It was David and Goliath as a Cornell team of engineers competed with more than 3,600 mathematics majors from around the world in the 2012 Mathematical Contest in Modeling this past spring. Alvin Wijaya ’15, electrical and computing engineering, Dennis Chua ’14, chemical engineering, and Jessie Lin ’15, electrical and computing engineering, used their programming skills to become finalists in the competion and won the Mathematical Association of America Award with their software program that simulates the growth of tree leaves based on sunlight patterns and calculates their masses. Among the 3,696 teams in the competition, only 10 teams were ranked higher than the Cornell team and only 16 other teams were named finalists.
Using MATLAB, a mathematical programming software, Wijaya, Chua, and Lin designed a program that would have real life application to scientists around the world. According to the team, their software will help researchers approximate two things: the most-likely leaf shape for a given tree in a given region, and the total mass of all the leaves in that tree.
By using the team’s software, researchers no longer have to physically go to a tree to categorize and count each of its leaves. Instead they can simply use the modeling system to approximate the information needed.
According to Lin, the process of creating, designing, and implementing a modeling software program was difficult, but rewarding.
“We racked our brains to come up with an implementable model that was reliable and flexible at the same time,” Lin said. “We began with a basic model that was built mainly on probability and then expanded it to take into account the geometry of the tree, the region of growth, and the season.”
The predicted leaf shape and mass numbers that come from their software are precise, according to Wijaya. He said that the team crosschecked their results with real data and found it to be accurate and applicable for scientists.
The team said they were thrilled with not only the accuracy and real life application of their program, but also with their success at the IMCM. Their competition — juniors and seniors majoring in mathematics — was intimidating, according to Wijaya, so winning was a pleasant surprise for them.
Historically, he said, the winning projects had primary foundation in mathematics, but their model mostly relied on programming skills and a simulation idea, rather than pure math knowledge.
“Going into the competition, we thought our design was pretty simple, but it turns out that we did it quite well. We went there without any hope of winning, but then we won it. It was mind-blowing,” said Wijaya
“My favorite part was writing the program for our rigorous models.” Chua said. “I ended up writing over 4000 lines of code over four practically sleepless nights. It was all worth it when we ran both models at the end and they produced highly corroborative results.”
According to Chua, the team had only four days to perform everything, including the design of the software program and the paper writing portion.
The team said working together as a unit was crucial.
“Dennis was our main software programmer and came up with the idea of using a fractal-based model,” Wijaya said. “I was the online researcher and the mathematical analyst and came up with the idea of a 3-D fractal-based model, and Jessie was the mathematics formulator and came up with the idea of time-based simulation model.”
The team said that they hope to extend their software beyond tree leaves and into various other types of plants across the world in various regions and climates.
Wijaya said he was proud of his team’s accomplishment. “If you’re a freshman, don’t be afraid to try projects like this. You can do it,” he said,
Wijaya and Chua also presented their award-winning software at MathFest 2012, the largest annual mathematics conference, in August in Madison, Wisconsin.
Correction: A previous version of this article incorrectly referred to the Cornell team as winners of the competion. In fact, among all 3,696 teams, 10 achieved a higher ranking than the Cornell team and 17 teams achieved the same "finalist" ranking.