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Low degree equations for phylogenetic group-based models
dc.contributor.author | Casanellas Rius, Marta |
dc.contributor.author | Fernández Sánchez, Jesús |
dc.contributor.author | Michalek, Mateusz |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2015-01-22T12:01:03Z |
dc.date.available | 2015-01-22T12:01:03Z |
dc.date.created | 2014-08-03 |
dc.date.issued | 2015 |
dc.identifier.citation | Casanellas, 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.issn | 0010-0757 |
dc.identifier.uri | http://hdl.handle.net/2117/26029 |
dc.description.abstract | Motivated 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.extent | 23 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject.lcsh | Biomathematics |
dc.title | Low degree equations for phylogenetic group-based models |
dc.type | Article |
dc.subject.lemac | Biomatemàtica |
dc.contributor.group | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
dc.identifier.doi | 10.1007/s13348-014-0120-0 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::92 Biology and other natural sciences::92D Genetics and population dynamics |
dc.subject.ams | Classificació AMS::14 Algebraic geometry::14H Curves |
dc.subject.ams | Classificació AMS::60 Probability theory and stochastic processes::60J Markov processes |
dc.relation.publisherversion | https://link.springer.com/article/10.1007/s13348-014-0120-0 |
dc.rights.access | Open Access |
local.identifier.drac | 15356381 |
dc.description.version | Postprint (published version) |
local.citation.author | Casanellas, M.; Fernández-Sánchez, J.; Michalek, M. |
local.citation.publicationName | Collectanea mathematica |
local.citation.volume | 66 |
local.citation.number | 2 |
local.citation.startingPage | 1 |
local.citation.endingPage | 225 |
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