diff --git a/Lectures_my/EMPP/2016/Lecture4/Exercises/Error_propagation/result.png b/Lectures_my/EMPP/2016/Lecture4/Exercises/Error_propagation/result.png
new file mode 100644
index 0000000..86e4ebe
--- /dev/null
+++ b/Lectures_my/EMPP/2016/Lecture4/Exercises/Error_propagation/result.png
Binary files differ
diff --git a/Lectures_my/EMPP/2016/Lecture4/Exercises/Integration_FOAM/foam_kanwa.C b/Lectures_my/EMPP/2016/Lecture4/Exercises/Integration_FOAM/foam_kanwa.C
new file mode 100755
index 0000000..138b29d
--- /dev/null
+++ b/Lectures_my/EMPP/2016/Lecture4/Exercises/Integration_FOAM/foam_kanwa.C
@@ -0,0 +1,167 @@
+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=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 kanwa(){
+ // TH2D *hst_xy = new TH2D("hst_xy" , "x-y plot", 50,0,1.0, 50,0,1.0);
+ Double_t *MCvect =new Double_t[2]; // 2-dim vector generated in the MC run
+ TRandom3 *PseRan = new TRandom3(); // Create random number generator
+ PseRan->SetSeed(4357); // Set seed
+ TFoam *FoamX = new TFoam("FoamX"); // Create Simulator
+ FoamX->SetkDim(2); // No. of dimensions, obligatory!
+ FoamX->SetnCells(500); // No. of cells, can be omitted, default=2000
+ FoamX->SetRhoInt(Camel2); // Set 2-dim distribution, included below
+ FoamX->SetPseRan(PseRan); // Set random number generator
+ FoamX->Initialize(); // Initialize simulator, takes a few seconds...
+ // From now on FoamX is ready to generate events according to Camel2(x,y)
+ for(Long_t 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); // fill scattergram
+ }// loop
+ Double_t mcResult, mcError;
+ FoamX->GetIntegMC( mcResult, mcError); // get MC integral, should be one
+ cout << " mcResult= " << mcResult << " +- " << mcError <cd();
+ // hst_xy->Draw("lego2");
+ return 1;
+}//kanwa
+
+
+double phi(int n, double *Xarg)
+{
+ double x=Xarg[0];
+ return exp(-x*x/2.)/sqrt(TMath::Pi()*2);
+}
+void PhimFoam()
+{
+ TRandom3 *PseRan = new TRandom3(); // Create random number generator
+ TFoam *FoamX = new TFoam("FoamX"); // Create Simulator
+ FoamX->SetkDim(1); // No. of dimensions, obligatory!
+ FoamX->SetRhoInt(phi); // Set 1-dim distribution, included below
+ FoamX->SetPseRan(PseRan); // Set random number generator
+ FoamX->Initialize(); // Initialize simulator, takes a few seconds...
+
+ for(Long_t 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); // fill scattergram
+ }
+ Double_t mcResult, mcError;
+ FoamX->GetIntegMC(mcResult,mcError); // get MC integral, should be one
+ cout<<"wartosc= "<Rndm();
+ wartf[i]=(f(x)+f(1.-x))/2.;
+ }
+ for(int i=0;iRndm();
+ wartf[i]=fsubg(x);
+ }
+ for(int i=0;iRndm());
+ double P;//P=(exp(-0.5)-1)*q*q/(2*sqrt(2*TMath::Pi()))+q/(2*sqrt(2*TMath::Pi()));
+ double a=2.*(exp(-0.5)/sqrt(2*TMath::Pi())-1.);
+ double b=2.-exp(-0.5)/sqrt(2*TMath::Pi());
+ while(1)
+ {
+
+ q=gRandom->Rndm();
+ // P=(exp(-0.5)-1)*q*q/(2*sqrt(2*TMath::Pi()))+q/(2*sqrt(2*TMath::Pi()));
+ P=a*q*q/2.+b*q;
+ // if((gRandom->Rndm()*(1+exp(-0.5))/(2*sqrt(2*TMath::Pi())))Rndm()
+\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/2016/Lecture4/beamerinnerthemeFlip.sty b/Lectures_my/EMPP/2016/Lecture4/beamerinnerthemeFlip.sty
new file mode 100755
index 0000000..9910f4d
--- /dev/null
+++ b/Lectures_my/EMPP/2016/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/2016/Lecture4/beamerouterthemeFlip.sty b/Lectures_my/EMPP/2016/Lecture4/beamerouterthemeFlip.sty
new file mode 100755
index 0000000..d12f6d6
--- /dev/null
+++ b/Lectures_my/EMPP/2016/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/2016/Lecture4/beamerouterthemedecolines.sty b/Lectures_my/EMPP/2016/Lecture4/beamerouterthemedecolines.sty
new file mode 100755
index 0000000..669e493
--- /dev/null
+++ b/Lectures_my/EMPP/2016/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/2016/Lecture4/beamerthemeFlip.sty b/Lectures_my/EMPP/2016/Lecture4/beamerthemeFlip.sty
new file mode 100755
index 0000000..a615ff5
--- /dev/null
+++ b/Lectures_my/EMPP/2016/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
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+\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/2016/Lecture4/mchrzasz.toc b/Lectures_my/EMPP/2016/Lecture4/mchrzasz.toc
new file mode 100644
index 0000000..429917f
--- /dev/null
+++ b/Lectures_my/EMPP/2016/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/2016/Lecture4/tikzfeynman.sty b/Lectures_my/EMPP/2016/Lecture4/tikzfeynman.sty
new file mode 100755
index 0000000..521fc65
--- /dev/null
+++ b/Lectures_my/EMPP/2016/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},
+}
+