Mathematics can reduce crowd deaths

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Stampedes and claustrophobia in crowded places leading to injuries and deaths has become quite the norm over the years. Be it a musical concert or a religious gathering, a sports event or a shopping fest, or even a local train, overly crowded places are quite popular for the disasters that come packaged with it.

In a fervent bid to prevent this, mathematicians are resorting to the numbers game to model crowd movement to establish safety measures.

Measuring crowd behavior with a mobile app

Mathematicians have also used highly accurate mathematical approaches from Density-Functional Theory (DFT) to predict crowd behavior. The objective of this approach is to study large collections of quantum mechanically interacting electrons. For instance, by using video data of crowds in public spaces this method is expected to predict how people would distribute themselves in a situation of extreme crowding. A smartphone app is used to measure density fluctuations in order to describe the current behavioral state or mood of a crowd. This approach is efficient in order to provide an early warning for crowds shifting towards such a dangerous behavior.

Fruit flies to the rescue test

To test the DFT theory, researchers used a model of walking fruit flies. They used two functions to demonstrate the mathematical approach. The first is the “vexation” function that quantifies how much flies like different locations in their environment. The second is the “frustration” function that explains how much flies mind crowding together. The two functions are based on details of how population densities change as these flies move around.

By comparing this information with the observations of a single fly in an entirely new environment, they could nearly accurate predict, before any observations of how a large crowd of flies would distribute themselves in that new environment.

By changing the social circumstances in their fly experiment and monitoring frustration values of the crowd, researchers showed that they could also detect changes in crowd “mood”.

The DFT approach, therefore, not only predicts crowd behaviors under new circumstances, but can also quickly and automatically detect changes in social behaviors. Granted in 2017, patent  US9691238B2 filed by Immersion Corporation and titled “Crowd-based haptics” describes a system that produces haptic effects. According to the patent, the system receives an input data that is associated with a crowd that attends the event and produces haptic effects via a haptic output device. These haptic effects include crowd key elements (e.g., crowd mood, cheers, boos, etc.). Ensemble methods leveraged to demonstrate multiple learning algorithms in order to obtain a better predictive performance. Particle filters method such as a sequential Monte Carlo method based on point mass (or “particle”) representations identifies probability densities.

Fig.1: The figure from patent US9691238B2 shows the block diagram of the system that produces haptic effects.

Patent CN206712964 (U), published in 2017 by Gao Shuoxin and titled “Potential mood intelligent analysis system for public safety precaution guards against “ relates to a potential mood intelligent analysis system for public safety. This system uses video analysis and mathematical formulae to provide real time monitoring of target emotions and to detect suspicious crowd behavior.

In the upcoming years, these mathematical models will prove to be a boon with reduced crowd disaster risks and better crowd management.

(Featured image is for representative purpose only and has been sourced from


A technology enthusiast who loves exploring gadgets by decoding the software used behind it. Shikha is an electronics and communication engineer and she keeps herself updated by reading technology blogs and whitepapers on cloud computing, networking and telecom.

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