From de8d63293d64deba8de105b019a90594e05e0a5e Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Fri, 30 May 2025 00:04:51 -0400 Subject: [PATCH] Remove commented out text --- paper.tex | 141 ------------------------------------------------------ 1 file changed, 141 deletions(-) diff --git a/paper.tex b/paper.tex index b5aa40b..12d1323 100644 --- a/paper.tex +++ b/paper.tex @@ -126,8 +126,6 @@ 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 @@ -179,14 +177,6 @@ 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) - %%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Experimental Results} @@ -235,9 +225,6 @@ 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 $\SI{673.92}{\milli\liter}$. \begin{figure}[H] \centering @@ -289,42 +276,6 @@ 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 $\todo{\Delta t = -% \SI{20}{\second}}$ Strangely, it is the consensus of current research that there is only a weak relationship between academic performance and hours studied @@ -342,18 +293,6 @@ 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} @@ -365,15 +304,6 @@ 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 +312,4 @@ 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}