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https://github.com/vale981/bachelor_thesis
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some theme polish
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1 changed files with 82 additions and 51 deletions
113
talk/slides.tex
113
talk/slides.tex
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@ -12,17 +12,25 @@
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\usepackage[list=true, font=small,
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labelformat=brace, position=top]{subcaption}
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%\setbeameroption{show notes on second screen} %
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\addbibresource{thesis.bib}
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\graphicspath{ {figs/} }
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\usepackage{animate}
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\usetheme{Antibes}
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% \usepackage{eulerpx}
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\usepackage{ifdraft}
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% \usefonttheme[onlymath]{serif}
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\graphicspath{ {figs/} }
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\addbibresource{thesis.bib}
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\sisetup{separate-uncertainty = true}
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\usetheme{default}
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\usecolortheme{dolphin}
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\usefonttheme{professionalfonts}
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%\usepackage{newmathpx}
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\institute[TUD] % (optional)
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{
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IKTP, TU Dresden
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}
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\setbeamertemplate{itemize items}[default]
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\setbeamertemplate{enumerate items}[default]
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\AtBeginSection[]
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{
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\begin{frame}
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@ -30,17 +38,23 @@ labelformat=brace, position=top]{subcaption}
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\end{frame}
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}
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\AtBeginSubsection[
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{\frame<beamer>{%
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\tableofcontents[currentsection,currentsubsection]}}%
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]
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\AtBeginSubsection[]
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{
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\begin{frame}
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\tableofcontents[currentsubsection]
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\end{frame}
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}
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\setbeamertemplate{footline}[frame number]
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\setbeamertemplate{bibliography item}{\insertbiblabel} %% Remove book
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%% symbol from references and add
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%% number
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\setbeamertemplate{bibliography item}{\insertbiblabel}
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\newtheorem{results}{Results}
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\newenvironment<>{results}[1][Results]{%
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\setbeamercolor{block example}{fg=white,bg=red!75!black}%
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\begin{exampleblock}#2{#1}}{\end{exampleblock}}
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\sisetup{separate-uncertainty = true}
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% Macros
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%% qqgg
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@ -232,7 +246,7 @@ labelformat=brace, position=top]{subcaption}
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\subsection{Result}
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\begin{frame}
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\begin{frame}{Result}
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\begin{equation}
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\label{eq:averagedm_final}
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\langle\abs{\mathcal{M}}^2\rangle = \frac{4}{3}(gZ)^4
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@ -352,11 +366,12 @@ labelformat=brace, position=top]{subcaption}
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\begin{frame}{Naive Integration Change of Variables}
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Choose \(\rho(\vb{x}) = \frac{1}{\abs{\Omega}}\)
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\onslide<2->{\(\implies I=\frac{\abs{\Omega}}{N}\sum_{i=1}^N
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\onslide<1->{\(\implies I=\frac{\abs{\Omega}}{N}\sum_{i=1}^N
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f(\vb{x_i})=\abs{\Omega}\cdot\bar{f}\) and
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\(\VAR{\frac{F}{P}}\approx\frac{\abs{\Omega}^2}{N-1}\sum_{i}\qty[f(\vb{x}_i)
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- \bar{f}]^2\)}
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\begin{block}{Results}
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\pause
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\begin{results}
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\begin{itemize}
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\item<3-> integrating \(\dv{\sigma}{\theta}\) with target error of
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\(\sigma = \SI{1e-3}{\pico\barn}\) takes
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@ -364,15 +379,15 @@ labelformat=brace, position=top]{subcaption}
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\item<4-> integrating \(\dv{\sigma}{\eta}\) takes just
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\result{xs/python/xs_mc_eta_N} samples
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\end{itemize}
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\end{block}
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\end{results}
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\begin{figure}[hb]
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\centering \onslide<3->{
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\begin{subfigure}[c]{.4\textwidth}
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\centering \plot[scale=.6]{xs/xs_integrand}
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\begin{subfigure}[c]{.41\textwidth}
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\centering \plot[width=\columnwidth]{xs/xs_integrand}
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\end{subfigure}
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} \onslide<4->{
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\begin{subfigure}[c]{.4\textwidth}
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\centering \plot[scale=.6]{xs/xs_integrand_eta}
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\begin{subfigure}[c]{.41\textwidth}
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\centering \plot[width=\columnwidth]{xs/xs_integrand_eta}
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\end{subfigure}
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}
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\end{figure}
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@ -396,11 +411,13 @@ labelformat=brace, position=top]{subcaption}
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\end{enumerate}
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\end{block}
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\pause
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\begin{block}{Result}
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Total function evaluations:
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\begin{results}
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\begin{itemize}
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\item Total function evaluations:
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\result{xs/python/xs_mc_θ_vegas_N}\\
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(for same accuracy as before)
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\end{block}
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\end{itemize}
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\end{results}
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\end{column}
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\begin{column}{.5\textwidth}
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\begin{figure}[ht]
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@ -468,27 +485,29 @@ labelformat=brace, position=top]{subcaption}
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\end{itemize}
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\end{block}
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\begin{block}<+->{Results with \(g=f_{\text{max}}\) }
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\begin{results}<+->[Results with \(g=f_{\text{max}}\)]
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\begin{itemize}[<+->]
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\item<.-> sampling \(\dv{\sigma}{\cos\theta}\):
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\result{xs/python/naive_th_samp}
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\item sampling \(\dv{\sigma}{\eta}\):
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\result{xs/python/eta_eff}
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\end{itemize}
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\end{block}
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\end{results}
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\end{frame}
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\begin{frame}{Hit or Miss}
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\begin{columns}
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\begin{column}{.4\textwidth}
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\begin{block}<+->{Results with \(g=a\cdot x^2 + b\)} Modest
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efficiency gain: \result{xs/python/tuned_th_samp}
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\end{block}
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\begin{results}<+->[Results with \(g=a\cdot x^2 + b\)]
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\begin{itemize}
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\item<+-> Modest efficiency gain:
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\result{xs/python/tuned_th_samp}
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\item<+-> Of course, we can use \vegas\ to provide a better
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\(g\implies\) \result{xs/python/strat_th_samp}
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\pnote{Has problems, not discussing now.}
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\(g\implies\) \result{xs/python/strat_th_samp} \pnote{Has
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problems, not discussing now.}
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\end{itemize}
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\end{results}
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\end{column}
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\begin{column}{.6\textwidth}
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\begin{figure}[ht]
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@ -501,18 +520,32 @@ labelformat=brace, position=top]{subcaption}
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\end{frame}
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\begin{frame}{Stratified Sampling}
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\begin{columns}
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\begin{column}{.6\textwidth}
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\begin{block}{Basic Idea}
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\begin{itemize}
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\item subdivide sampling volume \(\Omega\) into \(K\) subvolumes
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\(\Omega_i\)
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\item subdivide sampling volume \(\Omega\) into \(K\)
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subvolumes \(\Omega_i\)
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\item let \(A_i = \int_{\Omega_i}f(x)\dd{x}\)
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\item take \(N_i=\frac{A_i}{\sum_jA_j} \cdot N\) samples in each subvolume
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\item take \(N_i=\frac{A_i}{\sum_jA_j} \cdot N\) samples in
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each subvolume
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\item efficiency is given by:
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\(\mathfrak{e} = \frac{\sum_i A_i}{\sum_i A_i/\mathfrak{e}_i}\)
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\(\mathfrak{e} = \frac{\sum_i A_i}{\sum_i
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A_i/\mathfrak{e}_i}\)
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\end{itemize}
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\(\implies\) can optimize in each subvolume independently
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\end{block}
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How do choose the \(\Omega_i\)? \pause {\huge\vegas! :-)}
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\end{column}
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\pause
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\begin{column}{.4\textwidth}
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\begin{center}
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{\LARGE
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How do we choose the \(\Omega_i\)? \pause\\
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\vspace{1em}
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\(\implies\) \vegas! :-) }
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\end{center}
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\end{column}
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\end{columns}
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\end{frame}
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\begin{frame}{Observables}
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@ -528,12 +561,10 @@ labelformat=brace, position=top]{subcaption}
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\begin{figure}[p]
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\centering
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\begin{subfigure}[b]{.49\textwidth}
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\centering \plot[scale=.5]{xs_sampling/histo_sherpa_eta}
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\caption{histogram of the pseudo-rapidity (\(\eta\))}
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\centering \plot[scale=.7]{xs_sampling/histo_sherpa_eta}
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\end{subfigure}
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\begin{subfigure}[b]{.49\textwidth}
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\centering \plot[scale=.5]{xs_sampling/histo_sherpa_pt}
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\caption{histogram of the transverse momentum (\(\pt\))}
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\centering \plot[scale=.7]{xs_sampling/histo_sherpa_pt}
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\end{subfigure}
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\end{figure}
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\end{frame}
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