Title:
A combinatorial approach to biological structures and networks in predictive medicine

dc.contributor.advisor Tetali, Prasad
dc.contributor.advisor Mitchell, Cassie S.
dc.contributor.author Kirkpatrick, Anna
dc.contributor.committeeMember Cooper, Joshua
dc.contributor.committeeMember Randall, Dana
dc.contributor.committeeMember Steimle, Lauren
dc.contributor.committeeMember Storici, Francesca
dc.contributor.department Mathematics
dc.date.accessioned 2021-09-15T15:42:27Z
dc.date.available 2021-09-15T15:42:27Z
dc.date.created 2021-08
dc.date.issued 2021-08-09
dc.date.submitted August 2021
dc.date.updated 2021-09-15T15:42:27Z
dc.description.abstract 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.
dc.description.degree Ph.D.
dc.format.mimetype application/pdf
dc.identifier.uri http://hdl.handle.net/1853/65052
dc.language.iso en_US
dc.publisher Georgia Institute of Technology
dc.subject predictive 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.title A combinatorial approach to biological structures and networks in predictive medicine
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.advisor Mitchell, Cassie S.
local.contributor.advisor Tetali, Prasad
local.contributor.corporatename College of Sciences
local.contributor.corporatename School of Mathematics
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relation.isAdvisorOfPublication 85fa47ef-91b2-4aeb-b8a3-9ac5229276d3
relation.isOrgUnitOfPublication 85042be6-2d68-4e07-b384-e1f908fae48a
relation.isOrgUnitOfPublication 84e5d930-8c17-4e24-96cc-63f5ab63da69
thesis.degree.level Doctoral
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