\begin
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% Bayes Business School, City St George's, University of London.
% LaTeX Presentation Template
% Author: Emilio Luis Sáenz Guillén
% Email: emilio.saenz-guillen@bayes.city.ac.uk
% Webpage: emilioluissaenzguillen.github.io
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Requires compilation with XeLaTeX or LuaLaTeX
\documentclass[10pt,table,dvipsnames, t, compress, aspectratio=169]{beamer}
%% Packages
\usepackage{tikz} % Load TikZ for creating graphics
\usetikzlibrary{tikzmark,calc,arrows.meta,shapes.arrows,decorations.pathreplacing}
% tikzmark: mark locations in the document
% calc: do coordinate calculations in TikZ
% arrows.meta: customize arrow styles
% shapes.arrows: predefined arrow shapes for nodes
% decorations.pathreplacing: decorate or replace paths (e.g., with brackets)
\usepackage{caption, subcaption, bbm, mathtools, amsmath, lmodern}
\usepackage{graphicx, amssymb, cancel, pifont, bm}
\usefonttheme[onlymath]{serif}
% Bibliography
\usepackage[style=apa, backend=biber]{biblatex}
\addbibresource{sn-bibliography.bib}
% Theme
\usetheme{BayesBusinessSchool}
% Hyperref
\usepackage{hyperref}
% url in blue
\newcommand{\bluehref}[2]{%
\begingroup
\hypersetup{urlcolor=blue}%
\href{#1}{\color{blue}#2}%
\endgroup
}
% Color box
\usepackage{xcolor}
\usepackage{tcolorbox}
\newtcolorbox{mybox}{colback=BayesVeryLightGreen, colframe=BayesGreen, width=0.9\linewidth}
%% Math shortcut functions
% up/down arrow for math mode
\NewDocumentCommand{\overarrow}{O{=} O{\uparrow} m}{%
\overset{\makebox[0pt]{\begin{tabular}{@{}c@{}}#3\\[0pt]\ensuremath{#2}\end{tabular}}}{#1}
}
\NewDocumentCommand{\underarrow}{O{=} O{\downarrow} m}{%
\underset{\makebox[0pt]{\begin{tabular}{@{}c@{}}\ensuremath{#2}\\[0pt]#3\end{tabular}}}{#1}
}
% argmin/argmax operator
\DeclareMathOperator*{\argmin}{argmin}
\DeclareMathOperator*{\argmax}{argmax}
% permutation and combination
\newcommand\Myperm[2][n]{\prescript{^{#1}\mkern-2.5mu}{}P_{#2}}
\newcommand\Mycomb[2][n]{\prescript{^{#1}\mkern-0.5mu}{}C_{#2}}
% sign operator
\DeclareMathOperator{\sign}{sign}
% expectation operator
\DeclareMathOperator{\EX}{\mathbb{E}}
% sin, cos and tan with parentheses
\makeatletter
\newcommand*{\redefinesymbolwitharg}[1]{%
\expandafter\let\csname ltx#1\expandafter\endcsname\csname #1\endcsname
\@namedef{#1}{\@ifnextchar{^}{\@nameuse{#1@}}{\@nameuse{#1@}^{}}}%
\expandafter\def\csname #1@\endcsname^##1##2{%
\csname ltx#1\endcsname\ifx!##1!\else^{##1}\fi\mathopen{}\mathclose\bgroup\left(##2\aftergroup\egroup\right)
}%
}
\makeatother
\redefinesymbolwitharg{cos}
\redefinesymbolwitharg{sin}
\redefinesymbolwitharg{tan}
%% Title
\title{\textbf{\large Presentation Title}}
\author{Author Name}
\institute[Bayes Business School]{Faculty of Actuarial Science and Insurance,\\ Bayes Business School.}
\date{DD/MM/YYY}
\begin{document}
%----------------------------------------------------------------------------------------
% TITLE SLIDES
%----------------------------------------------------------------------------------------
% Select one of the 3 title slide types below and remove or comment out the others
%------------------------------------------------
% 1) Bunhill row background title slide
{
\usebackgroundtemplate{
\begin{tikzpicture}[remember picture, overlay]
\node[at=(current page.center)] { \includegraphics[width=\paperwidth,height=\paperheight,keepaspectratio]{background/City-St-Georges-Bayes-background-image-1_2024.jpg} % Use your image file here
};
\end{tikzpicture}
}
\begin{frame}[plain]
\titlepage
\end{frame}
}
% 2) Finsbury square background title slide (uncomment line 68 in beamerthemeBayesBusinessSchool.sty)
{
\usebackgroundtemplate{
\begin{tikzpicture}[remember picture, overlay]
\node[at=(current page.center)] { \includegraphics[width=\paperwidth,height=\paperheight,keepaspectratio]{background/City-St-Georges-Bayes-background-image-2_2024.jpg} % Use your image file here
};
\end{tikzpicture}
}
\begin{frame}[plain]
\titlepage
\end{frame}
}
% 3) Red background title slide example (uncomment line 68 in beamerthemeBayesBusinessSchool.sty)
{
\usebackgroundtemplate{
\begin{tikzpicture}[remember picture, overlay]
\node[at=(current page.center)] { \includegraphics[width=\paperwidth,height=\paperheight,keepaspectratio]{background/City-St-Georges-Bayes-background-image-3_2024.jpg} % Use your image file here
};
\end{tikzpicture}
}
\begin{frame}[plain]
\titlepage
\end{frame}
}
% Current section
\AtBeginSection[ ]
{
\begin{frame}{}
\tableofcontents[currentsection,currentsubsection,
sectionstyle=show/shaded]
\end{frame}
}
% Current subsection
\AtBeginSubsection[ ]
{
\begin{frame}{}
\tableofcontents[currentsection,currentsubsection,
sectionstyle=show/shaded]
\end{frame}
}
\smallframetitle
\section{Introduction}
\begin{frame}
\frametitle{\textbf{Administrative Details}}
\textbf{About myself:}
\begin{itemize}
\item Lorem ipsum dolor sit amet, consectetur adipiscing elit. Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
\item Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.
\item Email: \bluehref{dummy.email@domain.com}{dummy.email@domain.com}.\\
Personal website: \bluehref{https://loremipsum.example.com}{https://loremipsum.example.com}.
\end{itemize}
\pause
\textbf{Tutorials' details:}
\begin{itemize}
\item Cover around {\color{red}2-3} lorem ipsum questions every week.
\item Requirement: be \textit{minimally} familiar with the lorem ipsum dolor sit amet, and, if possible, also with the respective lorem exercises.
\item References: \cite{doe2024example} \& \cite{smith2025dummy}
\end{itemize}
\end{frame}
\section{Math examples}
\subsection{Sample Subsection}
\begin{frame}{Sample Title}
\begin{itemize}
\item Lorem ipsum dolor sit amet, consectetur adipiscing elit.
\begin{flalign*}
f(x) = \frac{p(x)}{q(x)}
\end{flalign*}
for $p(x)$ and $q(x)$ being polynomial functions.
\item Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. That is:
\begin{flalign*}
\frac{p(x)}{q(x)} &= \underbrace{s(x)}_{\text{quotient}} + \frac{\overbrace{r(x)}^{\text{remainder}}}{q(x)}
\end{flalign*}
where $\dfrac{r(x)}{q(x)}$ is now a proper rational function.
\end{itemize}
\end{frame}
\begin{frame}{}
\begin{block}{Block Title}
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
\end{block}
\vspace{0.15in}
\begin{table}[h!]
\centering
\scalebox{0.9}{
\begin{tabular}{|c|c|}
\hline
\textbf{Header 1} & \textbf{Header 2} \\ \hline
$\frac{px+q}{(x-a)(x-b)}$, $a \neq b$ & $\frac{A}{x-a} + \frac{B}{x-b}$ \\ \hline
$\frac{px+q}{(x-a)^2}$ & $\frac{A}{x-a} + \frac{B}{(x-a)^2}$ \\ \hline
$\frac{px^2+qx+r}{(x-a)(x-b)(x-c)}$ & $\frac{A}{x-a} + \frac{B}{x-b} + \frac{C}{x-c}$ \\ \hline
$\frac{px^2+qx+r}{(x-a)^2(x-b)}$ & $\frac{A}{x-a} + \frac{B}{(x-a)^2} + \frac{C}{x-b}$ \\ \hline
$\frac{px^2+qx+r}{(x-a)(x^2+bx+c)}$ & $\frac{A}{x-a} + \frac{Bx+C}{x^2+bx+c}$ \\ \hline
\multicolumn{2}{|c|}{\scriptsize{*where $x^2+bx+c$ cannot be factorised further}} \\ \hline
\end{tabular}}
\caption{Sample Table Caption}
\end{table}
\end{frame}
\subsection{Set Theory}
\begin{frame}{2.2. Set Theory Expressions}
\begin{itemize}
\item \textbf{Symmetric difference}:
\begin{equation*}
A\Delta B = (A\backslash B)\cup (B\backslash A)=(A\cap B^c)\cup (B\cap A^c)
\end{equation*}
\item \textbf{De Morgan's laws}:
\begin{equation*}
(A\cup B)^c\underarrow[=][\uparrow]{\scriptsize{up arrow}}A^c\cap B^c \quad\text{and}\quad (A\cap B)^c\overarrow[=][\downarrow]{\scriptsize{down arrow}}A^c\cup B^c
\end{equation*}
\end{itemize}
\end{frame}
\subsection{Permutations and Combinations}
\begin{frame}{2.3. Permutations and Combinations}
\textbf{Combinations}
\begin{equation*}
\Mycomb[n]{r} = \binom nr =\frac{\Myperm[n]{r}}{\Myperm[r]{r}} =\frac{n!}{r!(n-r)!}\quad
\end{equation*}
\ding{104} Number of possible arrangements in a collection of items where the order does not matter.
\textbf{Pascal's triangle.}
\centering
\resizebox{0.8\textwidth}{!}{$\displaystyle
\begin{array}{c@{\hskip 1cm}c}
\begin{array}{c}
\Mycomb[0]{0} \\
\Mycomb[1]{0} \quad \Mycomb[1]{1} \\
\Mycomb[2]{0} \quad \Mycomb[2]{1} \quad \Mycomb[2]{2} \\
\Mycomb[3]{0} \quad \Mycomb[3]{1} \quad \Mycomb[3]{2} \quad \Mycomb[3]{3} \\
\Mycomb[4]{0} \quad \Mycomb[4]{1} \quad \Mycomb[4]{2} \quad \Mycomb[4]{3} \quad \Mycomb[4]{4} \\
\Mycomb[5]{0} \quad \Mycomb[5]{1} \quad \Mycomb[5]{2} \quad \Mycomb[5]{3} \quad \Mycomb[5]{4} \quad \Mycomb[5]{5} \\
\Mycomb[6]{0} \quad \Mycomb[6]{1} \quad \Mycomb[6]{2} \quad \Mycomb[6]{3} \quad \Mycomb[6]{4} \quad \Mycomb[6]{5} \quad \Mycomb[6]{6} \\
\Mycomb[7]{0} \quad \Mycomb[7]{1} \quad \Mycomb[7]{2} \quad \Mycomb[7]{3} \quad \Mycomb[7]{4} \quad \Mycomb[7]{5} \quad \Mycomb[7]{6} \quad \Mycomb[7]{7} \\
\vdots
\end{array}
&
=\begin{array}{c}
1 \\
1 \quad 1 \\
1 \quad 2 \quad 1 \\
1 \quad 3 \quad 3 \quad 1 \\
1 \quad 4 \quad 6 \quad 4 \quad 1 \\
1 \quad 5 \quad 10 \quad 10 \quad 5 \quad 1 \\
1 \quad 6 \quad 15 \quad 20 \quad 15 \quad 6 \quad 1 \\
1 \quad 7 \quad 21 \quad 35 \quad 35 \quad 21 \quad 7 \quad 1 \\
\vdots
\end{array}
\end{array}
$}
\end{frame}
\subsection{Matrices}
\begin{frame}{2.4. Matrices. Diebold-Li model: state-space representation}
\begin{itemize}
\item Measurement equation:
\begin{equation}
\resizebox{.8\hsize}{!}{$
\begin{pmatrix}
y_{t}(\tau_1)\\
y_{t}(\tau_2)\\
\vdots\\
y_{t}(\tau_{43})
\end{pmatrix}=\begin{pmatrix}
1&\frac{1-e^{-\lambda_t\tau_{1}}}{\lambda_t\tau_{1}}&\frac{1-e^{-\lambda_t\tau_{1}}}{\lambda_t\tau}-e^{-\lambda_t\tau_{1}}\\
1&\frac{1-e^{-\lambda_t\tau_{2}}}{\lambda_t\tau_{2}}&\frac{1-e^{-\lambda_t\tau_{2}}}{\lambda_t\tau}-e^{-\lambda_t\tau_{2}}\\
\vdots&\vdots&\vdots\\
1&\frac{1-e^{-\lambda_t\tau_{43}}}{\lambda_t\tau_{1}}&\frac{1-e^{-\lambda_t\tau_{43}}}{\lambda_t\tau}-e^{-\lambda_t\tau_{43}}
\end{pmatrix}\times\begin{pmatrix}
L_{t}\\
S_{t}\\
C_{t}
\end{pmatrix}+\begin{pmatrix}
\varepsilon_{t}(\tau_{1})\\
\varepsilon_{t}(\tau_{2})\\
\vdots\\
\varepsilon_{t}(\tau_{43})
\end{pmatrix}
$}
\end{equation}
\item Transition equation:
\begin{equation}
\resizebox{.8\hsize}{!}{$
\begin{pmatrix}
L_{t}-\mu_{L}\\
S_{t}-\mu_{S}\\
C_{t}-\mu_{C}\\
\end{pmatrix}=\begin{pmatrix}
a_{11}&a_{12}&a_{13}&\\
a_{21}&a_{22}&a_{23}&\\
a_{31}&a_{32}&a_{33}&
\end{pmatrix}\times\begin{pmatrix}
L_{t-1}-\mu_{L}\\
S_{t-1}-\mu_{S}\\
C_{t-1}-\mu_{C}\\
\end{pmatrix}+\begin{pmatrix}
\eta_{t}(L)\\
\eta_{t}(S)\\
\eta_{t}(C)\\
\end{pmatrix}
$}
\end{equation}
\end{itemize}
where $\varepsilon$ and $\eta$ denote the disturbances in each equation respectively.
\end{frame}
\section{Other display examples}
\begin{frame}{Slide Title}
\frametitle{Slide Title}
\framesubtitle{Large Right Image Example}
\begin{columns}[T] % [T] ensures correct vertical alignment
\begin{column}{0.48\linewidth} % Left column
\textbf{Section Title}
\begin{itemize}
\item Sed ut perspiciatis unde omnis iste natus error sit voluptatem accusantium doloremque laudantium, totam rem aperiam, eaque ipsa quae ab illo inventore veritatis et quasi architecto beatae vitae dicta sunt explicabo.
\item Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit aut fugit, sed quia consequuntur magni dolores eos qui ratione voluptatem sequi nesciunt.
\end{itemize}
\end{column}
\begin{column}{0.48\linewidth} % Right column
\begin{figure}
\centering
\includegraphics[width=0.8\textwidth]{images/Bayes_resized.png}
\caption{Write picture caption here.}
\label{fig:enter-label1}
\end{figure}
\end{column}
\end{columns}
\end{frame}
\begin{frame}{Slide Title}
\frametitle{Slide Title}
\framesubtitle{Large Right Image Example}
\begin{columns}[T] % [T] ensures correct vertical alignment
\begin{column}{0.48\linewidth} % Right column
\begin{figure}
\centering
\includegraphics[width=0.8\textwidth]{images/Bayes_resized.png}
\caption{Write picture caption here.}
\label{fig:enter-label2}
\end{figure}
\end{column}
\begin{column}{0.48\linewidth} % Left column
\textbf{Section Title}
\begin{itemize}
\item Sed ut perspiciatis unde omnis iste natus error sit voluptatem accusantium doloremque laudantium, totam rem aperiam, eaque ipsa quae ab illo inventore veritatis et quasi architecto beatae vitae dicta sunt explicabo.
\item Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit aut fugit, sed quia consequuntur magni dolores eos qui ratione voluptatem sequi nesciunt.
\end{itemize}
\end{column}
\end{columns}
\end{frame}
\begin{frame}{Slide Title}{Three-Column Example}
\small % Reduce font size in this slide
\begin{columns}[T] % [T] ensures correct vertical alignment
\begin{column}{0.4\linewidth} % Left column
\includegraphics[width=0.6\linewidth]{images/Bayes_resized.png}\\
\textbf{Section Title}\\
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
\end{column}
\begin{column}{0.4\linewidth} % Center column
\includegraphics[width=0.6\linewidth]{images/Bayes_resized.png}\\
\textbf{Section Title}\\
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
\end{column}
\end{columns}
\end{frame}
\section{Conclusion}
\begin{frame}{Conclusion}
\begin{itemize}
\item[\ding{104}] Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur.
\item[\ding{104}] Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
\end{itemize}
\pause
\vspace{0.1in}
\begin{picture}(55,55)
\put(0,50){\makebox(340,5){\upbracefill}}
\end{picture}
\vspace{-0.75in}
\centering
\begin{mybox}
\begin{itemize}
\item[\ding{229}] Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.
\end{itemize}
\end{mybox}
\end{frame}
\frame[shrink=30] {\printbibliography}
\AtEndDocument{\usebeamertemplate{endpage}}
\end{document}