Arjun Ramani, an 18-year-old student from Indiana, won the third place honour worth $150,000 for blending the mathematical field of graph theory with computer programming to answer questions about networks in the oldest and most prestigious science and math competition in the US. Typically, these questions require statistical comparisons to hundreds or thousands of random graphs, a process that can take a relatively long time. He developed an algorithm that greatly accelerated the process by reducing the time required to generate these graphs. Arjun’s excellent Resume speaks all about his works and achievements that led to such a great discovery by this Indian-American teen.
In conversation with Arjun Ramani :
Q: Tell us a bit more about yourself.
Hi! I am currently a senior (12th grade) at West Lafayette Jr/Sr High School in West Lafayette Indiana. I am a huge tennis and basketball fan and actually got interested in statistics from watching NBA basketball in the first grade. My favourite pro tennis player is Andy Murrary. Other than research, my main activities are competitive debate, math competitions, and tennis.
Q: What led you to the idea of making this project? Where did you start from?
During my sophomore and junior years, I took several math classes at Purdue University in Multivariate Calculus, Linear Algebra, and Probability. My favourite area of mathematics from a young age has been counting and probability, so I emailed a professor at Purdue asking if they could help find a research project to work on. Professor David Gleich, a computer science professor, agreed to meet me and introduced me to the area of Kronecker Graph generation. I started by reading prior research papers in the field in order to gain an understanding of the area. In addition, I started by implementing simple algorithms that were simplifications of the my larger question. This allowed me to break my larger problem into a series of easier smaller problems.
Q: Brief us about the objective of this project.
How is it known if there is a pattern in a set of numbers? The set must be compared to sequence of random numbers. Similarly, in order to find abnormal properties in a graph, it must be compared to a random graph. In mathematics, a graph, or network, represents the connections between various objects. For example, a social network like facebook represents the friendships between people. Current methods for generating random networks are extremely slow. I sought to answer the question: How can random Kronecker graphs be more quickly generated? I worked on a new way to generate Kronecker graphs by “hopping” directly from edge to edge by using geometric random variables rather than going through each pair of nodes one by one. In addition, I solved the “unranking” problem, in which each edge is backward-mapped to its nodes allowing for more efficient random network generation. Thus, my algorithm eases the study of networks substantially by more quickly generating stochastic Kronecker graphs.
Q: How curious were you about the The Regeneron Science Talent Search competition? When and how did you start planning for it?
I have competed in the Intel International Science and Engineering Fair every year of high school so I have always been curious and interested in the Science Talent Search. Many of the students I have looked up to over the year have been finalists at the Science Talent Search. The Regeneron Science Talent Search is a unique competition in that it requires finalists to be able to problem-solve in all fields of science whether or not they are related to your project. Thus, in a way, I have been preparing for the competition since I started learning and doing research.
Q: Winning the Junior Nobel Prize and bagging the third position in one of the most prestigious competitions, how do you feel?
It feels incredible and even surreal. I did not expect to win this award because all my fellow finalists were extremely qualified and deserving. I am extremely grateful to everyone who has helped me along the way and also excited because I know there is so much more to explore in the world of science.
Q: What prior skills and studies were required to accomplish this project? What tools and resources did you use for the project?
I have been doing competition math since elementary school, which has given me a strong background in discrete math, specifically combinatorics. Furthermore, I have taken multiple math classes at Purdue University which gave me the more advanced techniques needed to do this project. I used the python programming language to write all of my algorithms and used several online programming forums and websites to gain information along the way.
Q: Who were your mentors in this journey? What difficulties did you face during its completion?
My primary research mentor is David Gleich, a professor of computer science at Purdue University. I also received substantial guidance from Dr. Clark Gedney of biological sciences at Purdue as well as my AP Statistics teacher, Pam Porterfield. Finally, my parents, Karthik and Sujatha Ramani have been my mentors from day one.
I faced many difficulties during my research. Oftentimes, I would get stuck trying to find the solution to an algorithm I was writing. Through reading many research papers in my field, I often stumbled upon solutions in the most unexpected of places. These times, when I was able to overcome a tough challenge were some of the most fruitful experiences in my research.
Q: Tell us about the broader vision of this project. What impact is it going to have on our lives in the near future?
Network analysis has grown in importance recently because of an explosion in big data in many fields ranging from protein-protein networks in our cells to social networks on the internet. It is important to be able to generate realistic random graphs in order to analyze the properties of real networks. The Kronecker model has been proven to have similar properties to real world networks. My algorithm eases the study of networks substantially by more quickly generating stochastic Kronecker graphs. Network scientists across fields can use fast Kronecker graph algorithms to sample thousands and thousands of graphs and create distributions of various graph properties called network motifs. Network motifs are statistically significant patterns of connectivity in graphs that appear more often than what would be expected at random. Identifying motifs allows researchers to better understand the structure and function of a network. For example, Uri Alon, a famous network scientist, used random graphs to identify motifs associated with specific properties in the transcription networks of E. Coli, yeast, and other organisms. Alon found that these motifs govern specific genes of the organism furthering the computational understanding of the biological network. My work would aid researchers like Alon by increasing the speed at which they can generate random graphs. Furthermore, researchers at companies like Facebook could use my algorithm to speed up the analysis of their social networks. In addition, they could help companies simulate how thy algorithm needs to be adopted to other random graph models other than the Kronecker model. This would require an in depth probabilistic analysis of the properties of these other network models.
Q: What are your future goals? Which occupation do you plan to pursue?
We are currently in the midst of the 4th industrial revolution of Big Data and information. Making sense of all the data we have around us will allow us to develop solutions to complex problems. I want to be on the forefront of this revolution which is why I plan on studying Computational and Applied Mathematics in college. I am not sure what occupation I plan on pursuing, but I know it must fit 2 criterion. First, I have to be stimulating my brain on the edge of whatever field I am in. Second, I have to be impacting the world around me in a positive manner. Thus, I could definitely see myself becoming a professor, working at a tech company, or even working for a place like the Federal Reserve. In today’s world, issues are becoming more and more complex and require people willing to let go of their preconceived notions to dig deep and find the truth and solutions. I think using mathematics to form an objective perspective on subjective issues is a good way to do that. I think I may be suited to combining mathematics with social science as I have always enjoyed interdisciplinary research.
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