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+\documentclass{article}
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+
+\usepackage[backend=biber]{biblatex}
+\addbibresource{sources.bib}
+
+\title{FNS25 Research Plan}
+\author{Aiden Woodruff}
+
+\begin{document}
+\maketitle
+
+\section{Selected paper}
+
+The selected paper is ``Experimental evidence for tipping points in social
+convention'' by Centola et al. \cite{centola_experimental_2018}. The social
+science report is cited across disciplines from swarm robotics to virology.
+
+\subsection{Main topic}
+
+Centola et al. collect experimental evidence to support theoretical models of
+tipping points in social conventions. The prior work on critical mass as
+defined in game theory and observational studies suggest dedicated minorities
+of anywhere from 10-40\% of a population are large enough to effect changes in
+conventions. The authors vary the size of minority groups to determine the
+threshold past which dedicated actors are able to disrupt the convention in
+a name game.
+
+\subsection{Methods}
+
+The study engaged 194 online subjects in a game where pairs of players
+coordinate in naming a picture of a person for their own gain. Participants
+were randomly assigned to independent groups of variable size. Within those
+groups, members were matched pairwise for a number of rounds. Each round, pairs
+of players interacted each round to gain 10\textcent{} if their names matched
+or else lose 10\textcent.
+
+When a naming convention was reached, dedicated confederates were introduced
+which simultaneously chose the same alternative (chosen from common previous
+played names). The theoretical tipping point was 25\% of the population, and so
+committed minorities in the range of 15\% to 35\% were introduced across
+different trials.
+
+Centola et al then developed a model based on a simple sliding window of memory
+which was able to predict 80\% of experimental results. They used the model to
+increase population size further and find a more exact critical mass
+percentage.
+
+The model was implemented in R and provided as part of supplementary materials
+on GitHub.
+
+\subsection{Data}
+
+The details of each round were recorded, including: group sizes, round counts,
+all names assigned by players in each round, and confederate sizes and
+behaviors. Experimental data were used to tune the sliding window memory model.
+Then minority and group sizes, memory, network density, and strategy preference
+were varied to achieve more accurate values for the tipping point.
+
+\subsection{Results and conclusions}
+
+The tipping point was found to be around 25-31\% of the population empirically
+and more precisely around 24.3\% for the developed model. The results of
+Centola et al. align well with certain qualitative studies in organizational
+settings, which they suggest may be due to the rewards of following convention
+being clearly defined. When they adjusted agent strategy preferences, the
+tipping point remained below 50\%.
+
+They extend their discussion to understanding intentional pushes to change
+social opinion and naturally evolving acceptability of different social
+behaviors.
+
+Centola et al. provided an emperical value for tipping points which is widely
+cited. Their work also supports the idea that the tipping point is precise in
+a population \cite{babitz_how_2025}.
+
+\subsection{Evaluation}
+
+Centola et al. build on similar games and their disciplines own conventions to
+devise this study. Their results are not general to every social convention but
+still serve as empirical evidence for the critical mass phenomenon. The
+proposed model provides a method to explore other hypotheses. The raw data can
+also be used to develop and test other models. Since their own sliding window
+memory model only predicted 80\% of experimental subject choices (even with
+longer memories), there may well be a better model which can be tuned to their
+data.
+
+Even without the more precise threshold predicted by Centola et al.'s model,
+their experimental threshold is a nice result.
+
+\section{Experimental proposal}
+
+\subsection{Goal and novelty}
+
+My goal is to replicate the sliding window memory model used by Centola et al.
+and vary the strategy preference among certain members of the network. I am
+hoping to more accurately model real world networks in which certain actors
+have much a greater aversion to changing conventions than others. Additionally,
+I want to try specifically adjusting the influence (i.e. node degree) of those
+individuals.
+
+\subsection{Data}
+
+I plan to run experiments on actor networks of the same type as Centola et al.
+I will choose different independent variables and determine tipping points for
+each configuration.
+
+I will also explore for data from similar studies to compare my results to.
+
+\subsection{Methods}
+
+I plan to use SNAP \cite{leskovec2016snap} for network infrastructure and
+analysis. The code implemented by Centola et al. is written in R and seems to
+run slowly on my machine. The code is short (less than 200 lines overall) and
+so I plan to re-implement it in C++.
+
+The tipping points found by Centola et al. were robust to network density, so I
+will plan to study less dense networks. Depending on the trial, I will
+introduce influential nodes of high degree.
+
+Smaller network were more susceptible to dedicated minorities, and so I am also
+interested in how variable strategy preference will affect small networks like
+those in the experiments (\(\le 30\) participants).
+
+Additionally, if I have time I may try to construct a different model that can
+more accurately predict the experimental data from Centola et al. Then it will
+be worth repeating the same experiments to see how the results differ.
+
+\subsection{Result evaluation criteria}
+
+Statistical significance will be a necessary result for a successful study. My
+hypothesis is that influential conservative nodes will cause the tipping point
+to be higher in small networks but not as much in large networks.
+
+\printbibliography
+
+\end{document}
+