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Geometry of phylogenetic group-based models

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2011

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https://doi.org/10.1016/j.jalgebra.2011.05.016
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http://arxiv.org/abs/1004.3012

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Journal of Algebra. Elsevier. 2011, 339(1), pp. 339-356. ISSN 0021-8693. eISSN 1090-266X. Available under: doi: 10.1016/j.jalgebra.2011.05.016

Zusammenfassung

We complete the results of Sullivant and Sturmfels (2005) [SS05] by proving that many of the algebraic group-based models for Markov processes on trees can be diagonalized, and we identify the cases when the resulting toric varieties are normal. This is done by the generalization of the discrete Fourier transform approach introduced by Evans and Speed (1993) [ES93]. We also characterize the lattice polytope of this toric variety. This involves extending the notions of sockets and networks introduced by Buczyńska and Wiśniewski (2007) [BW07] in their work on the binary symmetric model.

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Fachgebiet (DDC)
510 Mathematik

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Phylogenetics, G-models, Group-based models, Toric varieties

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ISO 690MICHALEK, Mateusz, 2011. Geometry of phylogenetic group-based models. In: Journal of Algebra. Elsevier. 2011, 339(1), pp. 339-356. ISSN 0021-8693. eISSN 1090-266X. Available under: doi: 10.1016/j.jalgebra.2011.05.016
BibTex
@article{Michalek2011Geome-52319,
  year={2011},
  doi={10.1016/j.jalgebra.2011.05.016},
  title={Geometry of phylogenetic group-based models},
  number={1},
  volume={339},
  issn={0021-8693},
  journal={Journal of Algebra},
  pages={339--356},
  author={Michalek, Mateusz}
}
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