor=center] (\source\dest) {};
 
                 \foreach \source/ \dest in {k/c, k/i, j/a, g/d, n/l}
                 \path<2->[right edge, opacity=0.35] (\source) -- (\dest)
@@ -785,16 +785,16 @@
             \node<2->[fill=blue,minimum size=10pt] at (\source\dest) {};
 
             \foreach \source/ \dest in {k/c, k/i, j/a, g/d, n/l}
-            \node<2->[fill=red,minimum size=10pt] at (\source\dest) {};    		
+            \node<2->[fill=red,minimum size=10pt] at (\source\dest) {};
 
             \begin{pgfonlayer}{midground}
                 \path<3->[edge, ultra thick] (kc.center) -- (ki.center) node[midway] {s};
                 \path<4->[edge, ultra thick] (me.center) -- (nl.center) node[midway, above] {v};
                 \path<5->[edge, ultra thick] (me.center) -- (kc.center) node[midway] {v};
-                \path<5->[edge, ultra thick] (fb.center) -- (kc.center) node[midway] {v};        
+                \path<5->[edge, ultra thick] (fb.center) -- (kc.center) node[midway] {v};
             \end{pgfonlayer}
         \end{tikzpicture}
-    \end{figure}	
+    \end{figure}
 \end{frame}
 
 \begin{frame}
@@ -819,13 +819,13 @@
 \begin{frame}
     \frametitle{Q \& A}
 
-    \begin{center} \LARGE Danke für die Aufmerksamkeit!\end{center} 	
-    \vspace{1em}	
-    \begin{center} \LARGE Fragen?\end{center} 	
+    \begin{center} \LARGE Danke für die Aufmerksamkeit!\end{center}
+    \vspace{1em}
+    \begin{center} \LARGE Fragen?\end{center}
 \end{frame}
 
 \begin{frame}[plain]
-    \begin{center} \LARGE Backup\end{center} 
+    \begin{center} \LARGE Backup\end{center}
 \end{frame}
 
 \begin{frame}
@@ -837,26 +837,26 @@
     \end{itemize}
 
     \begin{figure}
-        \begin{tikzpicture}[auto]	
+        \begin{tikzpicture}[auto]
             \foreach \pos/\name in {{(0,0)/a}, {(-3, 1)/b}, {(3, 1)/c},{(-2, 3)/d},
             {(2,2.5)/e}}
             \node[small vertex] (\name) at \pos {};
 
             \foreach \source/ \dest in {a/b, a/c, c/e, b/d,
             a/d, e/a}
-            \path[edge] (\source) -- (\dest);	
+            \path[edge] (\source) -- (\dest);
 
             \draw[dashed] (d) -- (-2, 4);
             \draw[dashed] (d) -- (-1, 2.5);
             \draw[dashed] (e) -- (2.5, 3);
-            \draw[dashed] (e) -- (1.5, 3.5);  
+            \draw[dashed] (e) -- (1.5, 3.5);
 
             \begin{pgfonlayer}{background}
-                \fill[red!50] (a.center) -- (b.center) -- (d.center);	
-                \fill[red!50] (a.center) -- (c.center) -- (e.center);	
+                \fill[red!50] (a.center) -- (b.center) -- (d.center);
+                \fill[red!50] (a.center) -- (c.center) -- (e.center);
             \end{pgfonlayer}
         \end{tikzpicture}
-    \end{figure}		
+    \end{figure}
 \end{frame}
 
 \begin{frame}
@@ -876,7 +876,7 @@
                 \item<3> Teilgraph als Segment
             \end{itemize}
         \end{column}
-        \begin{column}{.4\textwidth}	
+        \begin{column}{.4\textwidth}
             \begin{figure}
                 \begin{tikzpicture}[auto, scale=0.8]
                     \foreach \pos/\name in {{(0,0)/a}, {(0,2)/b}, {(4,0)/c},{(4,2)/d},
@@ -890,24 +890,24 @@
                         e/g, g/h, h/k, k/i, i/f,
                         g/k, h/f,
                     l/m, m/n, n/l, a/l, m/d}
-                    \path[edge] (\source) -- (\dest);        
+                    \path[edge] (\source) -- (\dest);
 
                     \foreach \vertex / \fr in {g/2, k/2, h/2, f/2,
                         l/3, m/3, n/3, a/3, d/3
                     }
                     \path<\fr> node[selected vertex] at (\vertex) {};
 
-                    \begin{pgfonlayer}{background}        
+                    \begin{pgfonlayer}{background}
                         \foreach \source / \dest / \fr in {g/k/2, h/f/2,
                             l/m/3, m/n/3, n/l/3, a/l/3, m/d/3
                         }
                         \path<\fr>[selected edge] (\source) -- (\dest);
-                    \end{pgfonlayer}  
+                    \end{pgfonlayer}
                 \end{tikzpicture}
             \end{figure}
             \vspace{1em}
         \end{column}
-    \end{columns}	
+    \end{columns}
 \end{frame}
 
 \begin{frame}
--- a/theme/LEA_beamer/beamerthemeLEA2.sty	Thu Dec 13 19:36:52 2012 +0100
+++ b/theme/LEA_beamer/beamerthemeLEA2.sty	Fri Dec 14 22:42:15 2012 +0100
@@ -38,16 +38,16 @@
 \logo{\pgfuseimage{uni}}
 
 \defbeamertemplate*{footline}{infolines theme}{%
-	\hspace*{2ex}\raisebox{1.5ex}[-1.5ex]{%
-	\tiny\insertframenumber{}/\inserttotalframenumber \hspace{5mm} \insertnavigation{0.8\paperwidth}}%
+    \hspace*{2ex}\raisebox{1.5ex}[-1.5ex]{%
+    \tiny\insertframenumber{}/\inserttotalframenumber \hspace{5mm} \insertnavigation{0.8\paperwidth}}%
 }
 
 \setbeamertemplate{frametitle}{
-	\begin{beamercolorbox}[wd=80mm,leftskip=0mm]{frametitle}
-		\usebeamerfont*{frametitle}
-		\insertframetitle\hfill\parbox{10mm}{\vspace{-2mm}\insertlogo}\hspace{-2mm}
-	\end{beamercolorbox}
-	\vspace{-3mm}\textcolor{tumblue}{\noindent\rule{\textwidth}{0.4px}}
+    \begin{beamercolorbox}[wd=80mm,leftskip=0mm]{frametitle}
+        \usebeamerfont*{frametitle}
+        \insertframetitle\hfill\parbox{10mm}{\vspace{-2mm}\insertlogo}\hspace{-2mm}
+    \end{beamercolorbox}
+    \vspace{-3mm}\textcolor{tumblue}{\noindent\rule{\textwidth}{0.4px}}
 }
 % hier kein Logo
 \setbeamertemplate{sidebar right}{\vfill\vskip2pt\llap{\usebeamertemplate***{navigation symbols}\hskip1mm}\vskip2pt}
--- a/theme/LEA_beamer/example.tex	Thu Dec 13 19:36:52 2012 +0100
+++ b/theme/LEA_beamer/example.tex	Fri Dec 14 22:42:15 2012 +0100
@@ -26,9 +26,9 @@
 \newcommand{\inter}   {\cap}                % Schnittmenge
 \newcommand{\union}   {\cup}                % Vereinigung
 \newcommand{\Oh}      {O}                   % O-Notation (Landau-Symbole)
-\newcommand{\mycite}[1]{\textcolor{tumgreen}{[#1]}} 
+\newcommand{\mycite}[1]{\textcolor{tumgreen}{[#1]}}
 
-\newenvironment{changemargin}[2]{% 
+\newenvironment{changemargin}[2]{%
   \begin{list}{}{%
     \setlength{\topsep}{0pt}%
     \setlength{\leftmargin}{#1}%
@@ -41,7 +41,7 @@
 
 \title{Title of the talk}
 \subtitle{Proseminar ``XY''}
-\author{\href{mailto:mail@example.com}{Vorname Nachname}} 
+\author{\href{mailto:mail@example.com}{Vorname Nachname}}
 \date{\today}
 %\date{2011-09-07}
 \institute{Technische Universität München}
--- a/theme/LEA_paper/example.tex	Thu Dec 13 19:36:52 2012 +0100
+++ b/theme/LEA_paper/example.tex	Fri Dec 14 22:42:15 2012 +0100
@@ -7,11 +7,11 @@
 \usepackage[pdftex]{hyperref}
 
 \ifpdf
-	\usepackage[pdftex]{graphicx}
-	\DeclareGraphicsExtensions{.pdf, .png, .jpg}
+    \usepackage[pdftex]{graphicx}
+    \DeclareGraphicsExtensions{.pdf, .png, .jpg}
 \else
-	\usepackage[dvips]{graphicx}
-	\DeclareGraphicsExtensions{.eps}
+    \usepackage[dvips]{graphicx}
+    \DeclareGraphicsExtensions{.eps}
 \fi
 
 \title{Ein kleines Beispiel}
@@ -64,7 +64,7 @@
 mathematische Formel im Text kommen $2^2=4$ oder wenn es etwas wichtiges
 ist, dann kann ich diese Formel auch hervorheben:
 \begin{align}
-	E = m \cdot c^2
+    E = m \cdot c^2
 \end{align}
 
 Dann kann wieder ein neuer Abschnitt kommen.
@@ -74,26 +74,26 @@
 Jetzt k\"onnen viele andere Latexkonstrukte eingebunden werden. Z.B.
 
 \begin{itemize}
-	\item Aufz\"ahlungen
-	\item Tabellen
-	\item \test
-	\item etc.
+    \item Aufz\"ahlungen
+    \item Tabellen
+    \item \test
+    \item etc.
 \end{itemize}
 
 \begin{theorem}[Mein Haupttheorem]
-	Hier steht dann die Behauptung meines Theorems
-	\begin{align}
-		1+1 = 2
-	\end{align}
+    Hier steht dann die Behauptung meines Theorems
+    \begin{align}
+        1+1 = 2
+    \end{align}
 \end{theorem}
 
 \begin{hypothesis} Hier steht dann die wichtige Vermutung
-	\begin{align}
-		2+2 = 4
-	\end{align}
+    \begin{align}
+        2+2 = 4
+    \end{align}
 \end{hypothesis}
 
-Nachdem alles ganz genau beschrieben ist, kommt ganz zum Schluss noch das 
+Nachdem alles ganz genau beschrieben ist, kommt ganz zum Schluss noch das
 Literaturverzeichnis.
 
 \bibliographystyle{alpha}
--- a/theme/LEA_paper/seminararbeit.tex	Thu Dec 13 19:36:52 2012 +0100
+++ b/theme/LEA_paper/seminararbeit.tex	Fri Dec 14 22:42:15 2012 +0100
@@ -7,11 +7,11 @@
 \usepackage[pdftex]{hyperref}
 
 \ifpdf
-	\usepackage[pdftex]{graphicx}
-	\DeclareGraphicsExtensions{.pdf, .png, .jpg}
+    \usepackage[pdftex]{graphicx}
+    \DeclareGraphicsExtensions{.pdf,.png,.jpg}
 \else
-	\usepackage[dvips]{graphicx}
-	\DeclareGraphicsExtensions{.eps}
+    \usepackage[dvips]{graphicx}
+    \DeclareGraphicsExtensions{.eps}
 \fi
 
 \title{Hier den Titel eintragen}
@@ -24,10 +24,9 @@
 \maketitle
 
 \begin{abstract}
-  Hier die Zusammenfassung eintragen
+Hier die Zusammenfassung eintragen.
 \end{abstract}
 
-...
 
 \bibliographystyle{alpha}
 \bibliography{seminararbeit}