296 lines
8.9 KiB
TeX
296 lines
8.9 KiB
TeX
\documentclass[a4paper, 12pt]{article}
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%%
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%% Python definition (c) 1998 Michael Weber
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%% Additional definitions (2013) Alexis Dimitriadis
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%%
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%
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%
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%
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morestring=[s]{r'''}{'''},%
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morestring=[s]{u"}{"},%
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morestring=[s]{u'''}{'''},%
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morestring=[s]{u"""}{"""},%
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%
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% *{-}{-}{1} will not replace in comments and so on
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literate=
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{á}{{\'a}}1 {é}{{\'e}}1 {í}{{\'i}}1 {ó}{{\'o}}1 {ú}{{\'u}}1
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{Á}{{\'A}}1 {É}{{\'E}}1 {Í}{{\'I}}1 {Ó}{{\'O}}1 {Ú}{{\'U}}1
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{à}{{\`a}}1 {è}{{\`e}}1 {ì}{{\`i}}1 {ò}{{\`o}}1 {ù}{{\`u}}1
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{À}{{\`A}}1 {È}{{\'E}}1 {Ì}{{\`I}}1 {Ò}{{\`O}}1 {Ù}{{\`U}}1
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{ä}{{\"a}}1 {ë}{{\"e}}1 {ï}{{\"i}}1 {ö}{{\"o}}1 {ü}{{\"u}}1
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{Ä}{{\"A}}1 {Ë}{{\"E}}1 {Ï}{{\"I}}1 {Ö}{{\"O}}1 {Ü}{{\"U}}1
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{â}{{\^a}}1 {ê}{{\^e}}1 {î}{{\^i}}1 {ô}{{\^o}}1 {û}{{\^u}}1
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{Â}{{\^A}}1 {Ê}{{\^E}}1 {Î}{{\^I}}1 {Ô}{{\^O}}1 {Û}{{\^U}}1
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{œ}{{\oe}}1 {Œ}{{\OE}}1 {æ}{{\ae}}1 {Æ}{{\AE}}1 {ß}{{\ss}}1
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{ç}{{\c c}}1 {Ç}{{\c C}}1 {ø}{{\o}}1 {å}{{\r a}}1 {Å}{{\r A}}1
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{€}{{\EUR}}1 {£}{{\pounds}}1
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%
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{^}{{{\color{ipython_purple}\^{}}}}1
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%
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{+}{{{\color{ipython_purple}+}}}1
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{*}{{{\color{ipython_purple}$^\ast$}}}1
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{/}{{{\color{ipython_purple}/}}}1
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%
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{+=}{{{+=}}}1
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{-=}{{{-=}}}1
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{*=}{{{$^\ast$=}}}1
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{/=}{{{/=}}}1,
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literate=
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{?}{{{\color{ipython_purple}?}}}1,
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%
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%
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rulecolor=\color{ipython_frame},
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%
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%
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% extendedchars=true,
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\usepackage[authordate, backend=bibtex, firstinits = true]{biblatex-chicago}
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\urlstyle{same}
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\bibliography{bibliograpy.bib}
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\numberwithin{figure}{section}
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\numberwithin{table}{section}
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\numberwithin{equation}{section}
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\sectionfont{\centering}
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\input{insbox}
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%\parindent0in
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\pagestyle{plain}
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\thispagestyle{plain}
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\newtheorem{Theorem}{Theorem}[section]
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\newtheorem{Definition}[Theorem]{Definition}
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\newtheorem{Lemma}[Theorem]{Lemma}
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\newtheorem{Algorithm}[Theorem]{Algorithm}
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\newtheorem{Example}[Theorem]{Example}
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\newtheorem{Assumption}[Theorem]{Assumption}
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\newtheorem{Proof}[Theorem]{Proof}
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\DeclareMathOperator*{\plim}{\mathbb{P}\text{-}\lim}
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\DeclareMathOperator{\supp}{supp}
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\DeclareMathOperator*{\argmin}{arg\,min}
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\DeclareMathOperator*{\argmax}{arg\,max}
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\DeclareMathOperator*{\po}{\mathbb{P}\text{-}\mathcal{O}}
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\DeclareMathOperator*{\equals}{=}
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\begin{document}
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\newcommand{\plimn}[0]{\plim\limits_{n \to \infty}}
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\newcommand{\norm}[1]{\left\lVert#1\right\rVert}
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\newcommand*\circled[1]{\tikz[baseline=(char.base)]{
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\node[shape=circle,draw,inner sep=2pt] (char) {#1};}}
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\newcommand{\abs}[1]{\ensuremath{\left\vert#1\right\vert}}
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\newcommand\Tstrut{\rule{0pt}{2.6ex}} % = `top' strut
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\newcommand\Bstrut{\rule[-0.9ex]{0pt}{0pt}} % = `bottom' strut
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\SetKwInput{KwInput}{Input}
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%\newcommand{\myrightarrow}[1]{\xrightarrow{\makebox[2em][c]{$\scriptstyle#1$}}}
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%Arndt Tobias \hfill 21.12.2017\newline
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%\textbf{Seminar Machine--Learning: Unsupervised %Learning} \newline
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%Institut für Mathematik der Universität %Augsburg\\
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%Lehrstuhl für Rechnerorientierte Statistik und %Datenanalyse\\
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\begin{center}
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\huge \textbf{Master Thesis}\\
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\vspace{1cm}
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\Large \textbf{University Augsburg\\Department of Mathematics\\Chair of
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Computational Statistics and Data Analysis}
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\vspace{1cm}
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\end{center}
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\begin{figure}[h]
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\centering
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\includegraphics[scale=1.3]{Figures/Uni_Aug_Siegel_32Grad_schwarz.png}
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\end{figure}
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\begin{center}
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\vspace{1cm}
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\huge \textbf{Neural Networks and their Application on Higher Complexity Problems}\\
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\vspace{1cm}
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\huge \textbf{Tim Tobias Arndt}\\
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\vspace{1cm}
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\Large \textbf{October 2020}
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\end{center}
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\pagenumbering{gobble}
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\clearpage
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%\setcounter{tocdepth}{4}
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\tableofcontents
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\clearpage
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\listoffigures
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\listoftables
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\newpage
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\pagenumbering{arabic}
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% Introduction
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\input{introduction}
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\newpage
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% Introduction Neural Networks
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\input{introduction_nn}
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\newpage
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% Theorem 3.8
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\input{theo_3_8}
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\newpage
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% Kapitel 4
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\input{further_applications_of_nn}
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\newpage
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\DeclareNameAlias{sortname}{last-first}
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\printbibliography
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% Appendix A
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\input{appendixA.tex}
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: t
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%%% End:
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