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\title{The effects of algorithmic flagging on fairness:}
\subtitle{Quasi-experimental evidence from Wikipedia}
\author[TeBlunthuis,Hill,Halfaker]{\textbf{Nathan TeBlunthuis}
  \footnotesize{nathante@uw.edu}\inst{1} \inst{2} \\ \and \textbf{Benjamin Mako Hill} \inst{1} \and \\ \textbf{Aaron Halfaker} \inst{2}}

\institute[UW,WMF]{\textbf{University of Washington\inst{1}} \\
  Department of Communication \\
{\textbf{Wikimedia Foundation}\inst{2}}
}

\date{June 19, 2020}
\IfFileExists{upquote.sty}{\usepackage{upquote}}{}
\begin{document}

% remove some of the space in the itemize to make it quite compact
% \let\olditemize\itemize
% \renewcommand\itemize{\olditemize\itemsep-1pt}

%% SLIDE: Title Slide
\begin{frame}
  \titlepage

  \tikz{\node at (current page.center) [anchor=center, yshift=-.75in, xshift=1.6in]
    {\includegraphics[width=0.25\textwidth]{figures/logo.pdf}};
  }

  % include version control stuff
  % \input{vc}
  % \credit{Revision:\ \VCRevision\  (\VCDateTEX)}
\end{frame}

% \section{How will algorithmic flagging shape fairness of human decision making?}

% \begin{frame}
% \larger
%   \sectionpage

%   \note{This is an example section page.}
% \end{frame}

\begin{frame}{What are we talking about?}

\larger \larger

\emph{Algorithmic predictions} that \emph{route attention} or \emph{provide information} to influence \emph{human decisions} that \emph{affect another person}.

\note{This project is about a kind of sociotechnical system where algorithmic predictions route attention or provide information to influence consequential human decisions
 that affect other people}
\end{frame}

% \begin{frame}
%   \frametitle{Simplifying a debate: Will algorithms help or hurt fairness?}

% \larger
% \larger
%   \e{Taste-based discrimination:}  \\ \emph{``I don't like people that look like you.''}

%   Algorithmic flagging can be \emph{biased}; \\ reproduce or encode problematic categories or ontologies;

%   \pause \vspace{1em}

%   \e{Statistical discrimination:} \\  \emph{``People that look like you are likely to cause problems.''}

% \end{frame}

% \begin{frame}
% \larger \larger
% \enspace
% \enspace
% \enspace

% Can algorithmic flagging help by better accounting for more information than human judges and thereby reduce statistical discrimination?

% \end{frame}

\begin{frame}\frametitle{High stakes, legally complicated algorithms}
\larger
\centering
\includegraphics[width=0.35\textwidth]{figures/court.pdf}  \\ \pause
\vspace{-2em}
\includegraphics[width=0.35\textwidth]{figures/job_application.jpg} \hfill \pause
\includegraphics[width=0.35\textwidth]{figures/house.png} \pause
\note{Some applications are high stakes, legally complicated: Should a judge grant bail to a defendant? Should a job applicant get an interview?  Should an applicant get a lease? These applications might be difficult to study for practical and ethical reasons.  }

\end{frame}

\begin{frame}\frametitle{Lower stakes applications in social media moderation}

\includegraphics[width=0.45\textwidth]{figures/wikipedia_logo.png}\hfill
\includegraphics[width=0.45\textwidth]{figures/reddit_logo.png}

\note{Similar kinds of systems are used in different contexts with lower stakes. In online moderation, how people are treated by moderators impacts who has voice in communities, whose views are represented in important knowledge bases, and the ability of moderators to prevent misbehavior, but not individual life courses or systematic oppression.}

\end{frame}

\section{Algorithmic flagging in online content moderation on Wikipedia}

\begin{frame}
  \sectionpage
\end{frame}

\begin{frame}\frametitle{Recent changes filters on Wikipedia}
\vspace{15em}
    \centering
\larger
\begin{tikzpicture}

  \node[anchor=west](flags) at (-7,2.7) {ORES Flags};
%  \node[anchor=west](pagetitle) at (-4.7,2.7) {Page titles};
  \node[anchor=west](userpagelink) at (-2.9,2.7) {Red user profile link};
  \node[anchor=west](unregistered) at (1.4,2.7) {Unregistered editor};

  \begin{scope}
  \node[anchor=south, inner sep=0] (image) at (0,0) {\includegraphics[width=\textwidth]{resources/rcfilters_example_2.png}};
  \draw [-stealth,ultra thick] (flags.220) -- ++(0,-0.4);
%  \draw [-stealth,ultra thick] (pagetitle.south) -- ++(0,-0.4);
  \draw [-stealth,ultra thick] (unregistered.200) -- (1.5,2);
  \draw [-stealth,ultra thick] (userpagelink.280) -- (0.2,1.6);
\end{scope}
\end{tikzpicture}

\raggedright

\note{Flags are triggered by arbitrary thresholds, so we can use a regression discontinuity to estimate the causal effects of being flagged on moderator actions?}

\end{frame}

\begin{frame}\frametitle{Moderation and fairness}

  \larger
\enspace

  Moderators use \emph{social signals} like \emph{registration} \\ and \emph{experience} to find and \emph{sanction} misbehavior.

  \enspace

  People displaying such signals might be \e{over-profiled} if moderators focus their attention on them but not on others engaged in similar behavior.

\enspace

  Moderator actions can be considered unfair if they are \e{controversial sanctions} (i.e. violates a meta-norm or a third person objects to the initial sanction).

  \note{When we think about how an algorithmic flagging system shapes fairness it's important to think about the baseline.  How are moderators making decisions without the algorithmic signals? How are they making them with the signals?

    Social signals like registration status and experience are clues that an editor might be misbehaving.  The moderators might use these signals the way that car insurance companies use sex as a sign that certain types of people are more risky than others.  This can lead to over-profiling if they focus their attention and their sanctioning actions on people that display these signals instead of others that might be up to equally bad if not even worse behavior.

    This might lead to unfairness in terms of disproportionate sanctioning or in terms of incorrect sanctioning in terms of meta-norms that tell moderators when they should issue sanctions
  }
  \end{frame}

\begin{frame}\frametitle{Research questions}
\vspace{7em}
\larger

  \e{RQ1:} How will flagging an action change the likelihood an action is sanctioned for over-profiled editors compared to others?

  \e{RQ2:} How will flagging an action by an over-profiled editor change the chances it receives a controversial sanction?

  \e{RQ3:} Within the set of sanctioned actions, how will the effect of flagging an action on controversial sanctions depend on whether contributors are over-profiled?

\end{frame}

\begin{frame}\frametitle{Research questions}
\vspace{7em}
\larger

  \e{RQ1:} How will flagging an action change the likelihood an action is sanctioned for over-profiled editors compared to others?

  \e{RQ2:} How will flagging an action by an over-profiled editor change the chances it receives a controversial sanction?

\textcolor{gray}{\textbf{RQ3:} Within the set of sanctioned actions, how will the effect of flagging an action on controversial sanctions depend on whether contributors are over-profiled?}

\end{frame}

\begin{frame}\frametitle{Research design: regression discontinuity}

\larger

An algorithmic predictor triggers flags when prediction \\
scores an \emph{arbitrary threshold}.

  So we infer the causal effects of flagging on moderation by \\ comparing edits right above the threshold with and  \\ conditioning  on the scores.

\begin{minipage}{0.45\textwidth}
\begin{knitrout}
\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}
\includegraphics[width=\textwidth]{figures/knitr-adoption_me_plot-1}

\end{knitrout}
\end{minipage}
\hfill
\begin{minipage}{0.45\textwidth}
By the way, we use Bayesian models fit with Rstanarm.

\note{This lets us draw a robust comparison between edits that are flagged and edits that are not flagged}
\end{minipage}

\end{frame}

\begin{frame}\frametitle{Data: Wikimedia History}

\larger

\begin{itemize}
\item Public data of Wikipedia edit history
\item Historical prediction scores maintained by Wikimedia \\ (to be released)
\item Thresholds (\textcolor{maybebad}{maybe damaging}, \textcolor{likelybad}{likely damaging})\\ reconstructed by loading old models and configuration files
\item Stratified sample with up to 23 different language editions of Wikipedia.
\end{itemize}

Unit of analysis: \emph{revision to an article}

\begin{description}

\item[overprofiling:] \emph{registration status} and \emph{redlink User pages}.
\item[sanction:] a revision is undone by a second party.
\item[controversial sanction:] a sanction is undone by a third party.

\end{description}

\note{We didn't find overall effects on sanctioning at the highest (very likely damaging) threshold, so we exclude it.}
\end{frame}

\section{Results}

\begin{frame}
  \sectionpage
  \end{frame}

\begin{frame}\frametitle{RQ1: Flagging and over-profiling: Registration status}

\begin{knitrout}
\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}
\includegraphics[width=\maxwidth]{figures/knitr-h1_unreg_me_plot-1}

\end{knitrout}
\end{frame}

\begin{frame}\frametitle{RQ2: Flagging and fair sanctioning: Unregistered editors}

\larger

Flagging decreases controversial sanctioning \\ for unregistered editors.

\includegraphics[width=1\linewidth]{figures/knitr-me_plot_H2_anon-1}

\end{frame}

% \begin{frame}\frametitle{RQ1: Flagging and over-profiling: Registration status}

%  \larger

% We find quite large effects of flagging on sanctioning.

% Unflagged actions by unregistered editors \\ are far more likely to be reverted.

% Once flagged, actions by registered and unregistered editors are reverted at relatively similar rates.

% This is evidence that Wikipedia moderators overprofile based on registration status and that algorithmic flagging reduces this over-profiling.

% % Being flagged at the ``maybe damaging'' increases the probability of sanctioning from  for unregistered contributors a change of between round((anon.md.proto.above$linpred.lower - anon.md.proto.below$linpred.upper)*100,1) and round((anon.md.proto.above$linpred.upper - anon.md.proto.below$linpred.lower)*100,1)
% % percentage points.

% % For registered contributors the increase is \emph{larger:} from format.percent(non.anon.md.proto.below$linpred,1) to format.percent(non.anon.md.proto.above$linpred,1), change of between round((non.anon.md.proto.above$linpred.lower - non.anon.md.proto.below$linpred.upper)*100,1) and round((non.anon.md.proto.above$linpred.upper - non.anon.md.proto.below$linpred.lower)*100,1) percentage points.

% % Similarly, at the ``likely damaging'' threshold we see an increases in sanctioning probability from format.percent(anon.ld.proto.below$linpred,1) to format.percent(anon.ld.proto.above$linpred,1) for unregistered contributors a change of between round((anon.ld.proto.above$linpred.lower - anon.ld.proto.below$linpred.upper)*100,1) and round((anon.ld.proto.above$linpred.upper - anon.ld.proto.below$linpred.lower)*100,1)
% % percentage points.

% % And for registered contributors the increase is \emph{larger:} from format.percent(non.anon.ld.proto.below$linpred,1) to format.percent(non.anon.ld.proto.above$linpred,1), change of between round((non.anon.ld.proto.above$linpred.lower - non.anon.ld.proto.below$linpred.upper)*100,1) and round((non.anon.ld.proto.above$linpred.upper - non.anon.ld.proto.below$linpred.lower)*100,1) percentage points.
% \end{frame}

% \begin{frame}\frametitle{Flagging improves fairness for unregistered editors}

% \begin{description}
% \item[Reducing overprofiling:] Once flagged, they were sanctioned \\ at a similar rate to \emph{registered} editors.
% \item[Improve moderator decisions:] Flagging makes sanctions against unregistered editors more fair in terms of Wikipedian norms.
% \end{description}

% \end{frame}

% \begin{frame}\frametitle{Recent changes filters on Wikipedia}
% \vspace{15em}
%     \centering
% \larger
% \begin{tikzpicture}

%   \node[anchor=west](flags) at (-7,2.7) {ORES Flags};
% %  \node[anchor=west](pagetitle) at (-4.7,2.7) {Page titles};
%   \node[anchor=west](userpagelink) at (-2.9,2.7) {Red user profile link};
%   \node[anchor=west](unregistered) at (1.4,2.7) {Unregistered editor};

%   \begin{scope}
%   \node[anchor=south, inner sep=0] (image) at (0,0) {\includegraphics[width=\textwidth]{resources/rcfilters_example_2.png}};
%   \draw [-stealth,ultra thick] (flags.220) -- ++(0,-0.4);
% %  \draw [-stealth,ultra thick] (pagetitle.south) -- ++(0,-0.4);
%   \draw [-stealth,ultra thick] (unregistered.200) -- (1.5,2);
%   \draw [-stealth,ultra thick] (userpagelink.280) -- (0.2,1.6);
% \end{scope}
% \end{tikzpicture}

% \raggedright

% %Flags are triggered by arbitrary thresholds, so we can use a regression discontinuity to estimate the causal effects of being flagged on moderator actions?

% \end{frame}

\begin{frame}\frametitle{RQ1: Flagging and over-profiling: User pages}

\begin{knitrout}
\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}
\includegraphics[width=\textwidth]{figures/knitr-h1_userpage_me_plot-1}

\end{knitrout}

\end{frame}

% \begin{frame}\frametitle{RQ1: Flagging and over-profiling: User pages}

% \larger

% Actions by editors \emph{without} User pages are more sensitive \\ to flagging than are edits \emph{with} User pages at the \\ ``maybe damaging'' threshold.

% %  There are few edits by editors with profile pages flagged at the ``likely damaging'' threshold.

%   This points to the opposite conclusion as when we looked at registration status: algorithmic flagging seems to amplify over-profiling of editors without User pages.

% \end{frame}

\begin{frame}\frametitle{RQ2: Flagging and fair sanctioning: No User pages}

\larger

We don't detect a change in controversial sanctioning \\ for editors without user pages.

\includegraphics[width=\textwidth]{figures/knitr-me_plot_H2_no_user_page-1}

\end{frame}

\begin{frame}\frametitle{Conclusion}

\larger

  Perhaps editors without User pages are not over profiled, \\ or the algorithm is biased against them. \pause

  While our estimates of the effects of flagging are causal, \\ comparison between types of editors is not. \pause

  This is about moderation on Wikipedia, but social and psychological processes might be similar in high stakes settings. \pause

  While algorithmic flagging can improve fariness for some classes of user, the general relationship seems complex and contingent. \pause

\end{frame}

\begin{frame}

  Thank you!

  \href{mailto:nathante@uw.edu}{nathante@uw.edu}

  \includegraphics[height=1.5em]{figures/Twitter_Logo_Blue.pdf} @groceryheist

  Manuscript on Arxiv:  \url{https://arxiv.org/abs/2006.03121}

  \url{https://teblunthuis.cc}

  \url{https://communitydata.science}

\end{frame}

\appendix

\end{document}

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text:
\chapter{Societal Issues}\label{ch:societal_issues}

If you do not think an issue, such as ethics for example, has any relation to your project, you can say so, but you should justify this. These responses need not be lengthy, but you should say something about each of the following issues:

\paragraph{Ethical.}
Ethical conduct is what one ought to do in working with others. It is the right thing to do, the moral action. It is not surprising that virtually all of our professional societies and groups, in all professions, have codes of ethical conduct. Professions realize that there are good and bad ways of working with others, and we need to make the distinction. Sometimes it can be difficult to know what is the right thing to do. What ethical questions were or could be raised about your project?

\paragraph{Social.}
Engineering is done within a social context, within a community of other people. Sometimes that community is defined very narrowly, sometimes very broadly. A focus on social issues allows us to consider the impact of our work on society. If we develop this product, or implement this system, what will be the effect? All of our human developments, in engineering and elsewhere, have unanticipated consequences, some good, some bad. We have an obligation to reflect on these consequences as well as we are able.

\paragraph{Political.}
Many of our projects are very political in nature, requiring us to take into consideration the will of the general public, usually through elected representatives. Engineers who work on public projects need to understand the political processes that make such work possible. What is the potential impact of your project or this type of project on society?

\paragraph{Economic.}
Economic considerations in engineering concern the costs of the various steps in the project. Such costs are usually dependent on the engineering decisions that are made during the design phase. Alternative approaches may offer cost options. We also need to consider the cost of money. How do we pay for the cost of a product development? If we must borrow significant amounts of money how do we account for the cost of the loan in the pricing of the product? What economic considerations arose in your project?

\paragraph{Health and Safety.}
We develop our products for the use of the public. Hence we must consider health and safety issues related to our product. How safe does a product have to be? Are there laws that determine this? Are there related ethical issues? What health effects are relevant? What health and safety issues arose in your project?

\paragraph{Manufacturability.}
Manufacturability issues are of great importance. Can the product be built? Is there an easier way to build this product than first imagined? What development time issues arise? What are the cost issues? Could your project be manufactured? What problems might arise?

\paragraph{Sustainability.}
Sustainability means two things in engineering; one is a narrow sense, one broad sense. In the former sense sustainability refers to the degree to which a product that is developed can continue to be viable and useful for a reasonable amount of time. A product that fails soon after it is built and cannot be repaired or updated or modified to fit new needs is not a sustainable product. In the broader sense a community or region or a world, perhaps, that uses its resources effectively so that it can sustain its life for a long time is said to be sustainable. We say that such a community has a sustainable economy. Engineering can help develop sustainable economies. What sustainability issues arise?

\paragraph{Environmental Impact.}
All of our products and systems have some environmental impact, in the uses of valuable resources, or in the production of pollution, or in other changes in our surroundings. The engineer is obliged to consider such impacts, and to point them out where they arise, or are a threat. What are the environmental issues related to your product?

\paragraph{Usability.}
Usability refers to what is sometimes called ``user-friendliness.'' Is the device straightforward, easily learned and easily used by the end user. Is your product usable?

\paragraph{Lifelong learning.}
Lifelong learning is a necessary part of all professions. You wouldn't want to have a doctor who did not know the latest procedures and medications to protect your life. And you wouldn't want an engineer who didn't know the analysis tools that had been developed since graduation, or the cost-effective materials that had just come along. We just have to keep up. Learning never stops. Did this project help prepare you for the time when you will have to learn on your own, or did it inspire you to study new material?

\paragraph{Compassion.}
One definition for compassion is an awareness of and sympathy for the suffering of another. Compassion means to recognize the suffering of another. But let’s look at a broader definition. Let’s define compassion as “the awareness of and sympathy for the suffering of another, and the desire to relieve that suffering.” What does that have to do with engineering? Simple! One of the things that engineers can choose to do in life is to look for and try to relieve suffering where they find it. Perhaps it means replacing an ancient water supply system that is leading to disease in some tiny village, or designing a communication system to protect seniors with illnesses, or designing prosthetic devices for crippled children. Even if we do not decide to make the relieving of suffering the focus of our life’s work, it is still critically important to our fullness as a human being that we feel compassion for the suffering. It is a part of the education that we hope you acquired at Santa Clara.

ext: tex

max_stars_repo_name: davidanastasiu/SCU-SOE-thesis

max_issues_repo_name: davidanastasiu/SCU-SOE-thesis

max_forks_repo_name: davidanastasiu/SCU-SOE-thesis


text:
\documentclass[simplex.tex]{subfiles}
% DO NOT INCLUDE PREAMBLES/PACKAGES HERE!!
% packages are inherited from preamble.tex; you can compile this on its own
\begin{document}
\subsection{FlashX}
%%% Jan
\begin{figure}[h!]
\begin{cframed}
\centering
\includegraphics[width=0.5\textwidth]{../../figs/FlashR.vs.RRO.png}
\caption{
Normalized runtime of FlashR vs. Revolution R when executing R implementations
of machine learning primitives on a dataset with one million data points and
1000 features on a large parallel machine with
48 CPU cores. FlashR outperforms Revolution R in all computations. When
the computation gets more complex, the speed advantage of FlashR
over Revolution R gets larger.
}
\label{fig:flashr}
\end{cframed}
\end{figure}

After having efficient matrix operations in the past months, including sparse
matrix multiplication and various dense matrix operations, we integrate all
matrix operations in a single computation framework called FlashR, which
provides both high compatibility with R and efficiency. FlashR now overrides
about 70 R matrix functions in the R
\textit{base} package. As such, we can run existing R code with little
modification or no modification at all. For example, we ported a few R
implementations of machine learning algorithms in the \textit{MASS} package
with little modification. We compare the speed of FlashR against Revolution R,
which is also designed to parallelize and accelerate R code, on a large parallel
machine with 48 CPU cores (Figure \ref{fig:flashr}).
Even for the simple matrix operation such as \textit{crossprod}, FlashR
outperforms Revolution R. As the computation gets more complex, the advantage
of FlashR over Revolution R gets larger. When executing the LDA implementation
(Linear Discriminant Analysis) in the MASS package, FlashR outperforms Revolution R
by over an order of magnitude.

\clearpage

%%%%% Feb

We use FlashR to process the billion-scale datasets to demonstrate its
scalability (Table \ref{tbl:scale}). We use three datasets here: \textit{(i)}
the Criteo dataset has over four billion data points with binary labels
(click vs. no-click), used for advertisement click prediction;
\textit{(ii)} PageGraph is the adjacency matrix of a graph, which has 3.5
billion vertices and 128 billion edges;
\textit{(iii)} PageGraph-32ev are 32 singular vectors that we computed on
the largest connected component of Pagegraph with the tools we built previously.
In these experiments, we run the iterative algorithms
(Logistic regression, k-means and PageRank) on the datasets until they converge.

\begin{table}[h!]
\begin{center}
\caption{The runtime and memory consumption of FlashR on the billion-scale
		datasets on the 48 CPU core machine. The runtime of iterative
		algorithms is measured when the algorithms converge. We run PageRank
		on the PageGraph dataset, run k-means on PageGraph-32ev and the remaining
		algorithms on Criteo.}
\vspace{-10pt}
\footnotesize
\begin{tabular}{|c|c|c|}
\hline
& Runtime (s) & Memory (GB) \\
\hline
Correlation & $91.23$ & $1.5$ \\
\hline
PCA & $136.71$ & $1.5$ \\
\hline
NaiveBayes & $76.55$ & $3$ \\
\hline
LDA & $2280$ & $8$ \\
\hline
Logistic regression & $4154.40$ & $26$ \\
\hline
k-means & $1110.82$ & $28$ \\
\hline
PageRank & $3900$ & $135$ \\
\hline
\end{tabular}
\normalsize
\label{tbl:scale}
\end{center}
\vspace{-10pt}
\end{table}

Even though we process the billion-scale datasets in a single machine (with
48 CPU cores), none of
the algorithms are prohibitively expensive. Simple algorithms, such as
Naive Bayes and PCA, require one or two passes over the datasets and take
only one or two minutes to complete. Logistic regression and k-means take
about $10-20$ iterations to converge. Because the PageRank implementation
uses the power method, it takes $100$ iterations to converge.
Nevertheless, all of the iterative algorithms take about one hour or less.

FlashR scales to datasets with billions of data points easily when running
out of core. Most of the algorithms have negligible memory consumption.
PageRank consumes more memory because the sparse matrix multiplication in
PageRank keeps vectors in memory for semi-external memory computation.
The scalability of FlashR is mainly bound by the capacity of SSDs.
The functional programming
interface generates a new matrix in each matrix operation, which potentially
leads to high memory consumption. Thanks to lazy evaluation and virtual matrices,
FlashR only needs to materialize the small matrices to effectively reduce
memory consumption.

\clearpage
%%%%%% March
We advance FlashR for exploratory analysis on a billion-scale
graph. This includes functions for filtering data points and plotting
histograms and heatmaps on billions of data points. Figure \ref{fig:FlashX}
shows an example of plotting the in-degree histogram of vertices in the page
graph and a heatmap for the distribution of the vertices of the page graph in
a two-dimension space.

\begin{figure}[!h]
\begin{cframed}
\centering
\includegraphics[width=0.4\textwidth]{../../figs/hist-indeg.pdf}
\includegraphics[width=0.4\textwidth]{../../figs/pg_xy_heatmap.pdf}
\caption{Left: the in-degree distribution of the Page graph.
	Right: a heatmap of the distribution of the vertices of the page graph
	in a two-dimension space; the coordinates of the vertices
	in the two-dimension space is determined by the first left and right
	singular vectors.}
\label{fig:FlashX}
\end{cframed}
\end{figure}

\clearpage
\end{document}


text:
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\begin{document}
    \title[Lecture 12]{Lecture 12: Two-Period Consumer Problem}
    \author[Hui-Jun Chen]{Hui-Jun Chen}
    \institute[OSU]{The Ohio State University}
    % \date{\today}
    \date{\today}
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%-------------------------------------------------------
{
%	\usebackgroundtemplate{\includegraphics[width=1\paperwidth]{../EveningSky_cropped_edit43_bright.jpg}}
    \begin{frame}
% \vspace{3em}
        \centering
%		{\footnotesize 	ECON 4002 Intermediate Macroeconomic Theory}
        \maketitle
% \vspace{-1.5em}
% \centering
% \includegraphics[width=0.55\linewidth]{Pictures/houses.jpeg}

    \end{frame}
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%------------------------------------------

\section{Budget}
\label{sec:Budget}

\begin{frame}{Variables and Notation}
\label{slide:Variables_and_Notation}
    Assume that consumer do NOT make consumption-leisure decision, but receive endowment of \alert{non-labor income} $ y $ and subject to \alert{lump-sum tax} $ t $.
    \begin{itemize}
        \item $ y $ \& $ t $: today (date 0), and $ y' $ \& $ t' $: tomorrow (date 1)
        \item in general, having a prime ``$'$'' represents tomorrow
    \end{itemize}
    If there's a \alert{saving technology} exists (may not be available!), then consumer saves $ s $ today for tomorrow consumption, i.e.,
    %
    \begin{equation*}
       c + s \le y - t
    ,\end{equation*}
    %
    where $ s > 0 $ represents ``saver'', and $ s < 0 $ represents ``borrower''.
\end{frame}

\begin{frame}{Savings and the Credit Market}
\label{slide:Savings_and_the_Credit_Market}
    Buying/selling \alert{Bonds} are the way to achieve saving $ s $.
    \begin{itemize}
        \item lenders/savers \red{buy} bonds; borrowers \red{sell} bonds.
    \end{itemize}
    Consumer will get $ 1+r $ unit of consumption goods tomorrow if he/she buys $ 1 $ unit of bond today, and thus tomorrow's budget constraint is
    %
    \begin{equation*}
       c'= y' - t'+ ( 1+r )s
    ,\end{equation*}
    %
    where $ r $ is the (net) \alert{real interest rate}, and ``$=$'' since \alert{no date 2}.
    \begin{itemize}
        \item \alert{relative price} of consumption between today and tmw: $ \frac{1}{1+r} $
        \item no default on bonds
        \item no middle man: bonds are trade directly between savers and borrowers
    \end{itemize}
\end{frame}

\begin{frame}{The Lifetime Budget Constraint}
\label{slide:The_Lifetime_Budget_Constraint}
    %
    \begin{align*}
        \text{Date 0}: \quad
            & c + s = y - t
        \\
        \text{Date 1}: \quad
            & c' = y' - t' + ( 1+r )s
        \\
        \text{Saving}: \quad
            & \Rightarrow s = \frac{c' - y' + t'}{1+r}
        \\
        \text{Plug saving back to Date 0}: \quad
            & c + \frac{c' - y' + t'}{1+r} = y - t
        \\
        \text{Rearrange}: \quad
            & \underbrace{%
                c + \frac{c'}{1+r}
              }_{\text{(1)}}
                =
              \underbrace{%
                y - t + \frac{y' - t'}{1+r};
              }_{\text{(2)}}
    \end{align*}
    %
    \begin{itemize}
        \item (1): \alert{present value of total lifetime consumption} (choice by consumer)
        \item (2): \alert{present value of total lifetime net worth}, also called $ we $ (fixed).
    \end{itemize}
\end{frame}

\begin{frame}{Numerical Example of Present Value}
\label{slide:Numerical_Example_of_Present_Value}
    Suppose we have data:
    \begin{tabular}{| c | c | c | c | c | }
        \hline
        $ y $
            & $ y' $
            & $ t $
            & $ t' $
            & $ r $
        \\
        \hline
        \hline
        $ 110 $
            & $120$
            & $ 20 $
            & $ 10 $
            & 0.1
        \\
        \hline
    \end{tabular}

    The face value of the net worth is
    %
    \begin{equation*}
        y - t + y' - t' = 110 - 20 + 120 - 10 = 200
    \end{equation*}
    %
    The present value of lifetime the net worth is
    %
    \begin{equation*}
        y - t + \frac{y' - t'}{1+r} = 110 - 20 + \frac{120 - 10}{1.1} = 190
    \end{equation*}
    %
    Future part has discounted $ 10\% $ to be evaluated in consumption goods today.
\end{frame}

\begin{frame}{Visualization: Lifetime Budget Constraint}
\label{slide:Visualization__Lifetime_Budget_Constraint}
    \begin{columns}
        \begin{column}{0.5\textwidth}
            \begin{figure}
                \caption{\scriptsize Figure 9.1 Consumer’s Lifetime Budget Constraint}
                \includegraphics[width=\textwidth]{./figures/Figure9_1.jpg}
            \end{figure}
        \end{column}
        \begin{column}{0.5\textwidth}
            On $ ( C, C' ) $ plane, $ \because $ substitution between current and future consumption.
            %
            \begin{equation*}
                 c' = \underbrace{we ( 1+r )}_{\text{y-intercept}} \underbrace{-( 1+r )}_{\text{slope}} c
            \end{equation*}
            %
            \begin{itemize}
                \item \textit{E}: \alert{endowment point}, where $ c = y-t $, and $ c' = y' - t' $.
                \item $\overline{BE}$: lending, give up $ c $ for $ c' $
                \item $\overline{AE}$: borrowing, the opposite
            \end{itemize}
        \end{column}
    \end{columns}
\end{frame}

\section{Preference}
\label{sec:Preference}

\begin{frame}{Consumer Preference in Two-Period Model}
\label{slide:Consumer_Preference_in_Two_Period_Model}
Since it is substitution between $ ( c, c' ) $, utility is $ U( c, c' ) $, so
\begin{columns}
    \begin{column}{0.4\textwidth}
        \begin{figure}
            \caption{\scriptsize Figure 9.2  A Consumer’s Indifference Curves}
            \includegraphics[width=\textwidth]{./figures/Figure9_2.jpg}
        \end{figure}
    \end{column}
    \begin{column}{0.6\textwidth}
        \begin{enumerate}
            \item \textbf{monotonicity}: more is preferred
            \begin{itemize}
                \item slope $ = -MRS_{c, c'}$ (substitution)
                \item $ U( I_{3} ) > U( I_{2} ) > U( I_{1} ) $
            \end{itemize}
            \item \textbf{convexity}: diversity is preferred
            \begin{itemize}
                \item Is bow in towards the origin
                \item \alert{consumption smoothing}: preferred equal amount of $ ( c, c' ) $
            \end{itemize}
            \item \textbf{normality}: if lifetime wealth $ \uparrow  $, both $ c $ and $ c' $ $ \uparrow  $
        \end{enumerate}
    \end{column}
\end{columns}
\end{frame}

\section{Consumer's Problem}
\label{sec:Consumer_s_Problem}

\begin{frame}{Consumer's Problem: Two-Period Model}
\label{slide:Consumer_s_Problem__Two_Period_Model}
    \begin{center}
        $\displaystyle \max_{c, c'} U( c, c' ) \quad \text{subject to} \quad c' = we( 1+r ) - c( 1+r )$
    \end{center}
    \begin{columns}
        \begin{column}{0.4\textwidth}
            \begin{figure}
                \caption{\scriptsize Figure 9.3 A Consumer Who Is a Lender}
                \includegraphics[width=\textwidth]{./figures/Figure9_3.jpg}
            \end{figure}
        \end{column}
        \begin{column}{0.6\textwidth}
            \begin{itemize}
                \item substitute $ c' $: $ \displaystyle \max_{c} U( c, we( 1+r ) - c( 1+r ) ) $
                \item FOC: $ \displaystyle D_{c} U( c, c' ) + D_{c'} U( c, c' ) ( -( 1+r ) ) = 0 $
                \item rearrange: $ \displaystyle \frac{D_{c}U( c, c' )}{D_{c'}U( c, c' )} = \alert{MRS_{c, c'} = 1+r} $
                \item Net worth at pt \textit{E}: excess endowment at date 0, so saving $ s = y - t - c^{*} > 0 $!
                \item $ c^{*} < y - t $; $ c'^{*} > y' - t'$
            \end{itemize}
        \end{column}
    \end{columns}
\end{frame}

\begin{frame}{Numerical Example}
\label{slide:Numerical_Example}
    \begin{columns}
        \begin{column}{0.5\textwidth}
            \begin{figure}
                \caption{\scriptsize Figure 9.3 A Consumer Who Is a Borrower}
                \includegraphics[width=\textwidth]{./figures/Figure9_3_2.jpg}
            \end{figure}
        \end{column}
        \begin{column}{0.5\textwidth}
            Let $ U( c, c' ) = \ln c + \ln c' $ and $ r = 0 $,

            $ \displaystyle MRS_{c, c'} = \frac{1/c}{1/c'} = \frac{c'}{c} = 1+r = 1 $

            optimal bundle: $ c^{*} = c'^{*} $
            \begin{itemize}
                \item if $ we = 1 \Rightarrow c + c' = 1 \Rightarrow c^{*} = c'^{*} = \frac{1}{2}$
                \item if $ E = ( 3/4, 1/4 ) $: consumer saves (last slide)
                \item if $ E = ( 1/4, 3/4 ) $: consumer borrows
            \end{itemize}
        \end{column}
    \end{columns}
\end{frame}

\section{Experiment}
\label{sec:Experiment}

\begin{frame}{Increase in Current income}
\label{slide:Increase_in_Current_income}
    Let consumer's \alert{current} income increases from $ y_1 $ to $ y_{2}$, $ y_{2} > y_{1} $
    \begin{columns}
        \begin{column}{0.5\textwidth}
            \begin{figure}
                \caption{\scriptsize Figure 9.5  The Effects of an Increase in Current Income for a Lender}
                \includegraphics[width=\textwidth]{./figures/Figure9_5.jpg}
            \end{figure}
        \end{column}
        \begin{column}{0.5\textwidth}
            \begin{itemize}
                \item parallel shift in budget line: $ r $ the same
                \item endowment: $ E_{1} $ to $ E_{2} $
                \item optimal bundle: $ A $ to $ B $
                \item consumption smoothing: $c_{1} = c'_{1}$, $c_{2} = c'_{2}$
                \item normality: $ c_{2} > c_{1} $, and $ c'_{2} > c'_{1} $
                \item To support normality, $ s_{2} > s_{1} $
            \end{itemize}
        \end{column}
    \end{columns}
\end{frame}

\begin{frame}{Increase in Future income}
\label{slide:Increase_in_Current_income}
    Let consumer's \alert{future} income increases from $ y'_1 $ to $ y'_{2}$, $ y'_{2} > y'_{1} $
    \begin{columns}
        \begin{column}{0.5\textwidth}
            \begin{figure}
                \caption{\scriptsize Figure 9.8  The Effects of an Increase in Future Income}
                \includegraphics[width=\textwidth]{./figures/Figure9_8.jpg}
            \end{figure}
        \end{column}
        \begin{column}{0.5\textwidth}
            \begin{itemize}
                \item shift in lifetime wealth:
                        $ \displaystyle \Delta we = we_{2} - we_{1} = \frac{y'_{2} - y'_{1}}{1+r} $
                \item optimal bundle: $ A $ to $ B $
                \item consumption smoothing: $c_{1} = c'_{1}$, $c_{2} = c'_{2}$
                \item normality: $ c_{2} > c_{1} $, and $ c'_{2} > c'_{1} $
                \item To support normality, \alert{$ s_{2} < s_{1} $}, shift income from date 1 to date 0!
            \end{itemize}
        \end{column}
    \end{columns}
\end{frame}

\begin{frame}{Intuition: Temporary vs Permanent Change in Income}
\label{slide:Intuition__Temporary_vs_Permanent_Change_in_Income}
    \textbf{Permanent Income Hypothesis} (PIH): changes in income that are permanent have large effects on
permanent income (lifetime wealth) and current consumption.
    \begin{itemize}
        \item temporary change in income: $ y_{1} \rightarrow y_{2}  $ \red{or} $ y'_{1} \rightarrow y'_{2} $
        \item permanent change in income: $ y_{1} \rightarrow y_{2}  $ \alert{and} $ y'_{1} \rightarrow y'_{2} $
        \item intuition: permanent change compounds through lifetime
        \item most of temporary increase saved (e.g. COVID stimulus), yet more permanent increase is consumed (e.g. Rich ppl buys houses)
    \end{itemize}
\end{frame}

\begin{frame}{Visualization: Permanent Income Hypothesis}
\label{slide:Visualization__Permanent_Income_Hypothesis}
    \begin{columns}
        \begin{column}{0.5\textwidth}
            \begin{figure}
                \caption{\scriptsize Figure 9.9  Temporary Versus Permanent Increases in Income}
                \includegraphics[width=\textwidth]{./figures/Figure9_9.jpg}
            \end{figure}
        \end{column}
        \begin{column}{0.5\textwidth}
            \textbf{Temporary}:
            \begin{itemize}
                \item budget line: $ \overline{AB} \rightarrow \overline{DE} $
                \item optimal bundle: $ H \rightarrow J $
            \end{itemize}
            \textbf{Permanent}:
            \begin{itemize}
                \item budget line: $ \overline{AB} \rightarrow \overline{GF} $
                \item optimal bundle: $ H \rightarrow K $
            \end{itemize}
            In conclusion,
            \begin{itemize}
                \item larger effect on current consumption when change is permanent
                \item temporary $ \Rightarrow  $ saving; not necessary for permanent
            \end{itemize}
        \end{column}
    \end{columns}
\end{frame}

\section{Data}
\label{sec:Data}

\begin{frame}{Consumption Smoothing in Data}
\label{slide:Consumption_Smoothing_in_Data}
    If all consumers act to smooth their consumption relative to their income, then
\alert{aggregate consumption} should likewise be smooth relative to \alert{aggregate income}.
    \begin{itemize}
        \item recall relative volatility: expect $ \sigma_{C}/\sigma_{Y} < 1 $
    \end{itemize}
    There are three main components of aggregate consumption:
    \begin{enumerate}
        \item \textbf{non-durables}: e.g. food, dishes...
        \item \textbf{durables}: e.g. cars, computers...
        \item \textbf{services}: haircuts, repairing...
    \end{enumerate}
    Does our prediction match the data in aggregate consumption? How about prediction with each component?
\end{frame}

\begin{frame}{Durables Behaves Similar to Investment}
\label{slide:Durables_Behaves_Similar_to_Investment}
    \begin{columns}
        \begin{column}{0.5\textwidth}
            \begin{figure}
                \caption{\scriptsize Figure 9.6  Percentage Deviations from Trend in Consumption of Durables and Real GDP, \alert{blue: Durables}, black: GDP}
                \includegraphics[width=\textwidth]{./figures/Figure9_6.jpg}
            \end{figure}
        \end{column}
        \begin{column}{0.5\textwidth}
            \begin{figure}
                \caption{\scriptsize Figure 3.10 Percentage Deviations from Trend in \alert{Real Investment} and Real GDP, \alert{blue: GDP}, black: investment}
                \includegraphics[width=\textwidth]{../Lecture_03/figures/Figure3_10.jpg}
            \end{figure}
        \end{column}
    \end{columns}
\end{frame}

\begin{frame}{Non-Durables \& Services Similar to Agg. Consumption}
\label{slide:Non_Durables_and_Services_Behaves_Similar_to_Agg__Consumption}
\begin{columns}
    \begin{column}{0.5\textwidth}
        \begin{figure}
            \caption{\scriptsize Figure 9.7 Percentage Deviations from Trend in Consumption of Nondurables and Services and Real GDP, \alert{blue: GDP}, \alert{lightblue: Nondurables + Service}}
            \includegraphics[width=\textwidth]{./figures/Figure9_7.jpg}
        \end{figure}
    \end{column}
    \begin{column}{0.5\textwidth}
        \begin{figure}
            \caption{\scriptsize Figure 3.9 Percentage Deviations from Trend in \alert{Real Consumption} and Real GDP, \alert{blue: GDP}, black: consumption}
            \includegraphics[width=\textwidth]{../Lecture_03/figures/Figure3_9.jpg}
        \end{figure}
    \end{column}
\end{columns}
\end{frame}

\end{document}


text:
\newpage
\section{Reflection on group work}
%The structure may be like..
%\begin{itemize}
%    \item What this reflection about
%    \item Explore the benefits of group work
%    \item Explore the challenge of group work
%    \item Give some example of challenge that we have faced or the benefits we have got
%    \item How we handling challenges
%    \item What we should perform next time
%\end{itemize}
\subsection{The benefits of group work}
Different people may have a different perspective, working with yourself may some time cause a lopsided view. Brainstorming with a group of people can always output a great idea.
\subsection{The challenge of group work}
Just like the benefits, the challenge also comes from the difference of individual. Sometimes we might encounter some confliction, or maybe the group is acting passively and wasting time while meeting. So a group must have a clear goal and support each other.
\subsection{The challenge our group have met}
For each of us, online teaching and study abord is a new thing. We need to adapt to it and came to a methodology while each member may have a different time zone and have other works to be done. And that's the most challenging issue we have.
\subsection{How we address those challenge}
First, by implementing an agreement. Then, we clarify our duty within the group and distribute the workload.
\subsection{How we can manage to make group agreement work}
\begin{itemize}
    \item As for participating fully (in spirit and actuality) and professionally, we should attend every meeting on time and emphasize that everyone must do their job independently and utilize their technical skills.
    \item As for the rule "Each member should abiding the rules of academic honesty", if anyone cheated or disobeyed academic honesty, we will warn for the first time and even repel him if the situation is serious.
    \item As for "Meeting responsibilities", we will supervise each other and help each other to make point short and clear.
    \item As for the rule "Respect each other", we are from the same culture background and we will keep silent when someone is talking.
\end{itemize}
\subsection{How we plan to prepare}
Firstly, we read carefully about the given information and  focus on the problems we ought to cope with. Secondly, we arrange a period of time for conversation. Finally, we talk about the questions and distribute the workload of each other.
\subsection{How do we plan to communicate}
The tool we use for communication is WeChat. Usually, we arrange a period of time when we are all free and start conversation.
\subsection{How we distribute the workload}
We usually split the task into several parts according to people and then randomly choose a part for each of us.

max_stars_repo_path: Group Agreement/Data/Section2.tex

max_stars_repo_name: SilentStars/GoupAssignmentACSS

max_issues_repo_path: Group Agreement/Data/Section2.tex

max_issues_repo_name: SilentStars/GoupAssignmentACSS

max_forks_repo_path: Group Agreement/Data/Section2.tex

max_forks_repo_name: SilentStars/GoupAssignmentACSS


text:
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\newcommand{\A}{\mathbf{A}}
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\newcommand{\qm}{q^{(-)}(x)}

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\author[JLC]{Jeremy Lloyd Conlin \\ \texttt{jlconlin@umich.edu}}

\institute[UM]{University of Michigan, Ann Arbor, Michigan}

\title[Monte Carlo Arnoldi]{Arnoldi's Method for Monte Carlo Criticality Calculations}

\date[ORNL]{Oak Ridge National Laboratory}

\begin{document}
\begin{abstract}
    The power method has been the algorithm of choice for Monte Carlo criticality codes for decades.  The power method can only calculate the fundamental eigenmode and suffers from slow convergence.  Despite its limitations, Monte Carlo codes have continued to use it because it is simple to implement and is consistent.

    Arnoldi's method of minimized iterations has been used in the computer science field for many years to calculate the eignvalues and eigenvectors of a matrix.  It is particularly interesting for sparse matrices or matrix-free applications where an explicit form of the matrix is not known.

    Arnoldi's method has a great advantage over the power method as it can calculate multiple eigenmodes.  Recent work has also shown the possibility of reducing the computational expense of calculating the matrix-vector product by reducing the precision of matrix-vector product.  This can be done without altering the convergence of the calculation.

    My PhD research has focused on using Arnoldi's method in a Monte Carlo criticality application.  I have implemented Arnoldi's method in a slab-geometry Monte Carlo code and have compared it to the power method.  In my talk I will present what I have learned about Arnoldi's method.  I will show comparisons between Arnoldi's method and the power method for slab geometry problems.  I will also discuss some work that remains to be done.
\end{abstract}

\begin{frame}
    \titlepage
\end{frame}

\begin{frame}
    \frametitle{Outline}
    \tableofcontents[pausesection]
\end{frame}

\section{Krylov Subspace Methods}
\begin{frame}
    \frametitle{Krylov Subspace Methods}
    Krylov Subspace:
    \begin{equation*}
        \mathcal{K}_m~=~\mathrm{span}\left\{v, \A v, \A^2v, \ldots , \A^{m-1}v\right\}
    \end{equation*}
    \begin{itemize}
        \item Constructed iteratively
            \note{We could construct the subspace the inefficient way by taking the power of the linear operator multiple times then operate on the vector.  Or we can just  operate on the previously calculated Krylov vector.}
        \item Don't require explicit knowledge of linear operator
        \item Perfect for Monte Carlo criticality applications
    \end{itemize}
\end{frame}

\begin{frame}
    \frametitle{Particle Transport Equation}
    \begin{itemize}
        \item Boltzmann Equation:
        \begin{equation*}
            \mathbf{\Omega}\cdot\mathbf{\nabla}\psi(\mathbf{r},\mathbf{\Omega})+\Sigma_t\psi(\mathbf{r},\mathbf{\Omega}) - \frac{\Sigma_s}{4\pi}\int \psi(\mathbf{r},\mathbf{\Omega})\;d\Omega =  \frac{1}{k}\frac{\nu\Sigma_f}{4\pi}\int \psi(\mathbf{r},\mathbf{\Omega})\;d\Omega
        \end{equation*}
        \item Operator Form:
        \begin{align*}
            \left(\mathbf{L} + \mathbf{C} - \mathbf{S}\right)\psi &= \frac{1}{k}\mathbf{F}\psi \\
            \mathbf{T}\psi &= \frac{1}{k}\mathbf{F}\psi
        \end{align*}
        \item Define:
        \begin{equation*}
            q \equiv \mathbf{F}\psi \hspace{5em} \A \equiv\mathbf{FT}^{-1}
        \end{equation*}
        \item Finally:
        \begin{equation*}
            \A q = kq
        \end{equation*}
    \end{itemize}
\end{frame}

\begin{frame}
    \frametitle{Monte Carlo Application of $\A$}
    \begin{align*}
        \A q &= kq \\
        q_{m+1} &= \frac{1}{k_m}\A q_m
    \end{align*}
    \begin{itemize}
        \item $q_m$ is a fission source
        \note{A fission source is a collection of fission sites}
        \item Neutron is sampled from $q_m$ and transported
        \item New fission sites are generated at points where neutron causes fission
    \end{itemize}
\end{frame}

\section{Power Method}
\begin{frame}
    \frametitle{Krylov Subspace---Power Method}
    \begin{equation*}
        \mathcal{K}_m~=~\mathrm{span}\left\{v, \A v, \A^2v, \ldots , \A^{m-1}v\right\}
    \end{equation*}
    \begin{itemize}
        \item Straightforward implementation of a Krylov Subspace
        \item Subspace becomes ``not-helpful'' because Krylov vectors are all nearly the same
    \end{itemize}
\end{frame}

\begin{frame}
    \frametitle{Krylov Subspace---Power Method}
    Power Iteration:
    \begin{gather*}
        q_{m+1} = \frac{1}{k_{m}}\mathbf{A}q_{m}, \\[2mm]
        k_{m+1} = k_{m}\frac{\int \A q_{m}}{\int q_{m}} = k_{m}\frac{\sum_{i=1}^{N} \omega_{m+1}^{(i)}}{\sum_{i=1}^{N} \omega_m^{(i)}}
    \end{gather*}
    \begin{itemize}
        \item As $m$ increases we are guaranteed to converge to the true eigenvector and eigenvalue (assuming no bias)
        \item Convergence is slow---proportional to dominance ratio $\left( \lambda_1/\lambda_0 \right)$
        \item Forgets/ignores information from previous iterations
    \end{itemize}
\end{frame}

\section{Arnoldi's Method}
\begin{frame}
    \frametitle{Arnoldi's Method}
    \begin{align*}
        \mathcal{K}_m &= \mathrm{span}\left\{v, \A v, \A^2v, \ldots , \A^{m-1}v\right\} \\
        \mathcal{K}_m &= \mathrm{span}\left\{q_0, q_1, q_2, \ldots , q_{m-1}\right\}
    \end{align*}
    \begin{itemize}
        \item Uses all previously calculated vectors
        \item $q_i$'s are called Arnoldi vectors
        \item Linear operator is applied in the same way as for the power method
            \note{Particle is sampled from fission source and transported causing new fissions}
    \end{itemize}
\end{frame}

\begin{frame}
    \frametitle{Arnoldi's Method}
    Arnoldi Iteration:
    \begin{itemize}
        \item Application of operator
        \begin{equation*}
            \tilde{q}_{m+1} = \A q_m
        \end{equation*}
        \item Orthogonalized against previous Arnoldi vectors
        \begin{equation*}
            \tilde{q}_{m+1} = \A q_m - \sum_{j=1}^m q_j h_{jm}
        \end{equation*}
        \item Normalized
        \begin{equation*}
            q_{m+1} = \frac{\tilde{q}_{m+1}}{h_{m+1,m}}
        \end{equation*}
    \end{itemize}
\end{frame}

\begin{frame}
    \frametitle{Arnoldi Iteration}
    Arnoldi iteration:
    \begin{gather*}
        \tilde{q}_{k+1} = \A q_k - \sum_{j=1}^k q_j h_{jk} \hspace{0.5in} q_{k+1} = \frac{\tilde{q}_{k+1}}{h_{k+1,k}} \\[2mm]
        h_{jk} = \langle Aq_k, q_j \rangle = \langle q_{k+1}, q_j \rangle.
    \end{gather*}
    \note{The inner products calculated during the orthogonalizing and normalizing of the Arnoldi vectors form an upper Hessenberg matrix.}
    \pause
    After $m$ iterations
    \begin{equation*}
        \A Q_m = Q_{m}H_{m} + q_{m+1}h_{m+1,m}e_m^T
    \end{equation*}
\end{frame}
\begin{frame}
    \frametitle{Eigenvalues from Arnoldi's Method}
    \begin{equation*}
        \A Q_m = Q_{m}H_{m} + q_{m+1}h_{m+1,m}e_m^T
    \end{equation*}
    The eigenvalues of $H_m$ can be calculated
    \begin{equation*}
        H_m x = \lambda x
    \end{equation*}
    \note{This is easy to do because $H_m$ is small.  Can be calculated using whatever algorithm one prefers}
    \pause
    Arnoldi factorization can gives us the Ritz pairs of $\A$:
    \begin{subequations}\begin{align*}
        \A Q_mx_m &= Q_{m}H_{m}x_m + q_{m+1}h_{m+1,m}e_m^Tx_m \\[2mm]
        \A Q_mx_m &= \lambda Q_{m}x_m + q_{m+1}h_{m+1,m}e_m^Tx_m \\[2mm]
        \A y_m &= \lambda y_m + q_{m+1}h_{m+1,m}e_m^Tx_m
    \end{align*}\end{subequations}
    \pause
    The Ritz pair $\left(\lambda, y_m\right)$ is an estimate of an eigenpair of $\A$.
\end{frame}

\begin{frame}
    \frametitle{Residual}
    \begin{equation*}
        \A y_m = \lambda y_m + q_{m+1}h_{m+1,m}e_m^Tx_m
    \end{equation*}
    \note{If $\left(\lambda, y_n\right)$ is an eigenpair of $\A$ then the residual $ \A y_m - \lambda y_m$ is zero.  If not an eigenpair, $\left\|\A y_m - \lambda y_m\right\|$ will not be zero, but it will be close to zero if it is a good approximation to an eigenpair.  In other words, a small residual guarantees that $\left(\lambda, y_m\right)$ is an eigenpair of an operator close to $\A$.}
    Residual:
    \begin{align*}
        r_m &= \left\|\A y_m - \lambda y_m\right\| \\
         &= \left|q_{m+1}h_{m+1,m}e_m^Tx_m\right| \\
         &= \left|h_{n+1,n}\right|\left|e_n^Tx_{n}\right|
    \end{align*}
    If $r_m$ is small, $\left(\lambda, y_n\right)$ is a good approximation of an eigenpair of $\A$.
    \note{I'll return to the residual later.}
\end{frame}

\subsection{Restarted Arnoldi's Method}
\begin{frame}
    \frametitle{Restarted Arnoldi's Method}
    What is a good starting vector?
    \pause
    \begin{equation*}
        q_0 = a_0x_0 + a_1x_1 + \cdots + a_nx_n
    \end{equation*}
    $x_i$'s are eigenvectors from desired portion of spectrum of $\A$.

    \pause
    \vspace{2ex}
    Restarting Arnoldi:
    \begin{itemize}
        \item Improves restart vector
        \item Reduces size of Krylov Subspace
        \item Reduces computational expense of orthogonalization
    \end{itemize}
\end{frame}

\subsection{Monte Carlo Implementation}
\subsubsection{Spatial Discretization}
\begin{frame}
    \frametitle{Spatial Discretization}
    What is the inner product of two fission sources?
    \begin{equation*}
        h_{jk} = \langle q_k,q_j\rangle = \int q_k(x)q_j(x) dx
    \end{equation*}

    \pause
    Must discretize fission source
    \begin{equation*}
        q(x) = \sum_{i=1}^B a_i \Pi_i(x),
    \end{equation*}
    \begin{equation*}
        \Pi_i(x) = \left \{
            \begin{array}{cc}
                1 ,& x_{i} \leq x < x_{i+1} \\
                0 ,& \mathrm{otherwise.}
            \end{array}\right.
    \end{equation*}
\end{frame}

\begin{frame}
    \frametitle{Spatial Discretization}
    Discretized fission source
    \begin{equation*}
        q(x) = \sum_{i=1}^B a_i \Pi_i(x), \hspace{0.5in}
        \Pi_i(x) = \left \{
            \begin{array}{cc}
                1 ,& x_{i} \leq x < x_{i+1} \\
                0 ,& \mathrm{otherwise.}
            \end{array}\right.
    \end{equation*}

    \pause
    Vector representation
    \begin{equation*}
        q_k = \left[a_1^{(k)}\; a_2^{(k)}\; \ldots\; a_B^{(k)}\right]^T
    \end{equation*}

    Inner product becomes dot product between two vectors:
    \begin{equation*}
        h_{jk} = \int q_k(x)q_j(x) dx = \sum_{i=1}^B a_i^{(k)}a_i^{(j)}
    \end{equation*}
\end{frame}

\subsubsection{Negative Sources}
\begin{frame}
    \frametitle{Negative Sources}
    \note{Through orthogonalization of Arnoldi vectors, some components of vectors will inevitably become negative}

    \only<1>{\includegraphics[width=\textwidth, keepaspectratio]{FullPDF}}
    \only<2>{\includegraphics[width=\textwidth, keepaspectratio]{SplitPDF}}
%   \only<3>{\includegraphics[width=\textwidth, keepaspectratio]{PosPDF}}
\end{frame}

\begin{frame}
    \frametitle{Negative Sources}
    \note{Through orthogonalization of Arnoldi vectors, some components of vectors will inevitably become negative}

    \begin{columns}[c]
    \column{0.5\textwidth}
        \begin{subequations}\begin{eqnarray*}
            \qp &=& \left\{
            \begin{array}{rc}
                q(x) ,& q(x) \geq 0 \\
                0 ,& \mathrm{else}
            \end{array}\right.  \\
            \qm &=& \left\{
            \begin{array}{rc}
                q(x) ,& q(x) < 0 \\
                0 ,& \mathrm{else}
            \end{array}\right.
        \end{eqnarray*}\end{subequations}

    \column{0.5\textwidth}
        \only<1>{
        \begin{align*}
            q(x) &\equiv \qp + \qm \\[2ex]
            \A q(x) &= \A \qp - \A \qm
        \end{align*}
        }

        \only<2>{
        \begin{align*}
            p(x) &\equiv \frac{|q(x)|}{\int|q(x)|\,dx} \\
             &= \frac{\qp + |\qm|}{\int|q(x)|\,dx}
        \end{align*}
        }
    \end{columns}

    \note{Subtracting the negative source is equivalent to giving particles negative weight transporting and scoring as usual.}
\end{frame}

\section{Numerical Results}
\begin{frame}
    \frametitle{Problem Parameters}
    \begin{itemize}
        \item Homogeneous slab geometry
        \item $\Sigma_s = 0.5$, $\nu\Sigma_f = 0.5$, $\Sigma_t = 1.0$
        \item Both methods tracked the same number of particles
    \end{itemize}

%   \vspace{0.25in}
    \begin{table}[h]
        \centering
        \begin{tabular}{cccccc}
            \toprule
            Width & Spatial & \multirow{2}{10ex}{Particles} & \multirow{2}{10ex}{Iterations} & Inactive & Active \\
            (mfp) & Bins & & & Restarts & Restarts \\
            \midrule
            \multirow{2}{\LL}{20} & \multirow{2}{\LL}{75} & \multirow{2}{\LL}{500,000} & 20 & 2 & 20 \\
            & & & \multicolumn{3}{c}{40/400 power cycles} \\
            \midrule
            \multirow{2}{\LL}{50} & \multirow{2}{\LL}{75} & \multirow{2}{\LL}{500,000} & 30 & 10 & 30 \\
            & & & \multicolumn{3}{c}{300/900 power cycles} \\
            \midrule
            \multirow{2}{\LL}{100} & \multirow{2}{\LL}{100} & \multirow{2}{\LL}{10,000,000} & 30 & 5 & 25 \\
            & & & \multicolumn{3}{c}{150/750 power cycles} \\
            \bottomrule
        \end{tabular}
    \end{table}
\end{frame}

\begin{frame}
    \frametitle{Numerical Results}
\begin{table}[h]
    \centering
    \begin{tabular}{ccccc}
        \toprule
        Width (mfp) & $\lambda_0$ & Method & Eigenvalue &  Runtime (s) \\
        \midrule
        \multirow{2}{5mm}{20} & \multirow{2}{15mm}{0.985928} & Power & 0.98590 $\pm$ 0.00006 & 833 \\
                           & & Arnoldi & 0.9857 $\pm$ 0.0002 & 767 \\
        \midrule
        \multirow{2}{5mm}{50} & \multirow{2}{15mm}{0.99752} & Power & 0.99753 $\pm$ 0.00004 & 2307 \\
                           & & Arnoldi & 0.9976 $\pm$ 0.0002 & 2156 \\
       \midrule
       \multirow{2}{5mm}{100} & \multirow{2}{15mm}{0.99933} & Power & 0.99929 $\pm$ 0.00001 & 42820 \\
                          & & Arnoldi & 0.99926 $\pm$ 0.00007 & 35240 \\
        \bottomrule
    \end{tabular}
    \label{tab:results}
\end{table}

\vspace{2ex}
{\scriptsize Jeremy Lloyd Conlin and James Paul Holloway, \emph{Arnoldi's method of minimized iterations for Monte Carlo criticality calculations}, PHYSOR 2008, Interlaken, Switzerland}
\end{frame}

\begin{frame}
    \only<1>{\frametitle{Eigenvalue Convergence---20 mfp}
    \begin{center}\includegraphics[width=0.90\textwidth, keepaspectratio]{ThinValue}\end{center}}
    \only<2>{\frametitle{Eigenvalue Convergence---50 mfp}
    \begin{center}\includegraphics[width=0.90\textwidth, keepaspectratio]{MedValue}\end{center}}
    \only<3>{\frametitle{Eigenvalue Convergence---100 mfp}
    \begin{center}\includegraphics[width=0.90\textwidth, keepaspectratio]{ThickValue}\end{center}}
\end{frame}

\begin{frame}
    \frametitle{Eigenvectors}
    \only<1>{\begin{center}\includegraphics[width=0.90\textwidth, keepaspectratio]{ThinVector}\end{center}}
%   \only<2>{\includegraphics[width=\textwidth, keepaspectratio]{MedVector}}
%   \only<3>{\includegraphics[width=\textwidth, keepaspectratio]{ThickVector}}
\end{frame}

\subsection{Discretization}
\begin{frame}
    \frametitle{Discretization Bias}
    \begin{center}\includegraphics[width=0.90\textwidth, keepaspectratio]{Bias}\end{center}
\end{frame}

\subsection{Relaxed Matrix-vector Products}

\subsection{Relaxed Arnoldi's Method}
\begin{frame}
    \frametitle{Relaxed Arnoldi's Method}
    \begin{equation*}
        r_m = \left\|\A y_m - \lambda y_m\right\| = \left|q_{m+1}h_{m+1,m}e_m^Tx_m\right|
    \end{equation*}
    \note{We know that as the residual decreases, our estimate of the Ritz value becomes a better estimate of the eigenvalue of $\A$}
    \pause

    Bouras and Frayss\'{e}:
    \begin{itemize}
        \item Can \emph{relax} application of linear operator
        \item Maintain convergence of Arnoldi's method
        \item Save computational expense
    \end{itemize}
\end{frame}

\begin{frame}
    \frametitle{Relaxed Arnoldi's Method}
    \begin{equation*}
        \hat{q}_{m+1} = \left(\A + \DA\right)q_m
    \end{equation*}
    \pause

    Magnitude of $\DA$ is prevented from growing too large
    \begin{gather*}
        \alpha_k = \frac{1}{\min\left(\left\|r_{k-1}\right\|, 1\right)} \\[2mm]
        \left\|\DA_k\right\| = \varepsilon_k \left\|\A\right\|
    \end{gather*}
    where $\varepsilon_k = \min\left(\alpha_k \eta, 1\right)$.

    \vspace{2ex}
    \pause
    As residual decreases, precision of application of linear operator decreases.

\end{frame}

\begin{frame}
    \frametitle{Monte Carlo Relaxation}
    \begin{align*}
        \hat{q}_{m+1} &= \left(\A + \DA\right)q_m \\
        \DA &\propto \frac{1}{\sqrt{N}}
    \end{align*}
    More than 80\% of time spent on tracking particles (application of $\A$)

    \pause
    \vspace{2ex}
    How to relax Monte Carlo\pause---track fewer particles when residual is small
    \begin{equation*}
        N_k = \left \{
            \begin{array}{ccc}
                N_0 &, & \eta < r_{k-1} \\
                N_0 \left( r_{k-1}/\eta \right) &, & \eta \geq r_{k-1},
            \end{array}
            \right.
    \end{equation*}
\end{frame}

\begin{frame}
    \frametitle{Problem Parameters}
    \begin{itemize}
        \item Homogeneous slab geometry
        \item 20mfp thick
        \item 1E6 particles per iteration
        \item $\eta = 0.1$ for relaxed Arnoldi
    \end{itemize}

    \begin{table}[h]
        \centering
        \begin{tabular}{ccccc}
            \toprule
            \multirow{2}{10ex}{Material} & \multirow{2}{10ex}{Method} & \multirow{2}{10ex}{Iterations} & Inactive & Active \\
            & & & Restarts & Restarts \\
            \midrule
            \multirow{3}{10ex}{Absorbing} & Power & \multicolumn{3}{c}{50/280 power cycles} \\
            & Arnoldi & 10 & 5 & 28 \\
            & Relaxed Arnoldi & 10 & 5 & 150 \\
            \midrule
            \multirow{3}{10ex}{Scattering} & Power & \multicolumn{3}{c}{150/250 power cycles} \\
            & Arnoldi & 10 & 15 & 25\\
            & Relaxed Arnoldi & 10 & 15 & 150\\
            \bottomrule
        \end{tabular}
    \end{table}
\end{frame}

\begin{frame}
    \frametitle{Numerical Results}
\begin{table}
    \centering
    \begin{tabular}{cccc}
        \toprule
        Material & $\lambda_0$ & Method & Eigenvalue \\
        \midrule
        \multirow{3}{15mm}{Absorbing} & \multirow{3}{15mm}{0.98593} & Power & 0.98593 $\pm$ 0.00004 \\ % 20mfp.Power.short
        & & Arnoldi & 0.98590 $\pm$ 0.00008 \\ % 20mfp.NotRelaxed4
        & & Relaxed Arnoldi & 0.98592 $\pm$ 0.00006 \\ % 20mfpRelaxed
        \midrule
        \multirow{3}{15mm}{Scattering} & \multirow{3}{15mm}{0.93339} & Power & 0.93335 $\pm$ 0.00008 \\ % 20mfp.Scattering.NotRelaxed.i15.Power.dat active: 250
        & & Arnoldi & 0.93331 $\pm$ 0.00023 \\ % 20mfp.Scattering.NotRelaxed.i15.dat Restart #: 24
        & & Relaxed Arnoldi & 0.93338 $\pm$ 0.00008 \\ % 20mfp.Scattering.x0.1.i15.Long.dat
        \bottomrule
    \end{tabular}
\end{table}

    \vspace{2ex}
    {\scriptsize Jeremy Lloyd Conlin and James Paul Holloway, \emph{Relaxation scheme for Monte Carlo explicitly restarted Arnoldi's method for criticality calculations}, M\&C 2009, Saratoga Springs, NY}
\end{frame}

\begin{frame}
    \only<1>{\frametitle{Eigenvalue Convergence---Absorbing Material}
    \begin{center}\includegraphics[width=0.9\textwidth,keepaspectratio]{ValueAbsorbing} \end{center}}
    \only<2>{\frametitle{Eigenvalue Convergence---Scattering Material}
    \begin{center}\includegraphics[width=0.9\textwidth,keepaspectratio]{ValueScattering} \end{center}}
\end{frame}

\begin{frame}
    \frametitle{Relaxed Timing Results}
    \begin{table}
        \centering
        \begin{tabular}{cccccc}
            \toprule
            Material & Method & Runtime (s) & Particles/sec & Cost \\
            \midrule
            \multirow{3}{15mm}{Absorbing} & Power & 1742 & $2.58 \times 10^5$  & 1 \\ % 20mfp.Power.short
            & Arnoldi & 1669 & $2.70 \times 10^5$ & 0.956 \\ % 20mfp.NotRelaxed4
            & Relaxed Arnoldi & 1972 & $2.34 \times 10^5$ & 1.100 \\ % 20mfpRelaxed
            \midrule
            \multirow{3}{15mm}{Scattering} & Power & 2310 & $1.73 \times 10^5$  & 1 \\ % 20mfp.Scattering.NotRelaxed.i15.Power.dat active:250
            & Arnoldi & 2340 & $1.71 \times 10^5$ & 1.01 \\ % 20mfp.Scattering.NotRelaxed.i15.dat Restart #: 24
            & Relaxed Arnoldi & 2272 & $1.75 \times 10^5$ & 0.989 \\ % 20mfp.Scattering.x0.1.i15.Long.dat
            \bottomrule
        \end{tabular}
        \label{tab:Timing}
    \end{table}
\end{frame}

\begin{frame}
    \only<1>{\frametitle{Uncertainty---Absorbing Material}
    \begin{center}\includegraphics[width=0.9\textwidth,keepaspectratio]{UncertaintyAbsorbing} \end{center}}
%   \begin{center}\includegraphics[width=0.9\textwidth,keepaspectratio]{UncertaintyAbsorbingLogLog}\end{center}}
    \only<2>{\frametitle{Uncertainty---Scattering Material}
    \begin{center}\includegraphics[width=0.9\textwidth,keepaspectratio]{UncertaintyScattering} \end{center}}
%   \begin{center}\includegraphics[width=0.9\textwidth,keepaspectratio]{UncertaintyScatteringLogLog}\end{center}}
\end{frame}

\subsection{Discussion}
\begin{frame}
    \frametitle{Discussion}
    Arnoldi's method:
    \begin{itemize}
        \item Can be used in Monte Carlo criticality applications
        \item Can calculate higher order eigenmodes
        \item Should be relaxed to reduce uncertainty and possibly save time
    \end{itemize}
\end{frame}

\section{Future Work}
\subsection{Implicitly Restarted Arnoldi's Method}
\begin{frame}
    \frametitle{Outline}
    \tableofcontents[pausesection]
\end{frame}

\begin{frame}
    \frametitle{Restarted Arnoldi}
    \begin{equation*}
        \A Q_m = Q_{m}H_{m} + r_m
    \end{equation*}
    \vspace{2ex}
    Restart vector:
    \begin{equation*}
        q_0 = a_0y_0 + a_1y_1 + \cdots + a_{n-1}y_{n-1}
    \end{equation*}

    \pause
    \begin{itemize}[<+->]
        \item Desire $j$ eigenpairs
        \item Want $a_j, \cdots, a_{n-1}$ to be small
        \item Explicit restarts force $a_j = \cdots = a_{n-1} = 0$
    \end{itemize}
\end{frame}

\begin{frame}
    \frametitle{Implicit Restarts}
    Replace Arnoldi Iterations with shifted QR-algorithm iterations on $H_m$
    \begin{gather*}
       \left(H_m - \mu_1I\right) = V_1R_1 \\[1ex]
       \hat{H}_1 = V_1^*H_mV_1
    \end{gather*}
    After $j$ iterations
    \begin{equation*}
        \hat{H}_p = \hat{V}_p^*H_m\hat{V}_p
    \end{equation*}
    where
    \begin{equation*}
        \hat{V}_p = V_1V_2\cdots V_p
    \end{equation*}
\end{frame}

\begin{frame}
    \frametitle{Implicit Restarts}
    Substitute $H_m = \hat{V}_pH_m\hat{V}_p^*$ into Arnoldi factorization

    \begin{align*}
        \A Q_m &= Q_{m}H_{m} + r_m \\
        \A Q_m &= Q_{m}\hat{V}_pH_m\hat{V}_p^* + r_m \\
        \A Q_m\hat{V}_p &= Q_{m}\hat{V}_pH_m\hat{V}_p^*\hat{V}_p + r_m\hat{V}_p \\
        \A \hat{Q}_m &= \hat{Q}_mH_m + r_m\hat{V}_p
    \end{align*}
    where $\hat{Q}_m = Q_m\hat{V}_p$.

\end{frame}

\begin{frame}
    \frametitle{Implicit Restarts}
    \begin{equation*}
        \A \hat{Q}_m = \hat{Q}_mH_m + r_m\hat{V}_p
    \end{equation*}

    \begin{itemize}
        \item Arnoldi factorization
        \item Restarted with $p$ iterations of shifted QR-algorithm
        \pause
        \item If shifts are chosen judiciously:
            \begin{itemize}
                \item Implicit restart equivalent to explicit restart
                \item Suppresses unwanted portion of spectrum of $\A$
                \item Implicit restarts can then proceed at iteration $p+1$
            \end{itemize}
        \pause
        \item Implicit restarts trade applications of $\A$ for shifted QR-algorithm iterations
    \end{itemize}

    \note{$\A \hat{Q}_m &= \hat{Q}_pH_m + r_m\hat{V}_p$ is an Arnoldi factorization.  It can be shown that performing the shifted QR-algorithm iterations will produce a restart vector with the unwanted portion of the spectrum suppressed and starting with }
\end{frame}

\begin{frame}
    \frametitle{Questions}
\end{frame}

\end{document}

max_stars_repo_name: jlconlin/PhDThesis

max_issues_repo_name: jlconlin/PhDThesis

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text:
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text:
\documentclass{article}

\usepackage{hyperref}

\textwidth13cm
\parindent0mm

\begin{document}

\thispagestyle{empty}

\begin{center}
\textsc{\large Question Answering over Linked Data}

\vspace{.2cm}

\textbf{\huge QALD-5: Evaluation results}

\vspace{.4cm}

\url{http://www.sc.cit-ec.uni-bielefeld.de/qald}

\end{center}

\vspace{.2cm}

\hrule

\subsubsection*{Column descriptions}

\begin{itemize}
\item The first column specifies the system name and the language it processed.
\item \emph{Processed} states for how many of the questions the system provided a query and/or answer.
\item \emph{Right} specifies how many of these questions were answered with an F-1 measure of 1.
\item \emph{Partial} specifies how many of the questions were answered with an F-1 measure strictly between 0 and 1.
\item \emph{Recall}, \emph{Precision} and \emph{F-1} report the measures with respect to the number of processed questions.
\item \emph{F-1 Global} in addition reports the F-1 measure with respect to the total number of questions.
Note that the HTML result files only report the global measures.
\end{itemize}

\subsection*{Multilingual question answering over DBpedia}

\emph{Total:} 50

\vspace{.6cm}

\begin{tabular}{r@{\ }lccccccc}
& & Processed & Right & Partial & Recall & Precision & F-1 & F-1 Global \\
\hline \\[1ex]
Xser & (en) & 42 & 26 & 7 & 0.72 & 0.74 & \textbf{0.73} & \textbf{0.63} \\
APEQ & (en) & 26 & 8 & 5 & 0.48 & 0.40 & \textbf{0.44} & \textbf{0.23} \\
QAnswer & (en) & 37 & 9 & 4 & 0.35 & 0.46 & \textbf{0.40} & \textbf{0.30} \\
SemGraphQA & (en) & 31 & 7 & 3 & 0.32 & 0.31 & \textbf{0.31} & \textbf{0.20} \\
YodaQA & (en) & 33 & 8 & 2 & 0.25 & 0.28 & \textbf{0.26} & \textbf{0.18} \\
\end{tabular}

\subsection*{Hybrid question answering}

\emph{Total:} 10

\begin{tabular}{rccccccc}
& Processed & Right & Partial & Recall & Precision & F-1 & F-1 Global \\
\hline \\[1ex]
ISOFT & 3 & 2 & 1 & 1.00 & 0.78 & \textbf{0.87} & \textbf{0.26} \\
HAWK & 3 & 1 & 0 & 0.33 & 0.33 & \textbf{0.33} & \textbf{0.10} \\
YodaQA & 10 & 1 & 0 & 0.10 & 0.10 & \textbf{0.10} & \textbf{0.10} \\
SemGraphQA & 6 & 0 & 0 & 0.00 & 0.20 & \textbf{0.00} & \textbf{0.00} \\
Xser & 3 & 0 & 0 & 0.0 & 0.00 & \textbf{0.00} & \textbf{0.00} \\
\end{tabular}

\end{document}

max_stars_repo_name: arademaker/QALD

max_issues_repo_name: arademaker/QALD

max_forks_repo_name: arademaker/QALD


text:
\cleardoublepage
\pdfbookmark{Acknowledgements}{Acknowledgements}
\chapter*{Acknowledgements}

Foremost, I would like to express my gratitude to my advisor, Prof.~Dr~Francisco M.\ Couto, whose expertise and undeniably scientifically oriented mind added considerably to my PhD. I appreciate his vast horizons and skills in many scientific areas (\eg semantic similarity, biomedical ontologies, Bioinformatics in general, just to list the ones more closely related to my research efforts), and his assistance in the extensive periods where writing was the major undertaking of my work (particularly the several manuscripts we jointly submitted for publication, as well as this document). Most of all, I look up to his ``relaxed'' yet serious attitude towards research, which always positively surprised me. Sometimes, research feels like a herculean task that we need to carry out in order to see some results, but more often it looks like a small train ride where we simply appreciate the landscape of knowledge to which we ourselves contribute.

My PhD companions, which are no longer students but Doctors, also deserve my gratitude: in no particular order, I thank Ana Teixeira, Catia M. Machado, Catia Pesquita, Daniel Faria, Hugo Bastos and Tiago Grego, with whom I collaborated in some way or another, and whom I could always count on to tag along on a brainstorming session over coffee. A further acknowledgement goes to André Lamúrias, with whom I collaborated towards the end of my PhD.

I recognize that this research would not have been possible without the financial assistance of the Fundação para a Ciência e Tecnologia, and express my gratitude to that agency for funding my PhD scholarship SFRH\slash BD\slash 69345\slash 2010.

I would also like to thank my parents for the infinite support they have been providing throughout my entire life, from the very first breath I took. The excellent upbringing you provided was the exact amount of motivation I needed to pursue the career in science that I now so dearly esteem. Thank you for always being there for me, for always helping me succeed. I also want to thank my brothers, André and Simão, for no other motive than that you are always present in my life. You are the best.

In particular, I must acknowledge my wife and best friend, Sandra, who stood by me every step of the way, who had to endure my absence whenever I needed to attend some conference, and without whose love, encouragement and unconditional assistance I would not have been able to finish this work. The biggest of my smiles is yours.

\vfill

{\flushright
\textit{Lisboa}, January 6\textsuperscript{th}, 2016\break
João Ferreira
\par}

max_stars_repo_name: jotomicron/phd-thesis

max_issues_repo_name: jotomicron/phd-thesis

max_forks_repo_name: jotomicron/phd-thesis


text:
\subsection{Contracts}

\input{res/sections/solidity/genericcontracts.tex}
\input{res/sections/solidity/storagecontracts.tex}
\input{res/sections/solidity/logiccontracts.tex}