Clean up document

paper.tex

@@ -1,43 +1,27 @@
 \documentclass[journal]{IEEEtran}
 
 \usepackage{amsmath,amsfonts}
+\usepackage{siunitx}
+\usepackage{mleftright}
 \usepackage{float}
 \usepackage{titlesec}
-\usepackage{algorithmic}
-\usepackage{algorithm}
-\usepackage{siunitx}
-\usepackage[normalem]{ulem}
-\usepackage{dsfont}
-\usepackage{mleftright}
-\usepackage{bbm}
 \usepackage[
     backend=biber,
     style=ieee,
     sorting=nty,
 ]{biblatex}
 
-\usepackage{tikz}
-\usetikzlibrary{spy, arrows.meta,arrows}
-
 \usepackage{pgfplots}
 \pgfplotsset{compat=newest}
 \usepgfplotslibrary{statistics}
 
-\usepackage{pgfplotstable}
-\usepackage{filecontents}
-
-\hyphenation{op-tical net-works semi-conduc-tor IEEE-Xplore}
-
 %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % Template modifications
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %
 
-% TODO: "The right strategy" pun
-
-\titlespacing*{\section}
-{0mm}{3mm}{1mm}
+\titlespacing*{\section}{0mm}{3mm}{1mm}
 
 \makeatletter
 \def\@maketitle{%
@@ -46,11 +30,11 @@
     \vspace*{-4mm}
     \begin{center}%
         {\Huge \linespread{0.9}\selectfont \@title \par}%
-        {\large
-            \lineskip .5em%
+        {\large \lineskip .5em%
             \begin{tabular}[t]{c}%
                 \@author
-        \end{tabular}\par}%
+            \end{tabular}
+        \par}%
     \end{center}%
     \vspace*{-8mm}
 }
@@ -111,12 +95,12 @@
 Performance}
 
 \author{Some concerned fellow students%
-    \thanks{The authors would like to thank their hard-working peers as well as
-        the staff of the KIT library for their unknowing - but vital -
-participation.}}
+    \thanks{The authors would like to thank their hard-working peers as
+        well as the staff of the KIT library for their unknowing - but vital
+- participation.}}
 
-\markboth{Journal of the Association of KIT Bibliophiles}{The
-Effect of the Choice of Hydration Strategy on Average Academic Performance}
+\markboth{Journal of the Association of KIT Bibliophiles}{The Effect
+of the Choice of Hydration Strategy on Average Academic Performance}
 
 \maketitle
 
@@ -126,14 +110,12 @@ Effect of the Choice of Hydration Strategy on Average Academic Performance}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %
 
-% \vspace*{-10mm}
-
 \begin{abstract}
     We evaluate the relationship between hydration strategy and
-    academic performance and project that by using the right button of
-    the water dispenser to fill up their water bottles, students can potentially
-    gain up to \SI{4.14}{\second} of study time per refill, which is amounts to
-    raising their grades by up to 0.00103 points.
+    academic performance and project that by using the right button
+    of the water dispenser to fill up their water bottles, students
+    can potentially gain up to \SI{4.14}{\second} of study time per
+    refill, which is amounts to raising their grades by up to 0.00103 points.
 \end{abstract}
 
 \begin{IEEEkeywords}
@@ -151,41 +133,37 @@ Effect of the Choice of Hydration Strategy on Average Academic Performance}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Introduction}
 
-\IEEEPARstart{T}{he} concepts of hydration and study have always been tightly
-interwoven. As an example, an investigation was once conducted by Bell Labs
-into the productivity of their employees that found that ``workers with the
-most patents often shared lunch or breakfast with a Bell Labs electrical
-engineer named Harry Nyquist'' \cite{gertner_idea_2012}, and we presume that
-they also paired their food with something to drink. We can see that
-intellectual achievement and fluid consumption are related even for the most
+% TODO: "The right strategy" pun?
+
+\IEEEPARstart{T}{he} concepts of hydration and study have always been
+tightly interwoven. As an example, an investigation was once
+conducted by Bell Labs into the productivity of their employees that
+found that ``workers with the most patents often shared lunch or
+breakfast with a Bell Labs electrical engineer named Harry Nyquist''
+\cite{gertner_idea_2012}, and we presume that they also paired their
+food with something to drink. We can see that intellectual
+achievement and fluid consumption are related even for the most
 prestigious research institutions.
 
-In this work, we quantify this relationship in the context of studying at the
-KIT library and subsequently develop a novel and broadly applicable strategy
-to leverage it to improve the academic performance of KIT students.
+In this work, we quantify this relationship in the context of
+studying at the KIT library and subsequently develop a novel and
+broadly applicable strategy to leverage it to improve the academic
+performance of KIT students.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Experimental Setup}
 
-Over a period of one week, we monitored the usage of the water dispenser
-on the ground floor of the KIT library at random times during the day.
-The experiment comprised two parts, a system measurement to determine the
-flowrate of the water dispenser, and a behavioural measurement, i.e.,
-a recording
-of the choice of hydration strategy of the participants: $S_\text{L}$ denotes
-pressing the left button of the water dispenser, $S_\text{R}$ the right one,
-and $S_\text{B}$ pressing both buttons.
+Over a period of one week, we monitored the usage of the water
+dispenser on the ground floor of the KIT library at random times
+during the day. The experiment comprised two parts, a system
+measurement to determine the flowrate of the water dispenser, and a
+behavioural measurement, i.e., a recording of the choice of hydration
+strategy of the participants: $S_\text{L}$ denotes pressing the left
+button of the water dispenser, $S_\text{R}$ the right one, and
+$S_\text{B}$ pressing both buttons.
 
-For the system measurement $10$ datapoints were recorded for each strategy,
-for the behavioural measurement $113$ in total.
-
-% As is always the case with measurements, care must be taken not to alter
-% quantities by measuring them. To this end, we made sure only to take system
-% measurements in the absence of participants and to only record data on the
-% behaviour of participants discreetly.
-
-% TODO: Describe the actual measurement setup? (e.g., filling up a 0.7l bottle
-% and timing with a standard smartphone timer)
+For the system measurement $10$ datapoints were recorded for each
+strategy, for the behavioural measurement $113$ in total.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Experimental Results}
@@ -227,17 +205,15 @@ for the behavioural measurement $113$ in total.
     \vspace*{-2mm}
 \end{figure}
 
-Fig. \ref{fig:System} shows the results of the system measurement.
-We observe that $S_\text{L}$ is the slowest strategy, while $S_\text{R}$
+Fig. \ref{fig:System} shows the results of the system measurement. We
+observe that $S_\text{L}$ is the slowest strategy, while $S_\text{R}$
 and $S_\text{B}$ are similar. Due to the small sample size and the
-unknown distribution, the test we chose to verify this observation is a Mann
-Whitney U test. We found that $S _\text{L}$ is faster than $S_\text{R}$ with a
-significance of $p < 0.0001$, while no significant statement could be made
-about $S_\text{R}$ and $S_\text{B}$.
-Fig. \ref{fig:Behavior} shows the results of the behavioural measurement.
-% During this part of the experiment, we also measured the time each participant
-% needed to fill up their bottle. Using the measured flowrates we calculated
-% the mean refill volume to be $\SI{673.92}{\milli\liter}$.
+unknown distribution, the test we chose to verify this observation is
+a Mann Whitney U test. We found that $S _\text{L}$ is faster than
+$S_\text{R}$ with a significance of $p < 0.0001$, while no
+significant statement could be made about $S_\text{R}$ and
+$S_\text{B}$. Fig. \ref{fig:Behavior} shows the results of the
+behavioural measurement.
 
 \begin{figure}[H]
     \centering
@@ -272,67 +248,34 @@ Fig. \ref{fig:Behavior} shows the results of the behavioural measurement.
 \end{figure}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Modelling}
+\section{Modelling the grade improvement}
 
-We can consider the water dispenser and students as comprising a queueing
-system, specifically an M/G/1 queue \cite{stewart_probability_2009}.
-The expected response time, i.e., the time spent waiting as well as
-the time dispensing water, is \cite[Section 14.3]{stewart_probability_2009}%
+We can consider the water dispenser and students as comprising a
+queueing system, specifically an M/G/1 queue
+\cite{stewart_probability_2009}. The expected response time, i.e.,
+the time spent waiting as well as the time dispensing water, is
+\cite[Section 14.3]{stewart_probability_2009}%
+%
 \begin{align*}
     W = E\mleft\{ S \mright\} + \frac{\lambda E\mleft\{ S^2
     \mright\}}{2\mleft( 1-\rho \mright)}
     ,%
 \end{align*}%
-where $S$ denotes the service time (i.e., the time spent refilling a bottle),
-$\lambda$ the mean arrival rate, and $\rho = \lambda \cdot E\mleft\{
-S \mright\}$ the system utilization. Using our
-experimental data we can approximate all parameters and obtain
-$W \approx \SI{23.3}{\second}$. The difference to always using
-the fastest strategy amounts to $\SI{4.14}{\second}$.
-% We examine the effects of the choice of hydration strategy. To
-% this end, we start by estimating the potential time savings possible by always
-% choosing the fastest strategy:%
-% %
-% % We can model the time needed for one person to refill their
-% bottle as a random
-% % variable (RV) $T_1 = V/R$ and the time saved by choosing the
-% fastest strategy
-% % as $\Delta T_1 = T_1 - V/\max r$, where $V$ and $R$ are RVs representing the
-% % bottle volume and flowrate. The potential time saving for the
-% last person in a
-% % queue of $N$ people is thus $\Delta T_N = N\cdot\Delta T_1$. We
-% can then model
-% % the total time savings as $\Delta T_\text{tot} = \sum_{n=1}^{N} \Delta T_n$,
-% % where N is an RV describing the queue length. Assuming the
-% independence of all
-% % RVs we can compute the mean total time savings as
-% %
-% \begin{gather*}
-%     T_1 = V/R, \hspace{3mm} \Delta T_1 = T_1 - V/\max R,
-% \hspace{3mm} \Delta T_n = n \cdot \Delta T_1 \\
-%     \Delta T_\text{tot} = \sum_{n=1}^{N} \Delta T_\text{n} =
-% \sum_{n=1}^{N} n \cdot \Delta T_1 = \Delta T_1 \frac{N\mleft( N+1
-% \mright)}{2} \\
-%     \Delta t := E\mleft\{ \Delta T_\text{tot} \mright\} = E\mleft\{
-% \Delta T_1 \mright\} \cdot \mleft[ E\mleft\{ N^2 \mright\} +
-% E\mleft\{ N \mright\} \mright]/2
-%     ,%
-% \end{gather*}
-% %
-% where $V$ and $R$ are random variables (RVs) representing the volume of a
-% bottle and the flowrate, $\Delta T_n$ describes the time the last of $n$
-% people saves, $\Delta T_\text{tot}$ the total time savings and $N$ the length
-% of the queue. It is plausible to assume independence of $R,V$ and $N$.
-% Using our experimental measurements we estimate $\todo{\Delta t =
-% \SI{20}{\second}}$
+%
+where $S$ denotes the service time (i.e., the time spent refilling a
+bottle), $\lambda$ the mean arrival rate, and $\rho = \lambda \cdot
+E\mleft\{ S \mright\}$ the system utilization. Using our experimental
+data we can approximate all parameters and obtain $W \approx
+\SI{23.3}{\second}$. The difference to always using the fastest
+strategy amounts to $\SI{4.14}{\second}$.
 
 Strangely, it is the consensus of current research that there is only
 a weak relationship between academic performance and hours studied
-\cite{plant_why_2005}.
-The largest investigation into the matter found a correlation of
-$\rho = 0.18$ \cite{schuman_effort_1985} between GPA and average time
-spend studying per day. Using a rather high estimate of 5 refills per
-day, we predict a possible grade gain of up to $0.00103$ points.
+\cite{plant_why_2005}. The largest investigation into the matter
+found a correlation of $\rho = 0.18$ \cite{schuman_effort_1985}
+between GPA and average time spend studying per day. Using a rather
+high estimate of 5 refills per day, we predict a possible grade gain
+of up to $0.00103$ points.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Discussion and Conclusion}
@@ -342,38 +285,14 @@ arrival process and the relationship between the response time gain
 the grade gain. Nevertheless, we believe this work serves as a solid
 first step on the path towards achieving optimal study behaviour.
 
-% Many attempts have been made in the literature to relate
-% the time spent studying to academic achievement -  see, e.g.
-% \cite{schuman_effort_1985, zulauf_use_1999, michaels_academic_1989,
-% dickinson_effect_1990}.
-% The overwhelming consensus is that there is a significant relationship,
-% though it is a weak one.
-%
-%Many of the studies were only performed over
-% a period of one week or even day, so we believe care should be taken when
-% generlizing these results. Nevertheless, the overwhelming consensus in the
-% literature is that a significant relationship exists, though it is a weak one.
-
-% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% \section{Conclusion}
-
 In this study, we investigated how the choice of hydration strategy
-affects average academic performance. We found that always
-choosing to press the right button leads to an average time gain of
+affects average academic performance. We found that always choosing
+to press the right button leads to an average time gain of
 \SI{4.14}{\second} per refill, which translates into a grade
 improvement of up to $0.00103$ levels. We thus propose a novel and
 broadly applicable strategy to boost the average academic performance
 of KIT students: always using the right button.
 
-% Further research is needed to develop a better model of how the choice of
-% hydration strategy is related to academic performance. We
-% suspect that there is a compounding effect that leads to $S_\text{L}$ being an
-% even worse choice of hydration strategy: When the queue is long, students are
-% less likely to refill their empty water bottles, leading to reduced mental
-% ability. Nevertheless, we believe that with this work we have laid a solid
-% foundation and hope that our results will find widespread acceptance among the
-% local student population.
-
 %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % Bibliography
@@ -382,75 +301,4 @@ of KIT students: always using the right button.
 
 \printbibliography
 
-% \appendix
-%
-% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% \section{Derivation of Service Time}
-% \label{sec:Derivation of Service Time}
-%
-%
-% We want to compute the response time of our queueing system, i.e.,
-% \cite[Section 14.3]{stewart_probability_2009}
-% \begin{align*}
-%     W = E\mleft\{ S \mright\} + \frac{\lambda E\mleft\{ S^2
-% \mright\}}{2\mleft( 1-\rho \mright)}
-%     .%
-% \end{align*}%
-% We start by modelling the service time and subsequently calculate $\lambda$
-% and $\rho$.
-%
-% Let $S, V$ and $R$ be random variables denoting the service time,
-% refill volume
-% and refill rate, respectively. Assuming that $V$ and $R$ are independent, we
-% have
-% \begin{gather*}
-%     S = \frac{V}{R} \hspace{5mm} \text{and} \hspace{5mm}
-%     P_R(r) = \left\{\begin{array}{rl}
-%         P(S_\text{L}), & r = r_{S_\text{L}} \\
-%         1-P(S_\text{L}), & r = r_{S_\text{R}}
-%     \end{array}\right.
-% \end{gather*}%
-% \begin{align*}
-%     E\mleft\{ S^2 \mright\} &= E\mleft\{ V^2 \mright\}E\mleft\{ 1 /
-% R^2  \mright\} \\
-%     & = E\mleft\{ V^2 \mright\} \mleft(
-% P(S_\text{L})\frac{1}{r^2_{S_\text{L}}} + \mleft( 1 - P(S_\text{L})
-% \mright)\frac{1}{r^2_{S_\text{R}}}  \mright)
-%     .%
-% \end{align*}
-% We now use our experimental data (having calculated $v_n, n\in [1:N]$ from the
-% measured fill times and flow rates) to compute
-% \begin{align*}
-%     \left.
-%     \begin{array}{r}
-%         E\mleft\{ V^2 \mright\} \approx \frac{1}{N+1}
-% \sum_{n=1}^{N} v_n^2 = \todo{15}\\
-%         P(S_\text{L}) \approx \frac{\text{\# times $S_\text{L}$ was
-% chosen}}{N} = \todo{123} \\
-%         r^2_{S_\text{L}} \approx \todo{125} \\
-%         r^2_{S_\text{R}} \approx \todo{250}
-%     \end{array}
-%     \right\} \Rightarrow
-%     \left\{
-%     \begin{array}{l}
-%         E\mleft\{ S \mright\} \approx \todo{678} \\
-%         E\mleft\{ S^2 \mright\} \approx \todo{123}
-%     \end{array}
-%     \right.
-%     .%
-% \end{align*}
-%
-% $\lambda$ is the mean arrival time.
-%
-% \todo{
-%     \textbf{TODOs:}
-%     \begin{itemize}
-%         \item Complete text describing / obtaining $\rho$ and $\lambda$
-%         \item Move model derivation to method section
-%         \item Move calculations with model to results section
-%         \item Add grade gain derivation
-%         \item Idea: Make the whole thing 2 pages and print on A3
-%     \end{itemize}
-% }
-
 \end{document}