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Quantifying Patterns in Dynamical Systems and Biological Data


From data clusters to fish swarms, patterns are widespread in both the natural world and in the era of big data. Across a range of applications, the identification and quantification of pattern features could provide a powerful means for predictions and classifications. Nevertheless, accurate and automated methods for quantifying pattern features are limited; existing methods commonly rely on manual inspection, restrict to global measures, require prior knowledge about the underlying system or data, or are difficult to interpret. In this work, we combine methods from topological data analysis and machine learning to develop novel tools for quantifying patterns for three distinct applications. First, we build a toolbox for quantifying zebrafish skin patterns. These tools are applied to thousands of simulations of in vivo zebrafish to study pattern variability and better understand the cellular mechanisms underlying pattern formation. Second, we develop an algorithm for identifying clusters of phenotypes in sizeable genomic data sets to identify groups of traits and diseases that share a core set of driving genes. We validate our algorithm through extensive simulation studies and then apply our method to identify shared genetic architecture among 81 case-control and seven quantitative phenotypes in 349,468 European-ancestry individuals from the UK Biobank. Third, we study time series data corresponding to spiral wave dynamics to quantify pattern abnormalities that arise from reaction-diffusion systems. We further demonstrate the theoretical guarantees of our topological-based approach to quantifying pattern defects in spiral wave dynamics. Overall, this research demonstrates the importance of accurate and practical tools for quantifying pattern features, and our results provide evidence that topological data analysis and machine learning are useful methods for pattern quantification, especially when used in tandem.
Thesis (Ph. D.)--Brown University, 2020

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McGuirl, Melissa Rose, "Quantifying Patterns in Dynamical Systems and Biological Data" (2020). Applied Mathematics Theses and Dissertations. Brown Digital Repository. Brown University Library.