Success can be measured at a variety of levels. Success in academics is something that most Stuyvesant students constantly strive to achieve. Success on a national level however, is more demanding and requires an amount of work that only a select group of Stuyvesant students are capable of doing. Fortunately, the Intel Science Talent Search is a yearly challenge that attracts the scientifically and mathematically geared population at Stuyvesant, giving such students the opportunity to compete at a national level. Stuyvesant students have consistently achieved victories and, this year, Stuyvesant produced two Intel finalists, seniors Adam Sealfon and Anissa Mak. Both projects were largely focused on graphs.

Sealfon’s dealt with a particular type of graph known as a hypergraph while Mak’s explored the applications offered in decomposing a graph. Sealfon described his project as “comparing the complexities of two types of algorithms for hypergraphs,” which examines “the properties of a generalization of graphs called a hypergraph, in which connections are not between pairs of vertices but between larger groups of vertices,” Sealfon said.

Sealfon not only examined the properties of hypergraphs, but also delved deeper to compare the efficiencies of two methods of studying hypergraphs’ natures. Between these approaches, which are adaptive algorithms that take into consideration previous experiments, and nonadaptive algorithms, which do not, Sealfon proved that adaptive algorithms are more effective.

He used the familiar optimization strategies learned in Pre-Calculus and Calculus classes to determine this result. Sealfon used one of the adaptive algorithms he discovered to determine the structure of a hypergraph.

Sealfon contributes part of his success to his work over the summer with Massachusetts Institute of Technology graduate student Victor Chen, who motivated Sealfon to choose this topic. Sealfon also found the Stuyvesant Mathematics department to be very helpful in his overall growth as both a mathematician and a researcher.

Mak’s project is titled “A Certifying Algorithm for the Modular Decomposition of Undirected Graphs.” Each module, which Mak defines as “a nonempty subset X of a graph’s vertex set such that for each vertex y not in X, y is either adjacent to all the vertices in X or none,” is arranged in the tree-shaped representation of the modular decomposition.  In other words, for all points that have y-coordinates that are not included in the subsets of their x-coordinates, the y coordinate is either adjacent to the subset or does not exist on the graph.

Mak’s findings could prove useful while performing a number of familiar tasks such as solving optimization problems, drawing graphs, or sequencing DNA in molecular biology.

Though Mak put in a large amount of work into her project, she remains in awe of her victory.  “I found out when the Intel people called my house in the afternoon to give me a head’s up before the public announcement and I was just speechless. That whole night, I thought it was a prank call,” Mak said.

Mak, like Sealfon, appreciates the support given by the Stuyvesant Mathematics department. She also worked with a mentor, Dr. Ross McConnell from Colorado State University, who was recommended to her by math teacher Gary Rubinstein.  Mak feels fortunate to have had the opportunity to work with Dr. McConnell. “Since he’s in Colorado, we communicated through emails and the telephone, which was difficult because it’s hard to talk about math on the phone, especially something as visual as graph theory,” Mak said.

Both Mak and Sealfon are looking forward to the experiences following their victories.  “I’m looking forward to going to Washington for the finals,” Sealfon said. “I’ve heard that the finalists last year got to meet the President, so I’m really hoping to meet Obama.”

“Being recognized is a great honor and I am excited to go to Washington D.C. to present my work,” Mak said. “I am a bit nervous about being judged, since this is still a competition, but I think I am just looking forward to the experience itself.”

For those who dream of following in Mak and Sealfon’s footsteps, “Although it is frustrating sometimes, especially when you are doing a math project, when you think you are going nowhere, stick with it. It really does pay off in the end when you discover something-however small it might be-because it is something you can call your own,” Mak said.