Title: Digraph Homology to study DNA Rearrangement
Speaker: Lina Fajardo Gomez
Date/Time/Location: Friday, September 9th at 12:00pm, NES 102
Abstract: In this work, we introduce tools to study DNA recombination pathways and measure their complexity. Genome rearrangement in some ciliate species can be modeled by subword pattern deletions in double-occurrence words (DOWs), words where each symbol appears exactly twice. The iterated deletions can be represented by a graph whose vertices are DOWs connected by an edge if one word can be obtained from the other through a pattern deletion. On this graph, called the ``word graph’’, we build a complex comprised of cells defined by Cartesian products of simplicial digraphs where we define a boundary operator and compute homology groups. These topological invariants are used to analyze the word graphs of DOWs from data sets and to make comparisons between the genomes of three ciliate species as well as to describe DOWs whose graphs attain arbitrarily large Betti numbers.