MEDFORD/SOMERVILLE, Mass. -- In a scene reminiscent of the popular crime-solving television show "Numbers," a team of Tufts University students have developed mathematical models designed to help police track down serial killers.
The models propelled the students to a top five finish in the 26th annual Mathematical Contest in Modeling which drew 2254 entries around the world. Using mathematical problem solving techniques, along with data taken from three actual serial murder cases, the Tufts teams was able to produce equations to help predict the possible locations of the killers' next crimes.
The three actual cases involved David Berkowitz, known as the "Son of Sam"; Angelo Buono and Kenneth Bianchi, who were convicted of the "Hillside Strangler" murders; and John Allen Muhammad, who was arrested, charged and later executed for a series of sniper shootings in the Washington, D.C. area in 2002.
The contest was sponsored by the Consortium for Mathematics and its Applications (COMAP). The Tufts team included Daniel Brady, a senior majoring in mathematics and engineering science; Liam Clegg, a junior majoring in quantitative economics and Victor Minden, a sophomore majoring in computer engineering and mathematics.
In their first model, the "centrographic model," the team began with the assumption that serial killers operate near their homes in areas with which they are familiar.
They pinpointed the locations of a connected series of crimes. They then established a geographical center, or centroid, for the crime spree. As the crimes continued, the location of the centroid changed. Using this movement, along with the rate at which crimes occurred, the team's equations were able to predict the potential locations of future crimes.
The team's second model, "the rational choice model," operated under the assumption that the serial killer weighs the possibility of getting caught before choosing the location of his next crime. To avoid capture, he is not likely to commit two crimes in the same location. By looking at such data as where the killer finds his victims and dumps their bodies, this model is able to predict not only where the killer is likely to strike next but where he lives.
The team tested each model in a computer simulation, using data from the real cases. The models' predictions about the locations of later crimes were compared with the actual locations where the crimes occurred.
In the MCM contest, the competing teams of up to three undergraduate or high school students worked from Feb. 18 to 22 to solve one of two problems. One was the serial murder problem. The other involved explaining the "sweet spot" on a baseball bat.
"I saw the criminology problem as being the more intriguing and challenging of the two," says Minden. "It was as if this was detective work and we were to predict where the killer would strike next. We really got into it."
Minden says that the predictions were not accurate in every instance. Both models could be improved with more data and would also require more testing. He adds that math is not a replacement for police work. "Mathematical models are tools for investigators to use," he says. '"Investigative experience is the best resources to catch a serial killer."
The team spent hours preparing for the contest with help from Tufts Assistant Professor of Mathematics Scott MacLachlan and Professor Misha Kilmer. "The long hours have paid off," says MacLachlan. "This award show how talented these students are."
The Consortium for Mathematics and its Applications is an award-winning non-profit organization whose mission is to improve mathematics education for students of all ages. Since 1980, COMAP has worked with teachers, students, and business people to create learning environments where mathematics is used to investigate and model real issues in the world.
About Tufts University
Tufts University, located on three Massachusetts campuses in Boston, Medford/Somerville, and Grafton, and in Talloires, France, is recognized among the premier research universities in the United States. Tufts enjoys a global reputation for academic excellence and for the preparation of students as leaders in a wide range of professions. A growing number of innovative teaching and research initiatives span all Tufts campuses, and collaboration among the faculty and students in the undergraduate, graduate and professional programs across the university's schools is widely encouraged.
