332 lines
10 KiB
TeX
332 lines
10 KiB
TeX
\documentclass[journal]{IEEEtran}
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\usepackage{amsmath,amsfonts}
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\usepackage{float}
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\usepackage{algorithmic}
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\usepackage{algorithm}
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\usepackage{siunitx}
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\usepackage[normalem]{ulem}
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\usepackage{dsfont}
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\usepackage{mleftright}
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\usepackage{bbm}
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\usepackage[
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backend=biber,
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style=ieee,
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sorting=nty,
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]{biblatex}
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\usepackage{tikz}
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\usetikzlibrary{spy, arrows.meta,arrows}
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\usepackage{pgfplots}
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\pgfplotsset{compat=newest}
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\usepgfplotslibrary{statistics}
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\usepackage{pgfplotstable}
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\usepackage{filecontents}
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\hyphenation{op-tical net-works semi-conduc-tor IEEE-Xplore}
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Inputs & Global Options
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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% Figures
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\input{common.tex}
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\pgfplotsset{colorscheme/rocket}
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\newcommand{\figwidth}{\columnwidth}
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\newcommand{\figheight}{0.5\columnwidth}
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\pgfplotsset{
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FERPlot/.style={
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line width=1pt,
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densely dashed,
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},
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BERPlot/.style={
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line width=1pt,
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},
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DFRPlot/.style={
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only marks,
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},
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}
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%
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% Bibliography
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\addbibresource{paper.bib}
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\AtBeginBibliography{\footnotesize}
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Title, Header, Footer, etc.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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\newcommand\todo[1]{\textcolor{red}{#1}}
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Title, Header, Footer, etc.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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\begin{document}
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\title{The Effect of the Choice of Hydration Strategy on Average Academic
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Performance}
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\author{Some concerned fellow students%
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\thanks{The authors would like to thank their hard-working peers as well as
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the staff of the KIT library for their unknowing - but vital -
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participation.}}
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\markboth{Journal of the Association of KIT Bibliophiles}{The
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Effect of the Choice of Hydration Strategy on Average Academic Performance}
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\maketitle
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Abstract & Index Terms
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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\begin{abstract}
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We evaluate the \todo{\ldots} and project that by using the right button of
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the water dispenser to fill up their water bottles, students can potentially
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gain up to \todo{5 minutes} of study time a day, which is equivalent to
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raising their grades by up to \todo{0.01} levels.
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\end{abstract}
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\begin{IEEEkeywords}
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KIT Library, Academic Performance, Hydration
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\end{IEEEkeywords}
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Content
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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\vspace*{-1mm}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Introduction}
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\IEEEPARstart{T}{he} concepts of hydration and study have always been tightly
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interwoven. As an example, an investigation was once conducted by Bell Labs
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into the productivity of their employees that found that ``workers with the
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most patents often shared lunch or breakfast with a Bell Labs electrical
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engineer named Harry Nyquist'' \cite{gertner_idea_2012}, and we presume that
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they also paired their food with something to drink. We can see that
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intellectual achievement and hydration are related even for the most
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prestigious research institutions.
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In this work, we quantify this relationship in the context of studying at the
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KIT library and subsequently develop a novel and broadly applicable strategy
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to leverage it to improve the academic performance of KIT students.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Experimental Setup}
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Over a period of one week, we monitored the usage of the water dispenser
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on the ground floor of the KIT library at random times during the day.
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The experiment comprised two parts, a system measurement to determine the
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flowrate of the water dispenser, and a behavioral measurement, i.e., a recording
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of the choice of hydration strategy of the participants: $S_\text{L}$ denotes
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pressing the left button of the water dispenser, $S_\text{R}$ the right one,
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and $S_\text{B}$ pressing both buttons.
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For the system measurement $10$ datapoints were recorded for each strategy,
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for the behavioral measurement it was $113$ in total.
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% As is always the case with measurements, care must be taken not to alter
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% quantities by measuring them. To this end, we made sure only to take system
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% measurements in the absence of participants and to only record data on the
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% behaviour of participants discreetly.
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% TODO: Describe the actual measurement setup? (e.g., filling up a 0.7l bottle
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% and timing with a standard smartphone timer)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Experimental Results}
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\begin{figure}[H]
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\centering
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\begin{tikzpicture}
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\begin{axis}[
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width=0.8\columnwidth,
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height=0.35\columnwidth,
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boxplot/draw direction = x,
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grid,
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ytick = {1, 2, 3},
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yticklabels = {$S_\text{B}$ (Both buttons), $S_\text{R}$ (Right button), $S_\text{L}$ (Left button)},
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xlabel = {Flowrate (\si{\milli\litre\per\second})},
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]
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\addplot[boxplot, fill, scol1, draw=black]
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table[col sep=comma, x=flowrate]
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{res/flowrate_both.csv};
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\addplot[boxplot, fill, scol2, draw=black]
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table[col sep=comma, x=flowrate]
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{res/flowrate_right.csv};
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\addplot[boxplot, fill, scol3, draw=black]
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table[col sep=comma, x=flowrate]
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{res/flowrate_left.csv};
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\end{axis}
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\end{tikzpicture}
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\vspace*{-3mm}
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\caption{Flow rate of the water dispenser depending on the hydration strategy.}
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\label{fig:System}
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\end{figure}
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\begin{figure}
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\centering
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\begin{tikzpicture}
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\begin{axis}[
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ybar,
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bar width=15mm,
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width=\columnwidth,
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height=0.35\columnwidth,
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area style,
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xtick = {0, 1, 2},
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grid,
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ymin = 0,
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enlarge x limits=0.3,
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xticklabels = {\footnotesize{$S_\text{L}$ (Left button)}, \footnotesize{$S_\text{R}$ (Right button)}, \footnotesize{$S_\text{B}$} (Both buttons)},
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ylabel = {No. chosen},
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]
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\addplot+[ybar,mark=no,fill=scol1] table[skip first n=1, col sep=comma, x=button, y=count]
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{res/left_right_distribution.csv};
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\end{axis}
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\end{tikzpicture}
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\vspace*{-3mm}
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\caption{Distribution of the choice of hydration strategy.}
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\label{fig:Behavior}
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\end{figure}
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Fig. \ref{fig:System} shows the results of the system measurement.
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We observe that $S_\text{L}$ is the slowest strategy, while $S_\text{R}$
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and $S_\text{B}$ are similar. Due to the small sample size and the
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unknown distribution, the test we chose to verify this observation is a Mann
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Whitney U test. We found that $S _\text{L}$ is faster than $S_\text{R}$ with a
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significance of $p < 0.0001$, while no significant statement could be made
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about $S_\text{R}$ and $S_\text{B}$.
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Fig. \ref{fig:Behavior} shows the results of the behavioral measurement.
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During this part of the experiment, we also measured the time each participant
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needed to fill up their bottle. Using the measured flowrates we calculated
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the mean bottle size to be $\SI{673.92}{\milli\liter}$.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Discussion}
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We examine the effects of the choice of hydration strategy. To
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this end, we start by estimating the potential time savings possible by always
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choosing the fastest strategy:%
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%
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% We can model the time needed for one person to refill their bottle as a random
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% variable (RV) $T_1 = V/R$ and the time saved by choosing the fastest strategy
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% as $\Delta T_1 = T_1 - V/\max r$, where $V$ and $R$ are RVs representing the
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% bottle volume and flowrate. The potential time saving for the last person in a
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% queue of $N$ people is thus $\Delta T_N = N\cdot\Delta T_1$. We can then model
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% the total time savings as $\Delta T_\text{tot} = \sum_{n=1}^{N} \Delta T_n$,
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% where N is an RV describing the queue length. Assuming the independence of all
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% RVs we can compute the mean total time savings as
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%
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\begin{gather*}
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T_1 = V/R, \hspace{3mm} \Delta T_1 = T_1 - V/\max r, \hspace{3mm} \Delta T_n = n \cdot \Delta T_1 \\
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\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} \\
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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
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,%
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\end{gather*}
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%
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where $V$ and $R$ are random variables (RVs) representing the volume of a
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bottle and the flowrate, $\Delta T_n$ describes the time the last of $n$
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people saves, $\Delta T_\text{tot}$ the total time savings and $N$ the length
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of the queue. It is plausible to assume independence of $R,V$ and $N$.
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Many attempts have been made in the literature to relate the time spent
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studying to academic achievement - see, e.g.
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\cite{schuman_effort_1985, zulauf_use_1999, michaels_academic_1989, dickinson_effect_1990}.
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The overwhelming consensus is that there is a significant relationship,
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though it is a weak one.
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%
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\todo{
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\begin{itemize}
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\item Compute possible grade gain
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\end{itemize}}
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%Many of the studies were only performed over
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% a period of one week or even day, so we believe care should be taken when
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% generlizing these results. Nevertheless, the overwhelming consensus in the
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% literature is that a significant relationship exists, though it is a weak one.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Conclusion}
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In this study, we investigated how the choice of hydration strategy affects
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the average academic performance. We found that always choosing to
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press the right button leads to an average time gain of \todo{\SI{10}{\second}}
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per day, which translates into a grade improvement of $\todo{0.001}$ levels.
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We thus propose a novel and broadly applicable strategy to boost the average
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academic performance of KIT students: always pressing the right button.
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% Further research is needed to develop a better model of how the choice of
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% hydration strategy is related to academic performance. We
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% suspect that there is a compounding effect that leads to $S_\text{L}$ being an
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% even worse choice of hydration strategy: When the queue is long, students are
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% less likely to refill their empty water bottles, leading to reduced mental
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% ability. Nevertheless, we believe that with this work we have laid a solid
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% foundation and hope that our results will find widespread acceptance among the
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% local student population.
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Bibliography
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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\printbibliography
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\end{document}
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