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dc.contributor.authorCasanellas Rius, Marta
dc.contributor.authorFernández Sánchez, Jesús
dc.contributor.authorMichalek, Mateusz
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.date.accessioned2015-01-22T12:01:03Z
dc.date.available2015-01-22T12:01:03Z
dc.date.created2014-08-03
dc.date.issued2015
dc.identifier.citationCasanellas, M.; Fernández-Sánchez, J.; Michalek, M. Low degree equations for phylogenetic group-based models. "Collectanea mathematica", 2015, vol. 66, núm. 2, p. 203-225.
dc.identifier.issn0010-0757
dc.identifier.urihttp://hdl.handle.net/2117/26029
dc.description.abstractMotivated by phylogenetics, our aim is to obtain a system of low degree equations that define a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic varieties defined via group-based models. For any finite abelian group G , we provide an explicit construction of codimX polynomial equations (phylogenetic invariants) of degree at most |G| that define the variety X on a Zariski open set U . The set U contains all biologically meaningful points when G is the group of the Kimura 3-parameter model. In particular, our main result confirms (Michalek, Toric varieties: phylogenetics and derived categories, PhD thesis, Conjecture 7.9, 2012) and, on the set U , Conjectures 29 and 30 of Sturmfels and Sullivant (J Comput Biol 12:204–228, 2005).
dc.format.extent23 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshBiomathematics
dc.titleLow degree equations for phylogenetic group-based models
dc.typeArticle
dc.subject.lemacBiomatemàtica
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.identifier.doi10.1007/s13348-014-0120-0
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::92 Biology and other natural sciences::92D Genetics and population dynamics
dc.subject.amsClassificació AMS::14 Algebraic geometry::14H Curves
dc.subject.amsClassificació AMS::60 Probability theory and stochastic processes::60J Markov processes
dc.relation.publisherversionhttps://link.springer.com/article/10.1007/s13348-014-0120-0
dc.rights.accessOpen Access
local.identifier.drac15356381
dc.description.versionPostprint (published version)
local.citation.authorCasanellas, M.; Fernández-Sánchez, J.; Michalek, M.
local.citation.publicationNameCollectanea mathematica
local.citation.volume66
local.citation.number2
local.citation.startingPage1
local.citation.endingPage225


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