Equations, autonomous systems and a very complex brain

What happens when undergraduate researchers are given the freedom to pursue complex questions across disciplines?

For SMU student Alexis Stus, it meant bringing together electrical and computer engineering, mathematics and cognitive science to study something particularly complex: the brain.

Stus was one of a select cohort of undergraduates who participated this summer in Modeling and Computations for Complex Systems, an interdisciplinary summer research program backed by the National Science Foundation through its Research Experiences for Undergraduates program.

Led by SMU professors Alejandro Aceves and Joe Camp, the six-week program brings together students in mathematics, engineering and computer science to experience the research process firsthand, from developing questions and studying existing research to testing ideas and presenting their findings.

For Stus, a junior studying electrical and computer engineering and mathematics with a minor in cognitive science, the experience offered an opportunity to bring her academic interests together, exploring how mathematical modeling could help researchers better understand the neurocircuitry associated with obsessive-compulsive disorder.

We spoke with Stus about her path to SMU, what she learned through undergraduate research and why some of the most interesting questions don’t fit neatly within a single discipline.

What drew you to SMU and the Lyle School of Engineering? Were there any specific memories or moments that made the Hilltop feel like home?

I originally began my studies at the University of the Arts, where I had planned to graduate with my Bachelor of Fine Arts in Dance and Choreography. After my first year, it was announced that the University of the Arts was closing due to financial constraints, forcing me to reconsider my academic path.

During my gap year, I worked as a marketing intern at a software company. I became particularly interested in its machine learning components, frequently speaking with engineers to better understand how the systems functioned. This curiosity led me to begin studying computation independently before formally applying to the engineering program here at SMU.

Growing up in Dallas, SMU was a crucial part of my childhood. From a young age, I looked up to the students at SMU, watching them walk around campus and imagining what it would truly be like to go to school here. I knew I wanted a smaller university with smaller class sizes and individualized learning, and SMU fit that bill perfectly.

SMU’s smaller environment has allowed me to get to know my classmates and become more involved in SMU’s diverse research landscape. I also wanted a school that was flexible and willing to work with its students. Choosing SMU and the Lyle School of Engineering was one of the greatest choices I could have made. SMU has been incredibly supportive of my integration of engineering and choreography, allowing me to pursue both of my passions.

What courses, mentors or experiences helped prepare you to take on a research project like this?

During my time at SMU, I think my courses involving digital logic design and microcontrollers really helped prepare me. We frequently discussed simplicity and efficiency rather than overcomplicating a specific topic. This idea stayed with me throughout the REU program, where I focused on simplicity to best represent a complicated system.

My project, entitled “Explosive Synchronization and Bifurcation in Underlying OCD Neurocircuitry,” focuses on dynamic mathematical modeling to develop a clinical staging model for obsessive-compulsive disorder (OCD). Specifically, I modeled how the underlying neurocircuitry may transition through different stages, from early neurocircuitry conditions to anxiety and behavioral addiction, using concepts from nonlinear dynamics and bifurcation theory.

Your research used mathematical modeling and computation to investigate a complex problem. What did a typical day in the program look like?

This REU program was surprisingly hands-off, really giving me the freedom and responsibility to self-manage and direct my project. We had brief meetings in the afternoon to check in with Aceves and the graduate student fellows and get feedback regarding our projects.

We had complete freedom to choose our project topic; the only requirement was to incorporate mathematics. This freedom allowed me to select a project that I was incredibly passionate about, making the required research reading feel more like a hobby.

What are your biggest takeaways from the experience: technical skills, a new perspective or something else entirely?

I think the biggest thing I learned is that a system as complex as the human brain cannot be simplified into one specific discipline, and that creativity has a definitive place in the research world.

What advice would you give Lyle students interested in pursuing research or an REU like this one?

Think interdisciplinary! Many projects today cannot be classified into one specific field. Just because you are studying engineering does not mean you can’t work on a chemistry-based project. You are NOT limited to one specific field or discipline!

Don’t let the fear of failure or the need to be perfect prevent you from learning. Research is rooted in failure and learning from those experiences. During this REU, I pushed myself to try something new that I had never done before. Ultimately, this experience allowed me to reshape my perspective on failure and understand that growth often occurs when something goes differently than expected.

How do you see this experience shaping your future academic or career plans?

This opportunity has served as a foundation for my future research and academics. I plan to continue working with dynamic modeling to explore how the human brain works. There is much work to be done in this evolving field, and I would love to be a part of it.

I am particularly interested in working with neurodegenerative diseases and mental disorders such as obsessive-compulsive disorder and borderline personality disorder, exploring how visual, auditory and kinesthetic stimuli can influence the treatment and severity of these conditions. My long-term goal is to use engineering and mathematics to model and visualize how these stimuli affect the brain and to help develop treatment approaches.

After graduation, I plan to work toward my master’s degree. My biggest goal is to work at the intersection of technology and human cognition, exploring how scientific systems, mathematics and creative expression attempt to understand what it means to be human. I am particularly interested in computational neuroscience, general biomedical engineering and brain-computer interfacing, with a focus on how these fields can be applied to better understand mental health, perception and communication differences.

Explore undergraduate research at SMU

Interested in pursuing research of your own? Explore opportunities to work alongside faculty, investigate complex questions and build research experience through SMU’s Office of Engaged Learning.

About the Bobby B. Lyle School of Engineering

SMU’s Lyle School of Engineering thrives on innovation that transcends traditional boundaries. We strongly believe in the power of externally funded, industry-supported research to drive progress and provide exceptional students with valuable industry insights. Our mission is to lead the way in digital transformation within engineering education, all while ensuring that every student graduates as a confident leader. Founded in 1925, SMU Lyle is one of the oldest engineering schools in the Southwest, offering undergraduate and graduate programs, including master’s and doctoral degrees.

About SMU

SMU is the nationally ranked teaching and research university in the dynamic city of Dallas, and a member of the prestigious Atlantic Coast Conference. SMU’s alumni, faculty and more than 12,000 students in eight degree-granting schools demonstrate an entrepreneurial spirit as they lead change in their professions, communities and the world.