Rocky Mountain Algebraic Combinatorics Seminar

Algorithms for Genome Assembly and Analysis

Christina Boucher
Colorado State University (Computer Science)

Assemblies of next generation sequencing data, while accurate, still contain a substantial number of errors that need to be corrected after the assembly process. In the first half of this talk, I will present an algorithm that corrects errors, i.e., insertions, deletions, and substitutions in assembled contigs. Fundamental to our method is the positional de Bruijn graph, which is a graph structure that models k-mers within reads while incorporating the approximate positions of reads into the model. The algorithm reduced the number of small insertions and deletions in the assemblies of standard multi-cell E. coli data by almost half, and corrected between 30the substitution errors. Further, we show the method is imperative to improving single-cell assembly, which is inherently more challenging due to higher error rates and non-uniform coverage; over half of the insertions, deletions, and substitutions in the single-cell assemblies were corrected. In the second half of this talk, I will present two algorithms for finding transcription factors in redundant sequences in genetic data that have important biological functions. Our algorithms are capable of detecting highly degenerate sequences that otherwise could not be detected by competing methods.


Equiangular lines and Seidel matrices with three eigenvalues

Sylvia Hobart
University of Wyoming

The maximum number of lines in Rn such that any pair form a constant angle was a favorite topic of J. J. Seidel, and it has connections with graphs, the Seidel matrix, and two-graphs. (Also, quantum information theory but I won't talk about that). Starting with some basics, this talk will describe some of these connections and show how Seidel matrices with three eigenvalues turn up in a natural way, based on recent work of Gary Greaves, Jack Koolen, Akihiro Munemasa, and Ferenc Szollosi.


Weber 223
4–6 pm
Friday, October 23, 2015
(Refreshments in Weber 117, 3:30–4 pm)
Colorado State University

This is a joint Denver U / UC Boulder / UC Denver / U of Wyoming / CSU seminar that meets biweekly. Anyone interested is welcome to join us at a local restaurant for dinner after the talks.

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Previous Seminars:

October 9, 2015
Josh Maglione, Ghodratollah Aalipour
September 25, 2015
Ross McConnell, Henry Adams
September 11, 2015
James B. Wilson, Tim Penttila
May 8, 2015
Amanda Schaeffer Fry, Peter Brooksbank
April 24, 2015
Heide Gluesing-Luerssen, Phil DeOrsey
March 6, 2015
Felice Manganiello, Eric Moorhouse
February 20, 2015
Anton Dzhamay, Anton Betten
February 6, 2015
Alexander Hulpke, Morgan Rodgers
December 5, 2014
Stefaan De Winter, Gretchen Matthews
November 14, 2014
Greg Coxson, Tom Dorsey
October 31, 2014
Octavio Paez Osuna, Sylvia Hobart
October 10, 2014
Takunari Miyazaki, Eric Moorhouse
September 26, 2014
Elissa Ross, Anton Betten
September 12, 2014
Petr Vojtěchovský, Alexander Hulpke
May 9, 2014
Philip DeOrsey, Tim Penttila
April 25, 2014
William J Martin, Jason Williford
April 11, 2014
Victor Pambuccian, George Shakan
March 7, 2014
Nathan Lindzey, Jens Harlander
February 21, 2014
Ross McConnell, Anton Betten
November 22, 2013
Justin Hughes, Josh Maglione

Department of Mathematics
Fort Collins, Colorado 80523