兔子先生

Mathematics鈥� Meagan Carney Uses Probability and Dynamics to Predict

The only predictable part about life is that it is inherently unpredictable. Accidents happen. Conditions change. Life contains surprises.

Chaos Theory: Study of 鈥淯npredictable鈥� Outcomes

In mathematics, chaos theory is the study of apparently random or unpredictable outcomes. Chaos theory is often referred to as 鈥渢he butterfly effect,鈥� a term coined by mathematician Edward Lorenz, who used the example of a tornado being influenced by a minor event, such as a far-away butterfly flapping its wings several weeks earlier.

Meagan Carney, a Ph.D. student in mathematics at the 兔子先生, has spent her time as a graduate student expanding on the mathematical principles and patterns underlying chaotic dynamical systems. Her research is advised by Matthew Nicol, professor of mathematics in the College of Natural Sciences and Mathematics.

Deterministic Systems: Initial Conditions Determine Outcome

In deterministic systems, the initial values determine the outcome. In deterministic chaos, unpredictability comes from the fact that two very similar initial conditions often lead to two very different outcomes.

Although at face value, chaos appears to be completely random, there are underlying patterns.

鈥淭here is a randomness within the system, which is where the use of statistics comes in,鈥� Carney said. 鈥淥ur research establishes statistical properties, such as Central Limit Theorems and the Strong Law of Large Numbers.鈥�

Statistical Properties Enable Predictions

One example would be weather. Even though day-to-day conditions can鈥檛 be forecast with complete certainty, in general, winter brings colder weather, while summer brings hotter temperatures.

These statistical properties enable certain predictions about chaotic dynamical systems.

鈥淚nstead of looking at the statistical properties of the averages in a system, we can also look at the statistical properties of the extremes in a system,鈥� Carney said.

Examples of extreme events could be the probability of a 100掳F day in March, a severe flooding event, or a major drop in the stock market.

During the course of her graduate studies, Carney has published two papers, with a third paper in submission, and attended conferences in cities as diverse as Marseille, San Francisco, Vancouver and Vienna.

鈥淢eagan is a talented researcher who is not only adept at pure mathematics but also has a comprehensive science background and excellent computational skills,鈥� Nicol said. 鈥淭his is a rare combination of abilities.鈥�

- Rachel Fairbank, College of Natural Sciences and Mathematics

January 16, 2019