Research

PhD Research at Johns Hopkins University

I have recently completed a paper with Nicolas Charon, Matteo Malgaroli, and Derrick Hull on unsupervised clustering methods for datasets of time series of unequal lengths and sampling rates entitled VISTA-SSM: Varying and Irregular Sampling Time-series Analysis via State Space Models. The arXiv preprint may be found here. This work was inspired by many real-world temporal datasets in the psychological sciences where each time series represents observations of an individual patient. Researchers are interested in grouping patients by their mental health status when no direct evaluations of condition exist - leading to an unsupervised approach. In self-reported settings, patients often supply data (through interactions with surveys, wearables, or messages to a provider) in non-uniform periods of time. Interpolating or sub-sampling obfuscates the problem, which is why we chose to develop a new approach to tackle these kinds of clustering problems.

Undergraduate Research at Lehigh University

Senior Thesis: A Mathematical Understanding of Red Blood Cell Dynamics with Dr. Miranda Teboh-Ewungkem

Abstract: Red blood cells are one of the most important components of life in humans and other mammals. Loss of red blood cells has consequences, such as anemia, while overproduction of red blood cells can also have negative consequences. Losses can be the result of phlebotomy, parasitemia, or other diseases, and overproduction can be due to myeloproliferative disorders such as Polycythemia Vera. Red blood cell dynamics within a human involve several stages of precursor cells before a red blood cell fully matures to an erythrocyte. Upon perturbation, a feedback mechanism contingent on loss and level of erythrocytes causes the production of more precursor cells to attempt to return the blood dynamics to equilibrium. We model this process using a system of nonlinear, deterministic, ordinary differential equations. Functions describing this feedback, the stem cell recruitment, and the erythrocyte loss are chosen to examine the system dynamics in different scenarios. Some parameter choices cause a Hopf bifurcation, demonstrating the sensitivity of blood dynamics to the selected parameters. Numerical methods are used to display bifurcation diagrams and transient dynamics for specific function choices. Methods of mathematical analysis such as nondimensionalization and proofs of invariance, positivity, boundedness, and uniqueness for arbitrary functions are given.