Abstract:
Although analysis of genome rearrangements was pioneered by Dobzhansky and Sturtevant 65 years ago, we still know very little about the rearrangement events that produced the existing varieties of genomic architectures. The genomic sequences of human and mouse provide evidence for a larger number of rearrangements than previously thought. We describe a new algorithm for constructing synteny blocks, study arrangements of synteny blocks in human and mouse, derive a most parsimonious human-mouse rearrangement scenario, and provide evidence that intrachromosomal rearrangements are more frequent than interchromosomal. Our analysis is based on the human-mouse breakpoint graph, which reveals related breakpoints and allows one to find a most parsimonious scenario.

Given n > 2, we would like determine if n is prime or composite in deterministic polynomial time. This talk covers the recient algorithm by Agrawal, Kayal, and Saxena, using subsequent insights by Daniel Bernstein.