Displaying similar documents to “On geometry of binary symmetric models of phylogenetic trees”

On the solidity of general varieties of tree languages

Magnus Steinby (2012)

Discussiones Mathematicae - General Algebra and Applications

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For a class of hypersubstitutions 𝓚, we define the 𝓚-solidity of general varieties of tree languages (GVTLs) that contain tree languages over all alphabets, general varieties of finite algebras (GVFAs), and general varieties of finite congruences (GVFCs). We show that if 𝓚 is a so-called category of substitutions, a GVTL is 𝓚-solid exactly in case the corresponding GVFA, or the corresponding GVFC, is 𝓚-solid. We establish the solidity status of several known GVTLs with respect to...

Toric varieties in phylogenetics

M. Michałek

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The paper contains a revised, and extended by new results, part of the author's PhD thesis. The main objects that we study are toric varieties naturally associated to special Markov processes on trees. Such Markov processes can be defined by a tree T and a group G. They are called group-based models. The main, but not unique, motivation to consider these processes comes from phylogenetics. We study the geometry, defining equations and combinatorial description of the associated toric...

Higher order duality and toric embeddings

Alicia Dickenstein, Sandra Di Rocco, Ragni Piene (2014)

Annales de l’institut Fourier

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The notion of higher order dual varieties of a projective variety, introduced by Piene in 1983, is a natural generalization of the classical notion of projective duality. In this paper we study higher order dual varieties of projective toric embeddings. We express the degree of the second dual variety of a 2-jet spanned embedding of a smooth toric threefold in geometric and combinatorial terms, and we classify those whose second dual variety has dimension less than expected. We also...

Nd-solid varieties

Klaus Denecke, Prisana Glubudom (2007)

Discussiones Mathematicae - General Algebra and Applications

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A non-deterministic hypersubstitution maps any operation symbol of a tree language of type τ to a set of trees of the same type, i.e. to a tree language. Non-deterministic hypersubstitutions can be extended to mappings which map tree languages to tree languages preserving the arities. We define the application of a non-deterministic hypersubstitution to an algebra of type τ and obtain a class of derived algebras. Non-deterministic hypersubstitutions can also be applied to equations of...

Binary relations on the monoid of V-proper hypersubstitutions

Klaus Denecke, Rattana Srithus (2006)

Discussiones Mathematicae - General Algebra and Applications

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In this paper we consider different relations on the set P(V) of all proper hypersubstitutions with respect to a given variety V and their properties. Using these relations we introduce the cardinalities of the corresponding quotient sets as degrees and determine the properties of solid varieties having given degrees. Finally, for all varieties of bands we determine their degrees.