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Density-functional fluctuation theory of crowds

Our collaborators developed a powerful theoretical approach to describing and predicting crowd behavior that is easiest to understand when you picture a human crowd. For example, imagine you go to a stadium to see your favorite band. The show is about to start, so you look for the best spot to watch. You walk up to the stage and politely pass by the people at the edge of the crowd. Those people have forgone the best view in order to have a little more personal space. As you near the front though, it gets more and more crowded. After all this searching, you find a spot which is a compromise between getting a good view without being too crowded. Simultaneously, all the other individuals of the crowd are doing the same thing until everyone is content.


Sounds reasonable, right? You balance your preference to be at the best location in the stadium with your preference for a comfortable crowd density. The proposal is that a wide variety of macroscopic crowd systems can be described in this same manner; separating out their interactions with each other from their interactions with their environment. What’s more exciting is that, using this approach, one can measure these independent interactions using only observations of the local densities and density fluctuations of the crowd. From data alone, one can quantify distinct social behaviors separately from the spatial preferences for a given environment. Lastly, once these interactions are measured, they can be used to predict how a crowd with a given behavior will distribute itself in a given environment, all directly from observations without the need to account for the individual preferences and motions of each member of the crowd


This work was purely theoretical, however, and completely untested! We thus developed a novel kind of crowd of living creatures that allowed us to carry out highly controlled experiments. Specifically, we confine crowds of 100+ fruit flies to different environments, as in human crowds, and then track their local densities as shown below. By doing so, we confirm for the first time that the DFFT approach indeed can be powerfully predictive and descriptive on a real living crowd system. Specifically, we can quantify the crowd's changing social interactions seperately from their spatial preference (shown in overlaid heatmap below) and even accurately predict the average distributions of a crowd exhibiting a previously observed behavior in a new arena. In addition to being easy to work with, fruit flies also provide us with a wide variety of genetic tools that we are currently exploiting so that we can independently control the social behaviors and spatial preferences of the flies. Additionally, using data collected by other groups, we have observed that this approach can describe systems that exhibit very different behaviors from those of our flies like zebrafish and midge swarms, which suggests that our DFFT approach is indeed general and not specific to just fruit flies.