There’s an App for That
Akil Narayan, Assistant Professor of Mathematics, is also a computer scientist who combines his expertise to develop computational tools and software.
Recently, Narayan helped biomedical engineers at the U build a simulation codebase for understanding how physiological factors influence the ability of human blood to carry and release oxygen. The codebase used mathematical work that Narayan had developed to understand optimal ways to build computational emulators for physical models.
“Much of my work is actually driven by scientists who seek tools to solve a particular problem,” he said. “In this sense, my research is motivated by an application that someone will find useful.”
Narayan has secured external research funding from the National Science Foundation and the Department of Defense, including the Air Force Office of Scientific Research.
“At the U, I’m fortunate to enjoy the support of two departments – Mathematics and the Scientific Computing and Imaging Institute (SCI Institute) – in creating a collaborative culture,” says Narayan, “and I find that there’s quite a bit of overlap between them.”
For example, work in the SCI Institute helps to provide a codified science that transforms mathematical formalisms – such as proofs and theorems – into simulation tools for modelers and engineers. At the same time, Narayan’s work in the Mathematics Department provides foundational theory and algorithms for accomplishing some of the most difficult computational tasks today.
“The modern availability of large experimental datasets makes the possibility of learning predictive models from data a realistic goal. However, the underlying mathematics and algorithms to accomplish this complex task in learning are still being developed,” says Narayan.
Narayan is currently investigating tools for approximations in higher dimensions, which is a necessary step to achieve many computational goals.
“There are situations when conducting research in the higher dimensions of math can overwhelm today’s technology, but by shifting focus and using the tools available in data science and machine learning, we can manipulate data and create predictive tools with exciting results.”
Historically, large data sets were analyzed manually, where scientists relied on human cognition to exploit patterns and structures to gain understanding of the data. Today, the mathematics, statistics, and computing power are sufficient to enable the mining of large data sets using computational cognition.
“Since computers can manipulate and investigate data much faster than humans, this advance has the potential to revolutionize the advancement of science,” says Narayan.