SAN DIEGO--How's this for a math problem: How many police officers does it take to make a neighborhood safe from crime?
And here's your second problem: is this really a matter for math?
In presentations at the 2010 AAAS Annual Meeting, applied mathematicians showed how their skills can be used to explore real-life problems, from crime "hotspots" to traffic pileups and crowded sidewalks. Urban planners and social scientists are increasingly turning to math as a way to understand these complex groups of unpredictable people, the speakers said.
Andrea Bertozzi, an applied mathematician at the University of California, Los Angeles, worked with anthropologists and criminologists to build mathematical models of how crime hotspots form and spread.
In a study published this week in the Proceedings of the National Academy of Sciences, the researchers plugged real-world data on crime--you're more likely to be be the victim of a home burglary if your neighbor's house was recently ransacked, for instance--into the models to see how hotspots might grow.
Some hotspots form when criminals drift through a neighborhood, finding easy targets near their homes and workplaces. The hotspot blossoms as each crime makes the neighborhood more unstable, and more prone to the next crime.
Other hotspots appear with a large local spike in crime, said UCLA anthropologist Jeffrey Brantingham, such as an open air drug market that attracts criminals to a central spot.
A heavy police presence might not stamp out the first kind of hotspot; the models suggest that the criminals would scatter to other areas, eventually creating another hotspot as their individual crimes again reach a critical level of overlap.
But the second type "could be quelled by policing" that would suppress the large but narrowly focused crime spike that caused the hotspot, said Bertozzi.
Applied mathematicians like Mehdi Moussaid, a researcher at the Swiss Federal Institute of Technology, use the same complex modeling to understand how people move in large groups. The models provide valuable information for street design and crowd control, he said.
In a commercial walkway, flows of people moving in opposite directions spontaneously separate, enhancing the traffic flow.[Courtesy Mehdi Moussaid]
In a commercial walkway, flows of people moving in opposite directions spontaneously separate, enhancing the traffic flow.
[Courtesy Mehdi Moussaid]
Moussaid used video cameras to watch pedestrians as they walked alone or in small groups, All walkers have individual quirks--whether to dodge left or right to avoid others, for instance--but in a large group these preferences combine to produce "the sudden emergence of collective behavior," he said. In France, he found, there seems to be a slight preference for dodging right, which creates distinct "lanes" of foot traffic on a busy sidewalk.
When friends walk together, the one in the middle of the group drops back while her companions move forward and toward the center, said Moussaid. The formation makes it easier to keep up with a conversation, although frustrated pedestrians trying to find a way around the chatting group will find that it "has no aerodynamic features at all," he joked.
Moussaid's colleagues have applied some of the same math models to studying crowds in Mecca during the annual Muslim pilgrimage to the city. In video of a deadly stampede during the 2006 pilgrimage, the mathematicians saw a new phenomenon: crowd turbulence, where extreme crowding leads to a strong ripple of movement as individuals jostle for more standing room.
Mathematicians are excited about the new collaborations with social scientists and other unexpected partners, according to Nicola Bellomo, a mathematician at the Polytechnic University of Turin in Italy. "The cultural growth of mathematics," he said, "is based on new motivation."