Applied Math - Seminar

December 31, 2019
Thursday, January 16, 2020 - 1:50pm to 2:45pm
Math Tower 154
Alexandria Volkening

Title: Topological data analysis to quantify zebrafish skin patterns

Speaker: Alexandria Volkening - Northwestern University

Abstract: Wild-type zebrafish feature black and yellow stripes across their body and fins, but mutants display a range of altered patterns, including spots and labyrinth curves. All these patterns form due to the interactions of pigment cells, which sort out through movement, birth, and competition during early development. Using an agent-based approach, we couple deterministic cell migration by ODEs with stochastic rules for updating population size to reproduce stripe pattern development. We then adjust parameters in our models to search for the cell interactions that may be altered in mutated patterns. Within a single zebrafish mutant, however, there is a lot of variability, and this makes it challenging to first identify the features of a pattern that we are trying to reproduce and then judge model success. Moreover, agent-based models have many parameters, and empirical descriptions of zebrafish patterns are largely qualitative. To help address these challenges, we draw on topological data analysis to develop a set of methods for automatically quantifying pattern features in a fully interpretable, cell-based way. We apply our techniques to both simulated data and real fish images, and we show how to quantitatively distinguish between and characterize different patterns. This is joint work with Melissa McGuirl (Brown Univ.) and Bjorn Sandstede (Brown Univ.).

Seminar Link

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