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- W2022954425 abstract "The general Markov model of the evolution of biological sequences along a tree leads to a parameterization of an algebraic variety. Understanding this variety and the polynomials, called phylogenetic invariants, which vanish on it, is a problem within the broader area of Algebraic Statistics. For an arbitrary trivalent tree, we determine the full ideal of invariants for the 2-state model, establishing a conjecture of Pachter–Sturmfels. For the κ-state model, we reduce the problem of determining a defining set of polynomials to that of determining a defining set for a 3-leaf tree. Along the way, we prove several new cases of a conjecture of Garcia–Stillman–Sturmfels on certain statistical models on star trees, and reduce their conjecture to a family of subcases." @default.
- W2022954425 created "2016-06-24" @default.
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- W2022954425 date "2008-02-01" @default.
- W2022954425 modified "2023-09-27" @default.
- W2022954425 title "Phylogenetic ideals and varieties for the general Markov model" @default.
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- W2022954425 doi "https://doi.org/10.1016/j.aam.2006.10.002" @default.
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