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trunk/doc/papers/PHR/uEA2014/slide/beamer/beamer-Warsaw.pdf Property changes : Added: svn:mime-type ## -0,0 +1 ## +application/octet-stream \ No newline at end of property Index: trunk/doc/papers/PHR/uEA2014/slide/beamer/template.tex =================================================================== --- trunk/doc/papers/PHR/uEA2014/slide/beamer/template.tex (nonexistent) +++ trunk/doc/papers/PHR/uEA2014/slide/beamer/template.tex (revision 246) @@ -0,0 +1,744 @@ +% Copyright 2007 by Till Tantau +% +% This file may be distributed and/or modified +% +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. +% +% See the file doc/licenses/LICENSE for more details. + + + +\documentclass{beamer} + +% +% DO NOT USE THIS FILE AS A TEMPLATE FOR YOUR OWN TALKS¡!! +% +% Use a file in the directory solutions instead. +% They are much better suited. +% + + +% Setup appearance: + +\usetheme{Darmstadt} +\usefonttheme[onlylarge]{structurebold} +\setbeamerfont*{frametitle}{size=\normalsize,series=\bfseries} +\setbeamertemplate{navigation symbols}{} + + +% Standard packages + +\usepackage[english]{babel} +\usepackage[latin1]{inputenc} +\usepackage{times} +\usepackage[T1]{fontenc} + + +% Setup TikZ + +\usepackage{tikz} +\usetikzlibrary{arrows} +\tikzstyle{block}=[draw opacity=0.7,line width=1.4cm] + + +% Author, Title, etc. + +\title[Block Partitioning and Perfect Phylogenies] +{% + On the Complexity of SNP Block Partitioning Under the Perfect + Phylogeny Model% +} + +\author[Gramm, Hartman, Nierhoff, Sharan, Tantau] +{ + Jens~Gramm\inst{1} \and + Tzvika~Hartman\inst{2} \and + Till~Nierhoff\inst{3} \and + Roded~Sharan\inst{4} \and + \textcolor{green!50!black}{Till~Tantau}\inst{5} +} + +\institute[Tübingen and others] +{ + \inst{1}% + Universität Tübingen, Germany + \and + \vskip-2mm + \inst{2}% + Bar-Ilan University, Ramat-Gan, Israel + \and + \vskip-2mm + \inst{3}% + International Computer Science Institute, Berkeley, USA + \and + \vskip-2mm + \inst{4}% + Tel-Aviv University, Israel + \and + \vskip-2mm + \inst{5}% + Universität zu Lübeck, Germany +} + +\date[WABI 2006] +{Workshop on Algorithms in Bioinformatics, 2006} + + + +% The main document + +\begin{document} + +\begin{frame} + \titlepage +\end{frame} + +\begin{frame}{Outline} + \tableofcontents +\end{frame} + + +\section{Introduction} + +\subsection{The Model and the Problem} + +\begin{frame}{What is haplotyping and why is it important?} + You hopefully know this after the previous three talks\dots +\end{frame} + +\begin{frame}[t]{General formalization of haplotyping.} + \begin{block}{Inputs} + \begin{itemize} + \item A \alert{genotype matrix} $G$. + \item The \alert{rows} of the matrix are \alert{taxa / individuals}. + \item The \alert{columns} of the matrix are \alert{SNP sites / + characters}. + \end{itemize} + \end{block} + \begin{block}{Outputs} + \begin{itemize} + \item A \alert{haplotype matrix} $H$. + \item Pairs of rows in $H$ \alert{explain} the rows of $G$. + \item The haplotypes in $H$ are \alert{biologically plausible}. + \end{itemize} + \end{block} +\end{frame} + + +\begin{frame}[t]{Our formalization of haplotyping.} + \begin{block}{Inputs} + \begin{itemize} + \item A genotype matrix $G$. + \item The rows of the matrix are individuals / taxa. + \item The columns of the matrix are SNP sites / characters. + \item + The problem is directed: one haplotype is known. + \item + The input is biallelic: there are only two homozygous + states (0 and 1) and one heterozygous state (2). + \end{itemize} + \end{block} + \begin{block}{Outputs} + \begin{itemize} + \item A haplotype matrix $H$. + \item Pairs of rows in $H$ explain the rows of $G$. + \item The haplotypes in $H$ form a perfect phylogeny. + \end{itemize} + \end{block} +\end{frame} + + +\begin{frame}{We can do perfect phylogeny haplotyping efficiently, but + \dots} + \begin{enumerate} + \item \alert{Data may be missing.} + \begin{itemize} + \item This makes the problem NP-complete \dots + \item \dots even for very restricted cases. + \end{itemize} + \textcolor{green!50!black}{Solutions:} + \begin{itemize} + \item Additional assumption like the rich data hypothesis. + \end{itemize} + \item \alert{No perfect phylogeny is possible.} + \begin{itemize} + \item This can be caused by chromosomal crossing-over effects. + \item This can be caused by incorrect data. + \item This can be caused by multiple mutations at the same sites. + \end{itemize} + \textcolor{green!50!black}{Solutions:} + \begin{itemize} + \item Look for phylogenetic networks. + \item Correct data. + \item + Find blocks where a perfect phylogeny is possible. + \end{itemize} + \end{enumerate} +\end{frame} + + +\subsection{The Integrated Approach} + +\begin{frame}{How blocks help in perfect phylogeny haplotyping.} + \begin{enumerate} + \item Partition the site set into overlapping contiguous blocks. + \item Compute a perfect phylogeny for each block and combine them. + \item Use dynamic programming for finding the partition. + \end{enumerate} + + \begin{tikzpicture} + \useasboundingbox (0,-1) rectangle (10,2); + + \draw[line width=2mm,dash pattern=on 1mm off 1mm] + (0,1) -- (9.99,1) node[midway,above] {Genotype matrix} + (0,0.6666) -- (9.99,0.6666) + (0,0.3333) -- (9.99,0.3333) + (0,0) -- (9.99,0) node[midway,below] {\only<1>{no perfect phylogeny}}; + + \begin{scope}[xshift=-.5mm] + \only<2-> + { + \draw[red,block] (0,.5) -- (3,.5) + node[midway,below] {perfect phylogeny}; + } + + \only<3-> + { + \draw[green!50!black,block] (2.5,.5) -- (7,.5) + node[pos=0.6,below] {perfect phylogeny}; + } + + \only<4-> + { + \draw[blue,block] (6.5,.5) -- (10,.5) + node[pos=0.6,below] {perfect phylogeny}; + } + \end{scope} + \end{tikzpicture} +\end{frame} + +\begin{frame}{Objective of the integrated approach.} + \begin{enumerate} + \item Partition the site set into \alert{noncontiguous} blocks. + \item Compute a perfect phylogeny for each block and combine them. + \item Compute partition while computing perfect + phylogenies. + \end{enumerate} + + \begin{tikzpicture} + \useasboundingbox (0,-1) rectangle (10,2); + + \draw[line width=2mm,dash pattern=on 1mm off 1mm] + (0,1) -- (9.99,1) node[midway,above] {Genotype matrix} + (0,0.6666) -- (9.99,0.6666) + (0,0.3333) -- (9.99,0.3333) + (0,0) -- (9.99,0) node[midway,below] {\only<1>{no perfect phylogeny}}; + + \only<2-> + { + \begin{scope}[xshift=-0.5mm] + \draw[red,block] (0,.5) -- (3,.5) + node[midway,below] {perfect phylogeny} + (8,.5) -- (9,.5); + + \draw[green!50!black,block] + (3,.5) -- (6,.5) + node[pos=0.6,below] {perfect phylogeny} + (6.4,.5) -- (8,.5) + (9,.5) -- (10,.5); + + \draw[blue,block] (6,.5) -- (6.4,.5) + node[midway,below=5mm] {perfect phylogeny}; + \end{scope} + } + \end{tikzpicture} +\end{frame} + + +\begin{frame}{The formal computational problem.} + We are interested in the computational complexity of \\ + \alert{the function \alert{$\chi_{\operatorname{PP}}$}}: + \begin{itemize} + \item It gets genotype matrices as input. + \item It maps them to a number $k$. + \item This number is minimal such that the sites can be + covered by $k$ sets, each admitting a perfect phylogeny. + \\ + (We call this a \alert{pp-partition}.) + \end{itemize} +\end{frame} + + +\section{Bad News: Hardness Results} + +\subsection{Hardness of PP-Partitioning of Haplotype Matrices} + +\begin{frame}{Finding pp-partitions of haplotype matrices.} + We start with a special case: + \begin{itemize} + \item The inputs $M$ are \alert{already haplotype matrices}. + \item The inputs $M$ \alert{do not allow a perfect phylogeny}. + \item What is $\chi_{\operatorname{PP}}(M)$? + \end{itemize} + \begin{example} + \begin{columns} + \column{.3\textwidth} + $M\colon$ + \footnotesize + \begin{tabular}{cccc} + 0 & 0 & 0 & 1 \\ + 0 & 1 & 0 & 0 \\ + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 1 \\ + 1 & 1 & 0 & 0 \\ + 0 & 0 & 1 & 0 \\ + 1 & 0 & 1 & 0 + \end{tabular}% + \only<2> + {% + \begin{tikzpicture} + \useasboundingbox (2.9,0); + + \draw [red, opacity=0.7,line width=1cm] (1.7 ,1.9) -- (1.7 ,-1.7); + \draw [blue,opacity=0.7,line width=5mm] (0.85,1.9) -- (0.85,-1.7) + (2.55,1.9) -- (2.55,-1.7); + \end{tikzpicture} + } + \column{.6\textwidth} + \begin{overprint} + \onslide<1> + No perfect phylogeny is possible. + + \onslide<2> + \textcolor{blue!70!bg}{Perfect phylogeny} + + \textcolor{red!70!bg}{Perfect phylogeny} + + $\chi_{\operatorname{PP}}(M) = 2$. + + \end{overprint} + \end{columns} + \end{example} +\end{frame} + +\begin{frame}{Bad news about pp-partitions of haplotype matrices.} + \begin{theorem} + Finding \alert{optimal pp-partition of haplotype matrices}\\ + is equivalent to finding \alert{optimal graph colorings}. + \end{theorem} + + \begin{proof}[Proof sketch for first direction] + \begin{enumerate} + \item Let $G$ be a graph. + \item Build a matrix with a column for each vertex of $G$. + \item For each edge of $G$ add four rows inducing\\the + submatrix $\left( + \begin{smallmatrix} + 0 & 0 \\ + 0 & 1 \\ + 1 & 0 \\ + 1 & 1 + \end{smallmatrix}\right)$. + \item The submatrix enforces that the columns lie in different + perfect phylogenies. \qedhere + \end{enumerate} + \end{proof} +\end{frame} + +\begin{frame}{Implications for pp-partitions of haplotype matrices.} + \begin{corollary} + If $\chi_{\operatorname{PP}}(M) = 2$ for a haplotype matrix $M$, + we can find an optimal pp-partition in polynomial time. + \end{corollary} + + \begin{corollary} + Computing $\chi_{\operatorname{PP}}$ for haplotype matrices is + \begin{itemize} + \item $\operatorname{NP}$-hard, + \item not fixed-parameter tractable, unless + $\operatorname{P}=\operatorname{NP}$, + \item very hard to approximate. + \end{itemize} + \end{corollary} +\end{frame} + + +\subsection{Hardness of PP-Partitioning of Genotype Matrices} + + +\begin{frame}{Finding pp-partitions of genotype matrices.} + Now comes the general case: + \begin{itemize} + \item The inputs $M$ are \alert{genotype matrices}. + \item The inputs $M$ \alert{do not allow a perfect phylogeny}. + \item What is $\chi_{\operatorname{PP}}(M)$? + \end{itemize} + \begin{example} + \begin{columns} + \column{.3\textwidth} + $M\colon$ + \footnotesize + \begin{tabular}{cccc} + 2 & 2 & 2 & 2 \\ + 1 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 1 \\ + 0 & 0 & 1 & 0 \\ + 0 & 2 & 2 & 0 \\ + 1 & 1 & 0 & 0 + \end{tabular}% + \only<2> + {% + \begin{tikzpicture} + \useasboundingbox (2.9,0); + + \draw [red, opacity=0.7,line width=1cm] (1.7 ,1.3) -- (1.7 ,-1.1); + \draw [blue,opacity=0.7,line width=5mm] (0.85,1.3) -- (0.85,-1.1) + (2.55,1.3) -- (2.55,-1.1); + \end{tikzpicture} + } + \column{.6\textwidth} + \begin{overprint} + \onslide<1> + No perfect phylogeny is possible. + + \onslide<2> + \textcolor{blue!70!bg}{Perfect phylogeny} + + \textcolor{red!70!bg}{Perfect phylogeny} + + $\chi_{\operatorname{PP}}(M) = 2$. + + \end{overprint} + \end{columns} + \end{example} +\end{frame} + + +\begin{frame}{Bad news about pp-partitions of haplotype matrices.} + \begin{theorem} + Finding \alert{optimal pp-partition of genotype matrices} + is at least as hard as finding \alert{optimal colorings of + 3-uniform hypergraphs}. + \end{theorem} + + \begin{proof}[Proof sketch] + \begin{enumerate} + \item Let $G$ be a 3-uniform hypergraph. + \item Build a matrix with a column for each vertex of $G$. + \item For each hyperedge of $G$ add four rows inducing\\ the submatrix + $\left( + \begin{smallmatrix} + 2 & 2 & 2 \\ + 1 & 0 & 0 \\ + 0 & 1 & 0 \\ + 0 & 0 & 1 + \end{smallmatrix}\right) + $. + \item The submatrix enforces that the three columns do not all lie + in the same perfect phylogeny. \qedhere + \end{enumerate} + \end{proof} +\end{frame} + +\begin{frame}{Implications for pp-partitions of genotype matrices.} + \begin{corollary} + Even if we know $\chi_{\operatorname{PP}}(M) = 2$ for a genotype matrix $M$,\\ + finding a pp-partition of any fixed size is still + \begin{itemize} + \item $\operatorname{NP}$-hard, + \item not fixed-parameter tractable, unless + $\operatorname{P}=\operatorname{NP}$, + \item very hard to approximate. + \end{itemize} + \end{corollary} +\end{frame} + + +\section{Good News: Tractability Results} + +\subsection{Perfect Path Phylogenies} + +\begin{frame}{Automatic optimal pp-partitioning is hopeless, but\dots} + \begin{itemize} + \item The hardness results are \alert{worst-case} results for\\ + \alert{highly artificial inputs}. + \item \alert{Real biological data} might have special properties + that make the problem \alert{tractable}. + \item One such property is that perfect phylogenies are often + perfect \alert{path} phylogenies: + + In HapMap data, in 70\% of the blocks where a perfect phylogeny + is possible a perfect path phylogeny is also possible. + \end{itemize} +\end{frame} + + +\begin{frame}{Example of a perfect path phylogeny.} + \begin{columns}[t] + \column{.3\textwidth} + \begin{exampleblock}{Genotype matrix} + $G\colon$ + \begin{tabular}{ccc} + A & B & C \\\hline + 2 & 2 & 2 \\ + 0 & 2 & 0 \\ + 2 & 0 & 0 \\ + 0 & 2 & 2 + \end{tabular} + \end{exampleblock} + + \column{.3\textwidth} + \begin{exampleblock}{Haplotype matrix} + $H\colon$ + \begin{tabular}{ccc} + A & B & C \\\hline + 1 & 0 & 0 \\ + 0 & 1 & 1 \\ + 0 & 0 & 0 \\ + 0 & 1 & 0 \\ + 0 & 0 & 0 \\ + 1 & 0 & 0 \\ + 0 & 0 & 0 \\ + 0 & 1 & 1 + \end{tabular} + \end{exampleblock} + + \column{.4\textwidth} + \begin{exampleblock}{Perfect path phylogeny} + \begin{center} + \begin{tikzpicture}[auto,thick] + \tikzstyle{node}=% + [% + minimum size=10pt,% + inner sep=0pt,% + outer sep=0pt,% + ball color=example text.fg,% + circle% + ] + + \node [node] {} [->] + child {node [node] {} edge from parent node[swap]{A}} + child {node [node] {} + child {node [node] {} edge from parent node{C}} + edge from parent node{B} + }; + \end{tikzpicture} + \end{center} + \end{exampleblock} + \end{columns} +\end{frame} + + +\begin{frame}{The modified formal computational problem.} + We are interested in the computational complexity of \\ + the function $\chi_{{\operatorname{PPP}}}$: + \begin{itemize} + \item It gets genotype matrices as input. + \item It maps them to a number $k$. + \item This number is minimal such that the sites can be + covered by $k$ sets, each admitting a perfect \alert{path} phylogeny. + \\ + (We call this a ppp-partition.) + \end{itemize} +\end{frame} + + + +\subsection{Tractability of PPP-Partitioning of Genotype Matrices} + +\begin{frame}{Good news about ppp-partitions of genotype matrices.} + \begin{theorem} + \alert{Optimal ppp-partitions of genotype matrices} can be + computed in \alert{polynomial time}. + \end{theorem} + \begin{block}{Algorithm} + \begin{enumerate} + \item Build the following partial order: + \begin{itemize} + \item Can one column be above the other in a phylogeny? + \item Can the columns be the two children of the root of a + perfect path phylogeny? + \end{itemize} + \item Cover the partial order with as few compatible chain pairs + as possible. + + For this, a maximal matching in a special graph needs to be + computed. + \end{enumerate} + \end{block} + \hyperlink{algorithm<1>}{\beamergotobutton{The algorithm in action}} + \hypertarget{return}{} +\end{frame} + +\section*{Summary} + +\begin{frame} + \frametitle{Summary} + + \begin{itemize} + \item + Finding optimal pp-partitions is \alert{intractable}. + \item + It is even intractable to find a pp-partition when \alert{just two + noncontiguous blocks are known to suffice}. + \item + For perfect \alert{path} phylogenies, optimal partitions can be + computed \alert{in polynomial time}. + \end{itemize} +\end{frame} + + +\appendix + +\section*{Appendix} + +\begin{frame}[label=algorithm]{The algorithm in action.}{Computation of + the partial order.} + \begin{columns}[t] + \column{.4\textwidth} + \begin{exampleblock}{Genotype matrix} + $G\colon$ + \begin{tabular}{ccccc} + A & B & C & D & E \\\hline + 2 & 2 & 2 & 2 & 2 \\ + 0 & 1 & 2 & 1 & 0 \\ + 1 & 0 & 0 & 1 & 2 \\ + 0 & 2 & 2 & 0 & 0 + \end{tabular} + \end{exampleblock} + \column{.6\textwidth} + \begin{exampleblock}{Partial order} + \begin{tikzpicture}[node distance=15mm] + \tikzstyle{every node}= + [% + fill=green!50!black!20,% + draw=green!50!black,% + minimum size=7mm,% + circle,% + thick% + ] + + \node (A) {A}; + \node (B) [right of=A] {B}; + \node (C) [below of=B] {C}; + \node (D) [above of=A] {D}; + \node (E) [below of=A] {E}; + + \path [thick,shorten >=1pt,-stealth'] (A) edge (E) + (B) edge (C) + (D) edge (A) + edge[bend right] (E); + + \uncover<2>{ + \path [-,blue,thick](A) edge (B) + edge (C) + (B) edge (E) + (C) edge (E);} + \end{tikzpicture} + + Partial order: \tikz[baseline] \draw[thick,-stealth'] (0pt,.5ex) + -- (5mm,.5ex); + + \uncover<2>{\textcolor{blue}{Compatible as children of root: + \tikz[baseline] \draw[thick] (0pt,.5ex) -- (5mm,.5ex);}} + \end{exampleblock} + \end{columns} +\end{frame} + +\begin{frame}{The algorithm in action.}{The matching in the special graph.} + \begin{columns}[t] + \column{.3\textwidth} + \begin{exampleblock}{Partial order} + \begin{tikzpicture}[node distance=15mm] + \tikzstyle{every node}=% + [% + fill=green!50!black!20,% + draw=green!50!black,% + minimum size=8mm,% + circle,% + thick% + ] + + \node (A) {$A$}; + \node (B) [right of=A] {$B$}; + \node (C) [below of=B] {$C$}; + \node (D) [above of=A] {$D$}; + \node (E) [below of=A] {$E$}; + + \path [thick,shorten >=1pt,-stealth'] (A) edge (E) + (B) edge (C) + (D) edge (A) + edge[bend right] (E); + + \path [-,blue,thick](A) edge (B) + edge (C) + (B) edge (E) + (C) edge (E); + + \only<3-> + { + \path[very thick,shorten >=1pt,-stealth',red] (D) edge (A) (B) edge (C); + \path [-,red,very thick](E) edge (B); + } + \end{tikzpicture} + \end{exampleblock} + \column{.7\textwidth} + \begin{exampleblock}{Matching graph} + \begin{tikzpicture}[node distance=15mm] + \tikzstyle{every node}=% + [% + fill=green!50!black!20,% + draw=green!50!black,% + minimum size=8mm,% + circle,% + thick,% + inner sep=0pt% + ] + + \node (A) {$A$}; + \node (B) [right of=A] {$B$}; + \node (C) [below of=B] {$C$}; + \node (D) [above of=A] {$D$}; + \node (E) [below of=A] {$E$}; + + \begin{scope}[xshift=4.75cm] + \node (A') {$A'$}; + \node (B') [right of=A'] {$B'$}; + \node (C') [below of=B'] {$C'$}; + \node (D') [above of=A'] {$D'$}; + \node (E') [below of=A'] {$E'$}; + \end{scope} + + \path [thick] (A) edge (E') + (B) edge (C') + (D) edge (A') + edge (E'); + + \path [blue,thick](A') edge (B') + edge (C') + (B') edge (E') + (C') edge (E'); + + \only<2-> + { + \path[very thick,red] (D) edge (A') + (B) edge (C') + (B') edge (E'); + } + \end{tikzpicture} + \end{exampleblock} + \end{columns} + + \medskip + \uncover<2->{A \alert{maximal matching} in the matching graph + \uncover<3>{induces\\ \alert{perfect path phylogenies}.}} + + \hfill\hyperlink{return}{\beamerreturnbutton{Return}} +\end{frame} + +\end{document} + +

trunk/doc/papers/PHR/uEA2014/slide/beamer/template.tex Property changes : Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +Author Date Id Rev URL \ No newline at end of property Index: trunk/doc/papers/PHR/uEA2014/slide/beamer/beamer-Warsaw.tex =================================================================== --- trunk/doc/papers/PHR/uEA2014/slide/beamer/beamer-Warsaw.tex (nonexistent) +++ trunk/doc/papers/PHR/uEA2014/slide/beamer/beamer-Warsaw.tex (revision 246) @@ -0,0 +1,194 @@ +% This text is proprietary. +% It's a part of presentation made by myself. +% It may not used commercial. +% The noncommercial use such as private and study is free +% Dec 2007 +% Author: Sascha Frank +% University Freiburg +% www.informatik.uni-freiburg.de/~frank/ +% +% +\documentclass{beamer} +\setbeamertemplate{navigation symbols}{} + + +\usetheme{Warsaw} + +\beamersetuncovermixins{\opaqueness<1>{25}}{\opaqueness<2->{15}} +\begin{document} +\title{Beamer Class Warsaw} +\author{Sascha Frank} +\date{\today} + + +\begin{frame} +\titlepage +\end{frame} + +\begin{frame}\frametitle{Table of contents}\tableofcontents +\end{frame} + + +\section{Section no.1} +\begin{frame}\frametitle{Title} +Each frame should have a title. +\end{frame} +\subsection{Subsection no.1.1 } +\begin{frame} +Without title somethink is missing. +\end{frame} + + +\section{Section no. 2} +\subsection{Lists I} +\begin{frame}\frametitle{unnumbered lists} +\begin{itemize} +\item Introduction to \LaTeX +\item Course 2 +\item Termpapers and presentations with \LaTeX +\item Beamer class +\end{itemize} +\end{frame} + +\begin{frame}\frametitle{lists with pause} +\begin{itemize} +\item Introduction to \LaTeX \pause +\item Course 2 \pause +\item Termpapers and presentations with \LaTeX \pause +\item Beamer class +\end{itemize} +\end{frame} + +\subsection{Lists II} +\begin{frame}\frametitle{numbered lists} +\begin{enumerate} +\item Introduction to \LaTeX +\item Course 2 +\item Termpapers and presentations with \LaTeX +\item Beamer class +\end{enumerate} +\end{frame} + +\begin{frame}\frametitle{numbered lists with pause} +\begin{enumerate} +\item Introduction to \LaTeX \pause +\item Course 2 \pause +\item Termpapers and presentations with \LaTeX \pause +\item Beamer class +\end{enumerate} +\end{frame} + +\section{Section no.3} +\subsection{Tables} +\begin{frame}\frametitle{Tables} +\begin{tabular}{|c|c|c|} +\hline +\textbf{Date} & \textbf{Instructor} & \textbf{Title} \\ +\hline +WS 04/05 & Sascha Frank & First steps with \LaTeX \\ +\hline +SS 05 & Sascha Frank & \LaTeX \ Course serial \\ +\hline +\end{tabular} +\end{frame} + + +\begin{frame}\frametitle{Tables with pause} +\begin{tabular}{c c c} +A & B & C \\ +\pause +1 & 2 & 3 \\ +\pause +A & B & C \\ +\end{tabular} +\end{frame} + + +\section{Section no. 4} +\subsection{blocs} +\begin{frame}\frametitle{blocs} + +\begin{block}{title of the bloc} +bloc text +\end{block} + +\begin{exampleblock}{title of the bloc} +bloc text +\end{exampleblock} + + +\begin{alertblock}{title of the bloc} +bloc text +\end{alertblock} +\end{frame} + +\section{Section no. 5} +\subsection{split screen} + +\begin{frame}\frametitle{splitting screen} +\begin{columns} +\begin{column}{5cm} +\begin{itemize} +\item Beamer +\item Beamer Class +\item Beamer Class Latex +\end{itemize} +\end{column} +\begin{column}{5cm} +\begin{tabular}{|c|c|} +\hline +\textbf{Instructor} & \textbf{Title} \\ +\hline +Sascha Frank & \LaTeX \ Course 1 \\ +\hline +Sascha Frank & Course serial \\ +\hline +\end{tabular} +\end{column} +\end{columns} +\end{frame} + +\subsection{Pictures} +\begin{frame}\frametitle{pictures in latex beamer class} +\begin{figure} +\includegraphics[width=0.5\textwidth]{PIC1} +\caption{show an example picture} +\end{figure} +\end{frame} + +\subsection{joining picture and lists} + +\begin{frame} +\frametitle{pictures and lists in beamer class} +\begin{columns} +\begin{column}{5cm} +\begin{itemize} +\item<1-> subject 1 +\item<3-> subject 2 +\item<5-> subject 3 +\end{itemize} +\vspace{3cm} +\end{column} +\begin{column}{5cm} +\begin{overprint} +\includegraphics<2>[width=0.4\textwidth]{PIC1} +\includegraphics<4>[width=0.4\textwidth]{PIC2} +\includegraphics<6>[width=0.4\textwidth]{PIC3} +\end{overprint} +\end{column} +\end{columns} +\end{frame} + + +\subsection{pictures which need more space} +\begin{frame}[plain] +\frametitle{plain, or a way to get more space} +\begin{figure} +\includegraphics[width=0.2\textwidth]{PIC1} +\caption{show an example picture} +\end{figure} +\end{frame} + + + +\end{document} \ No newline at end of file

trunk/doc/papers/PHR/uEA2014/slide/beamer/beamer-Warsaw.tex Property changes : Added: svn:eol-style ## -0,0 +1 ## +native \ No newline at end of property Added: svn:keywords ## -0,0 +1 ## +Author Date Id Rev URL \ No newline at end of property