Final doctoral examination and defense of dissertation of Anna Kirkpatrick, July 9, 2021
Date: July 9, 2021, 10:00am EST
Virtual Link via Microsoft Teams: https://teams.microsoft.com/l/meetup-join/19%3ameeting_ZmVkZDBhZjUtZGUxM...
Title: A combinatorial approach to biological structures and networks in predictive medicine
Advisors:
Dr. Cassie Mitchell, School of Biomedical Engineering, Georgia Institute of Technology
Dr. Prasad Tetali, School of Mathematics, Georgia Institute of Technology
Committee:
Dr. Joshua Cooper, Mathematics, University of South Carolina
Dr. Cassie Mitchell, Biomedical Engineering, Georgia Institute of Technology
Dr. Dana Randall, Computer Science, Georgia Institute of Technology
Dr. Lauren Steimle, Industrial and Systems Engineering, Georgia Institute of Technology
Dr. Francesca Storici, Biological Sciences, Georgia Institute of Technology
Dr. Prasad Tetali, Mathematics and Computer Science, Georgia Institute of Technology
Reader: Dr. Joshua Cooper, Mathematics, University of South Carolina
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The thesis is available here:
https://aco.gatech.edu/sites/default/files/documents/2021/dissertation-a...
Summary of the thesis is below.
Summary:
This work concerns the study of combinatorial models for biological structures and networks as motivated by questions in predictive medicine. Through multiple examples, the power of combinatorial models to simplify problems and facilitate computation is explored. First, continuous-time Markov models are used as a model to study the progression of Alzheimer’s disease and identify which variables best predict progression at each stage. Next, RNA secondary structures are modeled by a thermodynamic Gibbs distribution on plane trees. The limiting distribution (as the number of edges in the tree goes to infinity) is studied to gain insight into the limits of the model. Additionally, a Markov chain is developed to sample from the distribution in the finite case, creating a tool for understanding what tree properties emerge from the thermodynamics. Finally, knowledge graphs are used to encode relationships extracted from the biomedical literature, and algorithms for efficient computation on these graphs are explored.
