By Annette Hilton
Samantha Sherman has been searching for ways to share her passion for mathematics with the world. Sherman graduated with a bachelor’s degree in mathematics and went on to teach middle school math through AmeriCorps. After her AmeriCorps experience ended, Sherman enrolled in a doctoral degree in applied mathematics. “I wanted to learn how to make original contributions to subjects that could have an impact on a large audience,” Sherman said. “Applied mathematics does just that.”
Sherman thought her interests would be best suited to projects at a national laboratory, and applied to the National Science Foundation’s (NSF) Mathematical Sciences Graduate Internship (MSGI) Program to test if that was the right path for her.
Stationed at Sandia National Laboratories in Livermore, California, Sherman tackled a project to speed up data analysis.
To do so, Sherman conducted research into tensors. In mathematics, a tensor is a multidimensional array with rules for its mathematical manipulation. A tensor can have one or more dimensions depending on how it is being utilized. For example, a one-dimensional tensor is known as a vector, which can represent features of an object in a data-mining task. A three-dimensional tensor resembles a cube, and may be described as a higher-order matrix. The more complex the problem being solved is, the more dimensions are required of a tensor. Whenever a tensor is changed or manipulated, its components change accordingly by transformation laws. Essentially, tensors provide a mathematical framework for formulating, solving, and analyzing problems.
Tensors are great tools to solve complex mathematical problems; but, because they are so complex, forming them can take significant computational time and expense. Sherman’s goal was to find out if it is possible to obtain certain results from a special type of statistical tensor without having to actually build the entire tensor itself. The idea is to build a low-rank approximation of an empirical statistical moment tensor that is used in data analysis for understanding correlations between features in data mining analysis. Previous methods required forming the entire tensor in order to compute the low-rank approximation.
With the help of her mentor, Tamara Kolda, Ph.D., Sherman was able to develop a new way to compute a low-rank approximation without having to build the full tensor. In data analysis, it’s a big win for improving the speed, cost, and capabilities of the method.
“I had a wonderful experience that has opened up many opportunities for me,” Sherman said of the program. “I am now certain I want to pursue a career at a national laboratory after graduation, this has solidified my career goals.” Sherman returned to the University of Notre Dame to finish her doctoral degree in applied and computational mathematics and statistics.
Jesse Hamer, another NSF MSGI intern, didn’t always know what he wanted to do for a career. Like many students, his interests and ambitions have changed over time – from nuclear engineering to pre-pharmacy.
In his third semester of college, however, he realized something was missing. “It was my first semester without a math class, and I could tell that something wasn’t right,” Hamer said. “I missed the mindset math put me in, and the sense of accomplishment I felt from doing it.”
At that point, Hamer resolved to pursue a doctoral degree in pure mathematics, with the intent of becoming a professor. He obtained a bachelor’s degree in mathematics, and began a doctoral program in pure mathematics at the University of Iowa.
Four years into his doctoral degree, however, Hamer began to wonder if pure mathematics was the right path for him. With a growing appreciation for applied mathematics, he decided to switch career trajectories from academia to data science.
“The National Science Foundation’s (NSF) Mathematical Sciences Graduate Internship (MSGI) Program has been the most important milestone along that path yet,” Hamer said
For Hamer, it was the perfect opportunity to explore career possibilities in applied mathematics and data science. Stationed at Fermi National Accelerator Laboratory (Fermilab) near Chicago, Illinois, Hamer began research on artificial neural networks (ANNs), a type of machine learning system inspired by the human brain. ANNs are composed of interconnected processing elements that work in unison to solve specific problems, similar to how neurons work together in the brain to processes information. ANNs learn from examples and observational data, enabling them to recognize patterns in complex data sets that would be difficult to detect otherwise.
The use of ANNs has grown explosively in the past decade. ANNs are particularly effective at visual object recognition and natural language processing. They are ideal for large data computing used by entities such as Facebook and Google, as well as facial recognition technology in smartphones.
Despite their popularity, no systematic method or language currently exists to help users effectively choose the types of ANN that would deliver the best results for their specific needs. ANNs have complex structure; the various ways they are structured significantly influences how well they perform.
Under the mentorship of Gabriel Perdue, Ph.D., Hamer sought to make first attempts in establishing a systematic language that describes ANN types for researchers. To do so, Hamer utilized Fermilab’s MINERvA experiment as a case study. MINERvA is a giant detector 200 feet underground designed to study neutrino-nucleus interactions. Hamer analyzed ANNs that were trained on image data of the particle interactions collected by MINERvA.
Hamer used multiple programming languages during his internship. In total, he wrote upwards of 7,000 lines of code and 100 handwritten pages of notes for the project. In the end, he was able to design two generic methods for characterizing structural attributes of ANNs, called simple static network attributes and complex static network attributes. Simple static network attributes are computed without reference to the data set on which the ANN is trained, while complex static network attributes incorporate the original data set. Even if no patterns are uncovered in the methods,
Hamer and his mentor hope that the study will spark future interest in creating a language to describe ANN structure. They plan to submit their research to computer science conferences for publication.
“[The program] was fantastic. I only wish I had more time to continue the data analysis that I began. It really is a great opportunity to put pure mathematicians outside of their comfort zone, but with a problem they can still approach with their skill set. I felt valued for my unique perspective as a mathematician,” said Hamer.
Hamer returned to the University of Iowa to finish his doctoral degree. Though Hamer is not sure where he may land as a data scientist—researching at a national laboratory or in industry—he appreciates the path he has taken, particularly his internship with NSF MSGI. “It’s a dream come true, honestly, and I cannot be more grateful for the opportunity and experience,” said Hamer.
The NSF MSGI Program is funded by NSF and administered through the U.S. Department of Energy’s (DOE) Oak Ridge Institute for Science and Education (ORISE). ORISE is managed for DOE by ORAU.
Annette Hilton holds a bachelor’s degree in geology and is currently employed part time as a science communications specialist at Oak Ridge Associated Universities.