Abstract
Model selection based on experimental data is an essential challenge in biological data science. In decades, the volume of biological data from varied sources, including laboratory experiments, field observations, and patient health records has seen an unprecedented increase. Mainly when collecting data is expensive or time-consuming, as it is often in the case with clinical trials and biomolecular experiments, the problem of selecting information-rich data becomes crucial for creating relevant models.
Motivated by certain geometric relationships between data, we partitioned input data sets, especially data sets that correspond to a unique basis, into equivalence classes with the same basis to identify a unique algebraic model. The analysis of the data relationships and properties will facilitate the computations, storage, and access to sizable discrete data sets.
Degree Date
Fall 2019
Document Type
Dissertation
Degree Name
Ph.D.
Department
Mathematics
Advisor
Brandilyn Stigler
Format
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License
Recommended Citation
Zhang, Anyu, "Model Selection and Experimental Design of Biological Networks with Algebraic Geometry" (2019). Mathematics Theses and Dissertations. 4.
https://scholar.smu.edu/hum_sci_mathematics_etds/4
Included in
Algebraic Geometry Commons, Discrete Mathematics and Combinatorics Commons, Other Applied Mathematics Commons
