Senior project spotlight: Nicholas Lopez

Fourth-year applied mathematics concentrators at the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) have the option to write senior theses. Often taken for course credit through “AM91R: Supervised Reading and Research,” their theses use mathematical, statistical or computational modeling methods to explain a phenomenon, going beyond data analysis to answer questions of mechanism and causation.

Dynamic, Welfare-Maximizing Pooled Testing

Nicholas Lopez, A.B. '25, Applied Mathematics

Advisors: David Parkes and Francisco Marmolejo-Cossío

• Please give a brief summary of your project.

My thesis focuses on improvements to biological tests. From isolated cases to global pandemics, testing for disease is fundamental to modern medicine. However, shortages of time, testing supplies, and staff means that it is often not possible for each biological sample to be individually tested, so pooled testing is used. Under pooled testing, biological samples are grouped together and tested as one sample. To do this, assignment algorithms are used to group people for testing. My thesis focuses on improvements to these algorithms through the development of a dynamic model, where tests are performed sequentially to leverage tests' information, and the creation of new algorithms that apply this approach. 

• How did you come up with this idea for your final project?

My work built off of an original paper that both Dean Parkes and Dr. Marmolejo-Cossío helped develop. In their paper, they studied a specific model of pooled testing and applied it in Mexico. Attempting to build off this work, Dr. Marmolejo-Cossío and I developed an idea to expand the pooled testing model and evaluate the benefits of a new approach.

• What was the timeline of your project?

I spent 15 months on this project. The first three months were spent studying the specific model of pooled testing, implementing various algorithms in practice, and exploring ways to expand the model. From there, we spent nine months developing new algorithms followed by three months of testing and evaluating them.

• What part of the project proved the most challenging?

Creating the reinforcement learning algorithms was quite difficult, since there are many intricacies and heuristics in pooled testing that affect the results. I worked closely with my advisors and other researchers in SEAS, like J. Roberto Tello Ayala, to come with an approach that is optimized for both practicality and accuracy.

• What part of the project did you enjoy the most?

I greatly enjoyed getting to come up with brand new ideas that had never been attempted and working with my advisors to bring these ideas to reality. Creating new algorithms and getting to analyze their own unique properties and intricacies was especially interesting.

• What did you learn, or what skills did you gain, through this project?

I learned a lot about the academic research process in general, from ideation to formalizing the results into a 100+ page thesis. The model of pooled testing was also completely new to me, and it was great to apply statistical and computational ideas that I had learned in class to the field of biological modeling.