diff --git a/Lectures_my/MC_2016/Lecture1/mchrzasz.log b/Lectures_my/MC_2016/Lecture1/mchrzasz.log index ba9cccd..4724d9e 100644 --- a/Lectures_my/MC_2016/Lecture1/mchrzasz.log +++ b/Lectures_my/MC_2016/Lecture1/mchrzasz.log @@ -1,4 +1,4 @@ -This is XeTeX, Version 3.1415926-2.5-0.9999.3 (TeX Live 2013/Debian) (format=xelatex 2015.4.1) 25 FEB 2016 09:55 +This is XeTeX, Version 3.1415926-2.5-0.9999.3 (TeX Live 2013/Debian) (format=xelatex 2015.4.1) 3 MAR 2016 21:43 entering extended mode restricted \write18 enabled. %&-line parsing enabled. diff --git a/Lectures_my/MC_2016/Lecture1/mchrzasz.pdf b/Lectures_my/MC_2016/Lecture1/mchrzasz.pdf index 72b9786..e92de7e 100644 --- a/Lectures_my/MC_2016/Lecture1/mchrzasz.pdf +++ b/Lectures_my/MC_2016/Lecture1/mchrzasz.pdf Binary files differ diff --git a/Lectures_my/MC_2016/Lecture1/mchrzasz.tex b/Lectures_my/MC_2016/Lecture1/mchrzasz.tex index 8aa468c..6f060ef 100644 --- a/Lectures_my/MC_2016/Lecture1/mchrzasz.tex +++ b/Lectures_my/MC_2016/Lecture1/mchrzasz.tex @@ -626,7 +626,7 @@ \ARROW E(1.5) Calculate the above.\\ \ARROW From above we get: \begin{equation} -\dfrac{R_n-n/12}{\sqrt{n/12}} \xrightarrow{N\to \infty} N(0,1).\nonumber +\dfrac{R_n-n/2}{\sqrt{n/12}} \xrightarrow{N\to \infty} N(0,1).\nonumber \end{equation} aka we get a Gaussian distribution. \ARROW For $n=12$ $\Rightarrow~(R_{12}-6)$ ''practical'' Gauss generator.\\ diff --git a/Lectures_my/MC_2016/Lecture2/Makefile b/Lectures_my/MC_2016/Lecture2/Makefile new file mode 100644 index 0000000..e4cf8e8 --- /dev/null +++ b/Lectures_my/MC_2016/Lecture2/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/MC_2016/Lecture2/beamercolorthemeFlip.sty b/Lectures_my/MC_2016/Lecture2/beamercolorthemeFlip.sty new file mode 100755 index 0000000..d6b9c50 --- /dev/null +++ b/Lectures_my/MC_2016/Lecture2/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/MC_2016/Lecture2/beamerinnerthemeFlip.sty b/Lectures_my/MC_2016/Lecture2/beamerinnerthemeFlip.sty new file mode 100755 index 0000000..9910f4d --- /dev/null +++ b/Lectures_my/MC_2016/Lecture2/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/MC_2016/Lecture2/beamerouterthemeFlip.sty b/Lectures_my/MC_2016/Lecture2/beamerouterthemeFlip.sty new file mode 100755 index 0000000..d12f6d6 --- /dev/null +++ b/Lectures_my/MC_2016/Lecture2/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/MC_2016/Lecture2/beamerouterthemedecolines.sty b/Lectures_my/MC_2016/Lecture2/beamerouterthemedecolines.sty new file mode 100755 index 0000000..669e493 --- /dev/null +++ b/Lectures_my/MC_2016/Lecture2/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/MC_2016/Lecture2/beamerthemeFlip.sty b/Lectures_my/MC_2016/Lecture2/beamerthemeFlip.sty new file mode 100755 index 0000000..a615ff5 --- /dev/null +++ b/Lectures_my/MC_2016/Lecture2/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/MC_2016/Lecture2/images/buff.png b/Lectures_my/MC_2016/Lecture2/images/buff.png new file mode 100644 index 0000000..2bc83bd --- /dev/null +++ b/Lectures_my/MC_2016/Lecture2/images/buff.png Binary files differ diff --git a/Lectures_my/MC_2016/Lecture2/mchrzasz+mp.sh b/Lectures_my/MC_2016/Lecture2/mchrzasz+mp.sh new file mode 100644 index 0000000..1a24852 --- /dev/null +++ b/Lectures_my/MC_2016/Lecture2/mchrzasz+mp.sh @@ -0,0 +1 @@ +#!/bin/sh diff --git a/Lectures_my/MC_2016/Lecture2/mchrzasz-blx.bib b/Lectures_my/MC_2016/Lecture2/mchrzasz-blx.bib new file mode 100644 index 0000000..9e405b3 --- /dev/null +++ b/Lectures_my/MC_2016/Lecture2/mchrzasz-blx.bib @@ -0,0 +1,11 @@ +@Comment{$ biblatex control file $} +@Comment{$ biblatex version 2.3 $} +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 = {2.3:0:0:1:0:0:1:1:0:0:0:0:1:1:3:1:79:+}, +} diff --git a/Lectures_my/MC_2016/Lecture2/mchrzasz.aux b/Lectures_my/MC_2016/Lecture2/mchrzasz.aux new file mode 100644 index 0000000..3cf1eab --- /dev/null +++ b/Lectures_my/MC_2016/Lecture2/mchrzasz.aux @@ -0,0 +1,172 @@ +\relax +\providecommand\hyper@newdestlabel[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} +\providecommand*\HyPL@Entry[1]{} +\bibstyle{biblatex} 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b/Lectures_my/MC_2016/Lecture2/mchrzasz.out diff --git a/Lectures_my/MC_2016/Lecture2/mchrzasz.pdf b/Lectures_my/MC_2016/Lecture2/mchrzasz.pdf new file mode 100644 index 0000000..762e98a --- /dev/null +++ b/Lectures_my/MC_2016/Lecture2/mchrzasz.pdf Binary files differ diff --git a/Lectures_my/MC_2016/Lecture2/mchrzasz.run.xml b/Lectures_my/MC_2016/Lecture2/mchrzasz.run.xml new file mode 100644 index 0000000..3368f59 --- /dev/null +++ b/Lectures_my/MC_2016/Lecture2/mchrzasz.run.xml @@ -0,0 +1,91 @@ + + + + + + + + + + + + + + + + + + + + + + + + +]> + + + latex + + mchrzasz.aux + mchrzasz-blx.bib + + + mchrzasz.bbl + + + blx-compat.def + biblatex.def + numeric-comp.bbx + numeric.bbx + standard.bbx + numeric-comp.cbx + biblatex.cfg + english.lbx + + + + bibtex + + bibtex + + mchrzasz + + + mchrzasz.aux + + + mchrzasz.bbl + + + mchrzasz.bbl + + + mchrzasz.aux + mchrzasz-blx.bib + + + bib.bib + + + biblatex.bst + + + diff --git a/Lectures_my/MC_2016/Lecture2/mchrzasz.snm b/Lectures_my/MC_2016/Lecture2/mchrzasz.snm new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/Lectures_my/MC_2016/Lecture2/mchrzasz.snm diff --git a/Lectures_my/MC_2016/Lecture2/mchrzasz.tex b/Lectures_my/MC_2016/Lecture2/mchrzasz.tex index d0c78f3..80c4022 100644 --- a/Lectures_my/MC_2016/Lecture2/mchrzasz.tex +++ b/Lectures_my/MC_2016/Lecture2/mchrzasz.tex @@ -205,7 +205,7 @@ \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} +\title[Monte Carlo integration and variance reduction]{Monte Carlo integration and variance reduction} \date{\fixme} @@ -219,7 +219,7 @@ \begin{center} \begin{columns} \begin{column}{0.9\textwidth} - \flushright\fontspec{Trebuchet MS}\bfseries \Huge {Introduction to \\Monte Carlo methods} + \flushright\fontspec{Trebuchet MS}\bfseries \Huge {Monte Carlo integration\\ and variance reduction} \end{column} \begin{column}{0.2\textwidth} %\includegraphics[width=\textwidth]{SHiP-2} @@ -418,7 +418,7 @@ \ARROW The probability is described by the Bernoulli distribution: \begin{equation} -\mathcal{P}(n) = \binom{n}{k} P^n (1-P)^{N-n}, \nonumber +\mathcal{P}(n) = \binom{N}{n} P^n (1-P)^{N-n}, \nonumber \end{equation} where $P$ is the probability of success, N is the number of trials and n is the number of successes.\\ \ARROW The following are true: @@ -430,7 +430,7 @@ \end{equation} \ARROW Translating this into probability basis: \begin{equation} -E(\hat{P})=P,{~}{~}V(\hat{P})\dfrac{P(1-P)}{N}. \nonumber +E(\hat{P})=P,{~}{~}V(\hat{P})=\dfrac{P(1-P)}{N}. \nonumber \end{equation} \ARROW E2.1 prove the above. @@ -521,17 +521,17 @@ I=\int_0^1f(x)dx,~{\rm{and~}}0\leq f(x)\leq 1 {~} \forall x \in (0,1) \nonumber \end{equation} \ARROW The variation for the ''hit-or-miss''(HM) method: $V(\hat{I}_{HM})=\dfrac{1}{N}(I-I^2)$ -\ARROW The variation for the crude method: $V(\hat{I}_{HM})=\dfrac{1}{N}[\int_0^1 f^2(x)dx-I^2]$ +\ARROW The variation for the crude method: $V(\hat{I}_{Crude})=\dfrac{1}{N}[\int_0^1 f^2(x)dx-I^2]$ \ARROW Now the difference: \begin{align*} -V(\hat{I}_{HM}) - V(\hat{I}_{HM})= \dfrac{1}{N}[I-\int_0^1 f^2(x)dx]= \dfrac{1}{N}\int_0^1 f(x)[1-f(x)]dx\geq 0~{\rm{q.e.d}} +V(\hat{I}_{HM}) - V(\hat{I}_{Crude})= \dfrac{1}{N}[I-\int_0^1 f^2(x)dx]= \dfrac{1}{N}\int_0^1 f(x)[1-f(x)]dx\geq 0~{\rm{q.e.d}} \end{align*} \ARROW E2.3 Calculate the following integrals with uncertainties using ''hit or miss'' and crude methods: \begin{equation} -\int_0^1 \dfrac{1}{\sqrt{2\pi}} e^{-\dfrac{x^2}{2}} dxd \nonumber +\int_0^1 dx \dfrac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}} \nonumber \end{equation} \begin{equation} -\int_{x^2+y^2\leq 1} \dfrac{1}{4}\sqrt{1-(x^2+y^2)} dx dy\nonumber +\int_{x^2+y^2\leq 1} \dfrac{1}{4}\sqrt{1-(x^2+y^2)} dx dy \nonumber \end{equation} @@ -573,7 +573,7 @@ $\Omega \subset \mathcal{R}^n$ - some subspace in the n-dim space.\\ $V\equiv(\Omega)$ - volume of the $\Omega$ subspaces. \begin{equation} -I=\int_{\Omega} = \int_{\Omega} dx \int_{0}{f_{max}} dy \Theta(f(x)-y)=Vf_{max} \int_{\Omega} \dfrac{dx}{V} \int_{0}^{f_{max}} \dfrac{dy}{f_{max}} \Theta(f(x)-y) \nonumber +I = \int_{\Omega} dx \int_{0}^{f_{max}} dy \Theta(f(x)-y)=Vf_{max} \int_{\Omega} \dfrac{dx}{V} \int_{0}^{f_{max}} \dfrac{dy}{f_{max}} \Theta(f(x)-y) \nonumber \end{equation} where $(x,y)\in \mathcal{U}(\Omega \times [0,f_{max}]$. \ARROW Now we define $K$: @@ -599,7 +599,7 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame}\frametitle{Crude MC vs ”Hit and mishit”} +\begin{frame}\frametitle{Crude MC vs ”Hit and misss”} $\Rrightarrow$ We can repeat a toy MC studies as we did in the Euler needle case.\\ $\hookrightarrow$ In this example we want to calculate $\int_0^{\pi/2} \cos x dx$ @@ -699,6 +699,9 @@ Variance: $V(\hat{I})=\sum_{j=1}^k \dfrac{w_j^2}{n_j}V_j(f)$, \column{3in} + + + and it's estimator: $\hat{V} (\hat{I}) = \sum_{j=1}^k \dfrac{w_j^2}{n_j} \hat{V}_j(f)$ \end{columns} @@ -706,6 +709,61 @@ \end{footnotesize} \end{frame} + +\begin{frame}\frametitle{Stratified sampling in practice} +\begin{footnotesize} + \begin{exampleblock}{~} +One can show that splitting the integration region $\Omega$ into equal regions will not increase the variance! + \end{exampleblock} + \ARROW For example in case of two sub samples: +\begin{align*} +V(I_{{\rm{crude}}}) - V(I_{{\rm{SS}}}) = \dfrac{1}{N}\left[\int_{\omega_1} f(x)dx - \int_{\omega_2} f(x) dx \right]^{-2} \geq 0 +\end{align*} +{\color{red}{A2.1} Prove the above.} + \begin{exampleblock}{Practical advise:} +If we know very little about the integrating function the equal splitting of the $\Omega$ space is the best option! + \end{exampleblock} + + + +\end{footnotesize} +\end{frame} + + + + +\begin{frame}\frametitle{Stratified sampling for the Buffon needle} +\begin{footnotesize} +\ARROW Lets apply our Stratified sampling to my favourite :) Buffon needle with 5 samples. +\begin{columns} +\column{2in} +\includegraphics[width=0.95\textwidth]{images/buff.png} +\column{3in} +\ARROW We have $\omega_i=\Omega/5 = \dfrac{\pi}{10}$ and $n_i=\dfrac{N}{5}$.\\ +\ARROW The integral estimator: +\begin{align*} +\hat{P}=\dfrac{1}{\Omega}\sum_{j=1}^5 \sum_{i=1}^{N/5} p(x_i^j)=\dfrac{1}{N}\sum_{i=1}^N p(x_i) +\end{align*} +\ARROW The standard deviation (for $l=L$): +\begin{align*} +\sigma(\hat{\pi})_{SS} = \dfrac{0.34}{\sqrt{N}} < \sigma(\hat{\pi})_{Crude} = \dfrac{1.52}{\sqrt{N}} +\end{align*} +\end{columns} +\ARROW In the following example we generated a constant number of events ($N/5$) for each subsample independently of their impact on the integral.\\ +\ARROW We can improve this by generating events in each of the sub sample accordingly to the area of the blue rectangle.\\ +\ARROW E2.4 Using the Stratified Sampling please calculate the integrals from E2.3 by dividing the are into 5 samples. Compute the errors and compare them to the ones obtained from the Crude method. + + +\end{footnotesize} +\end{frame} + + + + + + + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}\frametitle{Importance sampling} @@ -777,7 +835,7 @@ \end{itemize} \end{itemize} - +\ARROW Calculate the first function from E2.3 using the importance sampling. As a weight function $g(x)$ take a linear function. \end{footnotesize} \end{frame} diff --git a/Lectures_my/MC_2016/Lecture2/mchrzasz.toc b/Lectures_my/MC_2016/Lecture2/mchrzasz.toc new file mode 100644 index 0000000..429917f --- /dev/null +++ b/Lectures_my/MC_2016/Lecture2/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/MC_2016/Lecture2/tikzfeynman.sty b/Lectures_my/MC_2016/Lecture2/tikzfeynman.sty new file mode 100755 index 0000000..521fc65 --- /dev/null +++ b/Lectures_my/MC_2016/Lecture2/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}, +} +