New mathematical law found to beautifully explain crowd phenomena

New mathematical law found to beautifully explain crowd phenomena

A new law of science has been found to beautifully explain crowd movements for first time. The as-yet unnamed law, which is a mathematical, universal power law for human interactions, was found by U of M researchers who analyzed complex datasets that have only recently been available. The movement of crowds is fundamentally anticipatory in nature, according to the researchers, and the new, simple energy law expresses, in the words of its lead author, “the beauty of human nature.”

“The law we identified is brand new; such a law would have been impossible to identify 10 years ago as we simply did not have the technology to track pedestrian crowds at a large-scale,” Dr Ioannis Karamouzas, Research Associate at the University of Minnesota’s Department of Computer Science and Engineering and first author of the report, told The Speaker.

New law of science found to beautifully explain crowd phenomena
Dr Ioannis Karamouzas

“Nowadays, though, in the era of big-data there is a plethora of publicly available human crowd data. By analyzing such data, we found that, unlike particle-based interactions, the interactions between pedestrians are anticipatory in nature,” Karamouzas told us, referring to previous models that had attempted to predict crowd behavior with data based on repulsive particles rather than humans.

“To be more specific, when two particles interact the amount of energy that they have to expend to avoid colliding with each other depends on how close they are. In contrast, when two pedestrians interact, their energy depends on the ‘time-to-collision,’ i.e., the time that it takes for the pedestrians to collide assuming that they do not change course; as a collision becomes more imminent, this energy increases drastically.”

Karamouzas and his team have discovered a universal parameter based on single variable that explains crowd movement.

New mathematical law found to beautifully explain crowd phenomena“Surprisingly, the relationship between interaction energy and time-to-collision consistently follows a simple mathematical law stating that the degree to which two pedestrians are willing to respond to each other is inversely proportional to the square of their projected time-to-collision.”

Karamouzas elaborated on the types of crowd phenomena that could be explained by the new law.

“This law is broadly applicable as it consistently holds across different crowd settings; we analyzed both sparse and dense human crowds and found that pedestrian interactions follow the same power-law relationship. Our law has allowed us to gain a better understanding into how human behave and interact in a crowd.

“Looking into the future, I believe that such a law will have broad applications into our everyday life, from simulating in a more accurate way pedestrian behaviors in games, training simulators and animated movies, to designing safer buildings and pedestrian facilities.”

Karamouzas also explained how a law could so simply cover such range in speeds, densities and situations.

“That’s the beauty of the human nature! Every person in a crowd is certainly unique with his/her own desires and individual goals. What our law captures is how people adapt their courses in response to others around them. And such adaptations directly follow from the psychology of anticipation. As we move through a crowd our brain is able to process visual and acoustic cues and recognize the future consequences of our actions allowing us to react accordingly. And it’s the interaction between each person’s individual goals and our inferred law that allows pedestrians to exhibit such a large variety of behaviors.”

The law could not have been found in the past, due to the complexity required of the analysis.

“When we move in a crowd, we typically experience a complex system of competing forces,” said Karamouzas. “On one hand we have a goal that we are tying to reach–e.g. grocery store–and on other hand we try not to bump into other people. On top of that, we hardly ever walk alone but in small groups–such as couples, families, friends, etc. As such, we have to account for all these factors and continuously make our own decisions, which makes very hard to isolate/identify the primary rule that describes our interactions in a crowd. Much of the work in our paper was developing a new analysis technique which can account for the effect of all these forces simultaneously. Because the technique we employed was statistical in nature, we needed to analyze thousands of trajectories to robustly determine the pedestrian interaction law.”

Karamouzas went into detail about how his team found the law.

“We turned into a large collection of publicly available pedestrian datasets that are nowadays available thanks to the advances in automated tracking and computer vision,” said Karamouzas. “Overall, we analyzed six datasets New mathematical law found to beautifully explain crowd phenomenaconsisting of students walking in college campuses, pedestrians interacting at commercial streets, and a few controlled experiments where participants navigate through narrow bottlenecks.

Previously, there had been formidable challenges facing researchers who wanted to find an accurate and general rule for pedestrian behavior.

“To overcome the challenges that I mentioned already and robustly quantify the interaction law of pedestrians we employed a novel approach rooted in condensed matter physics. We initially measured the probability that any pair of pedestrians in the data has of maintaining a certain separation distance. We basically hypothesized that similar to charged particles, the interaction between pedestrians is distance-dependent. However, we found that the probability plots were very different for different walking speeds; when two pedestrians approach each other very fast they tend to maintain a larger separation distance than when they move slowly, as opposed to particles. As such, we started looking into different variables that can describe the interactions between pedestrians and we found that the time-to-collision is a sufficient descriptor. The probability plots were the same for different speeds as well as different orientations at which pedestrians approach each other. In addition, the time-to-collision measure naturally accounts for pedestrians coming relatively close to one another when moving in roughly the same direction–e.g. a pair of friends walking line-abreast. Eventually, by analyzing all the data, we inferred a simple energy law for the interactions between pairs of pedestrians.”

The research is considered to hold new promise for improved public architecture and spaces, the failings of which in the past have caused deaths.

“First of all, the nice thing about our newly identified law is that it directly implies an accurate model of simulating crowd flows. And through such simulations, we can design safer buildings as well as improve the efficiency of New mathematical law found to beautifully explain crowd phenomena (4)existing facilities–e.g., better egress times at a stadium. Furthermore, our novel way of analyzing crowd data and directly measuring the “interaction energy” between pairs of pedestrians opens interesting avenues for future work. For example, we would like to analyze crowd data from mass gatherings, such as concerts, and see how the interaction energy can be used to identify critical areas preventing the likelihood of crowd disasters–like the Love Parade in 2010).

Karamouzas commented on what he thought may be the most important thing for readers to understand of the research.

“The main take-away message is that a lot of the complexity of pedestrian interactions can be captured using simple mathematical equations. The universality of how pedestrian respond to each other is really surprising, and understanding this can lead to more accurate simulations, safer building designs, and shed some light into the anticipatory nature of human interactions.

The report, Universal Power Law Governing Pedestrian Interactions, was authored by Drs. Ioannis Karamouzas, Brian Skinner, and Stephen J. Guy, and was published in Physical Letters Reviews last week.

Feature image: Karl Baron

Images belong to the work of the researchers

VIDEOS from the researchers

Agents positioned at two concentric circles have to walk to their antipodal points.

Self-directed agents form collective patterns.

Bi-directional flow through a corridor.

The “busiest intersection in the world,” Shibuya Crossing, Tokyo, Japan (LIVE)

When political parties reverse their policy stance, their supporters immediately switch their opinions too

At least a significant portion of their supporters, according to U of Aarhus researchers.

When two competing political parties in Denmark reversed their policy stance on an issue — suddenly they both supported reducing unemployment benefits — their voters immediately moved their opinions by around 15% into line with their party.

The same thing happened when one of these parties shifted from opposing to supporting ending Denmark’s early retirement.

The researchers were studying how public opinion is formed. Their recent paper sheds light on how much influence political parties have over their supporters, according to the researchers, who surveyed their panel of subjects in five successive waves between 2010 and 2011. They studied the same group of party supporters before, during and after a policy reversal.

“We can see that [the] welfare programs were actually quite popular … and many of the voters of the center-right party were in favor of these welfare programs,” commented one of the researchers, Rune Slothuus. “Nevertheless, we can see that they reversed their opinion from supporting these welfare programs to opposing these welfare programs.”

“I was surprised to see the parties appeared this powerful in shaping opinions,” Slothuus said. “Our findings suggest that partisan leaders can indeed lead citizens’ opinions in the real world, even in situations where the stakes are real and the economic consequences tangible.”

The researchers pondered Western democracy in light of their findings: “If citizens just blindly follow their party without thinking much about it, that should lead to some concern about the mechanisms in our democracy. Because how can partisan elites represent citizens’ views if the views of citizens are shaped by the very same elites who are supposed to represent them?”

Source: How Political Parties Shape Public Opinion in the Real World. Rune Slothuus and Martin Bisgaard. First published: 04 November 2020 https://doi.org/10.1111/ajps.12550

The brain listens for things it is trying to predict

The brain interprets sounds as they contrast with its expectations; it recognizes patterns of sounds faster when they’re in line with what it is predicting it will hear, but it only encodes sounds when they contrast with expectations, according to Technische U researchers.

The researchers showed this by monitoring the two principal nuclei of the subcortical pathway responsible for auditory processing: the inferior colliculus and the medial geniculate body, as their subjects listened to patterns of sounds which the researches modified so that sometimes they would hear an expected sound pattern, and other times something unexpected.

Source: Alejandro Tabas, Glad Mihai, Stefan Kiebel, Robert Trampel, Katharina von Kriegstein. Abstract rules drive adaptation in the subcortical sensory pathway. eLife, 2020; 9 DOI: 10.7554/eLife.64501

We have a particular way of understanding a room

When several research subjects were instructed to explore an empty room, and when they were instead seated in a chair and watched someone else explore the room, their brain waves followed a certain pattern, as recorded by a backpack hooked up to record their brain waves, eye movements, and paths. It didn’t matter if they were walking or watching someone else, according to UC researchers led by Dr Matthias Stangl.

The researchers also tested what happened when subjects searched for a hidden spot, or watched someone else do so, and found that brain waves flowed more strongly when they had a goal and hunted for something.

Source: Matthias Stangl, Uros Topalovic, Cory S. Inman, Sonja Hiller, Diane Villaroman, Zahra M. Aghajan, Leonardo Christov-Moore, Nicholas R. Hasulak, Vikram R. Rao, Casey H. Halpern, Dawn Eliashiv, Itzhak Fried, Nanthia Suthana. Boundary-anchored neural mechanisms of location-encoding for self and others. Nature, 2020; DOI: 10.1038/s41586-020-03073-y

Extroverts and introverts use different vocabularies

Extroverts use ‘positive emotion’ and ‘social process’ words more often than introverts, according to new research conducted at Nanyang Technological U.

‘Love,’ ‘happy,’ and ‘blessed’ indicate pleasant emotions, and ‘beautiful’ and ‘nice’ indicate positivity or optimism, and are among the words found to be used more often by extroverts. So too are ‘meet,’ ‘share,’ and ‘talk,’ which are about socializing. Extroverts use personal pronouns — except ‘I’ — more too, another indication of sociability.

The correlation, however, was small, and the researchers think that stronger linguistic indicators need to be found to achieve their general goal, which is improving machine learning approaches to targeting consumer marketing.

Source: Jiayu Chen, Lin Qiu, Moon-Ho Ringo Ho. A meta-analysis of linguistic markers of extraversion: Positive emotion and social process words. Journal of Research in Personality, 2020; 89: 104035 DOI: 10.1016/j.jrp.2020.104035

WhatsApp is changing today - Users must give the app permission to send their private data to Facebook or lose account

WhatsApp was bought by Facebook in 2014, but has thrived while promoting itself as a privacy-respecting messaging app that now has 1.5b monthly active users. This week, though, WhatApp sent out an update to users’ phones that they must ‘consent’ to a new policy or lose access.

Whatsapp will now share more of your data, including your IP address (your location) and phone number, your account registration information, your transaction data, and service-related data, interactions on WhatsApp, and other data collected based on your consent, with Facebook’s other companies. Facebook has been working towards more closely integrating Facebook, WhatsApp, Instagram and Messenger.

Users who do not agree to ‘consent’ to the new policy will see their WhatsApp account become inaccessible until they do ‘consent.’ These accounts will remain dormant for 120 days after which they will be ‘deleted.’

The biggest change to the user policy, which many people ignored and clicked ‘agree’ to, thinking it was just another unimportant app update message, now reads,

‘We collect information about your activity on our Services, like service-related, diagnostic, and performance information. This includes information about your activity (including how you use our Services, your Services settings, how you interact with others using our Services (including when you interact with a business), and the time, frequency, and duration of your activities and interactions), log files, and diagnostic, crash, website, and performance logs and reports. This also includes information about when you registered to use our Services; the features you use like our messaging, calling, Status, groups (including group name, group picture, group description), payments or business features; profile photo, “about” information; whether you are online, when you last used our Services (your “last seen”); and when you last updated your “about” information.’

Notably, Elon Musk tweeted on the news, saying that WhatsApp users should switch to Signal, one of several popular privacy-focused messaging apps similar to WhatsApp.

The data sharing policy change doesn’t affect people in Europe due to GDPR data protection regulations.