diff --git a/documents/GeoTopo/GeoTopo.tex b/documents/GeoTopo/GeoTopo.tex index b29d8b1..21691ac 100644 --- a/documents/GeoTopo/GeoTopo.tex +++ b/documents/GeoTopo/GeoTopo.tex @@ -75,10 +75,10 @@ \renewcommand{\headrulewidth}{0pt} } -\hypersetup{ - pdfauthor = {Martin Thoma}, - pdfkeywords = {Geometrie, Topologie}, - pdftitle = {Geometrie und Topologie} +\hypersetup{ + pdfauthor = {Martin Thoma}, + pdfkeywords = {Geometrie, Topologie}, + pdftitle = {Geometrie und Topologie} } \makeindex @@ -108,9 +108,9 @@ \clearpage \input{Abkuerzungen} \clearpage -\input{Definitionen} +\input{Definitionen} \clearpage -\input{Symbolverzeichnis} +\input{Symbolverzeichnis} \clearpage \addcontentsline{toc}{chapter}{Stichwortverzeichnis} \renewcommand{\indexname}{Stichwortverzeichnis} diff --git a/presentations/Sommerakademie-2015-Forschung/.gitignore b/presentations/Sommerakademie-2015-Forschung/.gitignore new file mode 100644 index 0000000..ad74c65 --- /dev/null +++ b/presentations/Sommerakademie-2015-Forschung/.gitignore @@ -0,0 +1,126 @@ +## Core latex/pdflatex auxiliary files: +*.aux +*.lof +*.log +*.lot +*.fls +*.out +*.toc + +## Intermediate documents: +*.dvi +*-converted-to.* +# these rules might exclude image files for figures etc. +# *.ps +# *.eps +# *.pdf + +## Bibliography auxiliary files (bibtex/biblatex/biber): +*.bbl +*.bcf +*.blg +*-blx.aux +*-blx.bib +*.brf +*.run.xml + +## Build tool auxiliary files: +*.fdb_latexmk +*.synctex +*.synctex.gz +*.synctex.gz(busy) +*.pdfsync + +## Auxiliary and intermediate files from other packages: + +# algorithms +*.alg +*.loa + +# achemso +acs-*.bib + +# amsthm +*.thm + +# beamer +*.nav +*.snm +*.vrb + +#(e)ledmac/(e)ledpar +*.end +*.[1-9] +*.[1-9][0-9] +*.[1-9][0-9][0-9] +*.[1-9]R +*.[1-9][0-9]R +*.[1-9][0-9][0-9]R +*.eledsec[1-9] +*.eledsec[1-9]R +*.eledsec[1-9][0-9] +*.eledsec[1-9][0-9]R +*.eledsec[1-9][0-9][0-9] +*.eledsec[1-9][0-9][0-9]R + +# glossaries +*.acn +*.acr +*.glg +*.glo +*.gls + +# gnuplottex +*-gnuplottex-* + +# hyperref +*.brf + +# knitr +*-concordance.tex +*.tikz +*-tikzDictionary + +# listings +*.lol + +# makeidx +*.idx +*.ilg +*.ind +*.ist + +# minitoc +*.maf +*.mtc +*.mtc0 + +# minted +_minted* +*.pyg + +# morewrites +*.mw + +# nomencl +*.nlo + +# sagetex +*.sagetex.sage +*.sagetex.py +*.sagetex.scmd + +# sympy +*.sout +*.sympy +sympy-plots-for-*.tex/ + +# todonotes +*.tdo + +# xindy +*.xdy + +# WinEdt +*.bak +*.sav diff --git a/presentations/Sommerakademie-2015-Forschung/Makefile b/presentations/Sommerakademie-2015-Forschung/Makefile new file mode 100644 index 0000000..31ec4ae --- /dev/null +++ b/presentations/Sommerakademie-2015-Forschung/Makefile @@ -0,0 +1,10 @@ +SOURCE = Sommerakademie-2015-Forschung + +make: + #latexmk -pdf -pdflatex="pdflatex -interactive=nonstopmode" -use-make $(SOURCE).tex + pdflatex -shell-escape $(SOURCE).tex -output-format=pdf #shellescape wird fürs logo benötigt + pdflatex -shell-escape $(SOURCE).tex -output-format=pdf # nochmaliges ausführen wegen Inhaltsverzeichnissen + make clean + +clean: + rm -rf $(TARGET) *.class *.html *.log *.aux *.out *.glo *.glg *.gls *.ist *.xdy *.1 *.toc *.snm *.nav *.vrb *.fls *.fdb_latexmk *.pyg diff --git a/presentations/Sommerakademie-2015-Forschung/README.md b/presentations/Sommerakademie-2015-Forschung/README.md new file mode 100644 index 0000000..4bd5bc4 --- /dev/null +++ b/presentations/Sommerakademie-2015-Forschung/README.md @@ -0,0 +1,28 @@ +# Interventions +Dieses Repository ist für einen 30-minütigen Vortrag bei einer Sommerakademie. +Das Thema lautet "Intervention distribution". + +Die kompilierte PDF kann [hier](https://github.com/MartinThoma/causality-presentation/raw/master/interventions.pdf) herutergeladen werden. + + +## Given + +* script 2.2. and ex. 3.1.1 + https://stat.ethz.ch/people/jopeters/index/edit/causalityHomepage/causality_files/scriptChapter1-4.pdf +* examples: intervention distribution, simpson's paradox +* Block: Causality +* Thema: interventions +* Nr: 11 +* Zeit: 30min + +## Plan + +* Einleitung: ca. 5 min +* Interventionsverteilung, def: ca. 2 min + +## Fragen + +1. Definition 2.2.1: "The set of noise variables in S now contains both ..." + - Soll hier wirklich "S" und nicht "\tilde{S}" stehen? +2. Was heißt "full support"? +3. A.2: Was ist Q? \ No newline at end of file diff --git a/presentations/Sommerakademie-2015-Forschung/Sommerakademie-2015-Forschung.tex b/presentations/Sommerakademie-2015-Forschung/Sommerakademie-2015-Forschung.tex new file mode 100644 index 0000000..4f1110e --- /dev/null +++ b/presentations/Sommerakademie-2015-Forschung/Sommerakademie-2015-Forschung.tex @@ -0,0 +1,93 @@ +\documentclass{beamer} +\usetheme{Frankfurt} +\usecolortheme{beaver} +\definecolor{links}{HTML}{2A1B81} +\hypersetup{colorlinks,linkcolor=,urlcolor=links} +\usepackage{hyperref} +\usepackage[utf8]{inputenc} % this is needed for german umlauts +\usepackage[ngerman]{babel} % this is needed for german umlauts +\usepackage[T1]{fontenc} % this is needed for correct output of umlauts in pdf +\usepackage{braket} % needed for \Set +\usepackage{csquotes} +% \usepackage{enumitem} +% \setitemize{label=\usebeamerfont*{itemize item}% +% \usebeamercolor[fg]{itemize item} +% \usebeamertemplate{itemize item}} +\usepackage{array} +\usepackage{amsmath, amssymb} +\usepackage{mathtools} +\usepackage{movie15} +\usepackage{bm} +\usepackage{dsfont} +\usepackage{nicefrac} +\usefonttheme[onlymath]{serif} +\usepackage{siunitx} % this package is for units! +\sisetup{range-phrase=--, range-units=single} + +\usepackage{booktabs} % for \toprule, \midrule and \bottomrule +\selectlanguage{ngerman} + +\usepackage{pgfplots} +\usepackage{tikz} + +\usetikzlibrary{arrows,positioning, calc} + +\newcommand {\framedgraphic}[2] { + \begin{frame}{#1} + \begin{center} + \includegraphics[width=\textwidth,height=0.8\textheight,keepaspectratio]{#2} + \end{center} + \end{frame} +} + +\setbeamertemplate{navigation symbols}{} +\addtobeamertemplate{navigation symbols}{}{% + \usebeamerfont{footline}% + \usebeamercolor[fg]{footline}% + \hspace{1em}% + \insertframenumber/\inserttotalframenumber +} +\makeatletter +\setbeamertemplate{footline} +{% + \pgfuseshading{beamer@barshade}% + \ifbeamer@sb@subsection% + \vskip-9.75ex% + \else% + \vskip-7ex% + \fi% + \begin{beamercolorbox}[ignorebg,ht=2.25ex,dp=3.75ex]{section in head/foot} + \insertnavigation{\paperwidth} + \end{beamercolorbox}% + \ifbeamer@sb@subsection% + \begin{beamercolorbox}[ignorebg,ht=2.125ex,dp=1.125ex,% + leftskip=.3cm,rightskip=.3cm plus1fil]{subsection in head/foot} + \usebeamerfont{subsection in head/foot}\insertsubsectionhead + \end{beamercolorbox}% + \fi% +}% +\setbeamertemplate{headline}{% +% \hskip1em\usebeamercolor[fg]{navigation symbols dimmed}% +% \insertslidenavigationsymbol% +% \insertframenavigationsymbol% +% \insertsectionnavigationsymbol% +% \insertsubsectionnavigationsymbol% +% \insertdocnavigationsymbol% +% \insertbackfindforwardnavigationsymbol% +} +\makeatother + +\begin{document} + +\title{On-line Recognition of Handwritten Mathematical Symbols} +\subtitle{Oder: Eine Einführung in Neuronale Netze} +\author{Martin Thoma} +\date{6. August 2015} +\subject{On-line Recognition of Handwritten Mathematical Symbols} + +\frame{\titlepage} + +\input{introduction} +% \input{main} +\input{end} +\end{document} diff --git a/presentations/Sommerakademie-2015-Forschung/end.tex b/presentations/Sommerakademie-2015-Forschung/end.tex new file mode 100644 index 0000000..fd82e0f --- /dev/null +++ b/presentations/Sommerakademie-2015-Forschung/end.tex @@ -0,0 +1,11 @@ +%!TEX root = Sommerakademie-2015-Forschung.tex +\section{Ende} +\subsection{Quellen} +\begin{frame}{Bildquellen} + \begin{itemize} + \item \href{http://imgur.com/a/Hqolp}{Visualizing Optimization Algos} + \item \href{http://blog.datumbox.com/tuning-the-learning-rate-in-gradient-descent/}{Tuning the learning rate in Gradient Descent} von Vasilis Vryniotis + \end{itemize} +\end{frame} + +\framedgraphic{Thanks for Your Attention!}{images/creative-users.png} \ No newline at end of file diff --git a/presentations/Sommerakademie-2015-Forschung/images/A-pixel.png 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b/presentations/Sommerakademie-2015-Forschung/images/function-machine.png differ diff --git a/presentations/Sommerakademie-2015-Forschung/images/gradient-descent.png b/presentations/Sommerakademie-2015-Forschung/images/gradient-descent.png new file mode 100644 index 0000000..7b0c42b Binary files /dev/null and b/presentations/Sommerakademie-2015-Forschung/images/gradient-descent.png differ diff --git a/presentations/Sommerakademie-2015-Forschung/introduction.tex b/presentations/Sommerakademie-2015-Forschung/introduction.tex new file mode 100644 index 0000000..44cfb91 --- /dev/null +++ b/presentations/Sommerakademie-2015-Forschung/introduction.tex @@ -0,0 +1,230 @@ +%!TEX root = Sommerakademie-2015-Forschung.tex +\section{Einleitung} +\subsection{Was ist On-Line Recognition?} + +\begin{frame}{Demo} + \begin{figure}[h] + \centering + \includegraphics*[width=0.7\linewidth, keepaspectratio]{images/Classification.png} + \end{figure} + + \href{http://write-math.com}{write-math.com} +\end{frame} + +\begin{frame}{Was ist On-Line Recognition?} +\medskip +\begin{columns}[t,onlytextwidth] +\begin{column}{.5\textwidth} +{\Large Off-line Recognition} +\begin{figure}[h] + \centering + \includegraphics*[width=0.7\linewidth, keepaspectratio]{images/A-pixel.png} +\end{figure} +\end{column} +\begin{column}{.5\textwidth} +{\Large On-line Recognition} +\begin{figure}[h] + \centering + \includegraphics*[width=0.7\linewidth, keepaspectratio]{images/A-vektor.png} +\end{figure} +\end{column} +\end{columns} +\end{frame} + +\begin{frame}{Was wollen wir?} + \[f(\text{Merkmale}) = \begin{pmatrix}0.7\\ 0.1\\ 0.2\end{pmatrix} = \begin{pmatrix} \mathbb{P}(\gamma)\\ \mathbb{P}(\text{ö})\\ \mathbb{P}(\heartsuit) \end{pmatrix}\] + \medskip + \visible<2->{ + \begin{center} + {\Large Gesucht: Funktion $f$}\\ + (und Merkmalsextraktion) + } + \end{center} +\end{frame} + +\begin{frame}{Merkmalsextraktion} + \begin{figure}[h] + \centering + \includegraphics*[width=0.7\linewidth, keepaspectratio]{images/A-vektor-merkmalsbildung.png} + \end{figure} + + Merkmalsvektor fester Länge ist praktisch +\end{frame} + +\section{Funktionen} +\subsection{Funktionen} + +\begin{frame}{Funktionen} +\begin{figure}[h] + \centering + \includegraphics*[width=0.7\linewidth, keepaspectratio]{images/function-machine.png} +\end{figure} +\end{frame} +\begin{frame}{Funktionen} + \medskip + \begin{columns}[t,onlytextwidth] + \begin{column}{.5\textwidth}{ + \begin{itemize}[<+->] + \item $f(x) = x^2$ ist $f: \mathbb{R} \rightarrow \mathbb{R}$ + \item $f(x, y) = x^2 + y^2$ ist $f: \mathbb{R}^2 \rightarrow \mathbb{R}$ + \item $f(x, y) = (x^2 + y^2, x \cdot y)$ ist $f: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ + \end{itemize} + } + \end{column} + \begin{column}{.4\textwidth} + \only<1>{ + \begin{tikzpicture} + \begin{axis}[ + legend pos=south west, + axis x line=middle, + axis y line=middle, + grid = major, + width=6.5cm, + height=6.5cm, + grid style={dashed, gray!30}, + xmin=-2, % start the diagram at this x-coordinate + xmax= 2, % end the diagram at this x-coordinate + ymin=-0.25, % start the diagram at this y-coordinate + ymax= 4.25, % end the diagram at this y-coordinate + axis background/.style={fill=white}, + xlabel=$x \in \mathbb{R}$, + ylabel=$f(x) \in \mathbb{R}$, + %xticklabels={-2,-1.6,...,7}, + %yticklabels={-8,-7,...,8}, + tick align=outside, + minor tick num=-3, + enlargelimits=true, + tension=0.08] + \addplot[domain=-2:2, red, thick,samples=40] {x*x}; + \end{axis} + \end{tikzpicture} + } + \only<2->{ + \pgfplotsset{ + colormap={whitered}{ + color(0cm)=(white); + color(1cm)=(orange!75!red) + } + } + \begin{tikzpicture} + \begin{axis}[ + colormap name=whitered, + width=5.5cm, + height=5.5cm, + view={340}{25}, + enlargelimits=false, + grid=major, + domain=-3:3, + y domain=-3:3, + samples=56, %57 : TeX capacity exceeded, sorry [main memory size=3000000]. + % see also http://tex.stackexchange.com/a/7954/5645 + xlabel=$x$, + ylabel=$y$, + zlabel={$f(x,y)$}, + ] + \addplot3[surf] {x^2 + y^2}; + \end{axis} + \end{tikzpicture} + } + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Funktionen mit Parametern} + \begin{columns} + \begin{column}{.5\textwidth} + {\Large Mit Parametern} + \begin{itemize}[<+->] + \item $f(x) = x^2$ + \item $f(x) = 2 \cdot x^2$ + \item $f(x) = \nicefrac{1}{2} \cdot x^2$ + \item $f(x) = a \cdot x^2$ + \item $f(x_1, \dots, x_{166}) = \sum_{i=1}^{166} a_i \cdot x_i$\\ + $\mathbb{R}^{166} \rightarrow \mathbb{R}$ + \item $f(x_1, \dots, x_{166}) = (\sum_{i=1}^{166} a_i \cdot x_i, \dots, \sum_{i=1}^{166} z_i \cdot x_i)$\\ + $\mathbb{R}^{166} \rightarrow \mathbb{R}^{\text(\# Klassen)}$ + \end{itemize} + \end{column} + \begin{column}{.4\textwidth} + \begin{tikzpicture} + \begin{axis}[ + legend pos=south west, + axis x line=middle, + axis y line=middle, + grid = major, + width=6.5cm, + height=6.5cm, + grid style={dashed, gray!30}, + xmin=-2, % start the diagram at this x-coordinate + xmax= 2, % end the diagram at this x-coordinate + ymin=-0.25, % start the diagram at this y-coordinate + ymax= 4.25, % end the diagram at this y-coordinate + axis background/.style={fill=white}, + xlabel=$x \in \mathbb{R}$, + ylabel=$f(x) \in \mathbb{R}$, + %xticklabels={-2,-1.6,...,7}, + %yticklabels={-8,-7,...,8}, + tick align=outside, + minor tick num=-3, + enlargelimits=true, + tension=0.08] + \only<1->{\addplot[domain=-2:2, red, thick,samples=40] {x*x};} + \only<2->{\addplot[domain=-2:2, blue, thick,samples=40] {2*x*x};} + \only<3->{\addplot[domain=-2:2, green, thick,samples=40] {0.5*x*x};} + \end{axis} + \end{tikzpicture} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Fehlerfunktion} + \begin{itemize}[<+->] + \item \textbf{Daten $(x_{i,1}, \dots, x_{i,n}, y_{i,1}, \dots, y_{i,\text{\# Klassen}})$}: Beispiele für den Computer + \item \textbf{Aktuelles Modell $f$}: Funktion mit vielen Parametern + \item \textbf{Fehlerfunktion}: Wie gut ist $f$ für die vorhandenen + Daten? + \end{itemize} +\end{frame} + +\begin{frame}{Fehlerfunktion} + Abbildung von \textbf{Parameterraum} auf den Fehler ($\mathbb{R}_0^+$) +\end{frame} + +\begin{frame}{Minimieren mit Ableitungen} + \begin{figure}[h] + \centering + \includegraphics*[width=0.7\linewidth, keepaspectratio]{images/derivative-function.png} + \end{figure} +\end{frame} + +\begin{frame}{Gradientenabstieg} + \begin{figure}[h] + \centering + \includegraphics*[width=0.7\linewidth, keepaspectratio]{images/gradient-descent.png} + \end{figure} +\end{frame} + + +\section{Neuronale Netze} +\subsection{Neuronale Netze} +\begin{frame}{Neuronale Netze}{} + \begin{itemize}[<+->] + \item Menge von parametrisierten Funktionen + $\mathbb{R}^n \rightarrow \mathbb{R}^{\text(\# Klassen)}$ + \item $\mathbb{R}^n$: Eingabe,\\z.B. Farbe von Pixel~1, Farbe von Pixel~2, \dots + \item $\mathbb{R}^{\text(\# Klassen)}$: Ausgabe,\\Wahrscheinlichkeit der Klasse (z.B. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) + \item Ableitbar + \end{itemize} +\end{frame} + +\section{Ausblick} +\subsection{Ausblick} +\begin{frame}{Ausblick} + Erkennung von Formeln + \begin{itemize}[<+->] + \item Aufbau eines Sprachmodells der Mathematik + \item Erweiterung der Symboldatenbank + \item Segmentierung + \end{itemize} +\end{frame} +