Math, physics, and video predict mood of big crowds

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Researchers are connecting the dots between electrons whizzing around each other and humans crammed together at a political rally, even if they don’t seem to have much in common at first.

They’ve developed a highly accurate mathematical approach to predict the behavior of crowds of living creatures, using Nobel Prize-winning methods originally developed to study large collections of quantum mechanically interacting electrons. The implications for the study of human behavior may be profound, researchers say.

For example, by using publicly available video data of crowds in public spaces, the approach could predict how people would distribute themselves under extreme crowding. By measuring density fluctuations using a smartphone app, the approach could describe the current behavioral state or mood of a crowd, providing an early warning system for crowds shifting toward dangerous behavior.

The researchers applied mathematical concepts and approaches from density-functional theory (DFT), a branch of many-body physics developed for quantum mechanical systems, to the behavior of crowds.

To test their theory, the researchers created a model system using walking fruit flies (Drosophila melanogaster). They first demonstrated a mathematical way to extract functions that quantify how much the flies like different locations in their environment—the “vexation” function—and how much they mind crowding together—the “frustration” function—based on the details of how the population densities change as the flies move around.

Then they showed that by mixing and matching this information with observations of a single fly in an entirely new environment, they could accurately predict, before any observations, how a large crowd of flies would distribute themselves in that new environment.

While fruit flies were “a convenient and ethical first test system,” says Tomas Arias, professor of physics at Cornell University, the behavior of a crowd at a political rally would provide a human example of DFT theory. Individuals will try to find the best location to stand—typically closest to the stage—while avoiding overcrowded areas. When new and better locations become available, individuals are likely to move toward them.

By varying the social circumstances in their fly experiments—such as changing the ratio of male and female, or inducing hunger and thirst—and monitoring the frustration values of the crowd, the researchers showed they can detect changes in the “mood” of the crowd. The DFT approach, therefore, not only predicts crowd behaviors under new circumstances, but also can quickly and automatically detect changes in social behaviors.

Another application, using cell-phone and census data, could analyze political or economic drivers and population pressures to describe and predict large-scale population flows, such as mass migrations.

“The resulting predictions of migration during acute events would enable better planning by all levels of government officials, from local municipalities to international bodies, with the potential to save millions of human lives,” the researchers note.

The research appears in Nature Communications.

Source: Cornell University