# Finiteness results for Abelian tree models

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 4, page 711-738
- ISSN: 1435-9855

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topDraisma, Jan, and Eggermont, Rob H.. "Finiteness results for Abelian tree models." Journal of the European Mathematical Society 017.4 (2015): 711-738. <http://eudml.org/doc/277264>.

@article{Draisma2015,

abstract = {Equivariant tree models are statistical models used in the reconstruction of phylogenetic trees from genetic data. Here equivariant§ refers to a symmetry group imposed on the root distribution and on the transition matrices in the model. We prove that if that symmetry group is Abelian, then the Zariski closures of these models are defined by polynomial equations of bounded degree, independent of the tree. Moreover, we show that there exists a polynomial-time membership test for that Zariski closure. This generalises earlier results on tensors of bounded rank, which correspond to the case where the group is trivial and the tree is a star, and implies a qualitative variant of a quantitative conjecture by Sturmfels and Sullivant in the case where the group and the alphabet coincide. Our proofs exploit the symmetries of an infinite-dimensional projective limit of Abelian star models.},

author = {Draisma, Jan, Eggermont, Rob H.},

journal = {Journal of the European Mathematical Society},

keywords = {phylogenetic tree models; tensor rank; noetherianity up to symmetry; applied algebraic geometry; phylogenetic tree models; tensor rank; noetherianity up to symmetry; applied algebraic geometry},

language = {eng},

number = {4},

pages = {711-738},

publisher = {European Mathematical Society Publishing House},

title = {Finiteness results for Abelian tree models},

url = {http://eudml.org/doc/277264},

volume = {017},

year = {2015},

}

TY - JOUR

AU - Draisma, Jan

AU - Eggermont, Rob H.

TI - Finiteness results for Abelian tree models

JO - Journal of the European Mathematical Society

PY - 2015

PB - European Mathematical Society Publishing House

VL - 017

IS - 4

SP - 711

EP - 738

AB - Equivariant tree models are statistical models used in the reconstruction of phylogenetic trees from genetic data. Here equivariant§ refers to a symmetry group imposed on the root distribution and on the transition matrices in the model. We prove that if that symmetry group is Abelian, then the Zariski closures of these models are defined by polynomial equations of bounded degree, independent of the tree. Moreover, we show that there exists a polynomial-time membership test for that Zariski closure. This generalises earlier results on tensors of bounded rank, which correspond to the case where the group is trivial and the tree is a star, and implies a qualitative variant of a quantitative conjecture by Sturmfels and Sullivant in the case where the group and the alphabet coincide. Our proofs exploit the symmetries of an infinite-dimensional projective limit of Abelian star models.

LA - eng

KW - phylogenetic tree models; tensor rank; noetherianity up to symmetry; applied algebraic geometry; phylogenetic tree models; tensor rank; noetherianity up to symmetry; applied algebraic geometry

UR - http://eudml.org/doc/277264

ER -

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