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% \title{The Spatio-Temporal Relationship Between Social Media Activism and Physical Protest: Evidence From \#JusticeForGeorgeFloyd}

\title{Tweets Matter: Quantifying the Spatio-Temporal Relationship Between Social Media Activism and Physical Protest}

\author[1,2,*]{Leonardo Nicoletti}
\author[2,+]{Trivik Verma}
% \author[1,2,+]{Paolo Santi}
\author[1,3,+]{Paolo Santi}
\author[2,+]{Martijn Warnier}
\affil[1]{MIT Senseable City Lab, Department of Urban and Social Planning, Cambridge, MA 02139, United States}
\affil[2]{TU Delft, Technology Policy Management, Delft, 2600 AA, Netherlands}
\affil[3]{Istituto di Informatica e Telematica del CNR, Pisa, 56124, Italy}

\affil[*]{info.leonardonicoletti@gmail.com}

\affil[+]{these authors contributed equally to this work}

% \keywords{social movements, hashtag activism, physical protest, big data}

\begin{abstract}
\textbf{Throughout history, social movements have often been catalysts for radical societal change. In the past two decades, hashtag activism, the use of social media platforms for internet activism, has become a driving force behind the development of social movements across the world. In the field of social movements science, a large body of research has studied the role of hashtag activism for the formation of social movements, but less efforts have been allocated towards the study of the spatio-temporal relationship that exists between hashtag activism and political mobilization processes. In this study, a large geo-located social media dataset pertaining to the \#JusticeForGeorgeFloyd social movement is used to quantify the spatio-temporal relationship between hashtag activism and physical protest activity. Results of this study indicate that at the national, state, and county scale, hashtag activism bears a strong positive temporal relationship with physical protest activity. Through the statistical modeling of this relationship, it is possible to predict the intensity of national, state, and county level protest activity on a given day based on the intensity of state and county level social movement related tweet counts the day before. At smaller scales (i.e. county), however, this research finds that the strength of this relationship is more variable, and it appears to be strongly dependent on population density. As such, this study reveals the existence of a critical population density threshold of 200 people/km$^2$, at which an increase in the number of social movement related tweets is likely to spark with an increase in the number of physical protests. These results represent novel insights that further contribute to our understanding of the complex spatio-temporal political mobilization processes that occur during social movements.}

% As such, this study found an optimal population density threshold  200 people/km$^2$, at which an increase in the number of social movement related tweets is likely to partner with an increase in the number of physical protests.
\end{abstract}
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% \noindent Please note: Abbreviations should be introduced at the first mention in the main text – no abbreviations lists. Suggested structure of main text (not enforced) is provided below.

\section*{Introduction}\label{cha:introduction}

% During a social movement, networks of actors with shared beliefs and solidarity are mobilized around contentious themes through the frequent use of various forms of protest with the objective of enabling different forms of social change \cite{della2015social}.

Throughout history, social movements have often been catalysts for radical societal change. As a most recent example, evidence has suggested that the 2020 \#JusticeForGeorgeFloyd social movement, characterized by sustained nation-wide (i.e. United States) and worldwide protests, may have influenced a range of subsequent societal and institutional changes \cite{mourtgos2021elevated, nguyen2021progress}. As exemplified by \#JusticeForGeorgeFloyd, physical protest is a key political resource for social movements. Activists use physical protest as a non-conventional form of political action to disrupt daily routines, attract public attention and apply political pressure on protest targets (e.g. policy-makers) \cite{della2015social, enos2019can, weldon2011protest, lipsky1968protest, heaney2020protest}. 

Similarly, hashtag activism, the use of social media platforms for internet activism, has recently become a driving force behind the development of social movements across the world \cite{jackson2020hashtagactivism}.  In greatly facilitating interactions between organizations and the public, social media platforms have fostered environments of political discussion and participation where rapid information diffusion beyond spatial boundaries facilitates the creation of communities that share values, characteristics, and interests \cite{kent2013using, fuchs2014introduction}. Indeed, through the use of social media data, scholars have demonstrated that hashtag activism is an effective tool for underrepresented social groups (e.g. ethnic minorities, youth, women) to shape political discourses and advance social movements \cite{carney2016all, li2021twitter, xiong2019hashtag}. For example, in an analysis of social media posts data from Twitter collected during the \#MeToo social movement, Xiong et al. (2019) \cite{xiong2019hashtag} found that hashtags functioned as a tool to empower and mobilize publics around the issue of sexual assault, and as a mechanism for Social Movement Organizations (SMOs) to effectively engage with the public. Xiong et al. (2019) \cite{xiong2019hashtag} conclude that such mechanisms allow for a more efficient organization of social movements. Through leveraging other case studies, scholars have demonstrated that hashtag activism is also effective for framing and re-framing social movements, and to maintain the vitality of social movements over time \cite{ince2017social, tan2013analyzing}.  Finally, there is consensus that, in the context of social justice and social change, decentralized networks such as those found on social media have allowed activist groups to position themselves as key actors to influence public discourse and call for collective action \cite{benford2000framing}.

In this context, while a large body of research has studied the role of hashtag activism for the formation of social movements, our understanding of the relationship between hashtag activism and political mobilization processes, such as physical protest, is very limited \cite{brantly2019cyberspace, howard2011states, shirky2011political}.  In a survey of participants from the Tahrir Square protests in Egypt, Tufekci and C. Wilson (2012) \cite{tufekci2012social} concluded that, during the 2011 Egyptian revolution,  use of social media increased the probability that an individual participated in physical protests. Similarly, through leveraging data from multiple social media platforms generated during Ukraine’s 2013-2014 euromaidan protests, Brantly (2019) \cite{brantly2019cyberspace} found evidence suggesting that social media plays a role in shifting protests from the digital to the physical space. Although statistically significant, such evidence was associated with a wide margin of error \cite{brantly2019cyberspace}. Following a similar methodology Bastos et al. (2015) \cite{bastos2015tents} found that, for the case of the Indignados, Occupy, and Vinegar social movements, Twitter and Facebook activity could be informative of next day’s protest activity. This study, however, found this relationship to be bi-directional, in that physical protest could also be predictive of next day’s social media activity. Due to its limited geographical scope, it also could not test whether these relationships exist across different geographical locations of a country. Moreover, similar research conducted by S. L. Wilson (2017) \cite{wilson2017detecting} with the use of geo-located tweets collected for the same case study generated conflicting results: while social media activity increased nationwide during mass protests, it decreased at sites of mass protest. More recently, a study of twitter data related to the 2016 Black Lives Matter (BLM) protests in Charlotte, NC, found a unidirectional causal relationship where physical protests appear to drive tweet activity \cite{karduni2020anatomy}. Because of such contradictory evidence, our understanding of the spatio-temporal relationship between hashtag activism and physical protest is very limited.

Such contradictions found in the literature motivate this research, where a data-driven framework is implemented to investigate the spatio-temporal relationship between hashtag activism and one important political mobilization process: physical protest. Through a combination of time-series analysis, regression, and geo-spatial analysis, and the use of a large Twitter data-set of geo-located social media posts, this relationship is quantified for the 2020 \#JusticeForGeorgeFloyd social movement across different spatial resolutions in the United States. Finally, this research proposes a general statistical law between hashtag activism, physical protest, and population density, that could help explain this relationship as well as the apparent contradictory results in the existing literature.


\section*{Results}
\label{cha:results}

\subsection{The temporal relationship between tweet activity and physical protests.}  In order to study the temporal relationship between hashtag activism and physical protest at different spatial scales, point data describing instances of hashtag activism (i.e. tweets related to \#JusticeForGeorgeFloyd) and physical protests were aggregated in time and space. Fig. \ref{fig:1_tweetsProtests_tot} shows, in the right half of the chart, the temporal patterns of both hashtag activism (measured in number of tweets) and physical protest at the national level. On the left side of the chart the temporal relationship between daily number of physical protests and daily number of tweets is illustrated through a scatter-plot. From Fig. \ref{fig:1_tweetsProtests_tot} it can be observed that, at the national scale, hashtag activism bears a very strong positive relationship with physical protest activity. On days where people protested more on social media, people also protested more in the street, and vice versa. In the case of \#JusticeForGeorgeFloyd, people may have used Twitter to express outrage about events of police brutality and to organize physical protests. During protests, more acts of police brutality were documented and shared on Twitter, which could have led to yet more protests and to more people showing up to protests, and so on. This trend can be modelled by a power regression function ($y_n = -0.004x_n^{1.116}$), represented by the red dashed line, where $y_n$ is the number of physical protests that take place on a given day and $x_n$ is the number of social movement tweets that are posted on a given day. This model is considerably accurate, with a Pearson correlation score $p$ of 0.852 and an $R^2$ score of 0.726.

Fig. \ref{fig:6_tpTotlag_crosscorr} illustrates the results of performing Time Lagged Cross Correlation on national level data using a time lag of $n=10$. The top subplot shows that the optimal Pearson correlation $p$ value and $R^2$ score is obtained when hashtag activism (i.e. daily number of tweets posted) leads physical protests by one day. In other words, at the national scale and during the case study of \#JusticeForGeorgeFloyd, social movement related tweets can best predict physical protest activity at time $t$ (in days) when tweets posted at time $t-1$ (i.e. the day before) are considered. This relationship is further illustrated in the bottom subplot of Fig. \ref{fig:6_tpTotlag_crosscorr}, where the outputs of power regression models using $x_t$ (left) and $x_{t-1}$ (right) can be compared, with higher values of accuracy achieved by the time-lagged model.

\begin{figure} 
\centering
    \includegraphics[width=0.85\textwidth]{figures/1_tweetsProtests_tot_paper.png}
    \caption[National-level power regressions: tweet count vs. physical protest count]{\label{fig:1_tweetsProtests_tot}Temporal (right) and statistical (left) relationship between hashtag activism and physical protests during \#JusticeForGeorgeFloyd, where each dot represents a day. The statistical relationship is modelled by the red dashed line as ($y_n = -0.004x_n^{1.116}$).}
\end{figure}

\begin{figure}
\centering
    \includegraphics[width=0.85\textwidth]{figures/6_tpTotlag_crosscorr.PNG}
    \caption[National-level time lagged cross correlation results]{\label{fig:6_tpTotlag_crosscorr}Time Lagged Cross Correlation results for hashtag activism and physical protests at $n=10$ time lags (top). Power regression models for hashtag activism and physical protests using same day tweet counts $x_t$ (bottom left) and previous day tweet counts $x_{t-1}$ (bottom right).}
\end{figure}

\subsection{The spatio-temporal relationship between hashtag activism and physical protest.} While Fig. \ref{fig:1_tweetsProtests_tot} and Fig. \ref{fig:6_tpTotlag_crosscorr} provide useful insight into the temporal relationship between hashtag activism and physical protest, they cannot answer whether this relationship exists in space as well. That is, if an \textit{overall} increase in hashtag activism results in an \textit{overall} increase in physical protest counts, does an increase in hashtag activism in \textit{a particular location} result in an increase in physical protest counts in \textit{that particular location}? With the use of data on social movement tweet counts and physical protest counts that is aggregated both in time and in space (i.e. at the state level), Figure \ref{fig:3_tweetsProtests_state} illustrates the temporal and statistical relationship between daily number of physical protests and daily number of tweets as scatter-plots for each of the U.S.'s 50 states. From this figure it is evident that the pattern previously observed at the national level also exists at the state level. Thus, in spite of the existence of a few outliers, the relationship between hashtag activism and physical protest counts in each state is described by a strong positive correlation. Across 50 states, the median Pearson correlation $p$ value is 0.74 and there are 44 states associated with Pearson correlation $p$ values greater than 0.6 (Supplementary Tab. S1). Additionally, similarly to the trend observed at the national scale, the relationship between state-level hashtag activism and physical protest counts can be modelled by a power regression function ($y_n = mx_n^{b}$), represented by the red dashed line in each subplot, where $y_n$ is the number of physical protests that take place on a given day in a given state and $x_n$ is the number of social movement tweets that are posted on a given day in a given state. 

\begin{figure}[!htb]
\centering
    \includegraphics[width=\textwidth]{figures/3_tweetsProtests_state_paper.png}
    \caption[State-level power regressions: tweet count vs. physical protest count]{\label{fig:3_tweetsProtests_state}State-level statistical relationships between hashtag activism and physical protests using the \#JusticeForGeorgeFloyd social movement as a case study.}
\end{figure}

In general, the accuracy of these models is described by a median $R^2$ value of 0.55 across 50 states, and 37 states that are associated with $R^2$ values greater than 0.5. Interestingly, Fig. \ref{fig:6_state_stats_} shows that across the 25\% most densely populated states, the power regression model yields considerably higher scores, with the median Pearson correlation $p$ value climbing to 0.8 and the median $R^2$ values climbing to 0.64. Across the 25\% least densely populated states, the opposite trend is observed. Summary statistics for each of the U.S. 50 states can be viewed in Tab. S2 of the Supplementary Information.

\begin{figure}[!htb]
\centering
    \includegraphics[width=0.85\textwidth]{figures/6_state_stats_.png}
    \caption[State-level power regressions: accuracy scores and population density]{\label{fig:6_state_stats_}Accuracy of Power regression models ($R^2$) across the 25\% most population dense U.S. states and the 25\% least population dense U.S. states (top). State-level results of Granger causality analysis for the hypothesis that tweet count Granger causes protest count and the hypothesis that protest count Granger causes tweet count (bottom).}
\end{figure}

With national and state-level data, Granger causality, a statistical hypothesis test developed to study the exchange of information between two or more time series, is implemented to study whether data on tweet counts can provide information that is statistically significant for the forecast of future physical protest counts. Results from this analysis are summarized in Fig. \ref{fig:6_state_stats_} and presented in Tab. S2 of the Supplementary Information. Overall, at 95\% confidence level, at the national level and for 49 states we can reject the null-hypothesis that tweet count does not \textit{Granger cause} protest count. Thus, it is found that tweet count \textit{Granger causes} protest count at the national level and in 49 out of 50 States. These results are in accordance with results obtained from the Time Lagged Cross Correlation method.

With national and state-level data, Granger causality is also implemented to study whether data on protest counts can provide information that is statistically significant for the forecast of future tweet counts. Results from this analysis are summarized in Fig. \ref{fig:6_state_stats_} and presented in Tab. S2 of the Supplementary Information. Overall, at 95\% confidence level, at the national level and for 27 states we cannot reject the null-hypothesis that protest count does not cause tweet count. Thus, it is found that protest count does not \textit{Granger cause} tweet count at the national level and in 27 out of 50 States.

% \begin{figure}
% \centering
%     \includegraphics[width=0.85\textwidth]{figures/6_state_granger_stats_.png}
%     \caption[State-level granger causality analysis results]{\label{fig:6_state_granger_stats}State-level results of Granger causality analysis for the hypothesis that tweet count Granger causes protest count (blue) and the hypothesis that protest count Granger causes tweet count (orange).}
% \end{figure}

Following the same methodology, the spatial scale is further disaggregated and the temporal relationship between hashtag activism and physical protest counts is investigated at the county level. Once again, we model this relationship as a power regression function ($y_n = mx_n^{b}$) for each of U.S. county where tweet and physical protest data was available (i = 2178 counties). Results from this analysis are illustrated by the bottom left and right subplots of Fig. \ref{fig:6_KDES_scores}, where the obtained Pearson correlation $p$ values and $R^2$ values are illustrated as kernel density distributions due to the large number of counties analysed. Fig. \ref{fig:6_KDES_scores} shows that, on average, the county level Pearson correlation $p$ value is positive and relatively high. Fig. \ref{fig:6_KDES_scores} also shows that while a power regression model achieves a high $R^2$ score in a majority of counties, there is more variance in the accuracy of the power regression model.

\begin{figure}
\centering
    \includegraphics[width=\textwidth]{figures/6_KDES_scores.PNG}
    \caption[County-level power regressions: distribution of correlation values and accuracy scores]{\label{fig:6_KDES_scores}Distribution of Pearson correlation $p$ values (left) and $R^2$ values (right) obtained from power regression modelling between tweet count and physical protest counts at the county level using the \#JusticeForGeorgeFloyd case study.}
\end{figure}

One reason that could explain this variance could be the lack of data-points available in some less densely populated counties. Another reason is that in some counties one of hashtag activism or physical protest was more commonly used to engage in activism during the \#JusticeForGeorgeFloyd social movement. In other words, in some counties people use physical protest to greater extents, while in other counties people may use hashtag activism more instead. In this context, modelling the relationship between hashtag activism and physical protest and visualizing this trade-off at the county level can provide unique insight into which locations experience synergy across digital and physical activism mediums, and which do not. Thus, on the one hand it can help identify which counties have activist groups that mobilize both digitally and physically, and thus where physical protests can be expected if people are already protesting on social media. On the other hand, for the counties that exhibit a weaker relationship between both forms of protest, it can generate insight as to \textit{why} this relationship is weak. Such tendency can be understood with the help of residual values resulting from each county's power regression model. As such, the number of positive residual values represents the number of data-points (i.e. days) in which physical protests were underestimated by the regression model, and thus where the proportion of physical protests was larger than that of social movement tweets. Instead, the number of negative residual values represents the number of data-points in which physical protests were overestimated by the regression model, and thus where the proportion of physical protests was smaller than that of social movement tweets.
 
 This type of classification can be achieved with the computation of a statistical index which we call the \textbf{\textit{Mobilization Synergy Index (MSI)}}. Such index is achieved by (a) calculating the number of positive and negative residuals $r_{pos}$ and $r_{neg}$ respectively from each individual county's power regression model where each residual $r$ is $r=y-y_{0}$, $y$ is the actual number of physical protests on a given day, and $y_{0}$ is the number of physical protests predicted by the regression model, and (b) calculating the proportions of positive residual values (days in which physical protest counts are disproportionally intense) and negative residual values (days in which tweets counts are disproportionally intense) as $r_p=r_{pos}/(r_{pos}+r_{neg})$ and $r_t=r_{neg}/(r_{pos}+r_{neg})$ respectively, and (c) multiplying each of these values by the product of the power regression model's slope $m$ and $R^2$ score (so as to capture both the strength of the power relationship between tweet count and physical protest activity and the accuracy of the power regression model). As such, two measurements are recorded for each individual county:
 
\begin{equation}
MSI_{protests}=r_p\times{(m\times{R^2})}
% (+d.res_pos/(+d.res_pos + +d.res_neg))*(+d.slope + +d.r2_value)
% (+d.res_neg/(+d.res_pos + +d.res_neg))*(+d.slope + +d.r2_value)
\end{equation}
\begin{equation}
MSI_{tweets}=r_t\times{(m\times{R^2})}
% (+d.res_pos/(+d.res_pos + +d.res_neg))*(+d.slope + +d.r2_value)
% (+d.res_neg/(+d.res_pos + +d.res_neg))*(+d.slope + +d.r2_value)
\end{equation}
 
Thus, if in a given county $MSI_{protests}>MSI_{tweets}$ then physical protest was disproportionately intense over the course of \#JusticeForGeorgeFloyd, if instead $MSI_{protests}<MSI_{tweets}$ then tweet activity was disproportionately intense over the course of \#JusticeForGeorgeFloyd, and finally if $MSI_{protests}\approx MSI_{tweets}$ then physical protests and tweet counts followed a strong power law relationship where more tweets on a given day translates in more physical protests on that same day.

\begin{figure}[!htb]
\centering
    \includegraphics[width=\textwidth]{figures/6_KDES_Map_index.PNG}
    \caption[Mobility Synergy Index (MSI)]{\label{fig:5_KDES_Map}Spatial (top) and statistical (bottom) distribution of the Mobility Synergy Index (MSI): darker shades represent counties in which people are likely to protest both digitally and physically on a given day. Shades of blue represent counties in which people are more likely to protest physically on a given day. Shades of red represent counties in which people are more likely to protest digitally on a given day.}
\end{figure}

The \textit{Mobilization Synergy Index (MSI)} and its spatial distribution is visualized through a bi-variate choropleth map in the top subplot of Fig. \ref{fig:5_KDES_Map}. In this map, darker shades represent counties in which $MSI_{protests}$ and $MSI_{tweets}$ converge, and thus where people are likely to protest both digitally and physically on a given day. In contrast, shades of blue represent counties where $MSI_{protests}$ outweighs $MSI_{tweets}$, and thus where people are more likely to protest physically on a given day. Finally, shades of red represent counties where $MSI_{tweets}$ outweighs $MSI_{protests}$, and thus where people are more likely to protest digitally on a given day. From  Fig. \ref{fig:5_KDES_Map}, it can be observed that the areas where the temporal relationship between tweets and physical protests is stronger are concentrated along the east and west coastlines, while the areas where this relationship is weaker are concentrated in the country's interior landmass. Areas where people choose to engage in hashtag activism over physical protest, and vice versa, does not exhibit any discernible spatial pattern.

\subsection{Population density as the best indicator.}  Results from quantile regressions are presented in Fig. \ref{fig:5_scaling_pop}, and in Fig. S1 of the Supplementary Information. The results reveal that, in the case of U.S. counties, population density (people/km$^2$) may serve as the strongest indicator of the temporal relationship between hashtag activism and physical protest activity. Indeed, while the Pearson correlation and slope between weekly number of tweets and weekly number of protests increase linearly with \% Urban Area and \% democratic votes (Supplementary Fig. S1), they increase very sharply with population density (Fig. \ref{fig:5_scaling_pop}). This sharp increase is halted and the value of regression metrics saturates once the minimum population density threshold is at around 200 people/km$^2$.

\begin{figure}[!htb]
\centering
    \includegraphics[width=\textwidth]{figures/quantileAnalysis_.PNG}
    \caption[Mobilization Synergy Scaling Law]{\label{fig:5_scaling_pop}Evolution of mean Pearson correlation (left), mean slope (middle), and mean intercept values (for the power relationship between daily number of tweets and daily number of protests) with population density.}
\end{figure}

While it could be possible that this pattern is due to a lack of data points available in less densely populated areas, our analysis shows that our population quantiles had on average 12 weeks of data or more, and that overall population density per county does not bear strong relationships with the number of data points per 100,000 (i.e. physical protests/100,000 and tweets/100,000) found in each county (Fig. \ref{fig:6_dtpts_pop}). Thus, in the case of U.S. counties, it can be said that if a county’s population density is at least 200 people/km$^2$, then an increase in the number of social movement related tweets originating from that county is likely to partner with an increase in the number of physical protests that occur inside that same county.


\begin{figure}[!htb]
\centering
    \includegraphics[width=\textwidth]{figures/6_dtpts_pop.PNG}
    \caption[Data Points and Population Density]{\label{fig:6_dtpts_pop}Statistical relationship between population density and
    the number of tweet data points per 100,000 people (left), and the number of physical protest data points per 100,000 people (right).}
\end{figure}


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\section*{Discussion and conclusions}

Contemporary social movements are characterized by sustained episodes of both physical and digital protest, but the interplay between these two forms of protest is largely undetermined. In an attempt to fill this gap, this study explored the spatio-temporal relationship between location-based hashtag activism and physical protest activity during the \#JusticeForGeorgeFloyd 2020 social movement. 

Through the analysis of geo-located social media and physical protest data, this research resulted in several key findings. First, in the case of \#JusticeForGeorgeFloyd, it was found that at the national scale, hashtag activism bears a very strong positive temporal relationship with physical protest activity. Through the statistical modelling of this relationship, it is possible to accurately predict the intensity of national level protest activity on a given day based on the intensity of national level hashtag activism the day before. This observation is in accordance with the qualitative evidence generated by Tufekci and C. Wilson (2012)\cite{tufekci2012social} on the role of social media in increasing the likelihood of participation in physical protest during the Tahrir Square protests, and more importantly with the empirical evidence generated by Brantly (2019)\cite{brantly2019cyberspace} and Bastos et al. (2015)\cite{bastos2015tents} on the potential existence of a one day time-lag between hashtag activism and physical protest activity. 

Second, it was found that this temporal relationship between hashtag activism and protest activity exists at the state level as well. By modelling this relationship at the state level, through the use of a simple power regression model, it is possible to predict the intensity of state level protest activity on a given day based on the intensity of state level hashtag activism the day before. In general, it was found that the accuracy of such predictions increases with population density. This could be explained by the fact that population dense states may have a larger number of urban centers, where social (media) networks may be more connected and thus where people are more aware of both local and national news. At the same time, urban centers may make it easier for people to gather in public spaces to engage in protest. The leader-follower relationship between hashtag activism and physical protest activity was further supported by the results of Granger causality analysis, where it was found at both the national and state level that hashtag activism Granger causes physical protest activity in the vast majority of areas. As a result, this research suggests that hashtag activism may act as a causal factor for physical protest activity, and not the other way around, where this causal relationship is also strongly related to physical space. This would be in accordance with other research within the broader topic of hashtag activism and social movements which has revealed unidirectional relationships between hashtag activism and other characteristics of social movements (e.g. the framing of political narratives; the polarization of social groups) \cite{kent2013using, carney2016all, li2021twitter, xiong2019hashtag, jackson2020hashtagactivism}. In this context, a causal spatial relationship between hashtag activism and physical protest would imply that today social media is not only a vital tool for activist groups to mobilize people physically, but also to mobilize people physically in targeted geographical locations. 

Third, it was found that the spatio-temporal relationship between hashtag activism and protest activity continues to hold at the county level. At such small scale, the accuracy of predictions remained generally high, but considerably more variance was observed and thus, a wider error margin is noted. Statistically, this is explained by the fact that in some "outlier" counties the temporal relationship between hashtag activism and physical protest is characterized by a disproportionate amount of physical protest compared to the intensity of hashtag activism, while in other counties this relationship is characterized by a disproportionate amount of hashtag activism compared to the intensity of physical protests. In order to make sense of this tendency this research first proposed the Mobilization Synergy Index, which makes it possible to statistically quantify this trade-off, and to visualize its spatial distribution in an intuitive way. Indeed, both policy makers and activists could gain valuable insight from this index. On the one hand, local policy makers could utilize it to understand how their communities mobilize in times of crisis, and become responsive to local demands accordingly. For example, if a specific county is categorized by the index as a county where the relationship between hashtag activism and physical protest is strong, local policy makers could avoid potential public disruption by fulfilling community needs rapidly once local levels of hashtag activism peak. In contrast, if a specific county is categorized by the index as a county where people use hashtag activism disproportionally, this could be a sign for local policy makers to pay closer attention to social media platforms for understanding community needs. On the other hand, activists could utilize the index to plan their mobilization efforts more efficiently and effectively. For example, by identifying counties in which people engage in hashtag activism intensely but do not mobilize physically, local activist groups could modify their strategies for physical mobilization so that more people show up at protests. In contrast, in counties where people engage in physical protest intensely but not in hashtag activism, local activist groups may increase their use of offline mobilization strategies to maximize protest turnout.

Finally, in an attempt to explain the variance  observed in relationship strength between physical protest and digital protest at small scales (i.e. county-level), this study revealed  the existence of a critical population density threshold of 200 people/km$^2$, at which relationship strength is always high (i.e. as indicated by regression metrics). That is, in counties where the population density is equal to or greater than 200 people/km$^2$ an increase in the number of social movement related tweets is likely to spark an increase in the number of physical protests. This is an interesting finding because, contrary to what we may expect, the value of this threshold is significantly lower than the population density threshold for urban areas in the U.S. (i.e. 978.5 persons per square kilometer or 2534.4 persons per square mile) \cite{USCensus}. Indeed, this study confirmed that an equally critical threshold in urban population is not observed. Instead, the relationship strength between physical protest and digital protest increases linearly with urban population. 

\subsection{Limitations and Outlook} 
Due to the scope of this research, this study comes with a number of limitations that may inform future scientific efforts:\\
\noindent\textbf{External validity}: Due to the analysis of a single case study, the results of this research could only be valid for the specific case of \#JusticeForGeorgeFloyd and may not be observed for other social movements in other parts of the world. Future research may address this limitation by implementing the proposed experimental framework to the case of other relevant social movements in other geographical areas. \\
\noindent\textbf{Spatial resolution}: While this research makes use of a large data-set with considerable geographical coverage, the spatial resolution of this data is still limited. For this reason, the analysis could not be implemented for sub-county level patterns in hashtag activism and physical protest activity (e.g. the neighborhood or precinct level). This limitation is difficult to address, as the availability of sub-city level geo-located social media data is scarce due to a number of ethical considerations (e.g. privacy). Nonetheless, future research could address this limitation by using sources of social media data that come with improved spatial resolution. \\
\noindent\textbf{Sampling bias}: While evidence has suggested that Twitter is the most popular social media platform for contemporary civil rights activists in the United States \cite{ince2017social, edrington2018tweeting}, as in \#JusticeForGeorgeFloyd, it is possible for some activists to have engaged in activism through other social media platforms during this social movement. The data used in this study does not consider such instances, and thus it is limited to instances where activists have engaged in activism through the Twitter platform. \\
\noindent\textbf{Causal inference}: While the Granger causality results that this research puts forth suggest that social movement tweets may have acted as a causal factor to the occurence of physical protests during the \#JusticeForGeorgeFloyd social movement, it is possible that a third factor may have acted as a causal factor for both hashtag activism and physical protests during the social movement. Thus, future research could explore the causal relationship between additional factors and both hashtag activism and physical protest activity.

\section*{Methods}

\subsection{Spatial and demographic data.}  In order to study geo-spatial relationships between social media activity and physical protest activity, data was aggregated across common spatial scales. For this research, the U.S. county and state spatial scales are chosen and the associated geo-spatial data is downloaded from the U.S. Census public API\cite{USCensus}. Additionally, data on population density and \% urban area at the U.S. county and State level are also retrieved from the U.S. Census public API.

\subsection{Social media data.} The primary data-set used for this research consists of a collection of geo-located social media posts (i.e. tweets) generated over the duration of the \#JusticeForGeorgeFloyd social movement (i.e. May 20th 2020 to November 10th 2020) across the United States. This data was collected through the Twitter API v2 via the "Academic Research product track", an exclusive license that provides academic researchers with full access to the Twitter historical archive since March 26, 2006 \cite{TWITTER:2021}. In order to retrieve this data the Python programming language was used to connect to the \url{https://api.twitter.com/2/tweets/search/all} endpoint. Finally, because the Twitter API v2 allows for a maximum search radius of 25 miles, a grid consisting of equally sized 1770 km\textsuperscript{2} hexagons covering the United States' landmass was created using the h3 Python library \cite{h3:2021}. Through an iterative process, tweets within a 25 mile radius of the centroid of each hexagon were collected. As a result, the API returned a collection of 1,066,440 tweets, where 267,033 tweets have location information at below-city level (i.e. exact location coordinates, coordinates of a point of interest such as a restaurant, an administrative bounding box such as for a neighborhood or a park), and 799,407 have location information at the city level. Table \ref{tab:features} describes the attributes returned for each tweet file.

\begin{table}[!htb]
\centering
\resizebox{\textwidth}{!}{%
\begin{tabular}{|l|l|}
\hline
 \textbf{Attribute} & \textbf{Description} \\
 \hline\hline
 id & The unique ID that serves to identify each tweet object. \\  
 \hline
 created\_at & The timestamp (year-month-day hour:min:second.timezone) at which the tweet was created. \\
 \hline
 public\_metrics & The number of retweets, replies, likes, and quotes that the tweet received. \\
 \hline
 entities & Any special entities extracted from the tweet text (urls, user mentions, hashtags, place mentions). \\
 \hline
 geo & The geographical location where the tweet was created (if user enabled), in the form of latitude and longitude coordinates for exact locations or polygon boundary coordinates for places.\\
 \hline
 author\_id & The unique ID that serves to identify the creator of the tweet. \\
 \hline
 text & The text that the user wrote when creating the tweet. \\
 \hline
 conversation\_id & If a tweet is part of a conversation (e.g. a reply in a thread), this attribute is the unique ID that serves to identify the conversation of which a tweet may be part of. \\
 \hline
\end{tabular}
}
\caption{\label{tab:features}Attributes returned by the Twitter API v2 with the specified search query, for each tweet object.}
\end{table}

In order to extract a set of latitude-longitude coordinates for each tweet, the geographic centroid is calculated for each tweet that has a bounding box as location information. The geographical scope of the resulting data-set is illustrated in \ref{fig:dataScope}.\\

% \vfill
\begin{figure}[!htb]
\centering
    \includegraphics[width=\textwidth]{figures/dataScope.PNG}
    \caption[Geographical scope of hashtag activism tweets and physical protests during \#JusticeForGeorgeFloyd from tweet and protest data-sets]{\label{fig:dataScope}Geographical scope of hashtag activism tweets during \#JusticeForGeorgeFloyd from tweet data-set (left) (Each dot represents one tweet). Geographical scope of physical protest events during \#JusticeForGeorgeFloyd from ACLED data-set (right) (Each dot represents one physical protest).}
\end{figure}
% \vfill

In order to allow comparison between physical protest counts and tweet counts, tweet data was aggregated at area and time units common to tweet and protest data-sets. The result is five processed data-sets:

\begin{enumerate}[topsep=0pt,itemsep=-1ex,partopsep=1ex,parsep=1ex]
\item Total number of daily tweets, irrespective of geographical location (168 records).
\item Total number of tweets by county, irrespective of time (3111 records).
\item Total number of tweets by State, irrespective of time (51 records).
\item Total number of daily tweets by county (522648 records).
\item Total number of daily tweets by state (3121 records).
\end{enumerate}

\subsection{Physical protest data.} Data on physical protest activity was retrieved from The Armed Conflict Location \& Event Data Project (ACLED) \cite{raleigh2010introducing}. ACLED is an event based data project that "codes the actions of rebels, governments, and militias within unstable states, specifying the exact location and date of battle events, transfers of military control, headquarter establishment, civilian violence, and rioting". In the case of \#JusticeForGeorgeFloyd, ACLED is particularly relevant as it includes the most complete and reliable information regarding every Black Lives Matter physical protest that took place in the United States during 2020. ACLED data was acquired through the ACLED website as a .csv tabular file, of which relevant attributes pertaining to the time-stamp, type, organizing actors, and location of each protest are extracted (\ref{tab:protests}).

\begin{table}[!htb]
\centering
\resizebox{.7\textwidth}{!}{%
\begin{tabular}{|l|l|}
\hline
 \textbf{Attribute} & \textbf{Description} \\
 \hline\hline
 event\_id\_cnty & An individual identifier	by number and country acronym. \\  
 \hline
 event\_date & The date the event occurred in the format: yyyy-mm-dd. \\
 \hline
 event\_type & The type of conflict event. \\
 \hline
 actor1 & The named	actor involved in the event. \\
 \hline
 assoc\_actor\_1 & The named actor allied with or identifying ACTOR1. \\
 \hline
 actor2 & The named	actor involved in the event. \\
 \hline
 assoc\_actor\_2 & The named actor allied with or identifying ACTOR2. \\
 \hline
 interaction & A numeric code indicating the interaction between types of ACTOR1 and ACTOR2. \\
 \hline
 location & The location in which the event took place. \\
 \hline
 latitude & The latitude of the location. \\
 \hline
 longitude & The longitude of the location. \\
 \hline
 fatalities & The number of reported fatalities which occured during the event. \\
 \hline
 \end{tabular}
 }
\caption{\label{tab:protests}Attributes extracted from ACLED data \cite{raleigh2010introducing}}
\end{table}

Once collected, the ACLED data was filtered (according to the "ASSOC\_ACTOR\_1", "ASSOC\_ACTOR\_2", "EVENT\_TYPE", and “EVENT\_DATE” fields) to contain only “Protests” and “Riots” events that are relevant to the \#JusticeForGeorgeFloyd case study. As a result, the ACLED data-set was reduced to 10278 protest events of which the geographical scope is illustrated in Fig. \ref{fig:dataScope}.\\

% \vfill
% \begin{figure}[!htb]
% \centering
%     \includegraphics[height=4.5in]{figures/protestsScope.PNG}
%     \caption[Geographical scope of physical protest events during \#JusticeForGeorgeFloyd from ACLED data-set]{\label{fig:protestsScope}Geographical scope of physical protest events during \#JusticeForGeorgeFloyd from ACLED data-set. Each dot represents one physical protest.}
% \end{figure}
% \vfill

In order to allow comparison between physical protest counts and tweet counts, ACLED data was aggregated at area and time units common to all three data-sets. The result is five processed data-sets:

\begin{enumerate}[topsep=0pt,itemsep=-1ex,partopsep=1ex,parsep=1ex]
\item Total number of daily physical protests, irrespective of geographical location (168 records).
\item Total number of physical protests by county, irrespective of time (3111 records).
\item Total number of physical protests by State, irrespective of time (51 records).
\item Total number of daily physical protests by county (522648 records).
\item Total number of daily physical protests by state (3121 records).
\end{enumerate}

\subsection{Power regression analysis.} In this research, regression is used to quantify the statistical relationship between hashtag activism and physical protest. More specifically, due to the left skewed distribution of both tweet counts and physical protest counts (please see the Results section) the power regression model is chosen for modelling such relationships. This regression model is used throughout all applications of regression modelling in this research. The power regression model is a non-linear regression model useful for modelling problems where the dependent variable is equal to the independent variable raised to a power, as such \cite{draper1998applied}:

\begin{equation}
y=\alpha x^{\beta}
\end{equation}

In this equation, $y$ is the dependent variable, $x$ is the independent variable, and $\alpha$ and $\beta$ are the regression coefficients that describe the relationship between $x$ and $y$. In this research, the performance of power regression models is evaluated by using the Pearson correlation score $p$ \cite{benesty2009pearson} and the coefficient of determination $R^2$\cite{fahrmeir2007regression}:

\begin{equation}
\label{eqn:r2}
R^{2}=1-\frac{R S S}{T S S}
\end{equation}

where $RSS$ is the Residual Sum of Squares, calculated as $R S S=\sum_{i=1}^{n}\left(y_{i}-f\left(x_{i}\right)\right)^{2}$, and $TSS$ is the Total Sum of Squares, calculated as $\mathrm{TSS}=\sum_{i=1}^{n}\left(y_{i}-\bar{y}\right)^{2}$, where $y_{i}$ is a given sample value to be predicted, $f(x_{i})$ is the predicted value of $y_i$, where $\bar{y}$ is the mean sample value, and $n$ is the total number of observations in the sample. The Pearson correlation score $p$ and the coefficient of determination $R^2$ are two of the most commonly used evaluation metrics in regression analysis \cite{fahrmeir2007regression}. 
\subsection{Time Lagged Cross Correlation analysis.} In this research, Time lagged cross correlation analysis is used to study the directionality between the tweet count and protest count time-series, such as the existence of a leader-follower relationship where one variable expresses occurrence before the other variable \cite{shen2015analysis}. Essentially, Time Lagged Cross Correlation studies the directionality between two time-series, $x_t$ an $y_t$, by identifying lags of $x$ that may be the best predictors of $y_t$. This method involves (a) choosing two time-series that cover the same temporal extent and (b) fitting a regression model $n*2$ times using the $y_t$ data and the $x_{t-n}$ and $x_{t+n}$ data, where |$n$| is the maximum number of time lags. In this research Time Lagged Cross Correlation is used to test the hypothesis that one of hashtag activism or physical protest happens before the other.

\subsection{Granger causality analysis.} A more comprehensive method for analyzing the relationship between two time-series is \textbf{Granger Causality Analysis}. Granger causality is a statistical hypothesis test developed to study the exchange of information between two or more time-series \cite{granger1969investigating, zhao2020dynamic}. In the field of social movements research, Granger causality analysis has proven useful in a number of instances, such as for the study of causal relationships between social network nodes \cite{ver2012information} and the study of causal relationships between protests and repression \cite{carey2006dynamic}. More relevantly, and as previously discussed in \ref{cha:introduction}, Bastos et al.
(2015)\cite{bastos2015tents} and Brantly (2019)\cite{brantly2019cyberspace} both implemented Granger causality to argue for the existence of causal relationships between social media activity and physical protest activity.\\

Essentially, Granger causality determines whether prior values from one time-series can be used to predict current and future values of another time-series. Thus, while Granger causality does not always imply \textit{True} Causality, it is said that a time-series $x2$ \textit{Granger-causes} another time-series $x1$ if \textit{lagged} values of $x2$ provide statistically significant information about future values of $x1$ \cite{granger1969investigating}. As such, the Null hypothesis that $x2$ does not Granger-cause $x1$ is tested by first identifying the correct lagged values of $x1$ to use in a uni-variate auto-regression of $x1$:

\begin{equation}
x1_{t}=a_{0}+a_{1} x1_{t-1}+a_{2} x1_{t-2}+\cdots+a_{m} x1_{t-m}+\text { error }_{t}
\end{equation}

Following this step, the auto-regression is modified to include lagged values of $x2$:

\begin{equation}
x1_{t}=a_{0}+a_{1} x1_{t-1}+a_{2} x1_{t-2}+\cdots+a_{m} x1_{t-m}+b_{1} x2_{t-1}+\cdots+b_{q} x2_{t-q}+\text { error }_{t}
\end{equation}

Next, the lagged values of $x2$ that (a) collectively add explanatory power to the auto-regression according to an F-test and (b) are found to be individually significant from the value of their t-statistic are retained in the auto-regression. In the above equation, $q$ is the smallest lag and $t-q$ is the largest lag for which a lagged value of $x2$ is significant. Finally, we accept the Null hypothesis that $x2$ does not Granger-cause $x1$ if no lagged values of $x2$ are retained in the auto-regression \cite{granger1969investigating}.\\

In this research, Granger causality analysis is implemented using the \textit{grangercausalitytests} function from the \textit{statsmodels} Python library \cite{seabold2010statsmodels}. This function performs four F-tests for granger non-causality of two time-series, where the Null hypothesis is that the second time-series $x2$ does not Granger cause the first time-series $x1$. In this implementation "Granger causality means that past values of $x2$ have a statistically significant effect on the current value of $x1$, taking past values of $x1$ into account as regressors. We reject the null hypothesis that $x2$ does not Granger cause $x1$ if the p-values are below a desired size of the test" \cite{mckinney2011time}. With national, state-level, and county-level data, Granger causality is implemented to study whether data on tweet counts can provide information that is statistically significant for the forecast of future physical protest counts.

\subsection{Geo-spatial analysis.} In this research, each data source contains explicit and implicit spatial information, such as geographical coordinates, the shapes of administrative regions, and the name of places and administrative regions. Thus, traditional geo-spatial analysis \cite{de2007geospatial} (i.e. spatial joins, geo-referencing, computation of centroids from shapes) procedures are used to process, manipulate and combine these different data sources, and analyze spatial relationships that exist between them.

\subsection{Quantile analysis.} To explore the nature of the relationship between hashtag activism and physical protests at small spatial scales (i.e. U.S. county level), three potential independent variables were considered: population density (people/km$^2$), urban area (\%), and democratic votes in the 2020 U.S. presidential elections (\%). In each case, the data (consisting of the weekly number of tweets and weekly number of physical protests for each of the U.S.’s 3,243 counties or county equivalents) was discretized into 25 equal-sized quantiles according to the distribution of the independent variable considered (i.e. 25 population density quantiles, 25 urban area quantiles, and 25 democratic votes quantiles). Next, for each such quantile, the power regression model was fit to each county’s weekly tweet and physical protest data where the independent variable (e.g. population density) was greater or equal to the quantile’s lower threshold. Finally, a quantile-specific average was computed for each of the resulting regression metrics. 

\section*{Data and code availability} All code used to reproduce the finding of this research can be found on \href{https://github.com/lnicoletti/hashtag_activism_reform}{Github}. All data used for this research can be found \href{https://figshare.com/s/f4c2d30e8a3fb51ea484}{here}.
\\\\

\bibliography{sample}

% \section*{Acknowledgements (not compulsory)}

% Acknowledgements should be brief, and should not include thanks to anonymous referees and editors, or effusive comments. Grant or contribution numbers may be acknowledged.
\section*{Acknowledgements}
The authors would like to acknowledge the Senseable City Lab at the Massachusetts Institute of Technology, and the Computational Urban Science and Policy lab at Delft University of Technology, for providing the academic environment that made this research possible.
\section*{Author contributions statement}

L.N. defined and implemented the research question, including literature review, conceptualization, data collection, data processing, data analysis and data visualization. T.V., P.S. and M.W. supervised the research, and informed the conceptualization and methods sections. L.N. wrote all sections of the manuscript. All authors reviewed the manuscript. 

\section*{Additional information}
\textbf{Supplementary Information} The online version contains supplementary material available at [SI URL].
\\\\
\noindent\textbf{Competing interests} The authors declare no competing interests.
 \\\\
\noindent\textbf{Correspondence} and requests for materials should be addressed to L.N.
\\\\
\noindent\textbf{Reprints and permissions information} is available at \hyperlink{www.nature.com/reprints}{www.nature.com/reprints}.


% \newpage
% \section*{Supplementary material}
% \label{cha:appendix}

% \begin{table}
% \centering
% \resizebox{0.2\textwidth}{!}{%
% \begin{tabular}{|l|l|l|}
% \hline
% state & pearson\_r & r2 \\ \hline
% AK & 0.627 & 0.393 \\ \hline
% WY & 0.575 & 0.331 \\ \hline
% MT & 0.629 & 0.396 \\ \hline
% ND & 0.480 & 0.230 \\ \hline
% SD & 0.715 & 0.512 \\ \hline
% NM & 0.742 & 0.551 \\ \hline
% ID & 0.447 & 0.200 \\ \hline
% NE & 0.764 & 0.583 \\ \hline
% NV & 0.505 & 0.255 \\ \hline
% KS & 0.663 & 0.439 \\ \hline
% UT & 0.715 & 0.511 \\ \hline
% ME & 0.709 & 0.503 \\ \hline
% OR & 0.807 & 0.651 \\ \hline
% CO & 0.768 & 0.589 \\ \hline
% IA & 0.868 & 0.754 \\ \hline
% OK & 0.524 & 0.275 \\ \hline
% AR & 0.643 & 0.414 \\ \hline
% MS & 0.711 & 0.505 \\ \hline
% AZ & 0.743 & 0.552 \\ \hline
% VT & 0.614 & 0.377 \\ \hline
% MN & 0.823 & 0.678 \\ \hline
% WV & 0.784 & 0.615 \\ \hline
% MO & 0.777 & 0.604 \\ \hline
% AL & 0.726 & 0.528 \\ \hline
% WI & 0.731 & 0.534 \\ \hline
% LA & 0.725 & 0.525 \\ \hline
% TX & 0.829 & 0.686 \\ \hline
% KY & 0.715 & 0.511 \\ \hline
% WA & 0.835 & 0.697 \\ \hline
% NH & 0.689 & 0.475 \\ \hline
% TN & 0.832 & 0.692 \\ \hline
% SC & 0.811 & 0.658 \\ \hline
% MI & 0.834 & 0.695 \\ \hline
% GA & 0.839 & 0.705 \\ \hline
% IN & 0.824 & 0.679 \\ \hline
% NC & 0.836 & 0.699 \\ \hline
% VA & 0.858 & 0.736 \\ \hline
% HI & 0.744 & 0.554 \\ \hline
% IL & 0.805 & 0.648 \\ \hline
% CA & 0.923 & 0.853 \\ \hline
% OH & 0.795 & 0.632 \\ \hline
% PA & 0.797 & 0.635 \\ \hline
% FL & 0.811 & 0.658 \\ \hline
% NY & 0.869 & 0.755 \\ \hline
% DE & 0.329 & 0.108 \\ \hline
% MD & 0.692 & 0.480 \\ \hline
% CT & 0.726 & 0.527 \\ \hline
% MA & 0.764 & 0.583 \\ \hline
% RI & 0.598 & 0.358 \\ \hline
% NJ & 0.757 & 0.573 \\ \hline
% DC & 0.391 & 0.153 \\ \hline
% \end{tabular}
% }
% \caption{\label{tab:state_reg_results}Results for state-level power regressions between daily number of tweets and daily number of physical protests.}
% \end{table}

% \begin{table}
% \centering
% \resizebox{\textwidth/3}{!}{%
% \begin{tabular}{|l|l|l|}
% \hline
% granger\_relationship                     & p\_value & state \\
% \hline\hline
% tweet\_count -\textgreater protest\_count & 0.0      & AK    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & AL    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & AR    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & AZ    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & CA    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & CO    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & CT    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & DC    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.4189   & DE    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & FL    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & GA    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & HI    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & IA    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0247   & ID    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & IL    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & IN    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & KS    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & KY    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & LA    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & MA    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & MD    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & ME    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & MI    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & MN    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & MO    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & MS    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0071   & MT    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & NC    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.2303   & ND    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & NE    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0061   & NH    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & NJ    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & NM    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & NV    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & NY    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & OH    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & OK    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & OR    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & PA    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0062   & RI    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & SC    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & SD    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & TN    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & TX    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & USA   \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & UT    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & VA    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & VT    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & WA    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & WI    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.0      & WV    \\
% \hline
% tweet\_count -\textgreater protest\_count & 0.1253   & WY
% \\
% \hline
% \end{tabular}
% }
% \caption{\label{tab:GrangerResults_tp}National and State-level results of Granger causality analysis for the hypothesis that tweet count Granger causes protest count.}
% \end{table}

% \begin{figure}[!htb]
% \centering
%     \includegraphics[width=\textwidth]{figures/quantileAnalysis_sup.PNG}
%     \caption[Mobilization Synergy Scaling Law]{\label{fig:5_scaling}Evolution of power regression parameters (for the power relationship between daily number of tweets and daily number of protests) with population density (top), urban area (middle), and democratic votes turnout (bottom).}
% \end{figure}

\end{document}