Jan 14, 2022

Ali Yang ’22, William Yue ’22, and Nathan Xiong ’22 were recognized as the Top 300 semifinalists in the Regeneron Science Talent Search (S.T.S.). According to its website, Regeneron S.T.S. is one of the nation’s oldest and most prestigious science and math competitions and is open exclusively for high school seniors.

In this program, students showcase extensive research of a mathematical or scientific field through a cohesive research paper. Students who are selected as one of the Top 300 Scholars receive a $2,000 reward, qualifying them to compete for the Top 40 finalists with prize money of $25,000 and a trip to Washington to display and present their research. In addition, Andover will receive $2,000 for each Scholar nominated to use for STEM-related purposes.

Yue’s research focused on applying combinatorics—an area of math primarily concerned with counting—and complex analysis—an area of math primarily concerned with functions of complex number variables—to theoretical computer science. He researched and developed an algorithm that could reconstruct some unknown data from a minimal number of noisy copies of that data.

“The problem of interest is called Trace Reconstruction. The idea is that you have some data and you want to reconstruct this data. You don’t know what the data is, but you can try to look at the data. However, when you try to do so, some of the data goes missing. Each piece of data goes missing with some probability, or chance. Basically, you can look at [the data many] times, and each time, some different pieces might go missing. And then from those many observations, you want to reconstruct what the original data was. You [also] want to minimize the number of times you have to look at the data,” said Yue.

Yue continued, “This has a lot of applications in computational biology. For example, you can take DNA sequencing. The sequencer may make a mistake when you try to sequence the DNA or some piece of the DNA mutates for some reason, and you want to recover what it originally said.”

Yang, another Andover student who was named a Top 300 Scholar, worked on machine learning for cancer genetics, a topic she was inspired to delve further after her summer project at the Research Science Institute. The project expands on already existing technology in an innovative and applicable way by developing a machine learning model which matches genetic data with diagnoses written in English.

“Typically, what people do when they study cancer genetics is they take the genetics as an input to the model, then have the model predict survival or severity or some sort of proxy for whatever they want. I used a different method where instead of trying to predict such a proxy directly, my model tries to match the English text with the genetic data. For example, you give the model maybe 256 genetic samples, then 256 diagnoses in English. So each English diagnosis would be something like ‘sarcoma, size 6.5 by 4 by 2 centimeters, moderately differentiated,’ and then you match it with the most similar genetic profile out of those 256 options,” said Yang.

Xiong started his project almost a year ago at the Massachusetts Institute of Technology Program for Research in Mathematics, Engineering and Science (MIT Primes), a free after school research program for high schoolers run by MIT, working with his mentor. Xiong studied Yang-Mills Theory, an attempt to mathematically understand the Standard Model, a famous and successful model in particle physics.

“In a lot of math and physics, we want to model the world, understand how it works. There is one very popular scientific model called the Standard Model. It’s [essentially] a model of how particles interact in the universe, about the physical nature of our world. It’s a very useful and powerful theory. The very general field which I was researching in tries to ground this in mathematics. I wasn’t actually dealing with the real world, but [rather] with [a] 2-dimensional space,” said Xiong.

Each research paper is at most 20 pages long, supported by extensive amounts of data, research, and models. According to Yue, the initial processes of learning the background and applying trial and error for finding valuable ideas towards proving the results were long and tedious, with numerous challenges along the way, but with the help of his mentor, he was able to brave through the learning process.

“Math research is very tough because you have to know a lot of background in that particular problem, and usually this background is maybe even graduate-level work. But I got a lot of help from my mentor and started reading a lot of papers, gradually learning the necessary things to understand all the background. This was the first main challenge. And then, actually proving the results was [also] very difficult since there are so many possibilities for what you could do. And oftentimes, you have some idea and you try it, [then] it doesn’t work. And then you try another idea [without knowing] which idea will actually get you closer to solving the problem. So it’s just a lot of effort that has to go into it until you actually get the results,” said Yue.

For Xiong, the Top 300 Scholar nomination was surprising as he didn’t expect any awards or ranking while preparing for this research. Instead, he appreciated the opportunity in sharing his research with other scientists and students.

“[I joined] mainly for the experience. Even though I got the Top 300 Scholar, I didn’t really expect to go much further. It’s just about the experience of doing research and being able to share with other people in a comprehensible way––being comfortable with talking about what you’ve done and being able to showcase it to other scientists and other students,” said Xiong.

*Editor’s Note: William Yue ’22 is a News Editor for *The Phillipian*.*