Mathematics Colloquia and Seminars

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Consider a particular quantitative trait, and suppose we want to discover a function that maps how n participating genes (or even environmental influences) interact to express the trait. Under plausible assumptions of how they evolved, certain traits can be viewed as “smooth” functions on the n-dimensional Boolean lattice of possible genomes. This allows approximation of their Fourier transforms, i.e., their gene networks, as sparse, dominated by “low-frequency” components.

From compressive sensing theory, we can observe the trait values from relatively few genomes, yet still accurately recover the gene network. Work is currently underway to see if empirical data fit the proposed model. If so, it could offer a radical reduction in the number of measurements — from exponential to polynomial in some cases — necessary to quantify the relationship between genomes and certain traits.

In the talk, we will review the Fourier theory connecting quantitative traits and their networks of gene interactions, with both concrete and theoretical examples to motivate the idea of “low-level concentration.” If time permits, we will present new results from a trait data set of mouse myopia.

We will have a 30 minute conversation with Dr. Herman after the talk where he will share about his career journey after getting his PhD from UC Davis. Please contact Mariel Vazquez (mrlvazquez@ucdavis.edu) for Zoom information or if you want to meet with the speaker.