diff --git a/README.md b/README.md
index c2ce8b3b92480c9a049b9fc15ebece49d082de24..1e06e506bb059ce7796d8649749c371bf3e72338 100644
--- a/README.md
+++ b/README.md
@@ -2,8 +2,9 @@
 
 This is my presentation about the Quantum Monte Carlo Loop Algorithm.
 
-The handout is available at [https://gitlab.cs.fau.de/oz73ifuv/qmc-loop-algorithm-report/-/jobs/artifacts/main/raw/build/qmc-loop-algorithm-report-handout.pdf?job=compile_pdf](https://gitlab.cs.fau.de/oz73ifuv/qmc-loop-algorithm-report/-/jobs/artifacts/main/raw/build/qmc-loop-algorithm-report-handout.pdf?job=compile_pdf).
-The presentation is available at [https://gitlab.cs.fau.de/oz73ifuv/qmc-loop-algorithm-report/-/jobs/artifacts/main/raw/build/qmc-loop-algorithm-report.pdf?job=compile_pdf](https://gitlab.cs.fau.de/oz73ifuv/qmc-loop-algorithm-report/-/jobs/artifacts/main/raw/build/qmc-loop-algorithm-report.pdf?job=compile_pdf).
+Download of the final PDF:
+- [handout](https://gitlab.cs.fau.de/oz73ifuv/qmc-loop-algorithm-report/-/jobs/artifacts/main/raw/build/qmc-loop-algorithm-report-handout.pdf?job=compile_pdf)
+- [presentation](https://gitlab.cs.fau.de/oz73ifuv/qmc-loop-algorithm-report/-/jobs/artifacts/main/raw/build/qmc-loop-algorithm-report.pdf?job=compile_pdf)
 
 If you want to compile the PDF yourself then do
 ```sh
diff --git a/src/qmc-loop-algorithm-report.tex b/src/qmc-loop-algorithm-report.tex
index 9629c9fd3b6b2cdfe12cc3a9ca370c33d8d314ee..96e8bfe7018c3ac46eac310b87a7476b40fc6dea 100644
--- a/src/qmc-loop-algorithm-report.tex
+++ b/src/qmc-loop-algorithm-report.tex
@@ -16,7 +16,7 @@
 %\usepackage{algpseudocode}
 \graphicspath{{../figures/}}
 
-\usepackage[backend=biber,urldate=iso,date=iso]{biblatex}
+\usepackage[backend=biber,urldate=iso,date=iso,style=authoryear]{biblatex}
 \addbibresource{references.bib}
 
 \date{2022-12-12}
@@ -26,25 +26,29 @@
 \institute[FAU]{Friedrich-Alexander Universität Erlangen-Nürnberg}
 
 \newcommand{\die}{\vcenter{\hbox{\includegraphics[width=1em]{die.png}}}}
+\newcommand\blfootnote[1]{%
+  \begingroup
+  \renewcommand\thefootnote{}\footnote{#1}%
+  \addtocounter{footnote}{-1}%
+  \endgroup
+}
+
 
 \begin{document}
 \begin{trueplainframe}
 \titlepage
 \end{trueplainframe}
 
-\begin{frame}{Outline}
-	\tableofcontents
-\end{frame}
+%\begin{frame}{Outline}
+%	\tableofcontents
+%\end{frame}
 
 \section{Classical Monte Carlo}
-\subsection{Classical Ising Model}
-\subsection{Markov Chain}
-\subsection{Detailed Balance Condition}
-\subsection{Metropolis Algorithm}
 \begin{frame}{Monte Carlo Basics}
 \begin{minipage}{0.48\linewidth}
 	%\only<2>{
 	%\visible<2>{
+\subsection{Classical Ising Model}
 \begin{block}{Classical Ising Model}
 	\begin{align*}
 		H(\vec{\sigma}) &= - \sum_{i}\left(J\sigma_i\sigma_{i+1} + \mu \sigma_i\right) \\
@@ -53,6 +57,7 @@
 	\end{align*}
 \end{block}
 	%}
+%\subsection{Markov Chain}
 \begin{block}{Markov Chain}
 	\begin{align*}
 		\vec{\sigma}_1\to \vec{\sigma}_2 \to \vec{\sigma}_3 \to \cdots
@@ -82,6 +87,7 @@
 	{\color{red} Significant configurations}
 	\end{minipage}
 \end{block}
+\subsection{Detailed Balance Condition}
 \begin{block}{Detailed Balance condition}
 	\begin{align*}
 			w_{\vec{\sigma}}\,	p(\vec{\sigma} \to \vec{\sigma}')
@@ -93,7 +99,9 @@
 	All configurations should be reachable after finitely many steps
 \end{block}
 \end{minipage}
+\blfootnote{\cite{Gubernatis2016}}
 \end{frame}
+\subsection{Metropolis Algorithm}
 \begin{frame}{Metropolis Algorithm}
 \begin{minipage}{0.45\linewidth}
 \begin{block}{Split the Probability}
@@ -121,13 +129,14 @@
 	&\die{} \begin{cases}
 		\visible<4->{\le \min\left(1,\frac{p_{\text{acc}}(\vec{\sigma}_A\to \vec{\sigma}_B)}{p_{\text{acc}}(\vec{\sigma}_B\to \vec{\sigma}_A)}\right) \\
 					 \implies \vec{\sigma}_1 \to \cdots \to \vec{\sigma}_A \to \vec{\sigma}_B} \\
-		\visible<5->{> \min\left(1,\frac{p_{\text{acc}}(\vec{\sigma}_A\to \vec{\sigma}_j)}{p_{\text{acc}}(\vec{\sigma}_j\to \vec{\sigma}_A)}\right) \\
+		\visible<5->{> \min\left(1,\frac{p_{\text{acc}}(\vec{\sigma}_A\to \vec{\sigma}_B)}{p_{\text{acc}}(\vec{\sigma}_B\to \vec{\sigma}_A)}\right) \\
 					 \implies \vec{\sigma}_1 \to \cdots \to \vec{\sigma}_A \to \vec{\sigma}_A}
 	\end{cases}}
 \end{align*}
 \end{block}
 }
 \end{minipage}
+\blfootnote{\cite{Gubernatis2016}}
 \end{frame}
 \begin{frame}{Hands-On Example}
 \begin{minipage}{0.48\linewidth}
@@ -177,6 +186,7 @@
 \end{align*}
 \end{block}
 \end{minipage}
+\blfootnote{\cite{Gubernatis2016}}
 \end{frame}
 \subsection{Heat-Bath Algorithm}
 \begin{frame}{Heat-Bath Algorithm}
@@ -219,6 +229,7 @@ Always accept the new configuration
 \end{frame}
 \begin{frame}{Observables}
 \begin{minipage}{0.45\linewidth}
+\begin{block}{Calculating Observables}
 \begin{enumerate}
 	\item<1-> \(N_{\text{eq}}\) sweeps to reach equilibrium
 	\item<2-> Use equilibrated MC steps for sampling
@@ -229,18 +240,23 @@ Always accept the new configuration
 		\tau_O = \frac{1}{2}(R_{\text{sat}}-1)
 	\end{align*}
 \end{enumerate}
-\visible<5->{\includegraphics[width=0.8\linewidth]{BoFoQoOo_gausshist_polarisation.pdf}}
+\end{block}
 \end{minipage}
 \hfill
 \begin{minipage}{0.45\linewidth}
-	\visible<5->{\includegraphics[width=\linewidth]{BoFoQoOo_rplot.pdf}}
+	\Centering
+	\visible<5->{\includegraphics[width=0.6\linewidth]{BoFoQoOo_rplot.pdf}}
+	\visible<5->{\includegraphics[width=0.6\linewidth]{BoFoQoOo_gausshist_polarisation.pdf}}
 \end{minipage}
+\blfootnote{\cite{Gubernatis2016}}
+\blfootnote{\cite{gehrbachelor}}
 \end{frame}
 \section{Quantum Monte Carlo}
 \subsection{XXZ Quantum Spin Chain}
 \subsection{Trotter Decomposition}
 \subsection{Updating Schemes}
 \subsection{Loop Updates}
+\subsection{Sign Problem}
 \begin{frame}{Quantum Monte Carlo}
 \begin{minipage}{0.45\linewidth}
 \begin{block}{XXZ Quantum Spin Chain}
@@ -275,9 +291,11 @@ Always accept the new configuration
 	\end{align*}
 \end{block}
 \end{minipage}
+\blfootnote{\cite{Assaad}}
 \end{frame}
 \begin{frame}{Trotter Decomposition}
 \begin{minipage}{0.5\linewidth}
+\begin{small}
 \begin{block}{Split Hamiltonian}
 	\begin{align*}
 		H &= \underbrace{\frac{J_x}{2}\sum_{\text{odd } i}(S_i^+S_{i+1}^-+S_i^-S_{i+1}^+) + J_z\sum_{\text{odd } i}S_i^zS_{i+1}^z}_{H'} \\
@@ -289,7 +307,7 @@ Always accept the new configuration
 		\tr\left[e^{-\beta H}\right]
 		&= \tr\left[\left(e^{-\Delta\tau H}\right)^m\right] \\
 		&= \tr\left[\left(e^{-\frac{\Delta\tau}{2}H''}e^{-\Delta\tau H'}e^{-\frac{\Delta\tau}{2}H''} + \mathcal{O}(\Delta\tau^3)\right)^m\right] \\
-		&= \tr\left[\left(e^{-\Delta\tau H'}e^{-\Delta\tau H''}\right)^m\right] + \mathcal{O}(\Delta\tau^2) \\
+		%&= \tr\left[\left(e^{-\Delta\tau H'}e^{-\Delta\tau H''}\right)^m\right] + \mathcal{O}(\Delta\tau^2) \\
 		&= \sum_{\vec{\sigma}_1\cdots\vec{\sigma}_{2m}}\bra{\vec{\sigma}_1}e^{-\Delta\tau H'}\ketbra{\vec{\sigma}_{2m}}
 		e^{-\Delta\tau H''}\ket{\vec{\sigma}_{2m-1}} \\
 		&\cdots\bra{\vec{\sigma}_3}e^{-\Delta\tau H'}\ketbra{\vec{\sigma}_{2}}
@@ -297,11 +315,15 @@ Always accept the new configuration
 		+ \mathcal{O}(\Delta\tau^2)
 	\end{align*}
 \end{block}
+\end{small}
 \end{minipage}
 \hfill
 \begin{minipage}{0.45\linewidth}
 	\includegraphics[width=0.8\linewidth]{worldline.pdf}
 \end{minipage}
+\blfootnote{\cite{Assaad}}
+\blfootnote{\cite{bchformula}}
+\blfootnote{\cite{Sandvik2010}}
 \end{frame}
 \begin{frame}{Updating Schemes}
 \begin{minipage}{0.48\linewidth}
@@ -322,6 +344,7 @@ Always accept the new configuration
 	\includegraphics[width=0.98\linewidth]{singleloopupdate.pdf}
 \end{block}
 \end{minipage}
+\blfootnote{\cite{Assaad}}
 \end{frame}
 \begin{frame}{Loop Updates}
 \begin{minipage}{0.48\linewidth}
@@ -329,7 +352,41 @@ Always accept the new configuration
 \end{minipage}
 \hfill
 \begin{minipage}{0.48\linewidth}
+\begin{align*}
+	\sum_G W(S,G) &= W(S) \\
+	P(S \to (S,G)) &= \frac{W(S,G)}{W(S)} \\
+	W(S,G) &= W(S',G) \\
+	P((S,G) \to (S',G)) &= \frac{W(S',G)}{W(S,G) + W(S',G)} = \frac{1}{2}
+\end{align*}
+\(\implies\) Each loop can be flipped with probability \(\frac{1}{2}\)
+\end{minipage}
+\blfootnote{\cite{Assaad}}
+\end{frame}
+\begin{frame}{Sign Problem}
+\begin{minipage}{0.48\linewidth}
+	\begin{block}{Partition Sum}
+		\begin{align*}
+			Z = \tr\left(e^{-\beta H}\right)
+			= \sum_{\vec{\sigma}} \bra{\vec{\sigma}}e^{-\beta H}\ket{\vec{\sigma}}
+			\overset{!}{=} \sum_{C}w_C
+		\end{align*}
+		\(\{\vec{\sigma}\}\) is not energy eigenbasis \\
+		\(\implies\) negative weights are possible
+	\end{block}
+\end{minipage}
+\hfill
+\begin{minipage}{0.48\linewidth}
+	\begin{block}{New Expectation Value}
+		\begin{align*}
+			\expval{O}
+			&= \tr\left(e^{-\beta H}O\right) \\
+			&\overset{!}{=} \frac{\sum_Cw_CO_C}{\sum_Cw_C}
+			= \frac{\sum_C\abs{w_C}\text{sign}_CO_C}{\sum_C\abs{w_C}\text{sign}_C} \\
+			&\approx \frac{\sum_{i=1}^{N} \text{sign}_{C_i}O_{C_i}}{\sum_{i=1}^{N} \text{sign}_{C_i}}
+		\end{align*}
+	\end{block}
 \end{minipage}
+\blfootnote{\cite{werner}}
 \end{frame}
 
 {
diff --git a/src/references.bib b/src/references.bib
index 327c7c22651452551e1157c53f6d24d8f45ccd3e..4f16a3d43894c3f05ebf1b1cb32e8bcc6fb48675 100644
--- a/src/references.bib
+++ b/src/references.bib
@@ -44,3 +44,12 @@
   title = {Computational Studies of Quantum Spin Systems},
   booktitle = {{AIP} Conference Proceedings}
 }
+
+@unpublished{gehrbachelor,
+	author = {Stefan Gehr},
+	title = {Investigation of a Two-level Emitter in a Cavity Using Continuous-time Quantum Monte Carlo Method},
+	institution = {Friedrich-Alexander-Universtität Erlangen-Nürnberg},
+	year = {2021},
+	url = {https://gitlab.cs.fau.de/oz73ifuv/two-level-emitter-qmc},
+	note = {Author's Bachelor's Thesis}
+}