Codes and Expansions (CodEx) Seminar

Matt Herman (Fourier Genetics)
Fourier Analysis on the Genome

We explore the genotype-phenotype relationship using Fourier expansion on a Boolean cube. Important features of a quantitative trait can be "read off" from its Fourier representation. Examples include the network of epistatic gene interactions (including possible existence of a Barabasi-Albert-Price scale-free network), the modularity of a trait, and the roughness of its fitness landscape.

In analogy with traditional low-frequency signals, we explain how and why many traits have their Fourier transform concentrated into the "lower levels." This can naturally lead to a (very) sparse representation, which can be exploited in different applications, such as compressive sensing and machine learning — in some cases, the number of necessary observations of a population can be significantly reduced from exponential to polynomial.

Joint work with Steve Doro, MD, PhD