A research team in the Department of Scientific Computing has expanded a 1950s math game and turned it into a project that helps undergraduate students practice and grow their skills.

Bryan Quaife, associate professor in the Department of Scientific Computing and faculty associate of the Geophysical Fluid Dynamics Institute, based the work on Martin Gardner’s 1957 puzzle “Four Bugs on a Square.” In the original problem, one bug starts at each corner of an imaginary square and moves toward the one ahead of it at the same speed. Their paths form matching spirals that curve inward until they meet at a single point.

“That problem appeared straightforward,” said undergraduate researcher Josh Briley. “It was just a brain teaser in a magazine, and Gardner published the solution in the next issue.”

Quaife and Briley’s new paper, “N Bugs on a Circle,” changes the setup in fundamental ways. The bugs are no longer placed at abstract corner points. Instead, they begin at random positions on a physical circle and are restricted to move along its perimeter, so they cannot spiral inward. The system can also involve any number of bugs, not just four.

Removing the spiral behavior and confining the bugs to a circular track leads to new dynamics and more complex patterns. Quaife developed the project to give undergraduate students a chance to apply computing and mathematical skills to a problem with simple rules but surprising behavior. Several students contributed over the years, but the project gained momentum when Briley joined.

“I’d tried three or four times to make progress with undergrads, but we never had someone who could stay with it long enough to see it through to publication,” Quaife said. “When Josh and I started working together, the results developed quickly and turned out to be worth publishing.”

When the bugs start at random positions on the circle, each one moves along the perimeter toward the specific bug it is assigned to pursue, a direction set at the beginning of the problem. The team found that the system has three possible long-term behaviors, known as “end states.”

One possible state occurs when the bugs split into two groups on opposite sides of the circle. This configuration is mathematically unstable and does not appear when the starting positions are random. The two stable outcomes are:

• The cycle state, where the bugs fall into an endless chase and never meet, and
• Coalescence, where all bugs eventually arrive at the same point on the circle.

“For large numbers of bugs, the cycle state becomes the most likely outcome,” Quaife said. “The probability that the bugs coalesce is proportional to one over the square root of the number of bugs. So, with 100 bugs, they coalesce only about one out of every ten trials.”

This project is not aimed at solving a real-world problem. Quaife describes it as “recreational math” that helps students turn theory into practice.

Briley said many math and computing students struggle to see how classroom tools relate to actual research. This project showed him how ideas evolve through experimentation, analysis and writing.

“In your classes, you build this toolbox, but sometimes you think, ‘I have all these tools, but nothing to use them on,’” Briley said. “This was a chance to use what I’d learned while also understanding the publication process.”

Quaife noted that moving from an imaginary square to a physical circle opens the door to even more possibilities. Future versions of the project may look at how the bugs behave on other curved surfaces, such as a sphere or a Möbius strip.

Quaife and Briley said they are grateful for the support of the Department of Scientific Computing, which helped them bring the project to publication.

To learn more about the Department of Scientific Computing, visit www.sc.fsu.edu.

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Machine learning and artificial intelligence have grabbed the spotlight with their potential to change the way we interact. Florida State University presents the 2023 Machine Learning Expo (MLX23) to explore the latest applications of machine learning and AI by FSU researchers.

The expo will be held from 9 a.m. to 5 p.m. Saturday, April 22, at the Jim Moran Building in downtown Tallahassee and is presented by the FSU Interdisciplinary Data Science Master’s Degree Program (IDS).

“We invite participants of this expo to open their minds to the possibilities these new tools offer, which are sprouting all around them,” said Gordon Erlebacher, FSU IDS program director and professor of scientific computing. “There’s an opportunity for Florida to become a leader in using advanced AI tools. This expo is an efficient way for the FSU community to become familiar with the tools, their use and the ethical considerations they raise.”

AI’s groundbreaking technology focuses on building systems that learn and improve from history and experience rather than explicit programming and is profoundly impacting many segments of business and industry including research activity.

MLX23 examines the newest machine learning and AI trends through presentations by FSU faculty, researchers, staff and students that illuminate how these tools are already being applied to solve complex problems. Each presentation will be accompanied by an objective analysis to compare the problem before and after machine learning integration, and hosted panel discussions will cover AI education, usage and ethics.

“Our lives are being transformed by AI,” said Zhe He, associate professor and co-chair of the information technology master’s program in the FSU School of Information. “Almost everyone is impacted by AI to a certain degree.”

This year’s presenters include researchers who contribute to the analysis of machine learning and AI from varied research perspectives including art, linguistics, physics, computer science, civil engineering, data administration and cyber security.

Peter Stone of the University of Texas Artificial Intelligence Laboratory and Sony AI America and founder and director of the Learning Agents Research Group, part of UT Austin’s Department of Computer Science Artificial Intelligence Laboratory, will deliver a keynote address.

“Machine learning, especially the generative kind, has made much progress in both language and images,” Erlebacher said. “More people have used AI chatbot ChatGPT since it launched in November 2022 than any other app or product in history. There are so many ways to use these new technologies, and we are excited to share them with attendees.”

Concerns are commonly articulated about the potential for AI software to be abused, not least by the scholars most invested in the technology’s development. The workshop will respond to these concerns and foster discussion on the importance of responsible use.

“It’s critical that we share our experiences using AI in research, education and our daily activities,” Zhe He said. “I hope attendees will also become aware of the unintended consequences of AI in our society.”

MLX23 is sponsored by FSU’s College of Arts and Sciences, College of Communication and Information, School of Information, Department of Computer Science, Department of Scientific Computing, Department of Mathematics, Department of Statistics and Jim Moran College of Entrepreneurship.

For the full schedule of presentations, topics, details on the presenters and more, visit datascience.fsu.edu/mlx.

About the FSU Interdisciplinary Data Science Master’s Degree Program:

Students in this professional degree program study the latest in machine learning, artificial intelligence, computer science, mathematics and statistics as they prepare for wide-ranging careers, from cybersecurity to the sciences and health care, from finance and economics to the humanities and more.

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