Aerial view of campus with Williamsport, the Susquehanna River and Bald Eagle Mountain as a backdrop

Lycoming College professor and students identify mathematical tool to analyze data

Lycoming College Physics Professor Christopher Kulp, Ph.D., and several students have identified a way to recognize whether certain types of phenomena are random.

“Researchers study a particular phenomenon to gain a better understanding of our world that can help scientists develop new technology and applications to enhance our lives. Our work focuses on one of the first steps in understanding any phenomenon — determining whether it occurs randomly or is governed by a set of rules,” said Kulp, who co-authored an article with J. M. Chobot ’16, B. J. Niskala ’16 and C. J. Needhammer ’15 that was published in “Chaos: An Interdisciplinary Journal of Nonlinear Science.” The faculty-student research documented in the paper began in the fall of 2014.

When studying data measured from a phenomenon, scientists look for patterns. In deterministic systems, the data follow rules that display certain patterns, but not others. These so-called forbidden patterns help scientists identify deterministic systems. If no forbidden patterns exist, the system is considered to be a random, or “stochastic,” system, Kulp explained.

“Once we know if a system is deterministic or random, we can then build predictive mathematical models of the system that researchers can use for a variety of applications,” he said.

Previously, work using forbidden patterns to detect determinism focused on regularly sampled data, where measurements are made at a regular rate (e.g. once per hour). The work presented in the paper extends the same technique to data that was not gathered on regular intervals, referred to as irregularly-sampled data.

Most data analyses are for regularly-sampled data and aren’t appropriate for irregularly-sampled data. New techniques that analyze irregularly-sampled data will benefit many fields of science where sampling irregularities are common. For example, in astronomy, cloudy nights may inhibit measurements. In the field of medicine, patients may not regularly self-report their condition.

“Our technique will allow researchers to develop better mathematical models for their systems that in turn, will help them better understand how use the information to benefit society,” said Kulp, who researches new ways to analyze irregularly-sampled data because if its wide applicability.

“My research group has successfully used the new technique, and others developed in our lab, on data from a variety of sources in a number of fields including biology, astrophysics, economics and climate science,” Kulp said.

“Involving students in ground-breaking research is an important aspect of our instructional methods and provides them with the detail-oriented skills they will need to tackle long-term societal problems,” he said. “Getting published in a prestigious scientific journal like Chaos gives them an edge over other students as they progress with their careers.”

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