\newcommand{\mat}[1]{\ensuremath{\mathbf #1}}
 \newcommand{\set}[1]{\ensuremath{\mathbf #1}}
 \newcommand{\cset}[1]{\ensuremath{\mathbf{\mathcal #1}}}
 \renewcommand{\vec}[1]{\ensuremath{\mathbf #1}}
 
 \newcommand{\nth}[1]{\ensuremath{#1^\mathrm{th}}}
 \newcommand{\fst}[1]{\ensuremath{#1^\mathrm{st}}}
 \newcommand{\snd}[1]{\ensuremath{#1^\mathrm{nd}}}
 
 \newcommand{\argmax}[1]{\ensuremath{\arg\hspace{-0.4ex}\max_{\hspace*{-3.0ex}#1}}}
 \newcommand{\argmin}[1]{\ensuremath{\arg\min_{\hspace*{-4.0ex}#1}}}
 
 \newcommand{\argmaxi}[1]{\ensuremath{\arg\hspace{-0.4ex}\max_{#1}}}
 \newcommand{\argmini}[1]{\ensuremath{\arg\hspace{-0.4ex}\min_{#1}}}
 
 % \newcommand{\argmin}[1]{\ensuremath{\begin{array}[t]{c} \arg \min \\
 % \vspace*{-0.1ex} #1 \end{array}}}
 
 \newcommand{\NP}{\ensuremath{\mathcal{NP}}}
 \newcommand{\PP}{\ensuremath{\mathcal{P}}}
 \newcommand{\e}[2]{\ensuremath{\{#1,#2\}}}
 \newcommand{\tup}[1]{\ensuremath{\langle#1\rangle}}
 \newcommand{\bigO}[1]{\ensuremath{\mathcal{O}\left(#1\right)}}
 
 \newcommand{\trans}[1]{\ensuremath{{#1}^\top}}
 \newcommand{\diag}[1]{\ensuremath{\mathrm{diag}\left(#1\right)}}
 
 \newcommand{\eq}[1]{equation \ref{#1}}
 \newcommand{\Eq}[1]{equation \ref{#1}}
 \newcommand{\fig}[1]{figure \ref{#1}}
 \newcommand{\Fig}[1]{figure \ref{#1}}
 \newcommand{\chap}[1]{chapter \ref{#1}}
 \newcommand{\Chap}[1]{chapter \ref{#1}}
 \newcommand{\sect}[1]{section \ref{#1}}
 \newcommand{\Sect}[1]{section \ref{#1}}
 
 \newcommand{\bydefn}{\ensuremath{\stackrel{\bigtriangleup}{=}}}
 \newcommand{\elmat}[2]{\ensuremath{#1 \odot #2}}
 
 \newcommand{\prune}[1]{\ensuremath{\mathrm{prune}\left(#1\right)}}
 
 \newcommand{\labelfig}[2]{\parbox[b]{0.2in}{\Large#1\normalsize\vspace{#2}}}
 % \newcommand{\labelfig}[1]{\parbox[b]{0.2in}{#1\vspace{1.8in}}}
 
 % \newcommand{\emptyset}{\ensuremath{\O}}
 
 \renewcommand{\Re}{\mathbb{R}}
 
 \newcommand{\incfig}[3]{\ifx\pdfoutput\undefined
                           \epsfig{#1.eps,#2,#3}
                         \else
                           \epsfig{#1.eps,#2,#3}
                         \fi}
           
 % Eigene Befehle %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \newcommand{\todo}[1]{
       {\colorbox{red}{ TODO: #1 }}
 }
 
 \newcommand{\todotext}[1]{
       {\color{red} TODO: #1} \normalfont
 }
 
 \newcommand{\info}[1]{
       {\colorbox{blue}{ (INFO: #1)}}
 }
 
 \newcommand{\infotext}[1]{
       {\color{blue}{ (INFO: #1)}}
 }
 
 % Hinweis auf Programme in Datei
 \newcommand{\datei}[1]{
       {\ttfamily{#1}}
 }
 
 \newcommand{\code}[1]{
       {\small \ttfamily {#1}}
 }