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dc.contributor.advisorTetali, Prasad
dc.contributor.advisorMitchell, Cassie
dc.contributor.authorKirkpatrick, Anna
dc.date.accessioned2021-09-15T15:42:27Z
dc.date.available2021-09-15T15:42:27Z
dc.date.created2021-08
dc.date.issued2021-08-09
dc.date.submittedAugust 2021
dc.identifier.urihttp://hdl.handle.net/1853/65052
dc.description.abstractThis 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.
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.publisherGeorgia Institute of Technology
dc.subjectpredictive medicine, combinatorics, Markov chains, hidden Markov models, Markov chain mixing, approximation algorithms, knowledge graph, heterogeneous information network, RNA, Alzheimer's disease, Catalan objects, plane trees
dc.titleA combinatorial approach to biological structures and networks in predictive medicine
dc.typeDissertation
dc.description.degreePh.D.
dc.contributor.departmentMathematics
thesis.degree.levelDoctoral
dc.contributor.committeeMemberCooper, Joshua
dc.contributor.committeeMemberRandall, Dana
dc.contributor.committeeMemberSteimle, Lauren
dc.contributor.committeeMemberStorici, Francesca
dc.date.updated2021-09-15T15:42:27Z


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