• Corpus ID: 23016110

Circular genome rearrangement models: applying representation theory to evolutionary distance calculations

@article{Terauds2017CircularGR,
  title={Circular genome rearrangement models: applying representation theory to evolutionary distance calculations},
  author={Venta Terauds and Jeremy G. Sumner},
  journal={arXiv: Populations and Evolution},
  year={2017}
}
We investigate the symmetry of circular genome rearrangement models, discuss the implementation of a new representation-theoretic method of calculating evolutionary distances between circular genomes, and give the results of some initial calculations for genomes with up to 11 regions. 

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References

SHOWING 1-10 OF 20 REFERENCES
A representation-theoretic approach to the calculation of evolutionary distance in bacteria
TLDR
This work shows, in a very general maximum likelihood setting, how to use elementary matrix algebra to sidestep intractable combinatorial computations and convert the problem into one of eigenvalue estimation amenable to standard numerical approximation techniques.
Position and Content Paradigms in Genome Rearrangements: The Wild and Crazy World of Permutations in Genomics
TLDR
The different ways in which permutations have been used to model genomes and genome rearrangement events are described, presenting some features and limitations of each approach, and how the various models are related are shown.
Dynamics of Genome Rearrangement in Bacterial Populations
TLDR
These findings represent the first characterization of genome arrangement evolution in a bacterial population evolving outside laboratory conditions and insight into the process of genomic rearrangement may further the understanding of pathogen population dynamics and selection on the architecture of circular bacterial chromosomes.
An algebraic view of bacterial genome evolution
  • A. Francis
  • Mathematics
    Journal of mathematical biology
  • 2014
TLDR
A family of biological problems in bacterial genome evolution for which an algebraic viewpoint may capture a deeper structure behind biological phenomena is discussed, and the prospect that the tools developed by algebraists over the last century might provide insight to this area of evolutionary biology is raised.
Phylogeny - discrete and random processes in evolution
  • M. Steel
  • Biology
    CBMS-NSF regional conference series in applied mathematics
  • 2016
TLDR
This self-contained book addresses the underlying mathematical theory behind the reconstruction and analysis of phylogenies, grounded in classical concepts from discrete mathematics and probability theory as well as techniques from other branches of mathematics (algebra, topology, differential equations).
Exact and approximation algorithms for sorting by reversals, with application to genome rearrangement
TLDR
The greedy algorithm is the first to come within a constant factor of the optimum; it guarantees a solution that uses no more than twice the minimum number of reversals, and the lower and upper bounds of the branch- and-bound algorithm are a novel application of maximum-weight matchings, shortest paths, and linear programming.
On the Enumeration of Polygons
(1960). On the Enumeration of Polygons. The American Mathematical Monthly: Vol. 67, No. 4, pp. 349-353.
The Symmetric Group
The first € price and the £ and $ price are net prices, subject to local VAT. Prices indicated with * include VAT for books; the €(D) includes 7% for Germany, the €(A) includes 10% for Austria.
The On-Line Encyclopedia of Integer Sequences
  • N. Sloane
  • Computer Science
    Electron. J. Comb.
  • 1994
TLDR
The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences which serves as a dictionary, to tell the user what is known about a particular sequence and is widely used.
Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
TLDR
A duality theorem is proved explaining this intriguing performance and it is shown that there exists a “hidden” parameter that allows one to compute the reversal distance between signed permutations in polynomial time.
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