Michael Bird, A16, Kathleen Cachel, A16, and Charles Colley,
E16 (From left to right,) winners of the 2014 Mathematical
Contest in Modeling contest, outside the Tisch Library. Michael Bird, A16,Charles Colley, E16, and Kathleen Cachel, A16 |

Three Tufts students, Michael Bird (A16), Kathleen Cachel (A16),
and Charles Colley (E16), received the Outstanding Award in the
annual Mathematics Contest in Modeling (MCM) competition from
COMAP, the
Consortium for Mathematics and Its Applications. Of 6,755
international teams of undergraduate students, only 13 teams
received the Outstanding Award designation.

The sophomores, who self-organized to form the 2014 Tufts team, are
students in Mathematical Modeling and Computation (Math 87), a
recent addition to the
Department of
Mathematics offerings. Math 87 serves as a key requirement in
the new Applied Mathematics major. The course introduces students to
both the concept of modeling physical systems and the manipulation
of these models to answer questions about the underlying physical
problem, says Department of Mathematics Associate Professor Scott
MacLachlan, who teaches the course and was the team's faculty
sponsor.

"The MCM is a challenging competition because it asks students to
exercise a wide range of skills," says MacLachlan. "A successful
paper will include detailed background research on the use of
mathematical modeling for the problem at hand, specialization of
these models to the particular questions posed, detailed
computational results in support of their conclusions, and critical
analysis of the mathematical models and computational results
obtained. All of this must be presented clearly and concisely, in a
compelling written document."

MacLachlan's participation is limited to preparing the team for the
four-day contest. During the period in which the contest runs, the
students cannot discuss the problem with anyone outside their team,
including their faculty sponsor. This year's competition began on
February 6, when the team saw the problems for the first time. By
8:00 pm, four nights later, they had to submit a copy of their paper
via email, explaining their mathematical model and how it answers
the questions posed.

"Many students are drawn to the competition because it shows them
just how much mathematics is present in the world around us, as well
as providing an intense experience beyond what is possible in the
classroom environment," says MacLachlan.

After selecting one of two modeling problems to solve, the Tufts
team was challenged to analyze the benefits and performance of a
"keep right except to pass" rule for highway travel. Michael Bird,
A16, a biochemistry and applied mathematics major, says he was
originally convinced the problem was beyond him. "Charlie and
Kathleen helped to get me off the ground in the first few hours of
the competition", he said. "By the time I broke out of my 'this is
impossible' haze, we'd found the Nagel-Schreckenberg model for
traffic flow on a freeway, which we eventually adapted to create our
model that was used for the paper."

However, says Bird, on Friday and Saturday the team still believed
they had plenty of time. "By Sunday, we had spent hours in Eaton
finishing the model and mining data from it, and then adapted it so
we could test different rules for passing on a highway." Colley
tested the models with different numbers of lanes, cars, max speeds,
and accident rates, and realized the team wouldn't have usable data
until some time in 2025. "We had to drop any further model building
we were doing so that I could come up with a script that would run
lots of the tests at once," says Bird, "and throw the results out as
a neat table that Charlie could convert into the informative charts
that make up much of the final paper." Earlier in the day the team
spent hours trying to fix broken code that frequently became stuck
in infinite loops.

As of Monday morning the team had not started writing the final
paper, recalls Bird, who says they spent the entire day writing it
in Hotung CafĂ©. The submitted paper was 17 pages, including
citations. No code is included says Bird: "it's all about drawing
conclusions from the data your model produced."

When Professor MacLachlan contacted team members on April 3 with the
news that they had been awarded the highest rank given to solution
papers, Bird was stunned. "At the time we were hoping we might be
able to produce a paper that just about earned the rank of
'successful participant', the second lowest score above
'unsuccessful', says Bird. "I was convinced the Outstanding Award
was some sort of belated April Fools joke for a few minutes after I
saw it."

This team's achievement is particularly notable, says Maclachlan,
since they are all sophomores, competing against many juniors and
seniors. He adds that they brought a great enthusiasm to the
contest. "They wrote a detailed and thoroughly researched report,"
adds Maclachlan. "They provided strong data in support of their
conclusions, as well as critical commentary on their results."