diff --git a/Lectures_my/EMPP/2017/Lecture1/Makefile b/Lectures_my/EMPP/2017/Lecture1/Makefile new file mode 100644 index 0000000..e4cf8e8 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/Makefile @@ -0,0 +1,9 @@ +all: mchrzasz.pdf + +mchrzasz.pdf: mchrzasz.tex + xelatex mchrzasz.tex +# bibtex mchrzasz + xelatex mchrzasz.tex +# xelatex mchrzasz.tex +clean: + rm *.aux *.bbl *.blg *.log *.out *.pdf *.sh *.xml *.snm *.toc *.nav diff --git a/Lectures_my/EMPP/2017/Lecture1/beamercolorthemeFlip.sty b/Lectures_my/EMPP/2017/Lecture1/beamercolorthemeFlip.sty new file mode 100755 index 0000000..d6b9c50 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/beamercolorthemeFlip.sty @@ -0,0 +1,179 @@ +% Color style file for the BEAMER FLIP THEME +% Copyright 2012 by Flip Tanedo +% This file may be distributed and/or modified +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. + + + +\mode +\newif\ifbeamer@Flip@dark +\beamer@Flip@darkfalse +\DeclareOptionBeamer{dark}{\beamer@Flip@darktrue} +\ProcessOptionsBeamer + + +% These are a few colors that I like. + +\definecolor{crimsonred}{RGB}{153,0,0} % Neurtal red, good for dark or light bg +\definecolor{darkcharcoal}{RGB}{25,25,25} % Darker gray +\definecolor{charcoal}{RGB}{51,51,51} % Darker gray +\definecolor{ash}{RGB}{100,100,100} % medium gray +\definecolor{paleblue}{RGB}{0,102,102} % More of an `ocean' color +\definecolor{turtlegreen}{RGB}{51,153,0} % A more neutral green +\definecolor{paleale}{RGB}{204,204,102} % Only for dark BG +\definecolor{lager}{RGB}{140,110,10} % Use instead of pale ale for white BG +\definecolor{regal}{RGB}{90,0,120} % A more neutral purple +\definecolor{jeans}{RGB}{20,30,150} % A more neutral blue + + +% Define some "invariant colors" so that a color that doen't work with a +% light/dark background will automatically be substituted with one that does. +% These will be rewritten in beamercolorthemeFlipDark + +\ifbeamer@Flip@dark + \definecolor{FlipSand}{RGB}{204,204,102} % paleale, Only for dark BG + \definecolor{FlipGreen}{RGB}{0,255,0} % Neon-like green, only for dark BG +\else + \definecolor{FlipSand}{RGB}{140,110,10} % lager, Only for light BG + \definecolor{FlipGreen}{RGB}{51,153,0} % turtlegreen, works for both +\fi + +%% Future revision: It would be nice to define these in terms of the palette. + + +\ifbeamer@Flip@dark + \setbeamercolor{normal text}{fg=white, bg=black} + \setbeamercolor{structure}{fg=gray, bg=black} % fg controls bullets + \setbeamercolor*{footerlike}{fg=white,bg=black} % Controls the footerline +\else + % Default to black on white + \setbeamercolor*{footerlike}{fg=white,bg=charcoal} % for charcoal footer + \setbeamercolor{structure}{fg=charcoal, bg=white} % fg controls bullets + % \setbeamercolor{normal text}{fg=white, bg=black} +\fi + + + + + +% These defined colors can be used in \textcolor{colorname}{text in that color}. + +% Colors for Keynote background: DARK +\definecolor{keynotebottom}{rgb}{0.32,0.3,0.38} +\definecolor{keynotemiddle}{rgb}{0.08,0.08,0.16} +\definecolor{keynotetop}{rgb}{0,0,0} +%%% Example of usage: +%% \setbeamertemplate{background canvas}[vertical shading] +%% [bottom=keynotebottom, middle=keynotemiddle, top=keynotetop] + + + + +% ALERT AND COMMENT COLORS (just copies of the above colors) +% (I don't know how ot do this more elegantly) +\ifbeamer@Flip@dark + \definecolor{ALERT}{RGB}{153,0,0} % crimsonred + \definecolor{Alert}{RGB}{51,153,0} % turtlegreen + \definecolor{alert}{RGB}{204,204,102} % paleale + \definecolor{charcoal}{RGB}{51,51,51} % charcoal + \definecolor{comment}{RGB}{80,80,80} % light charcoal + \definecolor{Comment}{RGB}{100,100,100} % ash + \definecolor{COMMENT}{RGB}{80,20,120} % regal +\else +% \definecolor{ALERT}{RGB}{153,0,0} % crimsonred + \definecolor{ALERT}{RGB}{28,134,238} % DodgerBlue2 +% \definecolor{Alert}{RGB}{51,153,0} % turtlegreen + \definecolor{Alert}{RGB}{255,127,36} % chocolate1 +% \definecolor{alert}{RGB}{140,110,10} % lager + \definecolor{alert}{RGB}{0,205,102} % SpringGreen3 + \definecolor{charcoal}{RGB}{80,80,80} % light charcoal + \definecolor{comment}{RGB}{51,51,51} % charcoal + \definecolor{Comment}{RGB}{100,100,100} % ash + \definecolor{COMMENT}{RGB}{80,20,120} % regal +\fi + + +% \definecolor{crimsonred}{RGB}{153,0,0} % Neurtal red, good for dark or light bg +% \definecolor{charcoal}{RGB}{51,51,51} % Darker gray +% \definecolor{ash}{RGB}{100,100,100} % medium gray +% \definecolor{paleblue}{RGB}{0,102,102} % More of an `ocean' color +% \definecolor{turtlegreen}{RGB}{51,153,0} % A more neutral green +% \definecolor{paleale}{RGB}{204,204,102} % Only for dark BG +% \definecolor{lager}{RGB}{140,110,10} % Use instead of pale ale for white BG +% \definecolor{regal}{RGB}{90,0,120} % A more neutral purple +% \definecolor{jeans}{RGB}{20,30,150} % A more neutral blue + + +% A few useful colors +\setbeamercolor{alerted text}{fg=alert} + +%% I would like ot use these colors, but there seems to be a bug in Beamer +%% where the footnote color infects the normal text color +%% See: http://tex.stackexchange.com/questions/8264/beamer-changing-the-footnote-color-also-changes-the-normal-text-color/8268#8268 + +% \setbeamercolor{footnote}{parent=normal text, fg=FlipSand} +% \setbeamercolor{footnote mark}{parent=normal text, fg=FlipSand} + +% Blocks +\setbeamercolor{block title}{fg=gray!30!white,bg=charcoal} +\setbeamercolor{block body}{parent=normal text,bg=gray, fg=white} + +\setbeamercolor{block title example}{fg=turtlegreen!30!white,bg=turtlegreen!40!black} +\setbeamercolor{block body example}{parent=normal text,bg=turtlegreen, fg=white} +% +\setbeamercolor{block title alerted}{fg=crimsonred!30!white,bg=crimsonred!40!black} +\setbeamercolor{block body alerted}{parent=normal text,bg=crimsonred, fg=white} + + + +% These "setbeamercolor" commands are more standardized. + + +%% From the Beamer User Guide: +% Outer themes base the color of navigational elements and, possibly, also of other elements, on the +% four palette colors. The “primary” palette should be used for the most important navigational elements, +% which are usually the ones that change most often and hence require the most attention by the audience. +% The “secondary” and “tertiary” are less important, the “quaternary” one is least important. +% By default, the palette colors do not have a background and the foreground ranges from structure.fg to black. +% For the sidebar, there is an extra set of palette colors, see palette sidebar primary. + +\setbeamercolor*{palette primary}{fg=crimsonred,bg=charcoal} +\setbeamercolor*{palette secondary}{fg=paleale,bg=lager} +\setbeamercolor*{palette tertiary}{fg=turtlegreen,bg=jeans} +\setbeamercolor*{palette quaternary}{fg=paleblue,bg=regal} + +% \setbeamercolor*{palette primary}{fg=crimsonred,bg=white} +% \setbeamercolor*{palette secondary}{fg=charcoal,bg=white} +% \setbeamercolor*{palette tertiary}{fg=paleblue,bg=white} +% \setbeamercolor*{palette quaternary}{fg=turtlegreen,bg=white} + + + +%% These are some structures that I define for use in the outer theme. + +\setbeamercolor*{crimsontown}{fg=paleblue,bg=crimsonred} +\setbeamercolor*{bluetown}{fg=white,bg=DodgerBlue2} +%\setbeamercolor*{titlelike}{fg=crimsonred} +\setbeamercolor*{titlelike}{fg=DodgerBlue2} +\setbeamercolor*{topbarlike}{fg=white, bg=charcoal} + + + + + +%% Some old definitions that I might want to get back to +% +% \setbeamercolor*{frametitle}{bg=white,fg=charcoal} +% \setbeamercolor*{part title}{bg=white,fg=charcoal} +% \setbeamercolor*{item}{fg=charcoal, bg=white} +% +% \setbeamercolor*{separation line}{} +% \setbeamercolor*{fine separation line}{} + + + + + +\mode + diff --git a/Lectures_my/EMPP/2017/Lecture1/beamerinnerthemeFlip.sty b/Lectures_my/EMPP/2017/Lecture1/beamerinnerthemeFlip.sty new file mode 100755 index 0000000..9910f4d --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/beamerinnerthemeFlip.sty @@ -0,0 +1,95 @@ +% Inner style file for the BEAMER FLIP THEME +% Copyright 2010 by Flip Tanedo +% This file may be distributed and/or modified +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. +% +% Based on: beamerinnerthemeFlip by Marco Barisione + +\mode + +% % Use alternative title page style. +% \DeclareOptionBeamer{alternativetitlepage}[true]{\def\beamer@Flip@alternativetitlepage{#1}} + +% Logo to use in the alternative title page. +% \def\beamer@Flip@titlepagelogo{} +% \DeclareOptionBeamer{titlepagelogo}{\def\beamer@Flip@titlepagelogo{#1}} + +% Bullet shape. +\DeclareOptionBeamer{bullet}{\def\beamer@Flip@bullet{#1}} +\DeclareOptionBeamer{shadow}[true]{\def\beamer@themerounded@shadow{#1}} +\ExecuteOptionsBeamer{shadow=false} + + +% \ExecuteOptionsBeamer{alternativetitlepage=false,bullet=square} +\ProcessOptionsBeamer + + + +% Margins. +\newlength{\beamer@Flip@normalmargin} +\setlength{\beamer@Flip@normalmargin}{.06\paperwidth} +\setbeamersize{text margin left=\beamer@Flip@normalmargin} +\setbeamersize{text margin right=\beamer@Flip@normalmargin} +\setlength\leftmargini{.6\beamer@Flip@normalmargin} +\setlength\leftmarginii{.6\beamer@Flip@normalmargin} +\setlength\leftmarginiii{.6\beamer@Flip@normalmargin} + +% Normal title page. +\defbeamertemplate*{title page normal}{Flip theme}[1][] +{ + \vbox{} + \vfill + \begin{centering} + \begin{beamercolorbox}[wd=\paperwidth,sep=8pt,center,#1]{title page header} + \usebeamerfont{title}\inserttitle\par% + \ifx\insertsubtitle\@empty% + \else% + \vskip0.25em% + {\usebeamerfont{subtitle}\usebeamercolor[fg]{subtitle}\insertsubtitle\par}% + \fi% + \end{beamercolorbox}% + \vskip1em\par + \begin{beamercolorbox}[sep=8pt,center,#1]{author} + \usebeamerfont{author}\insertauthor + \end{beamercolorbox} + \begin{beamercolorbox}[sep=8pt,center,#1]{institute} + \usebeamerfont{institute}\insertinstitute + \end{beamercolorbox} + \begin{beamercolorbox}[sep=8pt,center,#1]{date} + \usebeamerfont{date}\insertdate + \end{beamercolorbox}\vskip0.5em + {\usebeamercolor[fg]{titlegraphic}\inserttitlegraphic\par} + \end{centering} + \vfill +} + + +% Items. +\defbeamertemplate{itemize item}{squarealt}% +{\tiny\raise.5ex\hbox{\donotcoloroutermaths$\blacksquare$}} +\defbeamertemplate{itemize subitem}{squarealt}% +{\tiny\raise.4ex\hbox{\donotcoloroutermaths$\square$}} +\defbeamertemplate{itemize subsubitem}{squarealt}% +{\tiny\raise.3ex\hbox{\donotcoloroutermaths$\blacksquare$}} +% +\defbeamertemplate{itemize item}{circlealt}% +{\small\raise.2ex\hbox{\donotcoloroutermaths$\bullet$}} +\defbeamertemplate{itemize subitem}{circlealt}% +{\small\raise.1ex\hbox{\donotcoloroutermaths$\circ$}} +\defbeamertemplate{itemize subsubitem}{circlealt}% +{\scriptsize\raise.1ex\hbox{\donotcoloroutermaths$\bullet$}} +\setbeamertemplate{items}[circlealt] +% +\def\circletext{circle} +\ifx\beamer@Flip@bullet\circletext + \setbeamertemplate{items}[circlealt] +\else + \setbeamertemplate{items}[squarealt] +\fi + +\setbeamertemplate{blocks}[rounded][shadow=\beamer@themerounded@shadow] + + +\mode + diff --git a/Lectures_my/EMPP/2017/Lecture1/beamerouterthemeFlip.sty b/Lectures_my/EMPP/2017/Lecture1/beamerouterthemeFlip.sty new file mode 100755 index 0000000..d12f6d6 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/beamerouterthemeFlip.sty @@ -0,0 +1,189 @@ +% Outer style file for the BEAMER FLIP THEME 212 +% Copyright 2012 by Flip Tanedo +% This file may be distributed and/or modified +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. +% +% Based on: beamerouterthemesplit by Till Tantau + + +\mode + +% Watermark +\DeclareOptionBeamer{watermark}{\def\beamer@Flip@watermark{#1}} +\ExecuteOptionsBeamer{watermark=} % Default value is empty + + +\newif\ifbeamer@Flip@bigpagenumber +\beamer@Flip@bigpagenumberfalse +\DeclareOptionBeamer{bigpagenumber}{\beamer@Flip@bigpagenumbertrue} + + +\def\beamer@Flip@truetext{true} % Kludge for true/false so I can use ifx + +\DeclareOptionBeamer{topline}[true]{\def\beamer@Flip@topline{#1}} +\ExecuteOptionsBeamer{topline=false} % Default + + + +% \ExecuteOptionsBeamer{topline=} % Default value is empty + + +\ProcessOptionsBeamer + + +\usepackage{tikz} % For fancy decorations + + +% I should fix these up to be more robust against color changes +\setbeamercolor{section in head/foot}{parent=footerlike} +\setbeamercolor{subsection in head/foot}{parent=footerlike} +\setbeamercolor{author in head/foot}{parent=footerlike} +\setbeamercolor{title in head/foot}{parent=footerlike} + + +% \setbeamercolor{author in head/foot}{parent=section in head/foot} +% \setbeamercolor{title in head/foot}{parent=subsection in head/foot} + +%\setbeamercolor{topbar}{parent=crimsontown} +\setbeamercolor{topbar}{parent=bluetown} + + + + +\usesectionheadtemplate + {\hfill\insertsectionhead} + {\hfill\color{fg!50!bg}\insertsectionhead} + + +%%%%%%%%%%%%%%%%%% +% The footer bar % +%%%%%%%%%%%%%%%%%% + +\defbeamertemplate*{footline}{Flip theme} +{% + \leavevmode% +% OBSERVATION: the "%" symbols inside hbox are all very important here. +% The \hbox enviroment will insert spaces whenever there's whitespace +% Adding a % at the END of each line ensures that any hard returns aren't +% interpreted as white space. This allows the color boxes to be flush against +% one another. If a faint white line appears one could probably do something like +% hspace{-1px} and add an additional pixel-or-two wide beamercolorbox. + +\hbox{% +\begin{beamercolorbox}[wd=.4\paperwidth,ht=2.5ex,dp=1.125ex,leftskip=.3cm, rightskip=.3cm plus1fil]{author in head/foot}% + \usebeamerfont{author in head/foot}\insertshortauthor \end{beamercolorbox}% +% +\begin{beamercolorbox}[wd=.6\paperwidth,ht=2.5ex,dp=1.125ex,leftskip=.3cm,rightskip=.3cm plus1fil]{title in head/foot}% + \usebeamerfont{title in head/foot}{\textit \insertshorttitle}% + \hskip2ex plus1fill% + % \insertpagenumber\,/\,\insertpresentationendpage %% Want FRAME, not SLIDE number + \insertframenumber/\inserttotalframenumber + \end{beamercolorbox}% +}% + +% This is a complete kludge for the faint white line which appears +% between the beamer color boxes above. (It doesnt appear in presentation mode +% but sometimes looks funny when the pdfs are viewed in a window) +\begin{tikzpicture}[overlay] + \usebeamercolor[bg]{author in head/foot} + \draw[thick] (0,3.625ex) -- (\paperwidth,3.625ex); + \draw (.4\paperwidth,0) -- (.4\paperwidth,3.625ex); + \draw[thick] (0,0) -- (\paperwidth,0); +\end{tikzpicture} + + + +\ifbeamer@Flip@bigpagenumber + \begin{tikzpicture}[overlay] + \usebeamercolor[bg]{author in head/foot} + \draw[fill] (\paperwidth-5ex,3.625ex) circle (6ex); + \usebeamercolor[fg]{author in head/foot} + \draw[fill] (\paperwidth-5ex,3.625ex) circle (5ex); + \usebeamercolor[bg]{author in head/foot} + \node at (\paperwidth-5ex,4ex) {\small$^\text{\insertframenumber}/_\text{\inserttotalframenumber}$}; + \end{tikzpicture} +\fi +} + + + +\defbeamertemplate*{frametitle}{Flip theme}[1][left] +{ +% \ifbeamercolorempty[bg]{frametitle}{}{\nointerlineskip}% +\@tempdima=\textwidth% +\advance\@tempdima by\beamer@leftmargin% +\advance\@tempdima by\beamer@rightmargin% + +\vbox{}\vskip-3.5ex% +% +\begin{beamercolorbox}[sep=0.3cm,#1,wd=\the\@tempdima]{titlelike} + \usebeamerfont{frametitle}% + \vbox{}\vskip-1ex% + \if@tempswa\else\csname beamer@fte#1\endcsname\fi% + % \strut{\bf\insertframetitle}\strut\par% %% Include the \bf + \strut{\insertframetitle}\strut\par% + {% + \ifx\insertframesubtitle\@empty% + \else + {\usebeamerfont{framesubtitle} + \usebeamercolor[fg]{framesubtitle} + \insertframesubtitle\strut\par}% + \fi + }% + % + \vskip-1ex% + \if@tempswa\else\vskip-.3cm\fi% set inside beamercolorbox... evil here... +\end{beamercolorbox}% +%% + +% \def\beamer@fteright{\vskip0.35cm\advance\leftskip by 1.7cm\advance\rightskip by1.7cm} +} + + + + +% Sidebar right is important: anything placed here will be +% visible *behind* the main text. This is where to put any +% interesting watermarks. +% +% +\defbeamertemplate*{sidebar right}{Flip theme} +{ +% \llap{\includegraphics[width=50px]{footdecoration}} +% \llap{\includegraphics[width=\paperwidth,height=\paperheight]{upperleft_watermark_transp}} +% +% THIS WOULD BE A NICE WAY TO PUT THE PARTICLE BUBBLE CHAMBER BG +% ... make a png of the background with TRANSPARENT BG +% ... then put the image here (use \hfill to get it on the left) +% Now one can FURTHER apply a slight gradient in the BG +% +% +% % Top Line +\ifx\beamer@Flip@topline\beamer@Flip@truetext + \begin{tikzpicture}[overlay] + \usebeamercolor[fg]{titlelike} % alternately, topbarlike would be a good beamercolor +% \usebeamercolor[fg]{topbarlike} % alternately, topbarlike would be a good beamercolor + \draw[fill] (-\paperwidth,0) rectangle (0,-3pt); + \end{tikzpicture} +\fi +% +% + \vskip.2\beamer@leftmargin% + %\llap{\insertlogo\hskip.5\beamer@leftmargin}% + \llap{\insertlogo\hskip.08\beamer@leftmargin}% + \vfill% + \if \beamer@Flip@watermark\@empty + % This is kind of a kludge since if I put anything in here, I automatically get errors + % Somehow LaTeX wants to read the \else part! + \else% + \llap{\includegraphics[width=\paperwidth,height=\paperheight]{\beamer@Flip@watermark}} + \fi +} + + + +\mode +\endinput + + diff --git a/Lectures_my/EMPP/2017/Lecture1/beamerouterthemedecolines.sty b/Lectures_my/EMPP/2017/Lecture1/beamerouterthemedecolines.sty new file mode 100755 index 0000000..669e493 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/beamerouterthemedecolines.sty @@ -0,0 +1,168 @@ +% Copyright 2007 by Marco Barisione +% +% This file may be distributed and/or modified +% +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. + +\mode + +% String used between the current page and the total page count. +\def\beamer@decolines@pageofpages{/} +\DeclareOptionBeamer{pageofpages}{\def\beamer@decolines@pageofpages{#1}} + +% Show a line below the frame title. +\DeclareOptionBeamer{titleline}[true]{\def\beamer@decolines@titleline{#1}} + +% Image used for the watermark. +\def\beamer@decolines@watermarkorig{} +\DeclareOptionBeamer{watermark}{\def\beamer@decolines@watermarkorig{#1}} + +% Height of the watermark. +\def\beamer@decolines@watermarkheight{100px} +\DeclareOptionBeamer{watermarkheight}{\def\beamer@decolines@watermarkheight{#1}} + +% The original image height is watermarkheightmult * watermarkheight. +\def\beamer@decolines@watermarkheightmult{1} +\DeclareOptionBeamer{watermarkheightmult}{\def\beamer@decolines@watermarkheightmult{#1}} + +\ExecuteOptionsBeamer{titleline=false} +\ProcessOptionsBeamer + +% Enable/disable the watermark. +\def\watermarkon{% + \def\beamer@decolines@watermark{\beamer@decolines@watermarkorig}% +} +\def\watermarkoff{\def\beamer@decolines@watermark{}} + +% Initially enable the watermark. +\watermarkon + +% Colors. +\setbeamercolor*{lineup}{parent=palette primary} +\setbeamercolor*{linemid}{parent=palette secondary} +\setbeamercolor*{linebottom}{parent=palette tertiary} +\setbeamercolor*{page header}{parent=titlelike} + +% Lengths +\newlength{\headerheight} +\setlength{\headerheight}{.045\paperheight} +\newlength{\beamer@decolines@lineup} +\setlength{\beamer@decolines@lineup}{.025\paperheight} +\newlength{\beamer@decolines@linemid} +\setlength{\beamer@decolines@linemid}{.015\paperheight} +\newlength{\beamer@decolines@linebottom} +\setlength{\beamer@decolines@linebottom}{.01\paperheight} + +% The height of the watermark part below the 3 bottom lines. +\newlength{\beamer@decolines@watermarkheightbottom} +\addtolength{\beamer@decolines@watermarkheightbottom}{\beamer@decolines@lineup} +\addtolength{\beamer@decolines@watermarkheightbottom}{\beamer@decolines@linemid} +\addtolength{\beamer@decolines@watermarkheightbottom}{\beamer@decolines@linebottom} + +% The height of the watermark part over the 3 bottom lines before shrinking. +\newlength{\beamer@decolines@watermarkheightupperorig} +\setlength{\beamer@decolines@watermarkheightupperorig}{\beamer@decolines@watermarkheight} +\addtolength{\beamer@decolines@watermarkheightupperorig}{-\beamer@decolines@watermarkheightbottom} +\multiply\beamer@decolines@watermarkheightupperorig by \beamer@decolines@watermarkheightmult + +% % Footer. +% \defbeamertemplate*{footline}{decolines theme} +% { +% \leavevmode% +% % Page number. +% \hbox{% +% \begin{beamercolorbox}[wd=.2\paperwidth,ht=0ex,dp=0ex,center]{}% +% \usebeamerfont{palette primary}\insertframenumber{} \beamer@decolines@pageofpages{} \inserttotalframenumber% +% \end{beamercolorbox}% +% \begin{beamercolorbox}[wd=.8\paperwidth,ht=0ex,dp=0ex]{}% +% \end{beamercolorbox}% +% } % +% % First line. +% \hbox{% +% \begin{beamercolorbox}[wd=.2\paperwidth,ht=\beamer@decolines@lineup,dp=0pt]{}% +% \end{beamercolorbox}% +% \begin{beamercolorbox}[wd=.8\paperwidth,ht=\beamer@decolines@lineup,dp=0pt]{lineup}% +% \end{beamercolorbox}% +% } % +% % Second line. +% \hbox{% +% \begin{beamercolorbox}[wd=\paperwidth,ht=\beamer@decolines@linemid,dp=0pt]{linemid}% +% \end{beamercolorbox}% +% } % +% % Third line. +% \hbox{% +% \begin{beamercolorbox}[wd=.1\paperwidth,ht=\beamer@decolines@linebottom,dp=0pt]{}% +% \end{beamercolorbox}% +% \begin{beamercolorbox}[wd=.9\paperwidth,ht=\beamer@decolines@linebottom,dp=0pt]{linebottom}% +% \end{beamercolorbox}% +% }% +% % This seems to fix some alignment problems with the watermark. It has to be +% % always applied if you do not want to see the footer moving up and down when +% % moving from a page with watermark to a page without or vice versa. +% \vskip-.5px% +% % Watermark. +% \if\beamer@decolines@watermark\@empty\else% +% \vskip-\beamer@decolines@watermarkheightbottom% +% \llap{\includegraphics[height=\beamer@decolines@watermarkheightbottom,clip=true,% +% trim=0pt 0pt 0pt \beamer@decolines@watermarkheightupperorig]{\beamer@decolines@watermark}\hskip-\paperwidth}% +% \fi% +% } + +\defbeamertemplate*{headline}{decolines theme} +{ + \leavevmode% + \hbox{% + \begin{beamercolorbox}[wd=\paperwidth,ht=\headerheight,dp=0pt]{page header}% + \end{beamercolorbox}% + } % + \vskip0pt% +} + +\defbeamertemplate*{frametitle}{decolines theme}[1][left] +{ + \ifbeamercolorempty[bg]{frametitle}{}{\nointerlineskip}% + \@tempdima=\textwidth% + \advance\@tempdima by\beamer@leftmargin% + \advance\@tempdima by\beamer@rightmargin% + \vbox{}\vskip-.5\beamer@leftmargin% + \begin{beamercolorbox}[sep=\beamer@leftmargin,#1,wd=\the\@tempdima]{} + \usebeamerfont{frametitle}\usebeamercolor[bg]{framesubtitle}% + \vbox{}\vskip0ex% + \if@tempswa\else\csname beamer@fte#1\endcsname\fi% + \strut\insertframetitle\strut\par% + {% + \ifx\insertframesubtitle\@empty% + \else% + {\usebeamerfont{framesubtitle}\usebeamercolor[bg]{framesubtitle}\insertframesubtitle\strut\par}% + \fi + }% + \vskip-1ex% + \if@tempswa\else\vskip-\beamer@leftmargin\fi + \end{beamercolorbox}% + \def\beamer@decolines@truetext{true}% + \ifx\beamer@decolines@titleline\beamer@decolines@truetext% + \vskip-.5\beamer@leftmargin% + \begin{beamercolorbox}[wd=\textwidth,ht=.1ex,dp=0ex]{linemid}% + \end{beamercolorbox}% + \fi +} + +% Frame title continuations, default +\defbeamertemplate*{frametitle continuation}{decolines theme}{(\insertcontinuationcount)} + + + +\defbeamertemplate*{sidebar right}{decolines theme} +{ + \vskip.1\beamer@leftmargin% + \llap{\insertlogo\hskip.5\beamer@leftmargin}% + \vfill% + \if\beamer@decolines@watermark\@empty\else% + \llap{\includegraphics[height=\beamer@decolines@watermarkheight]{\beamer@decolines@watermark}}% + \vskip-\beamer@decolines@watermarkheightbottom% + \fi +} + +\mode + diff --git a/Lectures_my/EMPP/2017/Lecture1/beamerthemeFlip.sty b/Lectures_my/EMPP/2017/Lecture1/beamerthemeFlip.sty new file mode 100755 index 0000000..a615ff5 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/beamerthemeFlip.sty @@ -0,0 +1,59 @@ +% Main style file for the BEAMER FLIP THEME 2012 +% Copyright 2012 by Flip Tanedo +% This file may be distributed and/or modified +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. +% +% Comments: This is still a work in progress. +% A good way to present: http://www.cs.hmc.edu/~oneill/freesoftware/pdftokeynote.html + +% \usepackage{beamerthemesplit} +\mode + + +%% These are the options that are fed in through the driver file +%% Some of them get passed on to the other theme files +\DeclareOptionBeamer{bullet}{\PassOptionsToPackage{bullet=#1}{beamerinnerthemeFlip}} +\DeclareOptionBeamer{bigpagenumber}{\PassOptionsToPackage{bigpagenumber}{beamerouterthemeFlip}} +\DeclareOptionBeamer{topline}[true]{\PassOptionsToPackage{topline=#1}{beamerouterthemeFlip}} +\DeclareOptionBeamer{shadow}[false]{\PassOptionsToPackage{shadow=#1}{beamerinnerthemeFlip}} + +\DeclareOptionBeamer{watermark}{\PassOptionsToPackage{watermark=#1}{beamerouterthemeFlip}} + +\ProcessOptionsBeamer + +\useinnertheme{Flip} % Calls beamerinnerthemeFlip.sty +\useoutertheme{Flip} % Calls beamerouterthemeFlip.sty +\usecolortheme{Flip} % Calls beamercolorthemeFlip.sty + + + +%%%%%%%%%%%%%%%%%%%%%%%% +% Background Gradient % +%%%%%%%%%%%%%%%%%%%%%%%% + + +%% Usually I would leave this on +%% However, there seems to be problems with XeLaTeX +%% http://tex.stackexchange.com/questions/29497/xelatex-preventing-beamer-from-using-different-backgrounds +\setbeamertemplate{background canvas}[vertical shading][bottom=blue!.1, middle=white, top=white] + +%% HOWEVER: it seems to make it impossible to change this later on in the document + + +%% For a dark background: +% \setbeamertemplate{background canvas}[vertical shading][bottom=keynotebottom, middle=keynotemiddle, top=keynotetop] + + +%% An alternate way: \beamertemplateshadingbackground{blue!.1}{red!2} +%% In general: you want the gradient to be subtle! + + +%%%%%%%%%%%%%%%%%%%%%%% +% Navigation symbols % +%%%%%%%%%%%%%%%%%%%%%%% + +\setbeamertemplate{navigation symbols}{} % Turns off PDF navigation symbols + +\mode +\endinput \ No newline at end of file diff --git a/Lectures_my/EMPP/2017/Lecture1/images/BG_lower.png b/Lectures_my/EMPP/2017/Lecture1/images/BG_lower.png new file mode 100755 index 0000000..073034a --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/images/BG_lower.png Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture1/images/Higs_Ellis_SM.png b/Lectures_my/EMPP/2017/Lecture1/images/Higs_Ellis_SM.png new file mode 100644 index 0000000..7722291 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/images/Higs_Ellis_SM.png Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture1/images/bubble.gif b/Lectures_my/EMPP/2017/Lecture1/images/bubble.gif new file mode 100644 index 0000000..ecff282 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/images/bubble.gif Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture1/images/bubble.jpg b/Lectures_my/EMPP/2017/Lecture1/images/bubble.jpg new file mode 100644 index 0000000..ceb584d --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/images/bubble.jpg Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture1/images/bubble2.jpg b/Lectures_my/EMPP/2017/Lecture1/images/bubble2.jpg new file mode 100644 index 0000000..0fd03bb --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/images/bubble2.jpg Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture1/images/buffon.png b/Lectures_my/EMPP/2017/Lecture1/images/buffon.png new file mode 100644 index 0000000..b3c1f65 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/images/buffon.png Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture1/images/dupa.png b/Lectures_my/EMPP/2017/Lecture1/images/dupa.png new file mode 100644 index 0000000..70db5f7 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/images/dupa.png Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture1/images/result.png b/Lectures_my/EMPP/2017/Lecture1/images/result.png new file mode 100644 index 0000000..3617873 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/images/result.png Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture1/images/result_error.pdf b/Lectures_my/EMPP/2017/Lecture1/images/result_error.pdf new file mode 100644 index 0000000..f7a21bd --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/images/result_error.pdf Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture1/images/result_error_dep.pdf b/Lectures_my/EMPP/2017/Lecture1/images/result_error_dep.pdf new file mode 100644 index 0000000..8017f1e --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/images/result_error_dep.pdf Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture1/images/result_weight.png b/Lectures_my/EMPP/2017/Lecture1/images/result_weight.png new file mode 100644 index 0000000..afda7e1 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/images/result_weight.png Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture1/images/results_0.pdf b/Lectures_my/EMPP/2017/Lecture1/images/results_0.pdf new file mode 100644 index 0000000..cc9f45a --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/images/results_0.pdf Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture1/images/results_1.pdf b/Lectures_my/EMPP/2017/Lecture1/images/results_1.pdf new file mode 100644 index 0000000..b0c4fa9 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/images/results_1.pdf Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture1/images/results_fit_0.pdf b/Lectures_my/EMPP/2017/Lecture1/images/results_fit_0.pdf new file mode 100644 index 0000000..4ac392a --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/images/results_fit_0.pdf Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture1/images/results_fit_1.pdf b/Lectures_my/EMPP/2017/Lecture1/images/results_fit_1.pdf new file mode 100644 index 0000000..8bc7be0 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/images/results_fit_1.pdf Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture1/images/uzh-transp.pdf b/Lectures_my/EMPP/2017/Lecture1/images/uzh-transp.pdf new file mode 100644 index 0000000..977da67 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/images/uzh-transp.pdf Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture1/mchrzasz+mp.sh b/Lectures_my/EMPP/2017/Lecture1/mchrzasz+mp.sh new file mode 100644 index 0000000..1a24852 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/mchrzasz+mp.sh @@ -0,0 +1 @@ +#!/bin/sh diff --git a/Lectures_my/EMPP/2017/Lecture1/mchrzasz-blx.bib b/Lectures_my/EMPP/2017/Lecture1/mchrzasz-blx.bib new file mode 100644 index 0000000..0cd9139 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/mchrzasz-blx.bib @@ -0,0 +1,11 @@ +@Comment{$ biblatex control file $} +@Comment{$ biblatex version 2.8 $} +Do not modify this file! + +This is an auxiliary file used by the 'biblatex' package. +This file may safely be deleted. It will be recreated as +required. + +@Control{biblatex-control, + options = {2.8:0:0:1:0:1:1:0:0:0:0:1:3:1:79:+:nty}, +} diff --git a/Lectures_my/EMPP/2017/Lecture1/mchrzasz.aux b/Lectures_my/EMPP/2017/Lecture1/mchrzasz.aux new file mode 100644 index 0000000..ad74c5b --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture1/mchrzasz.aux @@ -0,0 +1,191 @@ +\relax +\providecommand\hyper@newdestlabel[2]{} +\providecommand\zref@newlabel[2]{} +\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} +\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined +\global\let\oldcontentsline\contentsline +\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} +\global\let\oldnewlabel\newlabel +\gdef\newlabel#1#2{\newlabelxx{#1}#2} +\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} +\AtEndDocument{\ifx\hyper@anchor\@undefined +\let\contentsline\oldcontentsline +\let\newlabel\oldnewlabel +\fi} +\fi} +\global\let\hyper@last\relax +\gdef\HyperFirstAtBeginDocument#1{#1} 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+\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{amssymb} +\usepackage{bm} +\usepackage{colortbl} +\usepackage{mathrsfs} % For Weinberg-esque letters +\usepackage{cancel} % For "SUSY-breaking" symbol +\usepackage{slashed} % for slashed characters in math mode +\usepackage{bbm} % for \mathbbm{1} (unit matrix) +\usepackage{amsthm} % For theorem environment +\usepackage{multirow} % For multi row cells in table +\usepackage{arydshln} % For dashed lines in arrays and tables +\usepackage{siunitx} +\usepackage{xhfill} +\usepackage{grffile} +\usepackage{textpos} +\usepackage{subfigure} +\usepackage{tikz} +\usepackage{hyperref} +%\usepackage{hepparticles} +\usepackage[italic]{hepparticles} + +\usepackage{hepnicenames} + +% Drawing a line +\tikzstyle{lw} = [line width=20pt] +\newcommand{\topline}{% + \tikz[remember picture,overlay] {% + \draw[crimsonred] ([yshift=-23.5pt]current page.north west) + -- ([yshift=-23.5pt,xshift=\paperwidth]current page.north west);}} + + + +% % % % % % % % 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height=3em, minimum width=6em] + + + + +\usetikzlibrary{backgrounds} +\usetikzlibrary{mindmap,trees} % For mind map +\newcommand{\degree}{\ensuremath{^\circ}} +\newcommand{\E}{\mathrm{E}} +\newcommand{\Var}{\mathrm{Var}} +\newcommand{\Cov}{\mathrm{Cov}} +\newcommand\Ts{\rule{0pt}{2.6ex}} % Top strut +\newcommand\Bs{\rule[-1.2ex]{0pt}{0pt}} % Bottom strut + +\graphicspath{{images/}} % Put all images in this directory. Avoids clutter. + +% SOME COMMANDS THAT I FIND HANDY +% \renewcommand{\tilde}{\widetilde} % dinky tildes look silly, dosn't work with fontspec +\newcommand{\comment}[1]{\textcolor{comment}{\footnotesize{#1}\normalsize}} % comment mild +\newcommand{\Comment}[1]{\textcolor{Comment}{\footnotesize{#1}\normalsize}} % comment bold +\newcommand{\COMMENT}[1]{\textcolor{COMMENT}{\footnotesize{#1}\normalsize}} % comment crazy bold +\newcommand{\Alert}[1]{\textcolor{Alert}{#1}} % louder alert +\newcommand{\ALERT}[1]{\textcolor{ALERT}{#1}} % loudest alert +%% "\alert" is already a beamer pre-defined +\newcommand*{\Scale}[2][4]{\scalebox{#1}{$#2$}}% + +\def\Put(#1,#2)#3{\leavevmode\makebox(0,0){\put(#1,#2){#3}}} + +\usepackage{gmp} +\usepackage[final]{feynmp-auto} + +\usepackage[backend=bibtex,style=numeric-comp,firstinits=true]{biblatex} +\bibliography{bib} +\setbeamertemplate{bibliography item}[text] + +\makeatletter\let\frametextheight\beamer@frametextheight\makeatother + +% suppress frame numbering for backup slides +% you always need the appendix for this! +\newcommand{\backupbegin}{ + \newcounter{framenumberappendix} + \setcounter{framenumberappendix}{\value{framenumber}} +} +\newcommand{\backupend}{ + \addtocounter{framenumberappendix}{-\value{framenumber}} + \addtocounter{framenumber}{\value{framenumberappendix}} +} + + +\definecolor{links}{HTML}{2A1B81} +%\hypersetup{colorlinks,linkcolor=,urlcolor=links} + +% For shapo's formulas: +\def\lsi{\raise0.3ex\hbox{$<$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}} +\def\gsi{\raise0.3ex\hbox{$>$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}} +\newcommand{\lsim}{\mathop{\lsi}} +\newcommand{\gsim}{\mathop{\gsi}} +\newcommand{\wt}{\widetilde} +%\newcommand{\ol}{\overline} +\newcommand{\Tr}{\rm{Tr}} +\newcommand{\tr}{\rm{tr}} +\newcommand{\eqn}[1]{&\hspace{-0.7em}#1\hspace{-0.7em}&} +\newcommand{\vev}[1]{\rm{$\langle #1 \rangle$}} +\newcommand{\abs}[1]{\rm{$\left| #1 \right|$}} +\newcommand{\eV}{\rm{eV}} +\newcommand{\keV}{\rm{keV}} +\newcommand{\GeV}{\rm{GeV}} +\newcommand{\im}{\rm{Im}} +\newcommand{\disp}{\displaystyle} +\def\be{\begin{equation}} +\def\ee{\end{equation}} +\def\ba{\begin{eqnarray}} +\def\ea{\end{eqnarray}} +\def\d{\partial} +\def\l{\left(} +\def\r{\right)} +\def\la{\langle} +\def\ra{\rangle} +\def\e{{\rm e}} +\def\Br{{\rm Br}} +\def\fixme{{\color{red} FIXME!}} +\def\mc{{\color{Magenta}{MC}}} +\def\pdf{{\rm p.d.f.}} + +\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (CERN)} +\institute{CERN} +\title[Introduction to \\Monte Carlo methods]{Introduction to \\Monte Carlo methods} +\date{\fixme} + + +\begin{document} +\tikzstyle{every picture}+=[remember picture] + +{ +\setbeamertemplate{sidebar right}{\llap{\includegraphics[width=\paperwidth,height=\paperheight]{bubble2}}} +\begin{frame}[c]%{\phantom{title page}} +\begin{center} +\begin{center} + \begin{columns} + \begin{column}{0.9\textwidth} + \flushright\fontspec{Trebuchet MS}\bfseries \Huge {Introduction to \\Monte Carlo methods} + \end{column} + \begin{column}{0.2\textwidth} + %\includegraphics[width=\textwidth]{SHiP-2} + \end{column} + \end{columns} +\end{center} + \quad + \vspace{3em} +\begin{columns} +\begin{column}{0.44\textwidth} +\flushright \vspace{-1.8em} {\fontspec{Trebuchet MS} \Large Marcin Chrząszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}} + +\end{column} +\begin{column}{0.53\textwidth} +\includegraphics[height=1.3cm]{uzh-transp} +\end{column} +\end{columns} + +\vspace{1em} +% \footnotesize\textcolor{gray}{With N. Serra, B. Storaci\\Thanks to the theory support from M. Shaposhnikov, D. Gorbunov}\normalsize\\ +\vspace{0.5em} + \textcolor{normal text.fg!50!Comment}{Experimental Methods in Particle Physics, \\ 5 October, 2016} +\end{center} +\end{frame} +} + + +\begin{frame}\frametitle{Literature} + +\begin{enumerate} +\item J. M. Hammersley, D. C. Hamdscomb, ``Monte Carlo Methods'', London: Methuen \& Co. Ltd., New York: J. Wiley \& Sons Inc., 1964 +\item I. M. Sobol, ``The Monte Carlo Method'', Mir Publishers, Moscow, 1975. +\item M. H. Kalos, P. A. Whitlock, ,,Monte Carlo Methods”, J. Wiley \& Sons Inc., New York, 1986 +\item G. S. Fishman, ,,Monte Carlo: Concepts, Algorithms and Applications”, Springer, 1996. +\item R. Y. Rubinstein, D. P. Kroese, ,,Simulation and the Monte Carlo Method”, Second Edition, J. Wiley \& Sons Inc., 2008. +\item R. Korn, E. Korn, G. Kroisandt, ,,Monte Carlo methods and models in finance and insurance”, CRC Press, +Taylor \& Francis Group, 2010. +\item S. Jadach, ,,Practical Guide to Monte Carlo”, \href{http://arxiv.org/abs/physics/9906056}{arXiv:physics/9906056}, \href{http://cern.ch/jadach/MCguide/}{http://cern.ch/jadach/MCguide/}. +\end{enumerate} + + +\end{frame} + + + + +\begin{frame}\frametitle{Course Plan} + +We will have 6 hours of Monte Carlo (MC) lectures. The lectures will be devoted:\\ + +\hspace{1.5cm} +\begin{itemize} +\item 1 h: Mathematical introduction to MC methods. +\item 1 h: MC integration methods. +\item 2 h: Random numbers generators. +\item 2 h: Markov Chain MC. +\item 2 h: Tutorial and examples. +\end{itemize} +\hspace{1cm} \\ +The hands-on tutorial will consist of program templates in which we will implement couple of algorithms that were explained in the lecture. \\ +$\Rrightarrow$ All examples shown in this course are available in the github repository:\\ +\url{https://github.com/mchrzasz/EMPP_MC}\\ +\color{RubineRed}{There will be an indication (in this color) on the adequate slide for each of the macro.} + + +\end{frame} + + +\begin{frame}\frametitle{Definitions} +\begin{footnotesize} +$\Rrightarrow$ Basic definition:\\ + \begin{exampleblock}{} + Monte Carlo method is any technique that uses {\it{random numbers}} to solve a given mathematical problem. + \end{exampleblock} +% \vspace{0.5cm} + +$\rightarrowtail$ Random number: For the purpose of this course we need to assume that we know what it is, although the formal definition is highly non-trivial.\\ +\vspace{0.05cm} +$\Rrightarrow$ My favourite definition (Halton 1970): \begin{scriptsize}more complicated, but more accurate.\end{scriptsize} + +\begin{exampleblock}{} +''Representing the solution of a problem as a parameter of a hypothetical population, and using a random sequence of numbers to construct a sample of the population, from which statistical estimates of the parameter can be obtained.'' + \end{exampleblock} +To put this definition in mathematical language:\\ +Let $F$ be a solution of a given mathematical problem. The estimate of the result $\hat{F}$:\\ +\begin{equation*} +\hat{F}=f( \lbrace r_1, r_2, r_3,...,r_n \rbrace; ...), +\end{equation*} +where $\lbrace r_1, r_2, r_3,...,r_n \rbrace$ are random numbers. +\begin{center} +\color{red}{The problem we are solving doesn't need to be stochastic!} +\end{center} +\begin{scriptsize} +$\twoheadrightarrow$ One could wonder why are we trying to add all the stochastic properties to a deterministic problem. Those are the properties that allow to use all well known statistic theorems. + \end{scriptsize} +\end{footnotesize} +\end{frame} + +\begin{frame}\frametitle{History of MC methods} +\begin{footnotesize} +\begin{itemize} +\item {\color{PineGreen}{G. Compte de Buffon (1777)}} - First documented usage of random numbers for integral computation (Buffon thrown niddle on the table with parrarel line; we will do a modern version of this exercise). +\item {\color{PineGreen}{Marquis de Laplace (1886)}} - Used the Buffon niddle to determine the value of $\pi$ number. +\item {\color{PineGreen}{Lord Kelvin (1901)}} - Thanks to drawing randomly numbered cards he managed he managed to calculate some integrals in kinematic gas theorem. +\item {\color{PineGreen}{W. S. Gosse (better knows as Student) (1908)}} - Used similar way as Lord Kelvin to get random numbers to prove \textit{t}-Student distribution. +\item {\color{PineGreen}{Enrico Fermi (1930) }} - First mechanical device (\texttt{FERMIAC}) for random number generations. Solved neutron transport equations in the nuclear plants. +\item {\color{PineGreen}{S. Ulam, R. Feynman, J. von Neumann et. al.}} - First massive usage of random numbers. Most applications were in Manhattan project to calculate neutron scattering and absorption. \\ +In {\color{NavyBlue}{Los Alamos}} the name {\color{Mahogany}{Monte Carlo}} was created as kryptonim of this kind of calculations. +\end{itemize} + + +\end{footnotesize} +\end{frame} + + + +\begin{frame}\frametitle{Euler number determination, $\rm \color{RubineRed}{Lecture1/Euler\_number}$ } +\begin{footnotesize} +$\Rrightarrow$ As mentioned before \mc~methods can be used to solve problems that \textbf{do not} have stochastic nature! All the integrals calculated in Los Alamos during the Manhattan project are nowadays solvable without any \mc~methods.\\ +$\rightarrowtail$ Let's give a trivial example of solving a non stochastic problem: calculating Euler number $e$. We know that $e=2.7182818...$. +$\Rrightarrow$ To calculate the $\hat{e}$ we will use the following algorithm: +\begin{itemize} +\item We generate a random number in range $(0,1)$ (in stat. $\mathcal{U}(0,1)$) until the number we generate is smaller then the previous one, aka we get the following sequence: +\begin{align*} +x_1x_{n} +\end{align*} +\item We store the number $n$. We repeat this experiment $N$ times and calculate the arithmetic average of $n$. The obtained value is an statistical estimator of $e$: +\begin{align*} +\hat{e}= \dfrac{1}{N}\sum_{i=1}^N n_i \xrightarrow{N\to \infty} e . +\end{align*} +\end{itemize} +$\Rrightarrow$ Numerical example: +\begin{tabular}{r c c c } +$N$ & $\hat{e}$ & $\hat{e} - e$ & \multirow{5}{*}{Is this $\sim\sqrt{N}$?} \\ +100 & $2.760000$ & $0.041718$ \\ +10000 & $2.725000$ & $0.006718$ \\ +1000000 & $2.718891$ & $0.000609$ \\ +100000000 & $2.718328$ & $0.000046$\\ +\end{tabular} + + +\end{footnotesize} +\end{frame} + +\begin{frame}\frametitle{Let's test the $\sqrt{N}$, $\rm \color{RubineRed}{Lecture1/Euler\_number}$ } + +\only<1> +{ +$\Rrightarrow$ In the last example we measured the Euler number using different number of pseudo-experiments.\\ +$\rightarrowtail$ We compared the obtained value to the true and observed roughly a $\sqrt{N}$ dependence on the difference between the true value and the obtained one.\\ +} +$\rightarrowtail$ Could we test this? YES! Lets put our experimentalist hat on!\\ +$\rightarrowtail$ From the begging of studies they tooth us to get the error you need to repeat the measurements. +\only<1> +{ +\begin{exampleblock}{The algorithm:} +Previous time we measured Euler number using $N$ events, where $N \in (100, 1000, 10000, 100000)$. Now lets repeat this measurement $n_N$ times (of course each time we use new generated numbers). From the distribution of $\hat{e} -e$ we could say something about the uncertainty of our estimator for given $N$. + \end{exampleblock} +} + +\begin{center} +\only<2> +{ +\includegraphics[angle=-90,width=0.8\textwidth]{images/result_error.pdf} +} +\only<3> +{ +\includegraphics[angle=-90,width=0.8\textwidth]{images/result_error_dep.pdf} +} +\end{center} + + + + + + + + + + + + +\end{frame} + +\begin{frame}\frametitle{Monte Carlo and integration} +\begin{footnotesize} +$\hookrightarrow$ {\color{BrickRed}{\textbf{All MC calculations are equivalent to preforming an integration.}}}\\ +$\rightrightarrows$ Assumptions: $r_i$ random numbers from $\mathcal{U}(0,1)$. The MC result: +\begin{align*} +F=F(r_1,r_2,...r_n) +\end{align*} +is unbias estimator of an integral: +\begin{align*} +I=\int_0^1...\int_0^1 F(x_1,x_2,...,x_n)dx_1,dx_2...,dx_n +\end{align*} +aka the expected value of the $I$ integral is: +\begin{align*} +E(F)=I. +\end{align*} + \begin{exampleblock}{} +$\Rrightarrow$ This mathematical identity is the most useful property of the MC methods. It is a link between mathematical analysis and statistic world. Now we can use the best of the both world! + \end{exampleblock} +If we want to calculate the integral in different range then $(0,1)$ we just scale the the previous result: +\begin{align*} +\dfrac{1}{N}\sum_{i=1}^N f(x_i) \xrightarrow{N\to \infty} E(f)=\dfrac{1}{b-a}\int_a^b f(x)dx +\end{align*} + + +\end{footnotesize} +\end{frame} + + +\begin{frame}\frametitle{Uncertainty from Monte Carlo methods} +\begin{footnotesize} +$\Rrightarrow$ In practice we do not have $N\to \infty$ so we will never know the exact result of an integral :(\\ +$\longmapsto$ Let's use the {\color{BrickRed}{statistical}} world and estimate the uncertainty of an integral in this case :)\\ +$\rightarrowtail$ A variance of a MC integral: +\begin{align*} +V(\hat{I}) = \dfrac{1}{n} \Big\lbrace E(f^2) - E^2(f) \Big\rbrace = \dfrac{1}{n} \Big\lbrace \dfrac{1}{b-a} \int_a^b f^2(x)dx - I^2 \Big\rbrace +\end{align*} + \begin{alertblock}{} +$\looparrowright$ To calculate $V(\hat{I})$ one needs to know the value of $I$! +\end{alertblock} +$\Rrightarrow$ In practice $V(\hat{I})$ is calculated via estimator: +\begin{columns} +\column{2in} +\begin{align*} +\hat{V}(\hat{I})=\dfrac{1}{n}\hat{V}(f), +\end{align*} +\column{3in} +\begin{align*} +\hat{V}(f) = \dfrac{1}{n-1}\sum_{i=1}^n \Big[ f(x_i)-\dfrac{1}{n} \sum_{i=1}^nf(x_i)\Big]^2. +\end{align*} +\end{columns} + + +$\Rrightarrow$ MC estimator of standard deviation: $\hat{\sigma}=\sqrt{\hat{V}(\hat{I})}$ + + +\end{footnotesize} +\end{frame} + + +\begin{frame}\frametitle{Buffon needle - $\pi$ number calculus} +\begin{footnotesize} + +$\Rrightarrow$ Buffon needle (Buffon 1777, Laplace 1886): +We are throwing a needle (of length $l$) on to a surface covered with parallel lines width distance $L$. If a thrown needle touches a line we count a hit, else miss. Knowing the number of hits and misses one can calculate the $\pi$ number. +\vspace{0.3cm} +\begin{columns} +\column{0.1in} +{~} +\column{2in} +{\color{ForestGreen}{Experiment:}} +\column{2.8in} +{\color{Cerulean}{Theory:}} + +\end{columns} + + +\begin{columns} +\column{0.1in} +{~} +\column{2in} + +\includegraphics[width=0.9\textwidth]{images/buffon.png}\\ +$n$ - number of hits\\ +$N$ number of hits and misses,\\ +aka number of tries. + +\column{2.8in} +$\Rightarrow$ x - angle between needle and horizontal line, $x \in \mathcal{U}(0,\pi)$. +$\Rightarrow$ the probability density function (\pdf) for x: +\begin{align*} +\rho(x)=\dfrac{1}{\pi} +\end{align*} +$\Rightarrow$ $p(x)$ probability to hit a line for a given x value: +\begin{align*} +p(x)=\dfrac{l}{L}\vert \cos x \vert +\end{align*} +$\Rightarrow$ Total hit probability: +\begin{align*} +P = E[p(x)]=\int_0^{\pi}p(x)\rho(x)dx=\dfrac{2l}{\pi L} +\end{align*} + +\end{columns} +Now one can calculate $\hat{P}$ from MC : $\hat{P}=\dfrac{n}{N} \xrightarrow{N\to \infty} P= \dfrac{2l}{\pi L} \Rightarrow \hat{\pi}=\dfrac{2Nl}{nL}$ + + +\end{footnotesize} +\end{frame} + + + + + + + + + + + +\begin{frame}\frametitle{Buffon needle - Simplest Carlo method} +\begin{footnotesize} +{\color{MidnightBlue}{Monte Carlo type ''heads or tails''}}\\ +Let's use the summery of $p(x)$ function nad take $0 p(x): & \text{miss}. +\end{cases} +\end{align*} + +\column{2.5in} +\includegraphics[width=0.75\textwidth]{images/result.png} + + + +\end{columns} +Let's define weight function: $w(x,y)=\Theta(p(x)-y)$, \\ +where $\Theta(x)$ is the step function.\\ +$\rightarrowtail$ \pdf : $\varrho(x,y)=\rho(x)g(y)=\frac{2}{\pi} \cdot 1$\\ +$\Rightarrow$ Integrated probability: +\begin{align*} +P=E(w)=\int w(x,y) \varrho(x,y)dx dy = \dfrac{2l}{\pi L} \xleftarrow{N\to \infty}\hat{P}=\frac{1}{N} \sum_{i=1}^N w(x_i,y_i)= \dfrac{n}{N} +\end{align*} +Standard deviation for $\hat{P}$: $\hat{\sigma}=\dfrac{1}{\sqrt{N-1}}\sqrt{\dfrac{n}{N}\Big(1-\dfrac{n}{N}\Big)} $ + + + +\end{footnotesize} +\end{frame} + + +\begin{frame}\frametitle{Buffon needle, $\rm \color{RubineRed}{Lecture1/Heads\_tails}$ } +\begin{small} + + +$\Rrightarrow$ Lets make this toy experiment and calculate the $\pi$ number.\\ +$\hookrightarrow$ We can simulate the central position $(y)$ of an needle between $(-L, L)$ from $\mathcal{U}(-L, L)$. + + \begin{exampleblock}{Symmetry:} +Please note the symmetry of the problem, if the position of the needle would be $>L$ then we can shift the needle by any number of $L$'s. + \end{exampleblock} + +$\hookrightarrow$ New we simulate the angle $(\phi)$ with a flat distribution from $(0,\pi)$. +$\hookrightarrow$ The maximum and minimum $y$ position of the needle are: +\begin{align*} +y_{\max}=y+\vert \cos \phi \vert l\\ +y_{\min}=y-\vert \cos \phi \vert l +\end{align*} +$\hookrightarrow$ Now we check if the needle touches any of the lines: $y=L$, $y=0$ or $y=-L$. If yes we count the events. +\end{small} +\begin{center} + + +\begin{footnotesize} + + +\begin{tabular}{r c c c } +$N$ & $\hat{\pi}$ & $\hat{\pi} - \pi$ & $\sigma(\hat{\pi})$ \\ +10000 & $3.12317$ & $-0.01842$ & $0.03047$\\ +100000 & $3.14707$ & $0.00547$ & $0.00979$\\ +1000000 & $3.13682$ & $-0.00477$ & $0.00307$\\ +10000000 & $3.14096$ & $-0.00063$ & $0.00097$\\ + + +\end{tabular} + +\end{footnotesize} +\end{center} +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame}\frametitle{Central Limit Theorem, $\rm \color{RubineRed}{Lecture1/CLT}$ } +\begin{footnotesize} + \begin{exampleblock}{} +Large independent random numbers assembly has always Gaussian distribution no matter from what distribution they were generated from as far as they have finite variances and expected values and the assembly is sufficiently large. + \end{exampleblock} +\includegraphics[width=0.9\textwidth]{images/dupa.png} + + +\end{footnotesize} +\end{frame} + + +\begin{frame}\frametitle{Crude Monte Carlo method of integration} +\begin{footnotesize} +$\Rrightarrow$ {\color{MidnightBlue}{Crude Monte Carlo method of integration is based on Central Limit Theorem (CLT): }}\\ +\begin{align*} +\dfrac{1}{N} \sum_{i=1}^N f(x_i) \xrightarrow{N\to \infty} \dfrac{1}{b-a}\int_a^b f(x)dx =E(f) +\end{align*} +$\Rrightarrow$ The standard deviation can be calculated: +\begin{align*} +\sigma = \dfrac{1}{\sqrt{N}} \sqrt{\Big[ E(f^2) -E^2(f)\Big] } +\end{align*} + +$\Rrightarrow$ From LNT we have: +\begin{align*} +P= \int w(x) \rho(x) dx = \int_0^{\pi/2} (\frac{l}{L} \cos x ) \frac{2}{\pi} dx= \dfrac{2l}{\pi L} \xrightarrow{N\to \infty} \frac{1}{N}\sum_{i=1}^N w(x_i) +\end{align*} +$\Rrightarrow$ Important comparison between ''Hit and mishit'' and Crude \mc~methods. One can analytically calculate: + +\begin{align*} +\hat{\sigma}^{{\rm{Crude}}} < \hat{\sigma}^{{\rm{Hit~and~mishit}}} +\end{align*} + + +$\Rrightarrow$ Crude \mc~is \textbf{always} better then ''Hit and mishit'' method. We will prove this on an example (can be proven analytically as well). + + +\end{footnotesize} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Crude MC vs ”Hit and mishit”, $\rm \color{RubineRed}{Lecture1/Crude\_vs\_HT}$} + +$\Rrightarrow$ We can repeat a toy MC studies as we did in the Euler needle case.\\ +$\hookrightarrow$ In this example we want to calculate $\int_0^{\pi/2} \cos x dx$ + +\only<1>{ +\begin{center} +\includegraphics[angle=-90,width=0.8\textwidth]{images/results_0.pdf} +\end{center} +} +\only<2>{ +\begin{center} +\includegraphics[angle=-90,width=0.8\textwidth]{images/results_1.pdf} +\end{center} +} +\only<3>{ +\begin{center} + +\includegraphics[angle=-90,width=0.4\textwidth]{images/results_fit_0.pdf} +\includegraphics[angle=-90,width=0.4\textwidth]{images/results_fit_1.pdf}\\ +\end{center} +$\Rrightarrow$ One clearly sees that both methods follow $1/\sqrt{N}$ dependence and that the Crude MC is always better then the ''Hit and mishit''.\\ +$\Rrightarrow$ Please note that for the ''Hit and mishit'' we are suing 2 times more random numbers than for the Crude method so in terms of timing the Crude MC is also much faster. + +} + + + +\end{frame} + +\begin{frame}\frametitle{Classical methods of variance reduction} +\begin{footnotesize} + +$\Rrightarrow$ In Monte Carlo methods the statistical uncertainty is defined as: +\begin{align*} +\sigma = \dfrac{1}{\sqrt{N}}\sqrt{V(f)} +\end{align*} +$\Rrightarrow$ Obvious conclusion: +\begin{itemize} +\item To reduce the uncertainty one needs to increase $N$.\\ +$\rightrightarrows$ Slow convergence. In order to reduce the error by factor of 10 one needs to simulate factor of 100 more points! +\end{itemize} +$\Rrightarrow$ How ever the other handle ($V(f)$) can be changed! $\longrightarrow$ Lot's of theoretical effort goes into reducing this factor.\\ +$\Rrightarrow$ We will discuss {\color{Mahogany}{four}} classical methods of variance reduction: +\begin{enumerate} +\item Stratified sampling. +\item Importance sampling. +\item Control variates. +\item Antithetic variates. +\end{enumerate} + + + + + +\end{footnotesize} +\end{frame} + + + + +\begin{frame}\frametitle{Stratified sampling} +\begin{footnotesize} +$\Rrightarrow$ The most intuitive method of variance reduction. The idea behind it is to divide the function in different ranges and to use the Riemann integral property: +\begin{align*} +I = \int_0^1 f(u) du = \int_0^a f(u)du + \int_a^1 f(u) du,~ 0$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}} +\newcommand{\lsim}{\mathop{\lsi}} +\newcommand{\gsim}{\mathop{\gsi}} +\newcommand{\wt}{\widetilde} +%\newcommand{\ol}{\overline} +\newcommand{\Tr}{\rm{Tr}} +\newcommand{\tr}{\rm{tr}} +\newcommand{\eqn}[1]{&\hspace{-0.7em}#1\hspace{-0.7em}&} +\newcommand{\vev}[1]{\rm{$\langle #1 \rangle$}} +\newcommand{\abs}[1]{\rm{$\left| #1 \right|$}} +\newcommand{\eV}{\rm{eV}} +\newcommand{\keV}{\rm{keV}} +\newcommand{\GeV}{\rm{GeV}} +\newcommand{\im}{\rm{Im}} +\newcommand{\disp}{\displaystyle} +\def\be{\begin{equation}} +\def\ee{\end{equation}} +\def\ba{\begin{eqnarray}} +\def\ea{\end{eqnarray}} +\def\d{\partial} +\def\l{\left(} +\def\r{\right)} +\def\la{\langle} +\def\ra{\rangle} +\def\e{{\rm e}} +\def\Br{{\rm Br}} +\def\fixme{{\color{red} FIXME!}} +\def\mc{{\color{Magenta}{MC}}} +\def\pdf{{\rm p.d.f.}} + +\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (Universit\"{a}t Z\"{u}rich)} +\institute{UZH} +\title[Introduction to \\Monte Carlo methods]{Introduction to \\Monte Carlo methods} +\date{\fixme} + + +\begin{document} +\tikzstyle{every picture}+=[remember picture] + +{ +\setbeamertemplate{sidebar right}{\llap{\includegraphics[width=\paperwidth,height=\paperheight]{bubble2}}} +\begin{frame}[c]%{\phantom{title page}} +\begin{center} +\begin{center} + \begin{columns} + \begin{column}{0.9\textwidth} + \flushright\fontspec{Trebuchet MS}\bfseries \Huge {Introduction to \\Monte Carlo methods} + \end{column} + \begin{column}{0.2\textwidth} + %\includegraphics[width=\textwidth]{SHiP-2} + \end{column} + \end{columns} +\end{center} + \quad + \vspace{3em} +\begin{columns} +\begin{column}{0.44\textwidth} +\flushright \vspace{-1.8em} {\fontspec{Trebuchet MS} \Large Marcin Chrząszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}} + +\end{column} +\begin{column}{0.53\textwidth} +\includegraphics[height=1.3cm]{uzh-transp} +\end{column} +\end{columns} + +\vspace{1em} +% \footnotesize\textcolor{gray}{With N. Serra, B. Storaci\\Thanks to the theory support from M. Shaposhnikov, D. Gorbunov}\normalsize\\ +\vspace{0.5em} + \textcolor{normal text.fg!50!Comment}{Experimental Methods in Particle Physics, \\ 5 October, 2016} +\end{center} +\end{frame} +} + + +\begin{frame}\frametitle{Literature} + +\begin{enumerate} +\item J. M. Hammersley, D. C. Hamdscomb, ``Monte Carlo Methods'', London: Methuen \& Co. Ltd., New York: J. Wiley \& Sons Inc., 1964 +\item I. M. Sobol, ``The Monte Carlo Method'', Mir Publishers, Moscow, 1975. +\item M. H. Kalos, P. A. Whitlock, ,,Monte Carlo Methods”, J. Wiley \& Sons Inc., New York, 1986 +\item G. S. Fishman, ,,Monte Carlo: Concepts, Algorithms and Applications”, Springer, 1996. +\item R. Y. Rubinstein, D. P. Kroese, ,,Simulation and the Monte Carlo Method”, Second Edition, J. Wiley \& Sons Inc., 2008. +\item R. Korn, E. Korn, G. Kroisandt, ,,Monte Carlo methods and models in finance and insurance”, CRC Press, +Taylor \& Francis Group, 2010. +\item S. Jadach, ,,Practical Guide to Monte Carlo”, \href{http://arxiv.org/abs/physics/9906056}{arXiv:physics/9906056}, \href{http://cern.ch/jadach/MCguide/}{http://cern.ch/jadach/MCguide/}. +\end{enumerate} + + +\end{frame} + + + + +\begin{frame}\frametitle{Course Plan} + +We will have 6 hours of Monte Carlo (MC) lectures. The lectures will be devoted:\\ + +\hspace{1.5cm} +\begin{itemize} +\item 1 h: Mathematical introduction to MC methods. +\item 1 h: MC integration methods. +\item 2 h: Random numbers generators. +\item 2 h: Markov Chain MC. +\item 2 h: Tutorial and examples. +\end{itemize} +\hspace{1cm} \\ +The hands-on tutorial will consist of program templates in which we will implement couple of algorithms that were explained in the lecture. \\ +$\Rrightarrow$ All examples shown in this course are available in the github repository:\\ +\url{https://github.com/mchrzasz/EMPP_MC}\\ +\color{RubineRed}{There will be an indication (in this color) on the adequate slide for each of the macro.} + + +\end{frame} + + +\begin{frame}\frametitle{Definitions} +\begin{footnotesize} +$\Rrightarrow$ Basic definition:\\ + \begin{exampleblock}{} + Monte Carlo method is any technique that uses {\it{random numbers}} to solve a given mathematical problem. + \end{exampleblock} +% \vspace{0.5cm} + +$\rightarrowtail$ Random number: For the purpose of this course we need to assume that we know what it is, although the formal definition is highly non-trivial.\\ +\vspace{0.05cm} +$\Rrightarrow$ My favourite definition (Halton 1970): \begin{scriptsize}more complicated, but more accurate.\end{scriptsize} + +\begin{exampleblock}{} +''Representing the solution of a problem as a parameter of a hypothetical population, and using a random sequence of numbers to construct a sample of the population, from which statistical estimates of the parameter can be obtained.'' + \end{exampleblock} +To put this definition in mathematical language:\\ +Let $F$ be a solution of a given mathematical problem. The estimate of the result $\hat{F}$:\\ +\begin{equation*} +\hat{F}=f( \lbrace r_1, r_2, r_3,...,r_n \rbrace; ...), +\end{equation*} +where $\lbrace r_1, r_2, r_3,...,r_n \rbrace$ are random numbers. +\begin{center} +\color{red}{The problem we are solving doesn't need to be stochastic!} +\end{center} +\begin{scriptsize} +$\twoheadrightarrow$ One could wonder why are we trying to add all the stochastic properties to a deterministic problem. Those are the properties that allow to use all well known statistic theorems. + \end{scriptsize} +\end{footnotesize} +\end{frame} + +\begin{frame}\frametitle{History of MC methods} +\begin{footnotesize} +\begin{itemize} +\item {\color{PineGreen}{G. Compte de Buffon (1777)}} - First documented usage of random numbers for integral computation (Buffon thrown niddle on the table with parrarel line; we will do a modern version of this exercise). +\item {\color{PineGreen}{Marquis de Laplace (1886)}} - Used the Buffon niddle to determine the value of $\pi$ number. +\item {\color{PineGreen}{Lord Kelvin (1901)}} - Thanks to drawing randomly numbered cards he managed he managed to calculate some integrals in kinematic gas theorem. +\item {\color{PineGreen}{W. S. Gosse (better knows as Student) (1908)}} - Used similar way as Lord Kelvin to get random numbers to prove \textit{t}-Student distribution. +\item {\color{PineGreen}{Enrico Fermi (1930) }} - First mechanical device (\texttt{FERMIAC}) for random number generations. Solved neutron transport equations in the nuclear plants. +\item {\color{PineGreen}{S. Ulam, R. Feynman, J. von Neumann et. al.}} - First massive usage of random numbers. Most applications were in Manhattan project to calculate neutron scattering and absorption. \\ +In {\color{NavyBlue}{Los Alamos}} the name {\color{Mahogany}{Monte Carlo}} was created as kryptonim of this kind of calculations. +\end{itemize} + + +\end{footnotesize} +\end{frame} + + + +\begin{frame}\frametitle{Euler number determination, $\rm \color{RubineRed}{Lecture1/Euler\_number}$ } +\begin{footnotesize} +$\Rrightarrow$ As mentioned before \mc~methods can be used to solve problems that \textbf{do not} have stochastic nature! All the integrals calculated in Los Alamos during the Manhattan project are nowadays solvable without any \mc~methods.\\ +$\rightarrowtail$ Let's give a trivial example of solving a non stochastic problem: calculating Euler number $e$. We know that $e=2.7182818...$. +$\Rrightarrow$ To calculate the $\hat{e}$ we will use the following algorithm: +\begin{itemize} +\item We generate a random number in range $(0,1)$ (in stat. $\mathcal{U}(0,1)$) until the number we generate is smaller then the previous one, aka we get the following sequence: +\begin{align*} +x_1x_{n} +\end{align*} +\item We store the number $n$. We repeat this experiment $N$ times and calculate the arithmetic average of $n$. The obtained value is an statistical estimator of $e$: +\begin{align*} +\hat{e}= \dfrac{1}{N}\sum_{i=1}^N n_i \xrightarrow{N\to \infty} e . +\end{align*} +\end{itemize} +$\Rrightarrow$ Numerical example: +\begin{tabular}{r c c c } +$N$ & $\hat{e}$ & $\hat{e} - e$ & \multirow{5}{*}{Is this $\sim\sqrt{N}$?} \\ +100 & $2.760000$ & $0.041718$ \\ +10000 & $2.725000$ & $0.006718$ \\ +1000000 & $2.718891$ & $0.000609$ \\ +100000000 & $2.718328$ & $0.000046$\\ +\end{tabular} + + +\end{footnotesize} +\end{frame} + +\begin{frame}\frametitle{Let's test the $\sqrt{N}$, $\rm \color{RubineRed}{Lecture1/Euler\_number}$ } + +\only<1> +{ +$\Rrightarrow$ In the last example we measured the Euler number using different number of pseudo-experiments.\\ +$\rightarrowtail$ We compared the obtained value to the true and observed roughly a $\sqrt{N}$ dependence on the difference between the true value and the obtained one.\\ +} +$\rightarrowtail$ Could we test this? YES! Lets put our experimentalist hat on!\\ +$\rightarrowtail$ From the begging of studies they tooth us to get the error you need to repeat the measurements. +\only<1> +{ +\begin{exampleblock}{The algorithm:} +Previous time we measured Euler number using $N$ events, where $N \in (100, 1000, 10000, 100000)$. Now lets repeat this measurement $n_N$ times (of course each time we use new generated numbers). From the distribution of $\hat{e} -e$ we could say something about the uncertainty of our estimator for given $N$. + \end{exampleblock} +} + +\begin{center} +\only<2> +{ +\includegraphics[angle=-90,width=0.8\textwidth]{images/result_error.pdf} +} +\only<3> +{ +\includegraphics[angle=-90,width=0.8\textwidth]{images/result_error_dep.pdf} +} +\end{center} + + + + + + + + + + + + +\end{frame} + +\begin{frame}\frametitle{Monte Carlo and integration} +\begin{footnotesize} +$\hookrightarrow$ {\color{BrickRed}{\textbf{All MC calculations are equivalent to preforming an integration.}}}\\ +$\rightrightarrows$ Assumptions: $r_i$ random numbers from $\mathcal{U}(0,1)$. The MC result: +\begin{align*} +F=F(r_1,r_2,...r_n) +\end{align*} +is unbias estimator of an integral: +\begin{align*} +I=\int_0^1...\int_0^1 F(x_1,x_2,...,x_n)dx_1,dx_2...,dx_n +\end{align*} +aka the expected value of the $I$ integral is: +\begin{align*} +E(F)=I. +\end{align*} + \begin{exampleblock}{} +$\Rrightarrow$ This mathematical identity is the most useful property of the MC methods. It is a link between mathematical analysis and statistic world. Now we can use the best of the both world! + \end{exampleblock} +If we want to calculate the integral in different range then $(0,1)$ we just scale the the previous result: +\begin{align*} +\dfrac{1}{N}\sum_{i=1}^N f(x_i) \xrightarrow{N\to \infty} E(f)=\dfrac{1}{b-a}\int_a^b f(x)dx +\end{align*} + + +\end{footnotesize} +\end{frame} + + +\begin{frame}\frametitle{Uncertainty from Monte Carlo methods} +\begin{footnotesize} +$\Rrightarrow$ In practice we do not have $N\to \infty$ so we will never know the exact result of an integral :(\\ +$\longmapsto$ Let's use the {\color{BrickRed}{statistical}} world and estimate the uncertainty of an integral in this case :)\\ +$\rightarrowtail$ A variance of a MC integral: +\begin{align*} +V(\hat{I}) = \dfrac{1}{n} \Big\lbrace E(f^2) - E^2(f) \Big\rbrace = \dfrac{1}{n} \Big\lbrace \dfrac{1}{b-a} \int_a^b f^2(x)dx - I^2 \Big\rbrace +\end{align*} + \begin{alertblock}{} +$\looparrowright$ To calculate $V(\hat{I})$ one needs to know the value of $I$! +\end{alertblock} +$\Rrightarrow$ In practice $V(\hat{I})$ is calculated via estimator: +\begin{columns} +\column{2in} +\begin{align*} +\hat{V}(\hat{I})=\dfrac{1}{n}\hat{V}(f), +\end{align*} +\column{3in} +\begin{align*} +\hat{V}(f) = \dfrac{1}{n-1}\sum_{i=1}^n \Big[ f(x_i)-\dfrac{1}{n} \sum_{i=1}^nf(x_i)\Big]^2. +\end{align*} +\end{columns} + + +$\Rrightarrow$ MC estimator of standard deviation: $\hat{\sigma}=\sqrt{\hat{V}(\hat{I})}$ + + +\end{footnotesize} +\end{frame} + + +\begin{frame}\frametitle{Buffon needle - $\pi$ number calculus} +\begin{footnotesize} + +$\Rrightarrow$ Buffon needle (Buffon 1777, Laplace 1886): +We are throwing a needle (of length $l$) on to a surface covered with parallel lines width distance $L$. If a thrown needle touches a line we count a hit, else miss. Knowing the number of hits and misses one can calculate the $\pi$ number. +\vspace{0.3cm} +\begin{columns} +\column{0.1in} +{~} +\column{2in} +{\color{ForestGreen}{Experiment:}} +\column{2.8in} +{\color{Cerulean}{Theory:}} + +\end{columns} + + +\begin{columns} +\column{0.1in} +{~} +\column{2in} + +\includegraphics[width=0.9\textwidth]{images/buffon.png}\\ +$n$ - number of hits\\ +$N$ number of hits and misses,\\ +aka number of tries. + +\column{2.8in} +$\Rightarrow$ x - angle between needle and horizontal line, $x \in \mathcal{U}(0,\pi)$. +$\Rightarrow$ the probability density function (\pdf) for x: +\begin{align*} +\rho(x)=\dfrac{1}{\pi} +\end{align*} +$\Rightarrow$ $p(x)$ probability to hit a line for a given x value: +\begin{align*} +p(x)=\dfrac{l}{L}\vert \cos x \vert +\end{align*} +$\Rightarrow$ Total hit probability: +\begin{align*} +P = E[p(x)]=\int_0^{\pi}p(x)\rho(x)dx=\dfrac{2l}{\pi L} +\end{align*} + +\end{columns} +Now one can calculate $\hat{P}$ from MC : $\hat{P}=\dfrac{n}{N} \xrightarrow{N\to \infty} P= \dfrac{2l}{\pi L} \Rightarrow \hat{\pi}=\dfrac{2Nl}{nL}$ + + +\end{footnotesize} +\end{frame} + + + + + + + + + + + +\begin{frame}\frametitle{Buffon needle - Simplest Carlo method} +\begin{footnotesize} +{\color{MidnightBlue}{Monte Carlo type ''heads or tails''}}\\ +Let's use the summery of $p(x)$ function nad take $0 p(x): & \text{miss}. +\end{cases} +\end{align*} + +\column{2.5in} +\includegraphics[width=0.75\textwidth]{images/result.png} + + + +\end{columns} +Let's define weight function: $w(x,y)=\Theta(p(x)-y)$, \\ +where $\Theta(x)$ is the step function.\\ +$\rightarrowtail$ \pdf : $\varrho(x,y)=\rho(x)g(y)=\frac{2}{\pi} \cdot 1$\\ +$\Rightarrow$ Integrated probability: +\begin{align*} +P=E(w)=\int w(x,y) \varrho(x,y)dx dy = \dfrac{2l}{\pi L} \xleftarrow{N\to \infty}\hat{P}=\frac{1}{N} \sum_{i=1}^N w(x_i,y_i)= \dfrac{n}{N} +\end{align*} +Standard deviation for $\hat{P}$: $\hat{\sigma}=\dfrac{1}{\sqrt{N-1}}\sqrt{\dfrac{n}{N}\Big(1-\dfrac{n}{N}\Big)} $ + + + +\end{footnotesize} +\end{frame} + + +\begin{frame}\frametitle{Buffon needle, $\rm \color{RubineRed}{Lecture1/Heads\_tails}$ } +\begin{small} + + +$\Rrightarrow$ Lets make this toy experiment and calculate the $\pi$ number.\\ +$\hookrightarrow$ We can simulate the central position $(y)$ of an needle between $(-L, L)$ from $\mathcal{U}(-L, L)$. + + \begin{exampleblock}{Symmetry:} +Please note the symmetry of the problem, if the position of the needle would be $>L$ then we can shift the needle by any number of $L$'s. + \end{exampleblock} + +$\hookrightarrow$ New we simulate the angle $(\phi)$ with a flat distribution from $(0,\pi)$. +$\hookrightarrow$ The maximum and minimum $y$ position of the needle are: +\begin{align*} +y_{\max}=y+\vert \cos \phi \vert l\\ +y_{\min}=y-\vert \cos \phi \vert l +\end{align*} +$\hookrightarrow$ Now we check if the needle touches any of the lines: $y=L$, $y=0$ or $y=-L$. If yes we count the events. +\end{small} +\begin{center} + + +\begin{footnotesize} + + +\begin{tabular}{r c c c } +$N$ & $\hat{\pi}$ & $\hat{\pi} - \pi$ & $\sigma(\hat{\pi})$ \\ +10000 & $3.12317$ & $-0.01842$ & $0.03047$\\ +100000 & $3.14707$ & $0.00547$ & $0.00979$\\ +1000000 & $3.13682$ & $-0.00477$ & $0.00307$\\ +10000000 & $3.14096$ & $-0.00063$ & $0.00097$\\ + + +\end{tabular} + +\end{footnotesize} +\end{center} +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{frame}\frametitle{Central Limit Theorem, $\rm \color{RubineRed}{Lecture1/CLT}$ } +\begin{footnotesize} + \begin{exampleblock}{} +Large independent random numbers assembly has always Gaussian distribution no matter from what distribution they were generated from as far as they have finite variances and expected values and the assembly is sufficiently large. + \end{exampleblock} +\includegraphics[width=0.9\textwidth]{images/dupa.png} + + +\end{footnotesize} +\end{frame} + + +\begin{frame}\frametitle{Crude Monte Carlo method of integration} +\begin{footnotesize} +$\Rrightarrow$ {\color{MidnightBlue}{Crude Monte Carlo method of integration is based on Central Limit Theorem (CLT): }}\\ +\begin{align*} +\dfrac{1}{N} \sum_{i=1}^N f(x_i) \xrightarrow{N\to \infty} \dfrac{1}{b-a}\int_a^b f(x)dx =E(f) +\end{align*} +$\Rrightarrow$ The standard deviation can be calculated: +\begin{align*} +\sigma = \dfrac{1}{\sqrt{N}} \sqrt{\Big[ E(f^2) -E^2(f)\Big] } +\end{align*} + +$\Rrightarrow$ From LNT we have: +\begin{align*} +P= \int w(x) \rho(x) dx = \int_0^{\pi/2} (\frac{l}{L} \cos x ) \frac{2}{\pi} dx= \dfrac{2l}{\pi L} \xrightarrow{N\to \infty} \frac{1}{N}\sum_{i=1}^N w(x_i) +\end{align*} +$\Rrightarrow$ Important comparison between ''Hit and mishit'' and Crude \mc~methods. One can analytically calculate: + +\begin{align*} +\hat{\sigma}^{{\rm{Crude}}} < \hat{\sigma}^{{\rm{Hit~and~mishit}}} +\end{align*} + + +$\Rrightarrow$ Crude \mc~is \textbf{always} better then ''Hit and mishit'' method. We will prove this on an example (can be proven analytically as well). + + +\end{footnotesize} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Crude MC vs ”Hit and mishit”, $\rm \color{RubineRed}{Lecture1/Crude\_vs\_HT}$} + +$\Rrightarrow$ We can repeat a toy MC studies as we did in the Euler needle case.\\ +$\hookrightarrow$ In this example we want to calculate $\int_0^{\pi/2} \cos x dx$ + +\only<1>{ +\begin{center} +\includegraphics[angle=-90,width=0.8\textwidth]{images/results_0.pdf} +\end{center} +} +\only<2>{ +\begin{center} +\includegraphics[angle=-90,width=0.8\textwidth]{images/results_1.pdf} +\end{center} +} +\only<3>{ +\begin{center} + +\includegraphics[angle=-90,width=0.4\textwidth]{images/results_fit_0.pdf} +\includegraphics[angle=-90,width=0.4\textwidth]{images/results_fit_1.pdf}\\ +\end{center} +$\Rrightarrow$ One clearly sees that both methods follow $1/\sqrt{N}$ dependence and that the Crude MC is always better then the ''Hit and mishit''.\\ +$\Rrightarrow$ Please note that for the ''Hit and mishit'' we are suing 2 times more random numbers than for the Crude method so in terms of timing the Crude MC is also much faster. + +} + + + +\end{frame} + +\begin{frame}\frametitle{Classical methods of variance reduction} +\begin{footnotesize} + +$\Rrightarrow$ In Monte Carlo methods the statistical uncertainty is defined as: +\begin{align*} +\sigma = \dfrac{1}{\sqrt{N}}\sqrt{V(f)} +\end{align*} +$\Rrightarrow$ Obvious conclusion: +\begin{itemize} +\item To reduce the uncertainty one needs to increase $N$.\\ +$\rightrightarrows$ Slow convergence. In order to reduce the error by factor of 10 one needs to simulate factor of 100 more points! +\end{itemize} +$\Rrightarrow$ How ever the other handle ($V(f)$) can be changed! $\longrightarrow$ Lot's of theoretical effort goes into reducing this factor.\\ +$\Rrightarrow$ We will discuss {\color{Mahogany}{four}} classical methods of variance reduction: +\begin{enumerate} +\item Stratified sampling. +\item Importance sampling. +\item Control variates. +\item Antithetic variates. +\end{enumerate} + + + + + +\end{footnotesize} +\end{frame} + + + + +\begin{frame}\frametitle{Stratified sampling} +\begin{footnotesize} +$\Rrightarrow$ The most intuitive method of variance reduction. The idea behind it is to divide the function in different ranges and to use the Riemann integral property: +\begin{align*} +I = \int_0^1 f(u) du = \int_0^a f(u)du + \int_a^1 f(u) du,~ 0 diff --git a/Lectures_my/EMPP/2017/Lecture3/beamerinnerthemeFlip.sty b/Lectures_my/EMPP/2017/Lecture3/beamerinnerthemeFlip.sty new file mode 100755 index 0000000..9910f4d --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture3/beamerinnerthemeFlip.sty @@ -0,0 +1,95 @@ +% Inner style file for the BEAMER FLIP THEME +% Copyright 2010 by Flip Tanedo +% This file may be distributed and/or modified +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. +% +% Based on: beamerinnerthemeFlip by Marco Barisione + +\mode + +% % Use alternative title page style. +% \DeclareOptionBeamer{alternativetitlepage}[true]{\def\beamer@Flip@alternativetitlepage{#1}} + +% Logo to use in the alternative title page. +% \def\beamer@Flip@titlepagelogo{} +% \DeclareOptionBeamer{titlepagelogo}{\def\beamer@Flip@titlepagelogo{#1}} + +% Bullet shape. +\DeclareOptionBeamer{bullet}{\def\beamer@Flip@bullet{#1}} +\DeclareOptionBeamer{shadow}[true]{\def\beamer@themerounded@shadow{#1}} +\ExecuteOptionsBeamer{shadow=false} + + +% \ExecuteOptionsBeamer{alternativetitlepage=false,bullet=square} +\ProcessOptionsBeamer + + + +% Margins. +\newlength{\beamer@Flip@normalmargin} +\setlength{\beamer@Flip@normalmargin}{.06\paperwidth} +\setbeamersize{text margin left=\beamer@Flip@normalmargin} +\setbeamersize{text margin right=\beamer@Flip@normalmargin} +\setlength\leftmargini{.6\beamer@Flip@normalmargin} +\setlength\leftmarginii{.6\beamer@Flip@normalmargin} +\setlength\leftmarginiii{.6\beamer@Flip@normalmargin} + +% Normal title page. +\defbeamertemplate*{title page normal}{Flip theme}[1][] +{ + \vbox{} + \vfill + \begin{centering} + \begin{beamercolorbox}[wd=\paperwidth,sep=8pt,center,#1]{title page header} + \usebeamerfont{title}\inserttitle\par% + \ifx\insertsubtitle\@empty% + \else% + \vskip0.25em% + {\usebeamerfont{subtitle}\usebeamercolor[fg]{subtitle}\insertsubtitle\par}% + \fi% + \end{beamercolorbox}% + \vskip1em\par + \begin{beamercolorbox}[sep=8pt,center,#1]{author} + \usebeamerfont{author}\insertauthor + \end{beamercolorbox} + \begin{beamercolorbox}[sep=8pt,center,#1]{institute} + \usebeamerfont{institute}\insertinstitute + \end{beamercolorbox} + \begin{beamercolorbox}[sep=8pt,center,#1]{date} + \usebeamerfont{date}\insertdate + \end{beamercolorbox}\vskip0.5em + {\usebeamercolor[fg]{titlegraphic}\inserttitlegraphic\par} + \end{centering} + \vfill +} + + +% Items. +\defbeamertemplate{itemize item}{squarealt}% +{\tiny\raise.5ex\hbox{\donotcoloroutermaths$\blacksquare$}} +\defbeamertemplate{itemize subitem}{squarealt}% +{\tiny\raise.4ex\hbox{\donotcoloroutermaths$\square$}} +\defbeamertemplate{itemize subsubitem}{squarealt}% +{\tiny\raise.3ex\hbox{\donotcoloroutermaths$\blacksquare$}} +% +\defbeamertemplate{itemize item}{circlealt}% +{\small\raise.2ex\hbox{\donotcoloroutermaths$\bullet$}} +\defbeamertemplate{itemize subitem}{circlealt}% +{\small\raise.1ex\hbox{\donotcoloroutermaths$\circ$}} +\defbeamertemplate{itemize subsubitem}{circlealt}% +{\scriptsize\raise.1ex\hbox{\donotcoloroutermaths$\bullet$}} +\setbeamertemplate{items}[circlealt] +% +\def\circletext{circle} +\ifx\beamer@Flip@bullet\circletext + \setbeamertemplate{items}[circlealt] +\else + \setbeamertemplate{items}[squarealt] +\fi + +\setbeamertemplate{blocks}[rounded][shadow=\beamer@themerounded@shadow] + + +\mode + diff --git a/Lectures_my/EMPP/2017/Lecture3/beamerouterthemeFlip.sty b/Lectures_my/EMPP/2017/Lecture3/beamerouterthemeFlip.sty new file mode 100755 index 0000000..d12f6d6 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture3/beamerouterthemeFlip.sty @@ -0,0 +1,189 @@ +% Outer style file for the BEAMER FLIP THEME 212 +% Copyright 2012 by Flip Tanedo +% This file may be distributed and/or modified +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. +% +% Based on: beamerouterthemesplit by Till Tantau + + +\mode + +% Watermark +\DeclareOptionBeamer{watermark}{\def\beamer@Flip@watermark{#1}} +\ExecuteOptionsBeamer{watermark=} % Default value is empty + + +\newif\ifbeamer@Flip@bigpagenumber +\beamer@Flip@bigpagenumberfalse +\DeclareOptionBeamer{bigpagenumber}{\beamer@Flip@bigpagenumbertrue} + + +\def\beamer@Flip@truetext{true} % Kludge for true/false so I can use ifx + +\DeclareOptionBeamer{topline}[true]{\def\beamer@Flip@topline{#1}} +\ExecuteOptionsBeamer{topline=false} % Default + + + +% \ExecuteOptionsBeamer{topline=} % Default value is empty + + +\ProcessOptionsBeamer + + +\usepackage{tikz} % For fancy decorations + + +% I should fix these up to be more robust against color changes +\setbeamercolor{section in head/foot}{parent=footerlike} +\setbeamercolor{subsection in head/foot}{parent=footerlike} +\setbeamercolor{author in head/foot}{parent=footerlike} +\setbeamercolor{title in head/foot}{parent=footerlike} + + +% \setbeamercolor{author in head/foot}{parent=section in head/foot} +% \setbeamercolor{title in head/foot}{parent=subsection in head/foot} + +%\setbeamercolor{topbar}{parent=crimsontown} +\setbeamercolor{topbar}{parent=bluetown} + + + + +\usesectionheadtemplate + {\hfill\insertsectionhead} + {\hfill\color{fg!50!bg}\insertsectionhead} + + +%%%%%%%%%%%%%%%%%% +% The footer bar % +%%%%%%%%%%%%%%%%%% + +\defbeamertemplate*{footline}{Flip theme} +{% + \leavevmode% +% OBSERVATION: the "%" symbols inside hbox are all very important here. +% The \hbox enviroment will insert spaces whenever there's whitespace +% Adding a % at the END of each line ensures that any hard returns aren't +% interpreted as white space. This allows the color boxes to be flush against +% one another. If a faint white line appears one could probably do something like +% hspace{-1px} and add an additional pixel-or-two wide beamercolorbox. + +\hbox{% +\begin{beamercolorbox}[wd=.4\paperwidth,ht=2.5ex,dp=1.125ex,leftskip=.3cm, rightskip=.3cm plus1fil]{author in head/foot}% + \usebeamerfont{author in head/foot}\insertshortauthor \end{beamercolorbox}% +% +\begin{beamercolorbox}[wd=.6\paperwidth,ht=2.5ex,dp=1.125ex,leftskip=.3cm,rightskip=.3cm plus1fil]{title in head/foot}% + \usebeamerfont{title in head/foot}{\textit \insertshorttitle}% + \hskip2ex plus1fill% + % \insertpagenumber\,/\,\insertpresentationendpage %% Want FRAME, not SLIDE number + \insertframenumber/\inserttotalframenumber + \end{beamercolorbox}% +}% + +% This is a complete kludge for the faint white line which appears +% between the beamer color boxes above. (It doesnt appear in presentation mode +% but sometimes looks funny when the pdfs are viewed in a window) +\begin{tikzpicture}[overlay] + \usebeamercolor[bg]{author in head/foot} + \draw[thick] (0,3.625ex) -- (\paperwidth,3.625ex); + \draw (.4\paperwidth,0) -- (.4\paperwidth,3.625ex); + \draw[thick] (0,0) -- (\paperwidth,0); +\end{tikzpicture} + + + +\ifbeamer@Flip@bigpagenumber + \begin{tikzpicture}[overlay] + \usebeamercolor[bg]{author in head/foot} + \draw[fill] (\paperwidth-5ex,3.625ex) circle (6ex); + \usebeamercolor[fg]{author in head/foot} + \draw[fill] (\paperwidth-5ex,3.625ex) circle (5ex); + \usebeamercolor[bg]{author in head/foot} + \node at (\paperwidth-5ex,4ex) {\small$^\text{\insertframenumber}/_\text{\inserttotalframenumber}$}; + \end{tikzpicture} +\fi +} + + + +\defbeamertemplate*{frametitle}{Flip theme}[1][left] +{ +% \ifbeamercolorempty[bg]{frametitle}{}{\nointerlineskip}% +\@tempdima=\textwidth% +\advance\@tempdima by\beamer@leftmargin% +\advance\@tempdima by\beamer@rightmargin% + +\vbox{}\vskip-3.5ex% +% +\begin{beamercolorbox}[sep=0.3cm,#1,wd=\the\@tempdima]{titlelike} + \usebeamerfont{frametitle}% + \vbox{}\vskip-1ex% + \if@tempswa\else\csname beamer@fte#1\endcsname\fi% + % \strut{\bf\insertframetitle}\strut\par% %% Include the \bf + \strut{\insertframetitle}\strut\par% + {% + \ifx\insertframesubtitle\@empty% + \else + {\usebeamerfont{framesubtitle} + \usebeamercolor[fg]{framesubtitle} + \insertframesubtitle\strut\par}% + \fi + }% + % + \vskip-1ex% + \if@tempswa\else\vskip-.3cm\fi% set inside beamercolorbox... evil here... +\end{beamercolorbox}% +%% + +% \def\beamer@fteright{\vskip0.35cm\advance\leftskip by 1.7cm\advance\rightskip by1.7cm} +} + + + + +% Sidebar right is important: anything placed here will be +% visible *behind* the main text. This is where to put any +% interesting watermarks. +% +% +\defbeamertemplate*{sidebar right}{Flip theme} +{ +% \llap{\includegraphics[width=50px]{footdecoration}} +% \llap{\includegraphics[width=\paperwidth,height=\paperheight]{upperleft_watermark_transp}} +% +% THIS WOULD BE A NICE WAY TO PUT THE PARTICLE BUBBLE CHAMBER BG +% ... make a png of the background with TRANSPARENT BG +% ... then put the image here (use \hfill to get it on the left) +% Now one can FURTHER apply a slight gradient in the BG +% +% +% % Top Line +\ifx\beamer@Flip@topline\beamer@Flip@truetext + \begin{tikzpicture}[overlay] + \usebeamercolor[fg]{titlelike} % alternately, topbarlike would be a good beamercolor +% \usebeamercolor[fg]{topbarlike} % alternately, topbarlike would be a good beamercolor + \draw[fill] (-\paperwidth,0) rectangle (0,-3pt); + \end{tikzpicture} +\fi +% +% + \vskip.2\beamer@leftmargin% + %\llap{\insertlogo\hskip.5\beamer@leftmargin}% + \llap{\insertlogo\hskip.08\beamer@leftmargin}% + \vfill% + \if \beamer@Flip@watermark\@empty + % This is kind of a kludge since if I put anything in here, I automatically get errors + % Somehow LaTeX wants to read the \else part! + \else% + \llap{\includegraphics[width=\paperwidth,height=\paperheight]{\beamer@Flip@watermark}} + \fi +} + + + +\mode +\endinput + + diff --git a/Lectures_my/EMPP/2017/Lecture3/beamerouterthemedecolines.sty b/Lectures_my/EMPP/2017/Lecture3/beamerouterthemedecolines.sty new file mode 100755 index 0000000..669e493 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture3/beamerouterthemedecolines.sty @@ -0,0 +1,168 @@ +% Copyright 2007 by Marco Barisione +% +% This file may be distributed and/or modified +% +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. + +\mode + +% String used between the current page and the total page count. +\def\beamer@decolines@pageofpages{/} +\DeclareOptionBeamer{pageofpages}{\def\beamer@decolines@pageofpages{#1}} + +% Show a line below the frame title. +\DeclareOptionBeamer{titleline}[true]{\def\beamer@decolines@titleline{#1}} + +% Image used for the watermark. +\def\beamer@decolines@watermarkorig{} +\DeclareOptionBeamer{watermark}{\def\beamer@decolines@watermarkorig{#1}} + +% Height of the watermark. +\def\beamer@decolines@watermarkheight{100px} +\DeclareOptionBeamer{watermarkheight}{\def\beamer@decolines@watermarkheight{#1}} + +% The original image height is watermarkheightmult * watermarkheight. +\def\beamer@decolines@watermarkheightmult{1} +\DeclareOptionBeamer{watermarkheightmult}{\def\beamer@decolines@watermarkheightmult{#1}} + +\ExecuteOptionsBeamer{titleline=false} +\ProcessOptionsBeamer + +% Enable/disable the watermark. +\def\watermarkon{% + \def\beamer@decolines@watermark{\beamer@decolines@watermarkorig}% +} +\def\watermarkoff{\def\beamer@decolines@watermark{}} + +% Initially enable the watermark. +\watermarkon + +% Colors. +\setbeamercolor*{lineup}{parent=palette primary} +\setbeamercolor*{linemid}{parent=palette secondary} +\setbeamercolor*{linebottom}{parent=palette tertiary} +\setbeamercolor*{page header}{parent=titlelike} + +% Lengths +\newlength{\headerheight} +\setlength{\headerheight}{.045\paperheight} +\newlength{\beamer@decolines@lineup} +\setlength{\beamer@decolines@lineup}{.025\paperheight} +\newlength{\beamer@decolines@linemid} +\setlength{\beamer@decolines@linemid}{.015\paperheight} +\newlength{\beamer@decolines@linebottom} +\setlength{\beamer@decolines@linebottom}{.01\paperheight} + +% The height of the watermark part below the 3 bottom lines. +\newlength{\beamer@decolines@watermarkheightbottom} +\addtolength{\beamer@decolines@watermarkheightbottom}{\beamer@decolines@lineup} +\addtolength{\beamer@decolines@watermarkheightbottom}{\beamer@decolines@linemid} +\addtolength{\beamer@decolines@watermarkheightbottom}{\beamer@decolines@linebottom} + +% The height of the watermark part over the 3 bottom lines before shrinking. +\newlength{\beamer@decolines@watermarkheightupperorig} +\setlength{\beamer@decolines@watermarkheightupperorig}{\beamer@decolines@watermarkheight} +\addtolength{\beamer@decolines@watermarkheightupperorig}{-\beamer@decolines@watermarkheightbottom} +\multiply\beamer@decolines@watermarkheightupperorig by \beamer@decolines@watermarkheightmult + +% % Footer. +% \defbeamertemplate*{footline}{decolines theme} +% { +% \leavevmode% +% % Page number. +% \hbox{% +% \begin{beamercolorbox}[wd=.2\paperwidth,ht=0ex,dp=0ex,center]{}% +% \usebeamerfont{palette primary}\insertframenumber{} \beamer@decolines@pageofpages{} \inserttotalframenumber% +% \end{beamercolorbox}% +% \begin{beamercolorbox}[wd=.8\paperwidth,ht=0ex,dp=0ex]{}% +% \end{beamercolorbox}% +% } % +% % First line. +% \hbox{% +% \begin{beamercolorbox}[wd=.2\paperwidth,ht=\beamer@decolines@lineup,dp=0pt]{}% +% \end{beamercolorbox}% +% \begin{beamercolorbox}[wd=.8\paperwidth,ht=\beamer@decolines@lineup,dp=0pt]{lineup}% +% \end{beamercolorbox}% +% } % +% % Second line. +% \hbox{% +% \begin{beamercolorbox}[wd=\paperwidth,ht=\beamer@decolines@linemid,dp=0pt]{linemid}% +% \end{beamercolorbox}% +% } % +% % Third line. +% \hbox{% +% \begin{beamercolorbox}[wd=.1\paperwidth,ht=\beamer@decolines@linebottom,dp=0pt]{}% +% \end{beamercolorbox}% +% \begin{beamercolorbox}[wd=.9\paperwidth,ht=\beamer@decolines@linebottom,dp=0pt]{linebottom}% +% \end{beamercolorbox}% +% }% +% % This seems to fix some alignment problems with the watermark. It has to be +% % always applied if you do not want to see the footer moving up and down when +% % moving from a page with watermark to a page without or vice versa. +% \vskip-.5px% +% % Watermark. +% \if\beamer@decolines@watermark\@empty\else% +% \vskip-\beamer@decolines@watermarkheightbottom% +% \llap{\includegraphics[height=\beamer@decolines@watermarkheightbottom,clip=true,% +% trim=0pt 0pt 0pt \beamer@decolines@watermarkheightupperorig]{\beamer@decolines@watermark}\hskip-\paperwidth}% +% \fi% +% } + +\defbeamertemplate*{headline}{decolines theme} +{ + \leavevmode% + \hbox{% + \begin{beamercolorbox}[wd=\paperwidth,ht=\headerheight,dp=0pt]{page header}% + \end{beamercolorbox}% + } % + \vskip0pt% +} + +\defbeamertemplate*{frametitle}{decolines theme}[1][left] +{ + \ifbeamercolorempty[bg]{frametitle}{}{\nointerlineskip}% + \@tempdima=\textwidth% + \advance\@tempdima by\beamer@leftmargin% + \advance\@tempdima by\beamer@rightmargin% + \vbox{}\vskip-.5\beamer@leftmargin% + \begin{beamercolorbox}[sep=\beamer@leftmargin,#1,wd=\the\@tempdima]{} + \usebeamerfont{frametitle}\usebeamercolor[bg]{framesubtitle}% + \vbox{}\vskip0ex% + \if@tempswa\else\csname beamer@fte#1\endcsname\fi% + \strut\insertframetitle\strut\par% + {% + \ifx\insertframesubtitle\@empty% + \else% + {\usebeamerfont{framesubtitle}\usebeamercolor[bg]{framesubtitle}\insertframesubtitle\strut\par}% + \fi + }% + \vskip-1ex% + \if@tempswa\else\vskip-\beamer@leftmargin\fi + \end{beamercolorbox}% + \def\beamer@decolines@truetext{true}% + \ifx\beamer@decolines@titleline\beamer@decolines@truetext% + \vskip-.5\beamer@leftmargin% + \begin{beamercolorbox}[wd=\textwidth,ht=.1ex,dp=0ex]{linemid}% + \end{beamercolorbox}% + \fi +} + +% Frame title continuations, default +\defbeamertemplate*{frametitle continuation}{decolines theme}{(\insertcontinuationcount)} + + + +\defbeamertemplate*{sidebar right}{decolines theme} +{ + \vskip.1\beamer@leftmargin% + \llap{\insertlogo\hskip.5\beamer@leftmargin}% + \vfill% + \if\beamer@decolines@watermark\@empty\else% + \llap{\includegraphics[height=\beamer@decolines@watermarkheight]{\beamer@decolines@watermark}}% + \vskip-\beamer@decolines@watermarkheightbottom% + \fi +} + +\mode + diff --git a/Lectures_my/EMPP/2017/Lecture3/beamerthemeFlip.sty b/Lectures_my/EMPP/2017/Lecture3/beamerthemeFlip.sty new file mode 100755 index 0000000..a615ff5 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture3/beamerthemeFlip.sty @@ -0,0 +1,59 @@ +% Main style file for the BEAMER FLIP THEME 2012 +% Copyright 2012 by Flip Tanedo +% This file may be distributed and/or modified +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. +% +% Comments: This is still a work in progress. +% A good way to present: http://www.cs.hmc.edu/~oneill/freesoftware/pdftokeynote.html + +% \usepackage{beamerthemesplit} +\mode + + +%% These are the options that are fed in through the driver file +%% Some of them get passed on to the other theme files +\DeclareOptionBeamer{bullet}{\PassOptionsToPackage{bullet=#1}{beamerinnerthemeFlip}} +\DeclareOptionBeamer{bigpagenumber}{\PassOptionsToPackage{bigpagenumber}{beamerouterthemeFlip}} +\DeclareOptionBeamer{topline}[true]{\PassOptionsToPackage{topline=#1}{beamerouterthemeFlip}} +\DeclareOptionBeamer{shadow}[false]{\PassOptionsToPackage{shadow=#1}{beamerinnerthemeFlip}} + +\DeclareOptionBeamer{watermark}{\PassOptionsToPackage{watermark=#1}{beamerouterthemeFlip}} + +\ProcessOptionsBeamer + +\useinnertheme{Flip} % Calls beamerinnerthemeFlip.sty +\useoutertheme{Flip} % Calls beamerouterthemeFlip.sty +\usecolortheme{Flip} % Calls beamercolorthemeFlip.sty + + + +%%%%%%%%%%%%%%%%%%%%%%%% +% Background Gradient % +%%%%%%%%%%%%%%%%%%%%%%%% + + +%% Usually I would leave this on +%% However, there seems to be problems with XeLaTeX +%% http://tex.stackexchange.com/questions/29497/xelatex-preventing-beamer-from-using-different-backgrounds +\setbeamertemplate{background canvas}[vertical shading][bottom=blue!.1, middle=white, top=white] + +%% HOWEVER: it seems to make it impossible to change this later on in the document + + +%% For a dark background: +% \setbeamertemplate{background canvas}[vertical shading][bottom=keynotebottom, middle=keynotemiddle, top=keynotetop] + + +%% An alternate way: \beamertemplateshadingbackground{blue!.1}{red!2} +%% In general: you want the gradient to be subtle! + + +%%%%%%%%%%%%%%%%%%%%%%% +% Navigation symbols % +%%%%%%%%%%%%%%%%%%%%%%% + +\setbeamertemplate{navigation symbols}{} % Turns off PDF navigation symbols + +\mode +\endinput \ No newline at end of file diff --git a/Lectures_my/EMPP/2017/Lecture3/images/BG_lower.png b/Lectures_my/EMPP/2017/Lecture3/images/BG_lower.png new file mode 100755 index 0000000..073034a --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture3/images/BG_lower.png Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture3/images/Focal_stability.png b/Lectures_my/EMPP/2017/Lecture3/images/Focal_stability.png 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modify this file! + +This is an auxiliary file used by the 'biblatex' package. +This file may safely be deleted. It will be recreated as +required. + +@Control{biblatex-control, + options = {2.3:0:0:1:0:0:1:1:0:0:0:0:1:1:3:1:79:+}, +} diff --git a/Lectures_my/EMPP/2017/Lecture3/mchrzasz.tex b/Lectures_my/EMPP/2017/Lecture3/mchrzasz.tex new file mode 100644 index 0000000..30582f8 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture3/mchrzasz.tex @@ -0,0 +1,999 @@ +\documentclass[11 pt,xcolor={dvipsnames,svgnames,x11names,table}]{beamer} + +\usepackage[english]{babel} +\usepackage{polski} +\usepackage[skins,theorems]{tcolorbox} +\tcbset{highlight math style={enhanced, + colframe=red,colback=white,arc=0pt,boxrule=1pt}} + +\usetheme[ + bullet=circle, % Other option: square + bigpagenumber, % circled page number on lower right + topline=true, % colored bar at the top of the frame + shadow=false, % Shading for beamer blocks + watermark=BG_lower, % png file for the watermark + ]{Flip} + +%\logo{\kern+1.em\includegraphics[height=1cm]{SHiP-3_LightCharcoal}} + + +\usepackage[lf]{berenis} +\usepackage[LY1]{fontenc} +\usepackage[utf8]{inputenc} + +\usepackage{emerald} +\usefonttheme{professionalfonts} +\usepackage[no-math]{fontspec} +\usepackage{listings} +\defaultfontfeatures{Mapping=tex-text} % This seems to be important for mapping glyphs properly + +\setmainfont{Gillius ADF} % Beamer ignores "main font" in favor of sans font +\setsansfont{Gillius ADF} % This is the font that beamer will use by default +% \setmainfont{Gill Sans Light} % Prettier, but harder to read + +\setbeamerfont{title}{family=\fontspec{Gillius ADF}} + +\input t1augie.fd + +%\newcommand{\handwriting}{\fontspec{augie}} % From Emerald City, free font +%\newcommand{\handwriting}{\usefont{T1}{fau}{m}{n}} % From Emerald City, free font +% \newcommand{\handwriting}{} % If you prefer no special handwriting font or don't have augie + +%% Gill Sans doesn't look very nice when boldfaced +%% This is a hack to use Helvetica instead +%% Usage: \textbf{\forbold some stuff} +%\newcommand{\forbold}{\fontspec{Arial}} + +\usepackage{graphicx} +\usepackage[export]{adjustbox} + +\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{amssymb} +\usepackage{bm} +\usepackage{colortbl} +\usepackage{mathrsfs} % For Weinberg-esque letters +\usepackage{cancel} % For "SUSY-breaking" symbol +\usepackage{slashed} % for slashed characters in math mode +\usepackage{bbm} % for \mathbbm{1} (unit matrix) +\usepackage{amsthm} % For theorem environment +\usepackage{multirow} % For multi row cells in table +\usepackage{arydshln} % For dashed lines in arrays and tables +\usepackage{siunitx} +\usepackage{xhfill} +\usepackage{grffile} +\usepackage{textpos} +\usepackage{subfigure} +\usepackage{tikz} +\usepackage{hyperref} +%\usepackage{hepparticles} +\usepackage[italic]{hepparticles} + +\usepackage{hepnicenames} + +% Drawing a line +\tikzstyle{lw} = [line width=20pt] +\newcommand{\topline}{% + \tikz[remember picture,overlay] {% + \draw[crimsonred] ([yshift=-23.5pt]current page.north west) + -- ([yshift=-23.5pt,xshift=\paperwidth]current page.north west);}} + + + +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +\usepackage{tikzfeynman} % For Feynman diagrams +\usetikzlibrary{arrows,shapes} +\usetikzlibrary{trees} +\usetikzlibrary{matrix,arrows} % For commutative diagram +% http://www.felixl.de/commu.pdf +\usetikzlibrary{positioning} % For "above of=" commands +\usetikzlibrary{calc,through} % For coordinates +\usetikzlibrary{decorations.pathreplacing} % For curly braces +% http://www.math.ucla.edu/~getreuer/tikz.html +\usepackage{pgffor} % For repeating patterns + +\usetikzlibrary{decorations.pathmorphing} % For Feynman Diagrams +\usetikzlibrary{decorations.markings} +\tikzset{ + % >=stealth', %% Uncomment for more conventional arrows + vector/.style={decorate, decoration={snake}, draw}, + provector/.style={decorate, decoration={snake,amplitude=2.5pt}, draw}, + antivector/.style={decorate, decoration={snake,amplitude=-2.5pt}, draw}, + fermion/.style={draw=gray, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow[draw=gray]{>}}}}, + fermionbar/.style={draw=gray, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow[draw=gray]{<}}}}, + fermionnoarrow/.style={draw=gray}, + gluon/.style={decorate, draw=black, + decoration={coil,amplitude=4pt, segment length=5pt}}, + scalar/.style={dashed,draw=black, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow[draw=black]{>}}}}, + scalarbar/.style={dashed,draw=black, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow[draw=black]{<}}}}, + scalarnoarrow/.style={dashed,draw=black}, + electron/.style={draw=black, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow[draw=black]{>}}}}, + bigvector/.style={decorate, decoration={snake,amplitude=4pt}, draw}, +} + +% TIKZ - for block diagrams, +% from http://www.texample.net/tikz/examples/control-system-principles/ +% \usetikzlibrary{shapes,arrows} +\tikzstyle{block} = [draw, rectangle, +minimum height=3em, minimum width=6em] + + + + +\usetikzlibrary{backgrounds} +\usetikzlibrary{mindmap,trees} % For mind map +\newcommand{\degree}{\ensuremath{^\circ}} +\newcommand{\E}{\mathrm{E}} +\newcommand{\Var}{\mathrm{Var}} +\newcommand{\Cov}{\mathrm{Cov}} +\newcommand\Ts{\rule{0pt}{2.6ex}} % Top strut +\newcommand\Bs{\rule[-1.2ex]{0pt}{0pt}} % Bottom strut + +\graphicspath{{images/}} % Put all images in this directory. Avoids clutter. + +% SOME COMMANDS THAT I FIND HANDY +% \renewcommand{\tilde}{\widetilde} % dinky tildes look silly, dosn't work with fontspec +%\newcommand{\comment}[1]{\textcolor{comment}{\footnotesize{#1}\normalsize}} % comment mild +%\newcommand{\Comment}[1]{\textcolor{Comment}{\footnotesize{#1}\normalsize}} % comment bold +%\newcommand{\COMMENT}[1]{\textcolor{COMMENT}{\footnotesize{#1}\normalsize}} % comment crazy bold +\newcommand{\Alert}[1]{\textcolor{Alert}{#1}} % louder alert +\newcommand{\ALERT}[1]{\textcolor{ALERT}{#1}} % loudest alert +%% "\alert" is already a beamer pre-defined +\newcommand*{\Scale}[2][4]{\scalebox{#1}{$#2$}}% + +\def\Put(#1,#2)#3{\leavevmode\makebox(0,0){\put(#1,#2){#3}}} + +\usepackage{gmp} +\usepackage[final]{feynmp-auto} + +\usepackage[backend=bibtex,style=numeric-comp,firstinits=true]{biblatex} +\bibliography{bib} +\setbeamertemplate{bibliography item}[text] + +\makeatletter\let\frametextheight\beamer@frametextheight\makeatother + +% suppress frame numbering for backup slides +% you always need the appendix for this! +\newcommand{\backupbegin}{ + \newcounter{framenumberappendix} + \setcounter{framenumberappendix}{\value{framenumber}} +} +\newcommand{\backupend}{ + \addtocounter{framenumberappendix}{-\value{framenumber}} + \addtocounter{framenumber}{\value{framenumberappendix}} +} + + +\definecolor{links}{HTML}{2A1B81} +%\hypersetup{colorlinks,linkcolor=,urlcolor=links} + +% For shapo's formulas: + +% For shapo's formulas: +\def\lsi{\raise0.3ex\hbox{$<$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}} +\def\gsi{\raise0.3ex\hbox{$>$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}} +\newcommand{\lsim}{\mathop{\lsi}} +\newcommand{\gsim}{\mathop{\gsi}} +\newcommand{\wt}{\widetilde} +%\newcommand{\ol}{\overline} +\newcommand{\Tr}{\rm{Tr}} +\newcommand{\tr}{\rm{tr}} +\newcommand{\eqn}[1]{&\hspace{-0.7em}#1\hspace{-0.7em}&} +\newcommand{\vev}[1]{\rm{$\langle #1 \rangle$}} +\newcommand{\abs}[1]{\rm{$\left| #1 \right|$}} +\newcommand{\eV}{\rm{eV}} +\newcommand{\keV}{\rm{keV}} +\newcommand{\GeV}{\rm{GeV}} +\newcommand{\im}{\rm{Im}} +\newcommand{\disp}{\displaystyle} +\def\be{\begin{equation}} +\def\ee{\end{equation}} +\def\ba{\begin{eqnarray}} +\def\ea{\end{eqnarray}} +\def\d{\partial} +\def\l{\left(} +\def\r{\right)} +\def\la{\langle} +\def\ra{\rangle} +\def\e{{\rm e}} +\def\Br{{\rm Br}} +\def\fixme{{\color{red} FIXME!}} +\def\mc{{\color{Magenta}{MC}}} +\def\pdf{{\rm p.d.f.}} +\def\cdf{{\rm c.d.f.}} +\def\ARROW{{\color{JungleGreen}{$\Rrightarrow$}}\xspace} +\def\ARROWR{{\color{WildStrawberry}{$\Rrightarrow$}}\xspace} + +\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (Universit\"{a}t Z\"{u}rich)} +\institute{UZH} +\title[Specific \pdf~generation]{Specific \pdf~generation} +\date{\fixme} +\newcommand*{\QEDA}{\hfill\ensuremath{\blacksquare}}% +\newcommand*{\QEDB}{\hfill\ensuremath{\square}}% + +\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (Universit\"{a}t Z\"{u}rich)} +\institute{UZH} +\title[Markov Chain MC]{Markov Chain MC} +\date{\fixme} + + +\begin{document} +\tikzstyle{every picture}+=[remember picture] + +{ +\setbeamertemplate{sidebar right}{\llap{\includegraphics[width=\paperwidth,height=\paperheight]{bubble2}}} +\begin{frame}[c]%{\phantom{title page}} +\begin{center} +\begin{center} + \begin{columns} + \begin{column}{0.9\textwidth} + \flushright\fontspec{Trebuchet MS}\bfseries \Huge {Markov Chain MC} + \end{column} + \begin{column}{0.2\textwidth} + %\includegraphics[width=\textwidth]{SHiP-2} + \end{column} + \end{columns} +\end{center} + \quad + \vspace{3em} +\begin{columns} +\begin{column}{0.44\textwidth} +\flushright \vspace{-1.8em} {\fontspec{Trebuchet MS} \Large Marcin Chrząszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}} + +\end{column} +\begin{column}{0.53\textwidth} +\includegraphics[height=1.3cm]{uzh-transp} +\end{column} +\end{columns} + +\vspace{1em} +% \footnotesize\textcolor{gray}{With N. Serra, B. Storaci\\Thanks to the theory support from M. Shaposhnikov, D. Gorbunov}\normalsize\\ +\vspace{0.5em} + \textcolor{normal text.fg!50!Comment}{Experimental Methods in Particle Physics, \\ 12 October, 2016} + +\end{center} +\end{frame} +} + + + +\begin{frame}\frametitle{Trivial example} +\begin{minipage}{\textwidth} +\ARROW Lets start with a TRIVIAL example: we want to calculate $S=A+B$. We can rewrite it in: +\begin{align*} +S=p \frac{A}{p}+(1-p) \frac{B}{1-p} +\end{align*} +and one can interpret the sum as expected value of: +\begin{align*} +W=\begin{cases} +\frac{A}{p}~~{ \rm with~propability~} p \\ +\frac{A}{1-p}~~{ \rm with~propability~} 1-p +\end{cases} +\end{align*} +\ARROW The algorithm: +\begin{itemize} +\item We generate a random variable $W$ and calculate: +\begin{align*} +\hat{S}=\frac{1}{N}\sum_{i=1}^N W_i +\end{align*} +\ARROW The $\hat{S}$ is an unbias estimator of $S$. +\end{itemize} + + + +\end{minipage} + +\end{frame} + +\begin{frame}\frametitle{Trivial example2 } +\begin{minipage}{\textwidth} +\begin{itemize} +\item Lets say we have a linear equation system: +\end{itemize} +\begin{equation} +\begin{array}{lcl} X & = & pY + (1-p) A \\ Y & = & qX + (1-q)B \end{array} \nonumber +\end{equation} +\begin{itemize} +\item We know $A,B,p,q$; $X$ and $Y$ are meant to be determined. +\item Algorithm: +\begin{enumerate} +\item We choose first element of the first equation with probability $p$ and second with probability $1-p$. +\item I we choose the second one, the outcome of this MCMC is $W=A$. +\item If we choose the first we go to second equation and choose the first element with probability $q$ and the second with $1-q$. +\item We we choose the second one, the outcome of this MCMC is $W=B$. +\item If we choose the first we go to the first equation back again. +\item We repeat the procedure. +\end{enumerate} +\item We can estimate the solution of this system: +\end{itemize} +\begin{equation} +\hat{X} = \dfrac{1}{N}\sum_{i=1} W_i{~}{~}{~}{~}{~} \hat{\sigma_X}=\dfrac{1}{\sqrt{N-1}}\sqrt{\dfrac{1}{N} \sum_{i=1}^N W_i^2-\hat{X}^2} \nonumber +\end{equation} + +\end{minipage} + +\end{frame} + + + + +\begin{frame}\frametitle{Random walk} +\begin{minipage}{\textwidth} +\begin{footnotesize} + +\begin{center} +\includegraphics[width=0.8\textwidth]{images/walk.png} +\end{center} +\ARROW We are in the point $x$ and we walk accordingly to the following rules: +\begin{itemize} +\item From point $x$ we walk with probability $p$ to point $y$ or with $1-p$ to $a$. +\item From point $y$ we walk with probability $q$ to point $x$ and with $1-Q$ to $b$. +\item The walks ends when you end up in $a$ or $b$. +\item You get a ''reward'' $A$ if you end up in point $a$ and $B$ if you end up in $b$. +\item $X$ is expected ''reward'' when you start the walk from $x$, $Y$ when you start from $y$. +\end{itemize} +\ARROW The algorithm above is so-called random walk on the set $\lbrace a,x,y,b \rbrace$\\ +\ARROW The described walked can solve the linear equation system that we discussed above. + +\end{footnotesize} + +\end{minipage} +\end{frame} + +\begin{frame}\frametitle{Markov Chain MC} +\begin{footnotesize} +\begin{itemize} + +\item Consider a finite (or Countable set) possible states: $S_1$, $S_2$, ... +\item The $X_t$ is the state of the system in the time $t$ +\item We are looking at discrete time steps: $1,2,3,...$ + + +\item The conditional probability is defined as: +\end{itemize} +\begin{equation} +P(X_t=S_j \vert X_{t-1}=S_{j-1},..., X_{1}=S_{1}) \nonumber +\end{equation} +\begin{itemize} +\item The Markov chain is then if the probability depends only on previous step. +\end{itemize} +\begin{equation} +P(X_t=S_j \vert X_{t-1}=S_{j-1},..., X_{1}=S_{1}) = P(X_t=S_j \vert X_{t-1}=S_{j-1} )\nonumber +\end{equation} +\begin{itemize} +\item For this reason MCMC is also knows as drunk sailor walk. +\item Very powerful method. Used to solve linear eq. systems, invert matrix, solve differential equations, etc. +\item Also used in physics problems: Brown motions, diffusion, etc. +\end{itemize} + + +\end{footnotesize} +\end{frame} + + + + +\begin{frame}\frametitle{Linear equations system} +\begin{footnotesize} +\ARROW Lets start from a linear equation system: +\begin{align*} +\textbf{A} \overrightarrow{x}=\overrightarrow{b},~~~~~\det \textbf{A} \neq 0, +\end{align*} +where $\textbf{A}=(a_{ij},i,j=1,2,...,n$ -matrix, $\overrightarrow{b}=(b_1,b_2,...,b_n)$-vector, $\overrightarrow{x}=(x_1,x_2,...,x_n)$ - vector of unknowns.\\ +\ARROW The solution we mark as $\overrightarrow{x}^0 = (x_1^0, x_2^0,..., x_n^0)$\\ +\ARROW The above system can be transformed into the iterative representation: +\begin{align*} + \overrightarrow{x}=\overrightarrow{a} + \textbf{H} \overrightarrow{x} +\end{align*} +where $\textbf{H}$ is a matrix, $\overrightarrow{a}$ is a vector.\\ +\ARROW We assume that the matrix norm: +\begin{align*} +\Vert H \Vert= \max_{1 \leq i \leq n} \sum_{j=1}^n \vert h_{h_{ij}} \vert <1 +\end{align*} +\pause +\ARROW We can always change transform every system to the iteration form: $\textbf{A}=\textbf{V}-\textbf{W}$. +\begin{align*} +(\textbf{V} - \textbf{W} )\overrightarrow{x} = \overrightarrow{b}~~~~ \mapsto ~~~~ \overrightarrow{x} = \textbf{V}^{-1} \overrightarrow{b} + \textbf{V}^{-1} \textbf{W} \overrightarrow{x} +\end{align*} + +\end{footnotesize} +\end{frame} + +\begin{frame}\frametitle{Linear equations system} +\begin{footnotesize} +\ARROW Now we further modify the equation system: +\begin{align*} +\overrightarrow{x}=\overrightarrow{a} + \textbf{H} \overrightarrow{x} \Rightarrow (\textbf{I} - \textbf{H})\overrightarrow{x}=\overrightarrow{a} +\end{align*} +where $\textbf{I}=\delta_{ij}$ - unit matrix, $\delta_{ij}$ is the Kronecker delta.\\ +\ARROW What one can do is to represent the solution in terns of Neumann series: +\begin{align*} +\overrightarrow{x}^0=(\textbf{I}-\textbf{H})^{-1}\overrightarrow{a}= \overrightarrow{a} + \textbf{H} \overrightarrow{a} + \textbf{H}^2 \overrightarrow{a}+ \textbf{H}^3 \overrightarrow{a}+ ... +\end{align*} +\ARROW So for the $i^{th}$ component we have: +\begin{align*} +x_i^0=a_i+\sum_{j=1}^nh_{ij} a_j + \sum_{j_1 =1}^n \sum_{j_2 =1}^n h_{ij_1} h_{j_1 j_2} a_{j_2} \\ ++...+\sum_{j_1 =1}^n ...\sum_{j_n =1}^n h_{ij_1}... h_{j_{n-1} j_n} a_{j_n} +\end{align*} +\ARROW We will construct a probabilistic interpretation using MCMC and then we show that the expected value is equal to the above formula. +\end{footnotesize} +\end{frame} + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Neumann-Ulam method} +\begin{footnotesize} + +\begin{itemize} +\item To do so we add to our matrix an additional column of the matrix: +\end{itemize} +\begin{equation} +h_{i,0} = 1-\sum_{j=1}^n h_{ij} > 0 \nonumber +\end{equation} +\begin{itemize} +\item The system has states: $\lbrace 0,1,2...,n\rbrace$ +\item State at $t$ time is denoted as $i_t(i_t=0,1,2,...,n;t=0,1,....)$ +\item We make a random walk accordingly to to the following rules: +\begin{itemize} +\item At the beginning of the walk ($t=0$) we are at $i_0$. +\item In the $t$ moment we are in the $i_t$ position then in $t+1$ time stamp we move to state $i_{t+1}$ with the probability $h_{i_t i_{t+1}}$. +\item We stop walking if we are in state $0$. +\end{itemize} +\item The path $\gamma = (i_0, i_1, i_2, ..., i_k, 0)$ is called trajectory. +\item For each trajectory we assign a number: +\begin{align*} +X(\gamma)=X(i_0, i_1, i_2, ..., i_k, 0)=\frac{a_{i_k}}{h_{i_k 0}} +\end{align*} +\end{itemize} + + +\end{footnotesize} + +\end{frame} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Neumann-Ulam method} +\begin{footnotesize} +\ARROW The $X(\gamma)$ variable is a random variable from: $\lbrace a_1/h_{1,0},a_2/h_{2,0},...,a_n/h_{n,0} \rbrace$. The probability that $X(\gamma)= a_j/h_{j,0}$ is equal to the probability that the last non zero state of the $\gamma$ trajectory is $j$.\\ +\ARROW The expected value of the $X(\gamma)$ trajectory if the trajectory begins from $i_0=s$ is: +\begin{align*} +E \lbrace X(\gamma) \vert i_0=s \rbrace=\sum_{k=0}^{\infty} \sum_{ \lbrace \gamma_k \rbrace} X(\gamma) P(\gamma) +\end{align*} +where $\gamma_k$ is a trajectory of length $k$, which starts in $i_0=s$ and $P(\gamma)$ is the probability of occurrence of this trajectory. +\ARROW Yes you guest it lets do Taylor expansion: +\begin{align*} +E \lbrace X(\gamma) \vert i_0=s \rbrace= \sum_{\gamma_0}X(\gamma)P(\gamma) + \sum_{\gamma_1}X(\gamma)P(\gamma)+...+ \sum_{\gamma_k}X(\gamma)P(\gamma) +\end{align*} +\ARROW Now let's examine the elements of the above series. + +\end{footnotesize} + +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Neumann-Ulam method} +\begin{footnotesize} +$\lbrace \gamma_0 \rbrace$: One trajectory: $\gamma_0=(i_0=s \vert 0)$, $P(\gamma_0)=h_{s,0}$ and $X(\gamma_0)=a_s/h_{s,0}$. So: +\begin{align*} +\sum_{\gamma_0}X(\gamma)P(\gamma) = \frac{a_s}{h_{s,0}} h_{s,0}=a_s +\end{align*} + + + +$\lbrace \gamma_1 \rbrace$: Trajectories: $\gamma_1=(i_0=s,i_1 \vert 0),~i_1 \neq 0$, $P(\gamma_1)= P(s,i_1,0)=h_{s,i_1}h_{i_1,0} $ and $X(\gamma_1)=a_{i_1}/h_{i_1,0}$. So: +\begin{align*} +\sum_{\gamma_1}X(\gamma)P(\gamma) = \sum_{i_1=1}^n \frac{a_{i_1}}{h_{i_1,0}} h_{s,i_1} h_{i_1,0}= \sum_{i=1}^n h_{s,i_1}a_{i_1} +\end{align*} + + +$\lbrace \gamma_2 \rbrace$: Trajectories: $\gamma_2=(i_0=s,i_1,i_2 \vert 0),~i_1,i_2 \neq 0$, $P(\gamma_2)= P(s,i_1, i_2,0)=h_{s,i_1}h_{i_1,i_2}h_{i_1,0} $ and $X(\gamma_2)=a_{i_2}/h_{i_2,0}$. So: +\begin{align*} +\sum_{\gamma_2}X(\gamma)P(\gamma) = \sum_{i_1=1}^n \sum_{i_2=1}^n \frac{a_{i_2}}{h_{i_2,0}} h_{s,i_1} h_{i_1,i_2} h_{i_2,0}= \sum_{i_1=1}^n \sum_{i_2=1}^n h_{s,i_1} h_{i_1,i_2} a_{i_2} +\end{align*} + +\ARROW etc... + +\end{footnotesize} + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Neumann-Ulam method} +\begin{footnotesize} +\ARROW After summing up: +\begin{align*} +E \lbrace X(\gamma) \vert i_0=s \rbrace= a_s+ \sum_{i_1 =1}^n h_{s,i_1} a_{i_1}+ \sum_{i_1 =1}^n \sum_{i_2 =1}^n h_{s,i_1} h_{i_1,i_2} a_{i_2}+....\\ + \sum_{i_1 =1}^n \sum_{i_2 =1}^n ... \sum_{i_k =1}^n h_{s,i_1} h_{i_1,i_2}... h_{i_{k-1},i_k} a_{i_k}+... +\end{align*} +\ARROW If you compare this expression with the Neumann series we will they are the same so: +\begin{align*} +x_i^0=E \lbrace X(\gamma) \vert i_0=i \rbrace +\end{align*} + +\begin{exampleblock}{To sum up:} +We have proven that solving a linear system can be represented by an expectation value of the random variable $X(\gamma)$. The error is computed using standard deviation equation. +\end{exampleblock} +\end{footnotesize} + +\end{frame} + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Neumann-Ulam method} +\begin{itemize} +\item For example lets try to solve this equation system: +\end{itemize} +\begin{equation} +\overrightarrow{x} = +\left(\begin{array}{c} + 1.5 \\ +-1.0\\ +0.7 \end{array} \right) ++ +\left(\begin{array}{ccc} +0.2 & 0.3 & 0.1 \\ +0.4 & 0.3 & 0.2 \\ +0.3 & 0.1 & 0.1 \end{array} \right) \overrightarrow{x} + \nonumber +\end{equation} +\begin{itemize} +\item The solution is $\overrightarrow{x}_0 = (2.154303, 0.237389, 1.522255)$. +\end{itemize} +\begin{columns} + +\column{0.1in} + +\column{2.5in} +\begin{itemize} +\item The propability matrix $h_{ij}$ has the shape: +\end{itemize} +\begin{tabular}{|c|cccc|} +\hline +$i/j$ & 1 & 2 & 3 & 0 \\ \hline +1 & 0.2 & 0.3 & 0.1 & 0.4 \\ +2 & 0.4 & 0.3 & 0.2 & 0.1 \\ +3 & 0.3 & 0.1 & 0.1 & 0.5 \\ \hline +\end{tabular} + +\column{2.5in} +\begin{itemize} +\item An example solution: +\end{itemize} +\includegraphics[width=0.95\textwidth]{images/mark.png} + +\end{columns} + + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\iffalse +\begin{frame}\frametitle{Neumann-Ulam dual method} +\begin{minipage}{\textwidth} + +\ARROW The main problem with the Neumann-Ulam method is the fact that one has to calculate each of the $x_0^i$ separately.\\ +\ARROW The generalization works as follows: +\begin{enumerate} +\item We set randomly a \pdf~of states: $q_1,q_2,q_3,...,q_n$, such that $q_i >0$ and $\sum_{i=1}^n =1$. +\item We choose the starting point accordingly to $q_i$ probability. +\item If in the $t$ moment the point is in position $i_t$ then the with the probability $p(i_{t+1} \vert i_t)=h_{i_{t+1}, i_t}$ the points moves to the $i_{t+1}$ state. +\item For the state $0$ we assign the probability: $h_{0,i_{t}}=1-\sum_{i=1}^n h_{i,i_t}$ +\item WARNING HERE THE MATRIX IS TRANSPOSED compared to method. +\item The walk ends while you reach $0$ state. +\item For each walk/trajectory $(\gamma=(i_0,i_1,...,i_k,0))$ we assign a vector: +\begin{align*} +\overrightarrow{Y}(\gamma)=\frac{a_{i_0}}{q_{i_0}p(0\vert i_k }) \widehat{e}_{i_k} +\end{align*} +\item The final result is: $\overrightarrow{x}^0=\frac{1}{N}\sum \overrightarrow{Y}$ + +\end{enumerate}\textbf{ + + + + +\end{minipage} + +\end{frame} +\fi +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Neumann-Ulam dual method} +\begin{itemize} +\item The problem with Neumann-Ulam method is that you need to repeat it for each of the coordinates of the $\overrightarrow{x}_0$ vector. +\item The dual method calculates the whole $\overrightarrow{x}_0$ vector. +\item The algorithm: +\begin{itemize} +\item On the indexes: $\lbrace0,1,...,n\rbrace$ we set a probability distribution:\\ $q_1, q_2,..., q_n$, $q_i>0$ and $\sum_{i=1}^n q_i=1$. +\item The starting point we select from $q_i$ distribution. +\item If in $t$ time we are in $i_t$ state then with probability $p(i_{t+1} \vert i_t) = h_{i_{t+1},i_{t}}$ in $t+1$ we will be in state $i_{t+1}$. For $i_{t+1}=0$ we define the probability: $h_{0,i_{t}}=1-\sum_{j=1}^n h_{j,i_{t}}$. Here we also assume that $h_{j,i_{t}} > 0$. +\item NOTE: there the matrix is transposed compared to previous method: $H^{T}$. +\item Again we end our walk when we are at state $0$. +\item For the trajectory: $\gamma = (i_0, i_1,...,i_k, 0)$, we assign the vector: +\end{itemize} +\begin{equation} +\overrightarrow{Y}(\gamma) = \dfrac{a_{i_0}}{ q_{i_{0}} p(0 \vert i_k) } \widehat{e}_{i_{k}} \in \mathcal{R}^n \nonumber +\end{equation} +\item The solution will be : $\overrightarrow{x}^0 = \dfrac{1}{N} \sum \overrightarrow{Y}(\gamma)$ +\end{itemize} + + +\end{frame} +\iffalse +\begin{frame}\frametitle{Neumann-Ulam dual method, proof} +\begin{footnotesize} +\ARROW If $Y_i(\gamma)$ is the i-th component of the $\overrightarrow{Y}(\gamma)$ vector. One needs to show: +\begin{align*} +E\lbrace Y_i(\gamma)\rbrace=x_j^0 +\end{align*} +\ARROW From definition: +\begin{align*} +Y_j(i_1,...,i_k,0)=\begin{cases} +\frac{a_{i_k}}{q_{i_0} p(0 \vert i_k)}~~~& i_k=j\\ +0 ~~~& i_k \neq j +\end{cases} +\end{align*} +\ARROW The expected value: +\begin{align*} +E \lbrace Y_j (\gamma) \rbrace=\sum_{ {\rm trajectories}} \frac{a_j}{q_{i_0}p(0 \vert i_k) } P(i_1,i_2,...,i_k,0), +\end{align*} +where $P(i_1,i_2,...,i_k,0)$ is the probability of this trajectory occurring.\\ +\ARROW But by our definition the probability: +\begin{align*} +P(i_0,i_1,...,i_{k-1},j,0)=q_{0}h_{i_1,i_0}...h_{k,i_{k-1}}p(0 \vert j) +\end{align*} +\ARROW In the end we get: +\begin{align*} +E(Y_j(\gamma))=\sum_{k=0}^{\infty} \sum_{i_{k-1}=1}^n ... \sum_{i_{1}=1}^n \sum_{i_{0}=1}^n h_{j,i_{k-1}} h_{j,i_{k-1}} ... h_{i_2,i_1} h_{i_1,i_0} a_{i_0} +\end{align*} + + +\end{footnotesize} +\end{frame} +\fi +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Neumann-Ulam dual method} +\begin{itemize} +\item Let's try to solve the equation system: +\end{itemize} +\begin{equation} +\overrightarrow{x} = +\left(\begin{array}{c} + 1.5 \\ +-1.0\\ +0.7 \end{array} \right) ++ +\left(\begin{array}{ccc} +0.2 & 0.3 & 0.1 \\ +0.4 & 0.3 & 0.2 \\ +0.1 & 0.1 & 0.1 \end{array} \right) \overrightarrow{x} + \nonumber +\end{equation} +\begin{itemize} +\item The solution is: $\overrightarrow{x}_0 = (2.0, 0.0, 1.0)$. +\item Let's put the initial probability as constant: +\end{itemize} +\begin{equation} +q_1=q_2=q_3=\dfrac{1}{3} \nonumber +\end{equation} +\begin{columns} + +\column{0.1in} + +\column{2.5in} +\begin{itemize} +\item The propability matrix $h_{ij}$ has the shape: +\end{itemize} +\begin{tabular}{|c|cccc|} +\hline +$i/j$ & 1 & 2 & 3 & 4 \\ \hline +1 & 0.2 & 0.4 & 0.1 & 0.3 \\ +2 & 0.3 & 0.3 & 0.1 & 0.3 \\ +3 & 0.1 & 0.2 & 0.1 & 0.6 \\ \hline +\end{tabular} + +\column{2.5in} +\begin{itemize} +\item An example solution: +\end{itemize} +\includegraphics[width=0.95\textwidth]{images/mark2.png} + +\end{columns} +\end{frame} + + + + +\begin{frame}\frametitle{Generalization, the algorithm} +\ARROW We set the $P$ matrix in a arbitrary way.\\ +\ARROW If in the $t$ moment the point is in the $i_t$ state, then with the probability $p_{i_t, i_{t+1}}$ he can go to $i_{t+1}$ state. \\ +\ARROW We stop the walk once we reach $0$.\\ +\ARROW For the given trajectory we assign the value: $X(\gamma_k)$\\ +\ARROW We repeat the procedure $N$ times and take the mean and RMS.\\ +\ARROW We repeat this also for every of the $\overrightarrow{x}^0$ vector components. + + + +\end{frame} + + +\iffalse +\begin{frame}\frametitle{Wasow method} + +\begin{footnotesize} + +\ARROW The main problem with the Neumann-Ulam methods is the fact that each time we estimate only one of the part of the taylor expansion.\\ +\ARROW W.Wasow (1956) was smarter: +\begin{itemize} + +\item For the trajectory: $\gamma(i_0,i_1,...,i_k,0)$ we look trajectories: +\begin{align*} +(i_0),~(i_0,i_1),~(i_0,i_1,...,i_k) +\end{align*} +and for each we associate a number: +\begin{align*} +(i_0,i_1,i_2,...,i_m),~0 \leq m \leq k +\end{align*} +we assign a number: +\begin{align*} +\nu_{i_0,i_1} \nu_{i_1,i_2}...\nu_{i_{m-1},i_m}a_{i_m} +\end{align*} + +\end{itemize} +\ARROW For the trajectory we define: +\begin{align*} +X^{\ast}(\gamma)=\sum_{m=0}^k \nu_{i_1,i_2}...\nu_{i_{m-1},i_m}a_{i_m} +\end{align*} +\ARROW One can proof that: +\begin{align*} +E \lbrace X^{\ast}(\gamma) \vert i_0=i \rbrace =x_i^0 +\end{align*} + +\end{footnotesize} + +\end{frame} + +\fi + + +\begin{frame}\frametitle{Partial differential equations, intro} +\begin{minipage}{\textwidth} +\begin{footnotesize} +\ARROW Let's say we are want to describe a point that walks on the $\mathbb{R}$ axis: +\begin{itemize} +\item At the beginning $(t=0)$ the particle is at $x=0$ +\item If in the $t$ the particle is in the $x$ then in the time $t+1$ it walks to $x+1$ with the known probability $p$ and to the point $x-1$ with the probability $q=1-p$. +\item The moves are independent. +\end{itemize} +\ARROW So let's try to described the motion of the particle. \\ +\ARROW The solution is clearly a probabilistic problem. Let $\nu(x,t)$ be a probability that at time $t$ particle is in position $x$. We get the following equation: +\begin{align*} +\nu(x,t+1)=p \nu(x-1,t)+q \nu(x+1,t) +\end{align*} +with the initial conditions: +\begin{align*} +\nu(0,0)=1,~~~~~\nu(x,0)=0~~{\rm if~}x \neq 0. +\end{align*} +\ARROW The above functions describes the whole system (every $(t,x)$ point). +\end{footnotesize} + +\end{minipage} + +\end{frame} + + + +\begin{frame}\frametitle{Partial differential equations, intro} +\begin{minipage}{\textwidth} +\begin{tiny} +\ARROW Now in differential equation language we would say that the particle walks in steps of $\Delta x$ in times: $k\Delta t$, $k=1,2,3....$: +\begin{align*} +\nu(x,t+\Delta t)=p\nu(x-\Delta x,t)+q\nu(x+\Delta x,t). +\end{align*} +\ARROW To solve this equation we need to expand the $\nu(x,t)$ funciton in the Taylor series: +\begin{align*} +\nu(x,t) + \frac{\partial \nu(x,t)}{\partial t} \Delta t = p \nu(x,t) - p \frac{\partial\nu(x,t) }{\partial x} \Delta x + \frac{1}{2} p \frac{\partial^2 \nu(x,t)}{\partial x^2} (\Delta x)^2\\ + q \nu(x,t) + q \frac{\partial\nu(x,t) }{\partial x} \Delta x + \frac{1}{2} q \frac{\partial^2 \nu(x,t)}{\partial x^2} (\Delta x)^2 +\end{align*} +\ARROW From which we get: +\begin{align*} +\frac{\partial \nu(x,t)}{\partial t} \Delta t = -(p-q) \frac{\partial \nu(x,t) }{\partial x}\Delta x + \frac{1}{2} \frac{\partial^2 \nu(x,t) }{\partial x^2}(\Delta x)^2 +\end{align*} +\ARROW Now We divide the equation by $\Delta t$ and take the $\Delta t \to 0$: +\begin{align*} +(p-q) \frac{\Delta x }{\Delta t} \to 2 c,~~~~~~\frac{ (\Delta x)^2}{\Delta t } \to 2D, +\end{align*} +\ARROW We get the Fokker-Planck equation for the diffusion with current: +\begin{align*} +\frac{\partial \nu(x,t)}{\partial t } = -2c \frac{\partial \nu(x,t) }{\partial x} + D \frac{\partial^2 \nu(x,t)}{\partial x^2} +\end{align*} +\ARROW The $D$ is the diffusion coefficient, $c$ is the speed of current. For $c=0$ it is a symmetric distribution. + +\end{tiny} + +\end{minipage} + +\end{frame} + + + + + + +\begin{frame}\frametitle{Laplace equation, Dirichlet boundary conditions} +\begin{minipage}{\textwidth} +\begin{footnotesize} +\ARROW The aforementioned example shows the way to solve the partial differential equation using Markov Chain MC. \\ +\ARROW We will see how different classes of partial differential equations can be approximated with a Markov Chain MC, whose expectation value is the solution of the equation. +\ARROW The Laplace equation: +\begin{align*} +\frac{\partial^2 u }{\partial x_1^2 } +\frac{\partial^2 u }{\partial x_2^2 }+...+\frac{\partial^2 u }{\partial x_k^2 }=0 +\end{align*} +The $u(x_1,x_2,...,x_k)$ function that is a solution of above equation we call harmonic function. If one knows the values of the harmonic function on the edges $\Gamma(D)$ of the $D$ domain one can solve the equation.\\ +\begin{exampleblock}{The Dirichlet boundary conditions:} +Find the values of $u(x_1,x_2,...,x_k)$ inside the $D$ domain knowing the values of the edge are given with a function: +\begin{align*} +u(x_1,x_2,...,x_k)=f(x_1,x_2,...,x_k) \in \Gamma(D) +\end{align*} +\end{exampleblock} +\ARROW Now I am lazy so I put $k=2$ but it's the same for all k! + +\end{footnotesize} + +\end{minipage} + +\end{frame} + + + + +\begin{frame}\frametitle{Laplace equation, Dirichlet boundary conditions} +\begin{minipage}{\textwidth} +\begin{footnotesize} +\begin{columns} +\column{0.1in} +{~}\\ +\column{3in} +\ARROW We will put the Dirichlet boundary condition as a discrete condition:\\ +\begin{itemize} +\item The domain $D$ we put a lattice with distance $h$. +\item Some points we treat as inside {\color{green}(denoted with circles)}. Their form a set denoted $D^{\ast}$. +\item The other points we consider as the boundary points and they form a set $\Gamma(D)$. +\end{itemize} + +\column{2in} +\begin{center} +\includegraphics[width=0.95\textwidth]{images/dir.png} +\end{center} + +\end{columns} +\ARROW We express the second derivatives with the discrete form: +\begin{align*} +\frac{ \frac{u(x+h)-u(x)}{h} -\frac{u(x)-u(x-h) }{h} }{h} = \frac{u(x+h)-2u(x)+u(x-h)}{h^2} +\end{align*} +\ARROW Now we choose the units so $h=1$. + +\end{footnotesize} +\end{minipage} +\end{frame} + + +\begin{frame}\frametitle{Laplace equation, Dirichlet boundary conditions} +\begin{minipage}{\textwidth} +\begin{footnotesize} +\begin{exampleblock}{The Dirichlet condition in the discrete form:} +Find the $u^{\ast}$ function which obeys the differential equation: +\begin{align*} +U^{\ast}(x,y)=\frac{1}{4}\left[ u^{\ast}(x-1,y)+u^{\ast}(x+1,y)+u^{\ast}(x,y-1)+u^{\ast}(x,y+1) \right] +\end{align*} +in all points $(x,y) \in D^{\ast}$ with the condition: +\begin{align*} +u^{\ast}(x,y)=f^{\ast}(x,y),~~~(x,y) \in \Gamma(D^{\ast}) +\end{align*} +where $f^{\ast}(x,y)$ is the discrete equivalent of $f(x,y)$ function. +\end{exampleblock} +\ARROW We consider a random walk over the lattice $D^{\ast} \cup \Gamma(D^{\ast})$. +\begin{itemize} +\item In the $t=0$ we are in some point $(\xi,\eta) \in D^{\ast})$ +\item If at the $t$ the particle is in $(x,y)$ then at $t+1$ it can go with equal probability to any of the four neighbour lattices: $(x-1,y)$, $(x+1,y)$, $(x,y-1)$, $(x,y+1)$. +\item If the particle at some moment gets to the edge $\Gamma(D^{\ast}$ then the walk is terminated. +\item For the particle trajectory we assign the value of: $\nu(\xi,\eta)=f^{\ast}(x,y)$, where $(x,y)\in \Gamma(D^{\ast})$. +\end{itemize} +\end{footnotesize} +\end{minipage} +\end{frame} + + + + +\begin{frame}\frametitle{Laplace equation, Dirichlet boundary conditions} +\begin{minipage}{\textwidth} +\begin{footnotesize} +\ARROW Let $p_{\xi,\eta}(x,y)$ be the probability of particle walk that starting in $(\xi,\eta)$ to end the walk in $(x,y)$.\\ +\ARROW The possibilities: +\begin{enumerate} +\item The point $(\xi,\eta) \in \Gamma(D^{\ast})$. Then: +\begin{align} +p_{\xi,\eta}(x,y)=\begin{cases} +1,~~(x,y)=\xi,\eta)\\ +0,~~(x,y)\neq \xi,\eta) +\end{cases}\label{eq:trivial} +\end{align} +\item The point $(\xi,\eta) \in D^{\ast}$: +\begin{align} +p_{\xi,\eta}(x,y) = \frac{1}{4}\left[ p_{\xi-1,\eta}(x,y) + p_{\xi+1,\eta}(x,y)+ p_{\xi,\eta-1}(x,y)+ p_{\xi,\eta+1}(x,y) \right] +\label{eq:1} +\end{align} + + +\end{enumerate} +this is because to get to $(x,y)$ the particle has to walk through one of the neighbours: $(x-1,y)$, $(x+1,y)$, $(x,y-1)$, $(x,y+1)$.\\ +\ARROW The expected value of the $\nu(\xi,\eta)$ is given by equation: +\begin{align} +E(\xi,\eta)=\sum_{(x,y)\in \Gamma^{\ast}} p_{\xi,\eta}(x,y) f^{\ast}(x,y)\label{eq:2} +\end{align} +where the summing is over all boundary points +\end{footnotesize} +\end{minipage} +\end{frame} + + + + + +\begin{frame}\frametitle{Laplace equation, Dirichlet boundary conditions} +\begin{minipage}{\textwidth} +\begin{footnotesize} +\ARROW Now multiplying the \ref{eq:1} by $f^{\ast}(x,y)$ and summing over all edge points $(x,y)$: +\begin{align*} +E(\xi,\eta)=\frac{1}{4}\left[ E(\xi-1,\eta) + E(\xi+1,\eta) + E(\xi,\eta-1) + E(\xi,\eta+1) \right] +\end{align*} +\ARROW Putting now \ref{eq:trivial} to \ref{eq:2} one gets: +\begin{align*} +E(x,y)=f^{\ast}(x,y),~~(\xi,\eta) \in \Gamma(D^{\ast}) +\end{align*} +\ARROW Now the expected value solves identical equation as our $u^{\ast}(x,y)$ function. From this we conclude: +\begin{align*} +E(x,y)=u^{\ast}(x,y) +\end{align*} +\ARROW The algorithm: +\begin{itemize} +\item We put a particle in $(x,y)$. +\item We observe it's walk up to the moment when it's on the edge $\Gamma(D^{\ast})$. +\item We calculate the value of $f^{\ast}$ function in the point where the particle stops. +\item Repeat the walk $N$ times taking the average afterwards. +\end{itemize} +\begin{alertblock}{Important:} +One can show the the error does not depend on the dimensions! +\end{alertblock} + +\end{footnotesize} +\end{minipage} +\end{frame} + + + + + +\backupbegin + +\begin{frame}\frametitle{Backup} + + +\end{frame} + +\backupend + +\end{document} diff --git a/Lectures_my/EMPP/2017/Lecture3/tikzfeynman.sty b/Lectures_my/EMPP/2017/Lecture3/tikzfeynman.sty new file mode 100755 index 0000000..521fc65 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture3/tikzfeynman.sty @@ -0,0 +1,43 @@ +% Tikz Feynman Diagrams +% by Flip Tanedo +% 4 January 2011, work in progress + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%% TIKZ - for drawing Feynman diagrams %%%% +%%% ... use with pdflatex %%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\usepackage{tikz} +\usetikzlibrary{arrows,shapes} +\usetikzlibrary{trees} +\usetikzlibrary{matrix,arrows} % For commutative diagram + % http://www.felixl.de/commu.pdf +\usetikzlibrary{positioning} % For "above of=" commands +\usetikzlibrary{calc,through} % For coordinates +\usetikzlibrary{decorations.pathreplacing} % For curly braces +\usepackage[tikz]{bclogo} % For cute logo boxes +\usepackage{pgffor} % For repeating patterns + +\usetikzlibrary{decorations.pathmorphing} % For Feynman Diagrams +\usetikzlibrary{decorations.markings} +\tikzset{ + % >=stealth', %% Different kind of arrows + vector/.style={decorate, decoration={snake}, draw}, + fermion/.style={postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow{>}}}}, + fermionbar/.style={draw, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow{<}}}}, + fermionnoarrow/.style={}, + gluon/.style={decorate, + decoration={coil,amplitude=4pt, segment length=5pt}}, + scalar/.style={dashed, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow{>}}}}, + scalarbar/.style={dashed, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow{<}}}}, + scalarnoarrow/.style={dashed,draw}, +% +%% Special vectors (when you need to fine-tune wiggles) + provector/.style={decorate, decoration={snake,amplitude=2.5pt}, draw}, + antivector/.style={decorate, decoration={snake,amplitude=-2.5pt}, draw}, +} + diff --git a/Lectures_my/EMPP/2017/Lecture4/Exercises/Error_propagation/err.py b/Lectures_my/EMPP/2017/Lecture4/Exercises/Error_propagation/err.py new file mode 100644 index 0000000..00c1615 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture4/Exercises/Error_propagation/err.py @@ -0,0 +1,42 @@ +from ROOT import * +import sys + +def main(argv): + NTOYS=100000 + SEED=1000 + + r=float(argv[1]) + r_err=float(argv[2]) + + rand = TRandom(SEED) + + r_list=[] + rsqr_list=[] + + print 'aaa' + + hist_r = TH1D("r", "r", 100, r-5.*r_err, r+5*r_err) + hist_r2= TH1D("1/r2", "1/r2", 100, 1/((r-10*r_err)*(r-10*r_err)), 1/((r+10*r_err)*(r+10*r_err))) + + for i in range(NTOYS): + tmp=rand.Gaus(r,r_err) + + hist_r.Fill(tmp) + hist_r2.Fill(1./(tmp*tmp)) + + + c1=TCanvas("c1", "c1", 1200, 600) + c1.Divide(2,1) + c1.cd(1) + hist_r.Draw() + hist_r.Fit('gaus') + c1.cd(2) + hist_r2.Draw() + hist_r2.Fit('gaus') + c1.SaveAs("result.png") + + + + +if __name__ == "__main__": + main(sys.argv) diff --git a/Lectures_my/EMPP/2017/Lecture4/Exercises/Error_propagation/result.png b/Lectures_my/EMPP/2017/Lecture4/Exercises/Error_propagation/result.png new file mode 100644 index 0000000..60424fa --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture4/Exercises/Error_propagation/result.png Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture4/Exercises/Integration_FOAM/foam_kanwa.C b/Lectures_my/EMPP/2017/Lecture4/Exercises/Integration_FOAM/foam_kanwa.C new file mode 100755 index 0000000..d6f9611 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture4/Exercises/Integration_FOAM/foam_kanwa.C @@ -0,0 +1,73 @@ +// This program can be execute from the command line as folows: +// +// root -l foam_kanwa.C +//_____________________________________________________________________________ + +#include "Riostream.h" +#include "TFoam.h" +#include "TCanvas.h" +#include "TH2.h" +#include "TMath.h" +#include "TFoamIntegrand.h" +#include "TRandom3.h" + +//_____________________________________________________________________________ +Double_t sqr(Double_t x){return x*x;}; +//_____________________________________________________________________________ +Double_t Camel2(Int_t nDim, Double_t *Xarg){ +// 2-dimensional distribution for Foam, normalized to one (within 1e-5) + Double_t x=Xarg[0]; + Double_t y=Xarg[1]; + Double_t GamSq= sqr(0.100e0); + Double_t Dist= 0; + Dist +=exp(-(sqr(x-1./3) +sqr(y-1./3))/GamSq)/GamSq/TMath::Pi(); + Dist +=exp(-(sqr(x-2./3) +sqr(y-2./3))/GamSq)/GamSq/TMath::Pi(); + return 0.5*Dist; +}// Camel2 +//_____________________________________________________________________________ + +Int_t foam_kanwa(){ + cout<<"--- kanwa started ---"<SetSeed(4357); + TFoam *FoamX = new TFoam("FoamX"); // Create Simulator + FoamX->SetkDim(2); // No. of dimensions, obligatory! + FoamX->SetnCells(500); // Optionally No. of cells, default=2000 + FoamX->SetRhoInt(Camel2); // Set 2-dim distribution, included below + FoamX->SetPseRan(PseRan); // Set random number generator + FoamX->Initialize(); // Initialize simulator, may take time... + // + // visualising generated distribution + TCanvas *cKanwa = new TCanvas("cKanwa","Canvas for plotting",600,600); + cKanwa->cd(); + // From now on FoamX is ready to generate events + int nshow=5000; + for(long loop=0; loop<100000; loop++){ + FoamX->MakeEvent(); // generate MC event + FoamX->GetMCvect( MCvect); // get generated vector (x,y) + Double_t x=MCvect[0]; + Double_t y=MCvect[1]; + if(loop<10) cout<<"(x,y) = ( "<< x <<", "<< y <<" )"<Fill(x,y); + // live plot + if(loop == nshow){ + nshow += 5000; + hst_xy->Draw("lego2"); + cKanwa->Update(); + } + }// loop + // + hst_xy->Draw("lego2"); // final plot + cKanwa->Update(); + // + Double_t MCresult, MCerror; + FoamX->GetIntegMC( MCresult, MCerror); // get MC integral, should be one + cout << " MCresult= " << MCresult << " +- " << MCerror < +#include +#include +#include +#include + + +using namespace std; + +int main(int argc, char **argv) +{ + double h[3][4]={ {0.4, 0.2, 0.3,0.1},{0.1,0.4,0.3,0.2},{0.5,0.3,0.1,0.1}}; + double a[3]={1.5,-1.0,0.7}; + int j = atoi(argv[1]); + int original =j; + int n_of_samples = atoi(argv[2]); + TRandom1 *rand = new TRandom1(2131); + double result =0; + double result2=0; + for(int i =0;i< n_of_samples;++i) + { + int last; + j=original; + while(1) + { + last =j; + double tmp =rand->Rndm(); + if(tmp h[j-1][0] && tmp h[j-1][1]+h[j-1][0] && tmp h[j-1][2]+h[j-1][1]+h[j-1][0] && tmp +#include +#include +#include "TStyle.h" + +#include + + +using namespace std; + +void solution(double &x,double &y,double &z,int traj, TRandom *gen) +{ + //double p[3]={0.9,0.8,0.7}; + double p[3]={0.3,0.3,0.6}; + double hPrim[3][3]={{0.3,0.5,0.9},{0.3,0.6,0.9},{0.6,0.7,0.9}}; + //double hPrim[3][3]={{0.9,1,1},{0.8,0.8,1},{0.7,0.7,0.7}}; + + double a[3]={1.5, -1.,0.7}; + double wynik[3]={0.,0.,0.}; + double ran; + double q[3]={1./3.,1./3.,1./3.}; + int i,ik; + int n; + ik=0; + for(int j=0;jRndm(); + if(ran<=q[0]){n=0;} + if(ran>q[0] && ranq[0]+q[1]){n=2;} + i=n+1; + while(i!=0) + { + ran=gen->Rndm(); + //if(n==2){cout<ran){ik=i; i=0;} + else + { + for(int m=2;m>=0;--m) + { + if(hPrim[i-1][m]SetOptFit(1); + gStyle->SetTitleFillColor(0); + gStyle->SetStatColor(0); + double x,y,z; + TRandom *gen=new TRandom3(); + solution(x,y,z, NTOYS,gen); + cout< +\newif\ifbeamer@Flip@dark +\beamer@Flip@darkfalse +\DeclareOptionBeamer{dark}{\beamer@Flip@darktrue} +\ProcessOptionsBeamer + + +% These are a few colors that I like. + +\definecolor{crimsonred}{RGB}{153,0,0} % Neurtal red, good for dark or light bg +\definecolor{darkcharcoal}{RGB}{25,25,25} % Darker gray +\definecolor{charcoal}{RGB}{51,51,51} % Darker gray +\definecolor{ash}{RGB}{100,100,100} % medium gray +\definecolor{paleblue}{RGB}{0,102,102} % More of an `ocean' color +\definecolor{turtlegreen}{RGB}{51,153,0} % A more neutral green +\definecolor{paleale}{RGB}{204,204,102} % Only for dark BG +\definecolor{lager}{RGB}{140,110,10} % Use instead of pale ale for white BG +\definecolor{regal}{RGB}{90,0,120} % A more neutral purple +\definecolor{jeans}{RGB}{20,30,150} % A more neutral blue + + +% Define some "invariant colors" so that a color that doen't work with a +% light/dark background will automatically be substituted with one that does. +% These will be rewritten in beamercolorthemeFlipDark + +\ifbeamer@Flip@dark + \definecolor{FlipSand}{RGB}{204,204,102} % paleale, Only for dark BG + \definecolor{FlipGreen}{RGB}{0,255,0} % Neon-like green, only for dark BG +\else + \definecolor{FlipSand}{RGB}{140,110,10} % lager, Only for light BG + \definecolor{FlipGreen}{RGB}{51,153,0} % turtlegreen, works for both +\fi + +%% Future revision: It would be nice to define these in terms of the palette. + + +\ifbeamer@Flip@dark + \setbeamercolor{normal text}{fg=white, bg=black} + \setbeamercolor{structure}{fg=gray, bg=black} % fg controls bullets + \setbeamercolor*{footerlike}{fg=white,bg=black} % Controls the footerline +\else + % Default to black on white + \setbeamercolor*{footerlike}{fg=white,bg=charcoal} % for charcoal footer + \setbeamercolor{structure}{fg=charcoal, bg=white} % fg controls bullets + % \setbeamercolor{normal text}{fg=white, bg=black} +\fi + + + + + +% These defined colors can be used in \textcolor{colorname}{text in that color}. + +% Colors for Keynote background: DARK +\definecolor{keynotebottom}{rgb}{0.32,0.3,0.38} +\definecolor{keynotemiddle}{rgb}{0.08,0.08,0.16} +\definecolor{keynotetop}{rgb}{0,0,0} +%%% Example of usage: +%% \setbeamertemplate{background canvas}[vertical shading] +%% [bottom=keynotebottom, middle=keynotemiddle, top=keynotetop] + + + + +% ALERT AND COMMENT COLORS (just copies of the above colors) +% (I don't know how ot do this more elegantly) +\ifbeamer@Flip@dark + \definecolor{ALERT}{RGB}{153,0,0} % crimsonred + \definecolor{Alert}{RGB}{51,153,0} % turtlegreen + \definecolor{alert}{RGB}{204,204,102} % paleale + \definecolor{charcoal}{RGB}{51,51,51} % charcoal + \definecolor{comment}{RGB}{80,80,80} % light charcoal + \definecolor{Comment}{RGB}{100,100,100} % ash + \definecolor{COMMENT}{RGB}{80,20,120} % regal +\else +% \definecolor{ALERT}{RGB}{153,0,0} % crimsonred + \definecolor{ALERT}{RGB}{28,134,238} % DodgerBlue2 +% \definecolor{Alert}{RGB}{51,153,0} % turtlegreen + \definecolor{Alert}{RGB}{255,127,36} % chocolate1 +% \definecolor{alert}{RGB}{140,110,10} % lager + \definecolor{alert}{RGB}{0,205,102} % SpringGreen3 + \definecolor{charcoal}{RGB}{80,80,80} % light charcoal + \definecolor{comment}{RGB}{51,51,51} % charcoal + \definecolor{Comment}{RGB}{100,100,100} % ash + \definecolor{COMMENT}{RGB}{80,20,120} % regal +\fi + + +% \definecolor{crimsonred}{RGB}{153,0,0} % Neurtal red, good for dark or light bg +% \definecolor{charcoal}{RGB}{51,51,51} % Darker gray +% \definecolor{ash}{RGB}{100,100,100} % medium gray +% \definecolor{paleblue}{RGB}{0,102,102} % More of an `ocean' color +% \definecolor{turtlegreen}{RGB}{51,153,0} % A more neutral green +% \definecolor{paleale}{RGB}{204,204,102} % Only for dark BG +% \definecolor{lager}{RGB}{140,110,10} % Use instead of pale ale for white BG +% \definecolor{regal}{RGB}{90,0,120} % A more neutral purple +% \definecolor{jeans}{RGB}{20,30,150} % A more neutral blue + + +% A few useful colors +\setbeamercolor{alerted text}{fg=alert} + +%% I would like ot use these colors, but there seems to be a bug in Beamer +%% where the footnote color infects the normal text color +%% See: http://tex.stackexchange.com/questions/8264/beamer-changing-the-footnote-color-also-changes-the-normal-text-color/8268#8268 + +% \setbeamercolor{footnote}{parent=normal text, fg=FlipSand} +% \setbeamercolor{footnote mark}{parent=normal text, fg=FlipSand} + +% Blocks +\setbeamercolor{block title}{fg=gray!30!white,bg=charcoal} +\setbeamercolor{block body}{parent=normal text,bg=gray, fg=white} + +\setbeamercolor{block title example}{fg=turtlegreen!30!white,bg=turtlegreen!40!black} +\setbeamercolor{block body example}{parent=normal text,bg=turtlegreen, fg=white} +% +\setbeamercolor{block title alerted}{fg=crimsonred!30!white,bg=crimsonred!40!black} +\setbeamercolor{block body alerted}{parent=normal text,bg=crimsonred, fg=white} + + + +% These "setbeamercolor" commands are more standardized. + + +%% From the Beamer User Guide: +% Outer themes base the color of navigational elements and, possibly, also of other elements, on the +% four palette colors. The “primary” palette should be used for the most important navigational elements, +% which are usually the ones that change most often and hence require the most attention by the audience. +% The “secondary” and “tertiary” are less important, the “quaternary” one is least important. +% By default, the palette colors do not have a background and the foreground ranges from structure.fg to black. +% For the sidebar, there is an extra set of palette colors, see palette sidebar primary. + +\setbeamercolor*{palette primary}{fg=crimsonred,bg=charcoal} +\setbeamercolor*{palette secondary}{fg=paleale,bg=lager} +\setbeamercolor*{palette tertiary}{fg=turtlegreen,bg=jeans} +\setbeamercolor*{palette quaternary}{fg=paleblue,bg=regal} + +% \setbeamercolor*{palette primary}{fg=crimsonred,bg=white} +% \setbeamercolor*{palette secondary}{fg=charcoal,bg=white} +% \setbeamercolor*{palette tertiary}{fg=paleblue,bg=white} +% \setbeamercolor*{palette quaternary}{fg=turtlegreen,bg=white} + + + +%% These are some structures that I define for use in the outer theme. + +\setbeamercolor*{crimsontown}{fg=paleblue,bg=crimsonred} +\setbeamercolor*{bluetown}{fg=white,bg=DodgerBlue2} +%\setbeamercolor*{titlelike}{fg=crimsonred} +\setbeamercolor*{titlelike}{fg=DodgerBlue2} +\setbeamercolor*{topbarlike}{fg=white, bg=charcoal} + + + + + +%% Some old definitions that I might want to get back to +% +% \setbeamercolor*{frametitle}{bg=white,fg=charcoal} +% \setbeamercolor*{part title}{bg=white,fg=charcoal} +% \setbeamercolor*{item}{fg=charcoal, bg=white} +% +% \setbeamercolor*{separation line}{} +% \setbeamercolor*{fine separation line}{} + + + + + +\mode + diff --git a/Lectures_my/EMPP/2017/Lecture4/beamerinnerthemeFlip.sty b/Lectures_my/EMPP/2017/Lecture4/beamerinnerthemeFlip.sty new file mode 100755 index 0000000..9910f4d --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture4/beamerinnerthemeFlip.sty @@ -0,0 +1,95 @@ +% Inner style file for the BEAMER FLIP THEME +% Copyright 2010 by Flip Tanedo +% This file may be distributed and/or modified +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. +% +% Based on: beamerinnerthemeFlip by Marco Barisione + +\mode + +% % Use alternative title page style. +% \DeclareOptionBeamer{alternativetitlepage}[true]{\def\beamer@Flip@alternativetitlepage{#1}} + +% Logo to use in the alternative title page. +% \def\beamer@Flip@titlepagelogo{} +% \DeclareOptionBeamer{titlepagelogo}{\def\beamer@Flip@titlepagelogo{#1}} + +% Bullet shape. +\DeclareOptionBeamer{bullet}{\def\beamer@Flip@bullet{#1}} +\DeclareOptionBeamer{shadow}[true]{\def\beamer@themerounded@shadow{#1}} +\ExecuteOptionsBeamer{shadow=false} + + +% \ExecuteOptionsBeamer{alternativetitlepage=false,bullet=square} +\ProcessOptionsBeamer + + + +% Margins. +\newlength{\beamer@Flip@normalmargin} +\setlength{\beamer@Flip@normalmargin}{.06\paperwidth} +\setbeamersize{text margin left=\beamer@Flip@normalmargin} +\setbeamersize{text margin right=\beamer@Flip@normalmargin} +\setlength\leftmargini{.6\beamer@Flip@normalmargin} +\setlength\leftmarginii{.6\beamer@Flip@normalmargin} +\setlength\leftmarginiii{.6\beamer@Flip@normalmargin} + +% Normal title page. +\defbeamertemplate*{title page normal}{Flip theme}[1][] +{ + \vbox{} + \vfill + \begin{centering} + \begin{beamercolorbox}[wd=\paperwidth,sep=8pt,center,#1]{title page header} + \usebeamerfont{title}\inserttitle\par% + \ifx\insertsubtitle\@empty% + \else% + \vskip0.25em% + {\usebeamerfont{subtitle}\usebeamercolor[fg]{subtitle}\insertsubtitle\par}% + \fi% + \end{beamercolorbox}% + \vskip1em\par + \begin{beamercolorbox}[sep=8pt,center,#1]{author} + \usebeamerfont{author}\insertauthor + \end{beamercolorbox} + \begin{beamercolorbox}[sep=8pt,center,#1]{institute} + \usebeamerfont{institute}\insertinstitute + \end{beamercolorbox} + \begin{beamercolorbox}[sep=8pt,center,#1]{date} + \usebeamerfont{date}\insertdate + \end{beamercolorbox}\vskip0.5em + {\usebeamercolor[fg]{titlegraphic}\inserttitlegraphic\par} + \end{centering} + \vfill +} + + +% Items. +\defbeamertemplate{itemize item}{squarealt}% +{\tiny\raise.5ex\hbox{\donotcoloroutermaths$\blacksquare$}} +\defbeamertemplate{itemize subitem}{squarealt}% +{\tiny\raise.4ex\hbox{\donotcoloroutermaths$\square$}} +\defbeamertemplate{itemize subsubitem}{squarealt}% +{\tiny\raise.3ex\hbox{\donotcoloroutermaths$\blacksquare$}} +% +\defbeamertemplate{itemize item}{circlealt}% +{\small\raise.2ex\hbox{\donotcoloroutermaths$\bullet$}} +\defbeamertemplate{itemize subitem}{circlealt}% +{\small\raise.1ex\hbox{\donotcoloroutermaths$\circ$}} +\defbeamertemplate{itemize subsubitem}{circlealt}% +{\scriptsize\raise.1ex\hbox{\donotcoloroutermaths$\bullet$}} +\setbeamertemplate{items}[circlealt] +% +\def\circletext{circle} +\ifx\beamer@Flip@bullet\circletext + \setbeamertemplate{items}[circlealt] +\else + \setbeamertemplate{items}[squarealt] +\fi + +\setbeamertemplate{blocks}[rounded][shadow=\beamer@themerounded@shadow] + + +\mode + diff --git a/Lectures_my/EMPP/2017/Lecture4/beamerouterthemeFlip.sty b/Lectures_my/EMPP/2017/Lecture4/beamerouterthemeFlip.sty new file mode 100755 index 0000000..d12f6d6 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture4/beamerouterthemeFlip.sty @@ -0,0 +1,189 @@ +% Outer style file for the BEAMER FLIP THEME 212 +% Copyright 2012 by Flip Tanedo +% This file may be distributed and/or modified +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. +% +% Based on: beamerouterthemesplit by Till Tantau + + +\mode + +% Watermark +\DeclareOptionBeamer{watermark}{\def\beamer@Flip@watermark{#1}} +\ExecuteOptionsBeamer{watermark=} % Default value is empty + + +\newif\ifbeamer@Flip@bigpagenumber +\beamer@Flip@bigpagenumberfalse +\DeclareOptionBeamer{bigpagenumber}{\beamer@Flip@bigpagenumbertrue} + + +\def\beamer@Flip@truetext{true} % Kludge for true/false so I can use ifx + +\DeclareOptionBeamer{topline}[true]{\def\beamer@Flip@topline{#1}} +\ExecuteOptionsBeamer{topline=false} % Default + + + +% \ExecuteOptionsBeamer{topline=} % Default value is empty + + +\ProcessOptionsBeamer + + +\usepackage{tikz} % For fancy decorations + + +% I should fix these up to be more robust against color changes +\setbeamercolor{section in head/foot}{parent=footerlike} +\setbeamercolor{subsection in head/foot}{parent=footerlike} +\setbeamercolor{author in head/foot}{parent=footerlike} +\setbeamercolor{title in head/foot}{parent=footerlike} + + +% \setbeamercolor{author in head/foot}{parent=section in head/foot} +% \setbeamercolor{title in head/foot}{parent=subsection in head/foot} + +%\setbeamercolor{topbar}{parent=crimsontown} +\setbeamercolor{topbar}{parent=bluetown} + + + + +\usesectionheadtemplate + {\hfill\insertsectionhead} + {\hfill\color{fg!50!bg}\insertsectionhead} + + +%%%%%%%%%%%%%%%%%% +% The footer bar % +%%%%%%%%%%%%%%%%%% + +\defbeamertemplate*{footline}{Flip theme} +{% + \leavevmode% +% OBSERVATION: the "%" symbols inside hbox are all very important here. +% The \hbox enviroment will insert spaces whenever there's whitespace +% Adding a % at the END of each line ensures that any hard returns aren't +% interpreted as white space. This allows the color boxes to be flush against +% one another. If a faint white line appears one could probably do something like +% hspace{-1px} and add an additional pixel-or-two wide beamercolorbox. + +\hbox{% +\begin{beamercolorbox}[wd=.4\paperwidth,ht=2.5ex,dp=1.125ex,leftskip=.3cm, rightskip=.3cm plus1fil]{author in head/foot}% + \usebeamerfont{author in head/foot}\insertshortauthor \end{beamercolorbox}% +% +\begin{beamercolorbox}[wd=.6\paperwidth,ht=2.5ex,dp=1.125ex,leftskip=.3cm,rightskip=.3cm plus1fil]{title in head/foot}% + \usebeamerfont{title in head/foot}{\textit \insertshorttitle}% + \hskip2ex plus1fill% + % \insertpagenumber\,/\,\insertpresentationendpage %% Want FRAME, not SLIDE number + \insertframenumber/\inserttotalframenumber + \end{beamercolorbox}% +}% + +% This is a complete kludge for the faint white line which appears +% between the beamer color boxes above. (It doesnt appear in presentation mode +% but sometimes looks funny when the pdfs are viewed in a window) +\begin{tikzpicture}[overlay] + \usebeamercolor[bg]{author in head/foot} + \draw[thick] (0,3.625ex) -- (\paperwidth,3.625ex); + \draw (.4\paperwidth,0) -- (.4\paperwidth,3.625ex); + \draw[thick] (0,0) -- (\paperwidth,0); +\end{tikzpicture} + + + +\ifbeamer@Flip@bigpagenumber + \begin{tikzpicture}[overlay] + \usebeamercolor[bg]{author in head/foot} + \draw[fill] (\paperwidth-5ex,3.625ex) circle (6ex); + \usebeamercolor[fg]{author in head/foot} + \draw[fill] (\paperwidth-5ex,3.625ex) circle (5ex); + \usebeamercolor[bg]{author in head/foot} + \node at (\paperwidth-5ex,4ex) {\small$^\text{\insertframenumber}/_\text{\inserttotalframenumber}$}; + \end{tikzpicture} +\fi +} + + + +\defbeamertemplate*{frametitle}{Flip theme}[1][left] +{ +% \ifbeamercolorempty[bg]{frametitle}{}{\nointerlineskip}% +\@tempdima=\textwidth% +\advance\@tempdima by\beamer@leftmargin% +\advance\@tempdima by\beamer@rightmargin% + +\vbox{}\vskip-3.5ex% +% +\begin{beamercolorbox}[sep=0.3cm,#1,wd=\the\@tempdima]{titlelike} + \usebeamerfont{frametitle}% + \vbox{}\vskip-1ex% + \if@tempswa\else\csname beamer@fte#1\endcsname\fi% + % \strut{\bf\insertframetitle}\strut\par% %% Include the \bf + \strut{\insertframetitle}\strut\par% + {% + \ifx\insertframesubtitle\@empty% + \else + {\usebeamerfont{framesubtitle} + \usebeamercolor[fg]{framesubtitle} + \insertframesubtitle\strut\par}% + \fi + }% + % + \vskip-1ex% + \if@tempswa\else\vskip-.3cm\fi% set inside beamercolorbox... evil here... +\end{beamercolorbox}% +%% + +% \def\beamer@fteright{\vskip0.35cm\advance\leftskip by 1.7cm\advance\rightskip by1.7cm} +} + + + + +% Sidebar right is important: anything placed here will be +% visible *behind* the main text. This is where to put any +% interesting watermarks. +% +% +\defbeamertemplate*{sidebar right}{Flip theme} +{ +% \llap{\includegraphics[width=50px]{footdecoration}} +% \llap{\includegraphics[width=\paperwidth,height=\paperheight]{upperleft_watermark_transp}} +% +% THIS WOULD BE A NICE WAY TO PUT THE PARTICLE BUBBLE CHAMBER BG +% ... make a png of the background with TRANSPARENT BG +% ... then put the image here (use \hfill to get it on the left) +% Now one can FURTHER apply a slight gradient in the BG +% +% +% % Top Line +\ifx\beamer@Flip@topline\beamer@Flip@truetext + \begin{tikzpicture}[overlay] + \usebeamercolor[fg]{titlelike} % alternately, topbarlike would be a good beamercolor +% \usebeamercolor[fg]{topbarlike} % alternately, topbarlike would be a good beamercolor + \draw[fill] (-\paperwidth,0) rectangle (0,-3pt); + \end{tikzpicture} +\fi +% +% + \vskip.2\beamer@leftmargin% + %\llap{\insertlogo\hskip.5\beamer@leftmargin}% + \llap{\insertlogo\hskip.08\beamer@leftmargin}% + \vfill% + \if \beamer@Flip@watermark\@empty + % This is kind of a kludge since if I put anything in here, I automatically get errors + % Somehow LaTeX wants to read the \else part! + \else% + \llap{\includegraphics[width=\paperwidth,height=\paperheight]{\beamer@Flip@watermark}} + \fi +} + + + +\mode +\endinput + + diff --git a/Lectures_my/EMPP/2017/Lecture4/beamerouterthemedecolines.sty b/Lectures_my/EMPP/2017/Lecture4/beamerouterthemedecolines.sty new file mode 100755 index 0000000..669e493 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture4/beamerouterthemedecolines.sty @@ -0,0 +1,168 @@ +% Copyright 2007 by Marco Barisione +% +% This file may be distributed and/or modified +% +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. + +\mode + +% String used between the current page and the total page count. +\def\beamer@decolines@pageofpages{/} +\DeclareOptionBeamer{pageofpages}{\def\beamer@decolines@pageofpages{#1}} + +% Show a line below the frame title. +\DeclareOptionBeamer{titleline}[true]{\def\beamer@decolines@titleline{#1}} + +% Image used for the watermark. +\def\beamer@decolines@watermarkorig{} +\DeclareOptionBeamer{watermark}{\def\beamer@decolines@watermarkorig{#1}} + +% Height of the watermark. +\def\beamer@decolines@watermarkheight{100px} +\DeclareOptionBeamer{watermarkheight}{\def\beamer@decolines@watermarkheight{#1}} + +% The original image height is watermarkheightmult * watermarkheight. +\def\beamer@decolines@watermarkheightmult{1} +\DeclareOptionBeamer{watermarkheightmult}{\def\beamer@decolines@watermarkheightmult{#1}} + +\ExecuteOptionsBeamer{titleline=false} +\ProcessOptionsBeamer + +% Enable/disable the watermark. +\def\watermarkon{% + \def\beamer@decolines@watermark{\beamer@decolines@watermarkorig}% +} +\def\watermarkoff{\def\beamer@decolines@watermark{}} + +% Initially enable the watermark. +\watermarkon + +% Colors. +\setbeamercolor*{lineup}{parent=palette primary} +\setbeamercolor*{linemid}{parent=palette secondary} +\setbeamercolor*{linebottom}{parent=palette tertiary} +\setbeamercolor*{page header}{parent=titlelike} + +% Lengths +\newlength{\headerheight} +\setlength{\headerheight}{.045\paperheight} +\newlength{\beamer@decolines@lineup} +\setlength{\beamer@decolines@lineup}{.025\paperheight} +\newlength{\beamer@decolines@linemid} +\setlength{\beamer@decolines@linemid}{.015\paperheight} +\newlength{\beamer@decolines@linebottom} +\setlength{\beamer@decolines@linebottom}{.01\paperheight} + +% The height of the watermark part below the 3 bottom lines. +\newlength{\beamer@decolines@watermarkheightbottom} +\addtolength{\beamer@decolines@watermarkheightbottom}{\beamer@decolines@lineup} +\addtolength{\beamer@decolines@watermarkheightbottom}{\beamer@decolines@linemid} +\addtolength{\beamer@decolines@watermarkheightbottom}{\beamer@decolines@linebottom} + +% The height of the watermark part over the 3 bottom lines before shrinking. +\newlength{\beamer@decolines@watermarkheightupperorig} +\setlength{\beamer@decolines@watermarkheightupperorig}{\beamer@decolines@watermarkheight} +\addtolength{\beamer@decolines@watermarkheightupperorig}{-\beamer@decolines@watermarkheightbottom} +\multiply\beamer@decolines@watermarkheightupperorig by \beamer@decolines@watermarkheightmult + +% % Footer. +% \defbeamertemplate*{footline}{decolines theme} +% { +% \leavevmode% +% % Page number. +% \hbox{% +% \begin{beamercolorbox}[wd=.2\paperwidth,ht=0ex,dp=0ex,center]{}% +% \usebeamerfont{palette primary}\insertframenumber{} \beamer@decolines@pageofpages{} \inserttotalframenumber% +% \end{beamercolorbox}% +% \begin{beamercolorbox}[wd=.8\paperwidth,ht=0ex,dp=0ex]{}% +% \end{beamercolorbox}% +% } % +% % First line. +% \hbox{% +% \begin{beamercolorbox}[wd=.2\paperwidth,ht=\beamer@decolines@lineup,dp=0pt]{}% +% \end{beamercolorbox}% +% \begin{beamercolorbox}[wd=.8\paperwidth,ht=\beamer@decolines@lineup,dp=0pt]{lineup}% +% \end{beamercolorbox}% +% } % +% % Second line. +% \hbox{% +% \begin{beamercolorbox}[wd=\paperwidth,ht=\beamer@decolines@linemid,dp=0pt]{linemid}% +% \end{beamercolorbox}% +% } % +% % Third line. +% \hbox{% +% \begin{beamercolorbox}[wd=.1\paperwidth,ht=\beamer@decolines@linebottom,dp=0pt]{}% +% \end{beamercolorbox}% +% \begin{beamercolorbox}[wd=.9\paperwidth,ht=\beamer@decolines@linebottom,dp=0pt]{linebottom}% +% \end{beamercolorbox}% +% }% +% % This seems to fix some alignment problems with the watermark. It has to be +% % always applied if you do not want to see the footer moving up and down when +% % moving from a page with watermark to a page without or vice versa. +% \vskip-.5px% +% % Watermark. +% \if\beamer@decolines@watermark\@empty\else% +% \vskip-\beamer@decolines@watermarkheightbottom% +% \llap{\includegraphics[height=\beamer@decolines@watermarkheightbottom,clip=true,% +% trim=0pt 0pt 0pt \beamer@decolines@watermarkheightupperorig]{\beamer@decolines@watermark}\hskip-\paperwidth}% +% \fi% +% } + +\defbeamertemplate*{headline}{decolines theme} +{ + \leavevmode% + \hbox{% + \begin{beamercolorbox}[wd=\paperwidth,ht=\headerheight,dp=0pt]{page header}% + \end{beamercolorbox}% + } % + \vskip0pt% +} + +\defbeamertemplate*{frametitle}{decolines theme}[1][left] +{ + \ifbeamercolorempty[bg]{frametitle}{}{\nointerlineskip}% + \@tempdima=\textwidth% + \advance\@tempdima by\beamer@leftmargin% + \advance\@tempdima by\beamer@rightmargin% + \vbox{}\vskip-.5\beamer@leftmargin% + \begin{beamercolorbox}[sep=\beamer@leftmargin,#1,wd=\the\@tempdima]{} + \usebeamerfont{frametitle}\usebeamercolor[bg]{framesubtitle}% + \vbox{}\vskip0ex% + \if@tempswa\else\csname beamer@fte#1\endcsname\fi% + \strut\insertframetitle\strut\par% + {% + \ifx\insertframesubtitle\@empty% + \else% + {\usebeamerfont{framesubtitle}\usebeamercolor[bg]{framesubtitle}\insertframesubtitle\strut\par}% + \fi + }% + \vskip-1ex% + \if@tempswa\else\vskip-\beamer@leftmargin\fi + \end{beamercolorbox}% + \def\beamer@decolines@truetext{true}% + \ifx\beamer@decolines@titleline\beamer@decolines@truetext% + \vskip-.5\beamer@leftmargin% + \begin{beamercolorbox}[wd=\textwidth,ht=.1ex,dp=0ex]{linemid}% + \end{beamercolorbox}% + \fi +} + +% Frame title continuations, default +\defbeamertemplate*{frametitle continuation}{decolines theme}{(\insertcontinuationcount)} + + + +\defbeamertemplate*{sidebar right}{decolines theme} +{ + \vskip.1\beamer@leftmargin% + \llap{\insertlogo\hskip.5\beamer@leftmargin}% + \vfill% + \if\beamer@decolines@watermark\@empty\else% + \llap{\includegraphics[height=\beamer@decolines@watermarkheight]{\beamer@decolines@watermark}}% + \vskip-\beamer@decolines@watermarkheightbottom% + \fi +} + +\mode + diff --git a/Lectures_my/EMPP/2017/Lecture4/beamerthemeFlip.sty b/Lectures_my/EMPP/2017/Lecture4/beamerthemeFlip.sty new file mode 100755 index 0000000..a615ff5 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture4/beamerthemeFlip.sty @@ -0,0 +1,59 @@ +% Main style file for the BEAMER FLIP THEME 2012 +% Copyright 2012 by Flip Tanedo +% This file may be distributed and/or modified +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. +% +% Comments: This is still a work in progress. +% A good way to present: http://www.cs.hmc.edu/~oneill/freesoftware/pdftokeynote.html + +% \usepackage{beamerthemesplit} +\mode + + +%% These are the options that are fed in through the driver file +%% Some of them get passed on to the other theme files +\DeclareOptionBeamer{bullet}{\PassOptionsToPackage{bullet=#1}{beamerinnerthemeFlip}} +\DeclareOptionBeamer{bigpagenumber}{\PassOptionsToPackage{bigpagenumber}{beamerouterthemeFlip}} +\DeclareOptionBeamer{topline}[true]{\PassOptionsToPackage{topline=#1}{beamerouterthemeFlip}} +\DeclareOptionBeamer{shadow}[false]{\PassOptionsToPackage{shadow=#1}{beamerinnerthemeFlip}} + +\DeclareOptionBeamer{watermark}{\PassOptionsToPackage{watermark=#1}{beamerouterthemeFlip}} + +\ProcessOptionsBeamer + +\useinnertheme{Flip} % Calls beamerinnerthemeFlip.sty +\useoutertheme{Flip} % Calls beamerouterthemeFlip.sty +\usecolortheme{Flip} % Calls beamercolorthemeFlip.sty + + + +%%%%%%%%%%%%%%%%%%%%%%%% +% Background Gradient % +%%%%%%%%%%%%%%%%%%%%%%%% + + +%% Usually I would leave this on +%% However, there seems to be problems with XeLaTeX +%% http://tex.stackexchange.com/questions/29497/xelatex-preventing-beamer-from-using-different-backgrounds +\setbeamertemplate{background canvas}[vertical shading][bottom=blue!.1, middle=white, top=white] + +%% HOWEVER: it seems to make it impossible to change this later on in the document + + +%% For a dark background: +% \setbeamertemplate{background canvas}[vertical shading][bottom=keynotebottom, middle=keynotemiddle, top=keynotetop] + + +%% An alternate way: \beamertemplateshadingbackground{blue!.1}{red!2} +%% In general: you want the gradient to be subtle! + + +%%%%%%%%%%%%%%%%%%%%%%% +% Navigation symbols % +%%%%%%%%%%%%%%%%%%%%%%% + +\setbeamertemplate{navigation symbols}{} % Turns off PDF navigation symbols + +\mode +\endinput \ No newline at end of file diff --git a/Lectures_my/EMPP/2017/Lecture4/images/BG_lower.png b/Lectures_my/EMPP/2017/Lecture4/images/BG_lower.png new file mode 100755 index 0000000..073034a --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture4/images/BG_lower.png Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture4/images/FOAM.png b/Lectures_my/EMPP/2017/Lecture4/images/FOAM.png new file mode 100644 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a/Lectures_my/EMPP/2017/Lecture4/mchrzasz.synctex.gz b/Lectures_my/EMPP/2017/Lecture4/mchrzasz.synctex.gz new file mode 100644 index 0000000..c19bd1b --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture4/mchrzasz.synctex.gz Binary files differ diff --git a/Lectures_my/EMPP/2017/Lecture4/mchrzasz.tex b/Lectures_my/EMPP/2017/Lecture4/mchrzasz.tex new file mode 100644 index 0000000..747ff3b --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture4/mchrzasz.tex @@ -0,0 +1,496 @@ +\documentclass[11 pt,xcolor={dvipsnames,svgnames,x11names,table}]{beamer} + +\usepackage[english]{babel} +\usepackage{polski} +\usepackage[skins,theorems]{tcolorbox} +\tcbset{highlight math style={enhanced, + colframe=red,colback=white,arc=0pt,boxrule=1pt}} + +\usetheme[ + bullet=circle, % Other option: square + bigpagenumber, % circled page number on lower right + topline=true, % colored bar at the top of the frame + shadow=false, % Shading for beamer blocks + watermark=BG_lower, % png file for the watermark + ]{Flip} + +%\logo{\kern+1.em\includegraphics[height=1cm]{SHiP-3_LightCharcoal}} + + +\usepackage[lf]{berenis} +\usepackage[LY1]{fontenc} +\usepackage[utf8]{inputenc} + +\usepackage{emerald} +\usefonttheme{professionalfonts} +\usepackage[no-math]{fontspec} +\usepackage{listings} +\defaultfontfeatures{Mapping=tex-text} % This seems to be important for mapping glyphs properly + +\setmainfont{Gillius ADF} % Beamer ignores "main font" in favor of sans font +\setsansfont{Gillius ADF} % This is the font that beamer will use by default +% \setmainfont{Gill Sans Light} % Prettier, but harder to read + +\setbeamerfont{title}{family=\fontspec{Gillius ADF}} + +\input t1augie.fd + +%\newcommand{\handwriting}{\fontspec{augie}} % From Emerald City, free font +%\newcommand{\handwriting}{\usefont{T1}{fau}{m}{n}} % From Emerald City, free font +% \newcommand{\handwriting}{} % If you prefer no special handwriting font or don't have augie + +%% Gill Sans doesn't look very nice when boldfaced +%% This is a hack to use Helvetica instead +%% Usage: \textbf{\forbold some stuff} +%\newcommand{\forbold}{\fontspec{Arial}} + +\usepackage{graphicx} +\usepackage[export]{adjustbox} + +\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{amssymb} +\usepackage{bm} +\usepackage{colortbl} +\usepackage{mathrsfs} % For Weinberg-esque letters +\usepackage{cancel} % For "SUSY-breaking" symbol +\usepackage{slashed} % for slashed characters in math mode +\usepackage{bbm} % for \mathbbm{1} (unit matrix) +\usepackage{amsthm} % For theorem environment +\usepackage{multirow} % For multi row cells in table +\usepackage{arydshln} % For dashed lines in arrays and tables +\usepackage{siunitx} +\usepackage{xhfill} +\usepackage{grffile} +\usepackage{textpos} +\usepackage{subfigure} +\usepackage{tikz} +\usepackage{hyperref} +%\usepackage{hepparticles} +\usepackage[italic]{hepparticles} + +\usepackage{hepnicenames} + +% Drawing a line +\tikzstyle{lw} = [line width=20pt] +\newcommand{\topline}{% + \tikz[remember picture,overlay] {% + \draw[crimsonred] ([yshift=-23.5pt]current page.north west) + -- ([yshift=-23.5pt,xshift=\paperwidth]current page.north west);}} + + + +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +\usepackage{tikzfeynman} % For Feynman diagrams +\usetikzlibrary{arrows,shapes} +\usetikzlibrary{trees} +\usetikzlibrary{matrix,arrows} % For commutative diagram +% http://www.felixl.de/commu.pdf +\usetikzlibrary{positioning} % For "above of=" commands +\usetikzlibrary{calc,through} % For coordinates +\usetikzlibrary{decorations.pathreplacing} % For curly braces +% http://www.math.ucla.edu/~getreuer/tikz.html +\usepackage{pgffor} % For repeating patterns + +\usetikzlibrary{decorations.pathmorphing} % For Feynman Diagrams +\usetikzlibrary{decorations.markings} +\tikzset{ + % >=stealth', %% Uncomment for more conventional arrows + vector/.style={decorate, decoration={snake}, draw}, + provector/.style={decorate, decoration={snake,amplitude=2.5pt}, draw}, + antivector/.style={decorate, decoration={snake,amplitude=-2.5pt}, draw}, + fermion/.style={draw=gray, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow[draw=gray]{>}}}}, + fermionbar/.style={draw=gray, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow[draw=gray]{<}}}}, + fermionnoarrow/.style={draw=gray}, + gluon/.style={decorate, draw=black, + decoration={coil,amplitude=4pt, segment length=5pt}}, + scalar/.style={dashed,draw=black, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow[draw=black]{>}}}}, + scalarbar/.style={dashed,draw=black, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow[draw=black]{<}}}}, + scalarnoarrow/.style={dashed,draw=black}, + electron/.style={draw=black, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow[draw=black]{>}}}}, + bigvector/.style={decorate, decoration={snake,amplitude=4pt}, draw}, +} + +% TIKZ - for block diagrams, +% from http://www.texample.net/tikz/examples/control-system-principles/ +% \usetikzlibrary{shapes,arrows} +\tikzstyle{block} = [draw, rectangle, +minimum height=3em, minimum width=6em] + + + + +\usetikzlibrary{backgrounds} +\usetikzlibrary{mindmap,trees} % For mind map +\newcommand{\degree}{\ensuremath{^\circ}} +\newcommand{\E}{\mathrm{E}} +\newcommand{\Var}{\mathrm{Var}} +\newcommand{\Cov}{\mathrm{Cov}} +\newcommand\Ts{\rule{0pt}{2.6ex}} % Top strut +\newcommand\Bs{\rule[-1.2ex]{0pt}{0pt}} % Bottom strut + +\graphicspath{{images/}} % Put all images in this directory. Avoids clutter. + +% SOME COMMANDS THAT I FIND HANDY +% \renewcommand{\tilde}{\widetilde} % dinky tildes look silly, dosn't work with fontspec +%\newcommand{\comment}[1]{\textcolor{comment}{\footnotesize{#1}\normalsize}} % comment mild +%\newcommand{\Comment}[1]{\textcolor{Comment}{\footnotesize{#1}\normalsize}} % comment bold +%\newcommand{\COMMENT}[1]{\textcolor{COMMENT}{\footnotesize{#1}\normalsize}} % comment crazy bold +\newcommand{\Alert}[1]{\textcolor{Alert}{#1}} % louder alert +\newcommand{\ALERT}[1]{\textcolor{ALERT}{#1}} % loudest alert +%% "\alert" is already a beamer pre-defined +\newcommand*{\Scale}[2][4]{\scalebox{#1}{$#2$}}% + +\def\Put(#1,#2)#3{\leavevmode\makebox(0,0){\put(#1,#2){#3}}} + +\usepackage{gmp} +\usepackage[final]{feynmp-auto} + +\usepackage[backend=bibtex,style=numeric-comp,firstinits=true]{biblatex} +\bibliography{bib} +\setbeamertemplate{bibliography item}[text] + +\makeatletter\let\frametextheight\beamer@frametextheight\makeatother + +% suppress frame numbering for backup slides +% you always need the appendix for this! +\newcommand{\backupbegin}{ + \newcounter{framenumberappendix} + \setcounter{framenumberappendix}{\value{framenumber}} +} +\newcommand{\backupend}{ + \addtocounter{framenumberappendix}{-\value{framenumber}} + \addtocounter{framenumber}{\value{framenumberappendix}} +} + + +\definecolor{links}{HTML}{2A1B81} +%\hypersetup{colorlinks,linkcolor=,urlcolor=links} + +% For shapo's formulas: + +% For shapo's formulas: +\def\lsi{\raise0.3ex\hbox{$<$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}} +\def\gsi{\raise0.3ex\hbox{$>$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}} +\newcommand{\lsim}{\mathop{\lsi}} +\newcommand{\gsim}{\mathop{\gsi}} +\newcommand{\wt}{\widetilde} +%\newcommand{\ol}{\overline} +\newcommand{\Tr}{\rm{Tr}} +\newcommand{\tr}{\rm{tr}} +\newcommand{\eqn}[1]{&\hspace{-0.7em}#1\hspace{-0.7em}&} +\newcommand{\vev}[1]{\rm{$\langle #1 \rangle$}} +\newcommand{\abs}[1]{\rm{$\left| #1 \right|$}} +\newcommand{\eV}{\rm{eV}} +\newcommand{\keV}{\rm{keV}} +\newcommand{\GeV}{\rm{GeV}} +\newcommand{\im}{\rm{Im}} +\newcommand{\disp}{\displaystyle} +\def\be{\begin{equation}} +\def\ee{\end{equation}} +\def\ba{\begin{eqnarray}} +\def\ea{\end{eqnarray}} +\def\d{\partial} +\def\l{\left(} +\def\r{\right)} +\def\la{\langle} +\def\ra{\rangle} +\def\e{{\rm e}} +\def\Br{{\rm Br}} +\def\fixme{{\color{red} FIXME!}} +\def\mc{{\color{Magenta}{MC}}} +\def\pdf{{\rm p.d.f.}} +\def\cdf{{\rm c.d.f.}} +\def\ARROW{{\color{JungleGreen}{$\Rrightarrow$}}\xspace} +\def\ARROWR{{\color{WildStrawberry}{$\Rrightarrow$}}\xspace} + +\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (Universit\"{a}t Z\"{u}rich)} +\institute{UZH} +\title[Specific \pdf~generation]{Specific \pdf~generation} +\date{\fixme} +\newcommand*{\QEDA}{\hfill\ensuremath{\blacksquare}}% +\newcommand*{\QEDB}{\hfill\ensuremath{\square}}% + +\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (Universit\"{a}t Z\"{u}rich)} +\institute{UZH} +\title[Application of MC methods]{Application of MC methods} +\date{\fixme} + + +\begin{document} +\tikzstyle{every picture}+=[remember picture] + +{ +\setbeamertemplate{sidebar right}{\llap{\includegraphics[width=\paperwidth,height=\paperheight]{bubble2}}} +\begin{frame}[c]%{\phantom{title page}} +\begin{center} +\begin{center} + \begin{columns} + \begin{column}{0.9\textwidth} + \flushright\fontspec{Trebuchet MS}\bfseries \Huge {Application of MC methods} + \end{column} + \begin{column}{0.2\textwidth} + %\includegraphics[width=\textwidth]{SHiP-2} + \end{column} + \end{columns} +\end{center} + \quad + \vspace{3em} +\begin{columns} +\begin{column}{0.44\textwidth} +\flushright \vspace{-1.8em} {\fontspec{Trebuchet MS} \Large Marcin Chrząszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}} + +\end{column} +\begin{column}{0.53\textwidth} +\includegraphics[height=1.3cm]{uzh-transp} +\end{column} +\end{columns} + +\vspace{1em} +% \footnotesize\textcolor{gray}{With N. Serra, B. Storaci\\Thanks to the theory support from M. Shaposhnikov, D. Gorbunov}\normalsize\\ +\vspace{0.5em} + \textcolor{normal text.fg!50!Comment}{Experimental Methods in Particle Physics, \\ 12 October, 2016} + +\end{center} +\end{frame} +} + + + + + +\begin{frame}\frametitle{Classical methods of variance reduction} +\begin{footnotesize} + +\ARROW In Monte Carlo methods the statistical uncertainty is defined as: +\begin{align*} +\sigma = \dfrac{1}{\sqrt{N}}\sqrt{V(f)} +\end{align*} +\ARROW Obvious conclusion: +\begin{itemize} +\item To reduce the uncertainty one needs to increase $N$.\\ +$\rightrightarrows$ Slow convergence. In order to reduce the error by factor of 10 one needs to simulate factor of 100 more points! +\end{itemize} +\ARROW How ever the other handle ($V(f)$) can be changed! $\longrightarrow$ Lot's of theoretical effort goes\ + into reducing this factor.\\ +\ARROW We will discuss {\color{Mahogany}{four}} classical methods of variance reduction: +\begin{enumerate} +\item Stratified sampling. +\item Importance sampling. +\item Control variates. +\item Antithetic variates. +\end{enumerate} + + +\end{footnotesize} +\end{frame} + + + + +\begin{frame}\frametitle{Disadvantages of classical variance reduction methods} +\begin{footnotesize} + + \ARROW All aforementioned methods(beside the Stratified sampling) require knowledge of the integration function!\\ + \ARROW If you use the method in the incorrect way, you can easily get the opposite effect than intendant. \\ + + \ARROW Successful application of then require non negligible effort before running the program.\\ + \ARROW A natural solution would be that our program is ''smart'' enough that on his own, he will learn something about our function while he is trying to calculate the integral.\\ + \ARROW Similar techniques were already created for numerical integration!\\ +\ARROW Truly adaptive methods are nontrivial to code but are widely available in external packages as we will learn.\\ +\ARROW Naming conventions: +\begin{itemize} +\item Integration \mc - software that is able to compute JUST! integrals. +\item Generator \mc - software that BESIDES! beeing able to perform the integration is also capable of performing a generation of points accordingly to the integration function. +\end{itemize} + + + +\end{footnotesize} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Now the Foam algorithm +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{\texttt{FOAM} algorithm } +\begin{footnotesize} +\ARROW S.Jadach (2000), \href{http://arxiv.org/abs/physics/9910004}{arXiv:physics/9910004, Comp. Phys. Commun. 152 (2003) 55}. Adaptive method with recursive division of the integration domain in cells. \\ +\ARROW There are two algorithms in dividing the integration domain: +\begin{itemize} +\item Symplectic: Cells are sympleces(hiper-triangles). This method can be applied to not so large number of dimensions. $(\leq 5)$. +\item Qubic: Cells are hiper-cubes. This might be applied in higher number dimensions. $(\leq20)$. +\end{itemize} +\ARROW The algorithm: +\begin{itemize} +\item Exploration phase:\\ +The integration domain (hipper-cube) is divided recursively into cells. In each step only one cell is split. The splitting is not event! The procedure is stop when the number of cells reach a certain number that is set by us. One constructs an approximation function and based on this the integral is calculated. +\item Generation/Calculation Phase:\\ +We generate random points accordingly to the distribution of approximation function and the integral is calculated using the Importance sampling based on the approximation function. + +\end{itemize} + +\end{footnotesize} +\end{frame} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{\texttt{FOAM} algorithm } +\begin{footnotesize} +\begin{center} +\includegraphics[width=0.95\textwidth]{FOAM.png} +\end{center} +\end{footnotesize} +\end{frame} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{\texttt{FOAM} algorithm } +\begin{footnotesize} +\begin{center} +\includegraphics[width=0.75\textwidth]{FOAM2.png}\\ +\end{center} + +\end{footnotesize} +\end{frame} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Neumann-Ulam method} +\begin{itemize} +\item For example lets try to solve this equation system: +\end{itemize} +\begin{equation} +\overrightarrow{x} = +\left(\begin{array}{c} + 1.5 \\ +-1.0\\ +0.7 \end{array} \right) ++ +\left(\begin{array}{ccc} +0.2 & 0.3 & 0.1 \\ +0.4 & 0.3 & 0.2 \\ +0.3 & 0.1 & 0.1 \end{array} \right) \overrightarrow{x} + \nonumber +\end{equation} +\begin{itemize} +\item The solution is $\overrightarrow{x}_0 = (2.154303, 0.237389, 1.522255)$. +\end{itemize} +\begin{columns} + +\column{0.1in} + +\column{2.5in} +\begin{itemize} +\item The propability matrix $h_{ij}$ has the shape: +\end{itemize} +\begin{tabular}{|c|cccc|} +\hline +$i/j$ & 1 & 2 & 3 & 0 \\ \hline +1 & 0.2 & 0.3 & 0.1 & 0.4 \\ +2 & 0.4 & 0.3 & 0.2 & 0.1 \\ +3 & 0.3 & 0.1 & 0.1 & 0.5 \\ \hline +\end{tabular} + +\column{2.5in} +\begin{itemize} +\item An example solution: +\end{itemize} +\includegraphics[width=0.95\textwidth]{images/mark.png} + +\end{columns} + + +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Neumann-Ulam dual method} +\begin{itemize} +\item Let's try to solve the equation system: +\end{itemize} +\begin{equation} +\overrightarrow{x} = +\left(\begin{array}{c} + 1.5 \\ +-1.0\\ +0.7 \end{array} \right) ++ +\left(\begin{array}{ccc} +0.2 & 0.3 & 0.1 \\ +0.4 & 0.3 & 0.2 \\ +0.1 & 0.1 & 0.1 \end{array} \right) \overrightarrow{x} + \nonumber +\end{equation} +\begin{itemize} +\item The solution is: $\overrightarrow{x}_0 = (2.0, 0.0, 1.0)$. +\item Let's put the initial probability as constant: +\end{itemize} +\begin{equation} +q_1=q_2=q_3=\dfrac{1}{3} \nonumber +\end{equation} +\begin{columns} + +\column{0.1in} + +\column{2.5in} +\begin{itemize} +\item The propability matrix $h_{ij}$ has the shape: +\end{itemize} +\begin{tabular}{|c|cccc|} +\hline +$i/j$ & 1 & 2 & 3 & 4 \\ \hline +1 & 0.2 & 0.4 & 0.1 & 0.3 \\ +2 & 0.3 & 0.3 & 0.1 & 0.3 \\ +3 & 0.1 & 0.2 & 0.1 & 0.6 \\ \hline +\end{tabular} + +\column{2.5in} +\begin{itemize} +\item An example solution: +\end{itemize} +\includegraphics[width=0.95\textwidth]{images/mark2.png} + +\end{columns} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +\begin{center} +\begin{huge} +Q \& A + +\end{huge} +\end{center} + + +\end{frame} + + + + + + +\backupbegin + +\begin{frame}\frametitle{Backup} + + +\end{frame} + +\backupend + +\end{document} diff --git a/Lectures_my/EMPP/2017/Lecture4/mchrzasz.toc b/Lectures_my/EMPP/2017/Lecture4/mchrzasz.toc new file mode 100644 index 0000000..429917f --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture4/mchrzasz.toc @@ -0,0 +1,5 @@ +\boolfalse {citerequest}\boolfalse {citetracker}\boolfalse {pagetracker}\boolfalse {backtracker}\relax +\defcounter {refsection}{0}\relax +\beamer@endinputifotherversion {3.24pt} +\defcounter {refsection}{0}\relax +\select@language {english} diff --git a/Lectures_my/EMPP/2017/Lecture4/tikzfeynman.sty b/Lectures_my/EMPP/2017/Lecture4/tikzfeynman.sty new file mode 100755 index 0000000..521fc65 --- /dev/null +++ b/Lectures_my/EMPP/2017/Lecture4/tikzfeynman.sty @@ -0,0 +1,43 @@ +% Tikz Feynman Diagrams +% by Flip Tanedo +% 4 January 2011, work in progress + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%% TIKZ - for drawing Feynman diagrams %%%% +%%% ... use with pdflatex %%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\usepackage{tikz} +\usetikzlibrary{arrows,shapes} +\usetikzlibrary{trees} +\usetikzlibrary{matrix,arrows} % For commutative diagram + % http://www.felixl.de/commu.pdf +\usetikzlibrary{positioning} % For "above of=" commands +\usetikzlibrary{calc,through} % For coordinates +\usetikzlibrary{decorations.pathreplacing} % For curly braces +\usepackage[tikz]{bclogo} % For cute logo boxes +\usepackage{pgffor} % For repeating patterns + +\usetikzlibrary{decorations.pathmorphing} % For Feynman Diagrams +\usetikzlibrary{decorations.markings} +\tikzset{ + % >=stealth', %% Different kind of arrows + vector/.style={decorate, decoration={snake}, draw}, + fermion/.style={postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow{>}}}}, + fermionbar/.style={draw, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow{<}}}}, + fermionnoarrow/.style={}, + gluon/.style={decorate, + decoration={coil,amplitude=4pt, segment length=5pt}}, + scalar/.style={dashed, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow{>}}}}, + scalarbar/.style={dashed, postaction={decorate}, + decoration={markings,mark=at position .55 with {\arrow{<}}}}, + scalarnoarrow/.style={dashed,draw}, +% +%% Special vectors (when you need to fine-tune wiggles) + provector/.style={decorate, decoration={snake,amplitude=2.5pt}, draw}, + antivector/.style={decorate, decoration={snake,amplitude=-2.5pt}, draw}, +} +