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Finiteness results for Abelian tree models

Jan Draisma, Rob H. Eggermont (2015)

Journal of the European Mathematical Society

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....

Formalisation and methods of analysis of the fast xenobiotic mass transfer in the body

Volodymir G. Zinkovsky, Olga V. Zhuk, Michał Teodorczyk, Natalia Karpinchik (2009)

Applicationes Mathematicae

A novel discrimination and regression method for a quantitative determination of the relative efficiency of "fast" distribution processes of xenobiotics is discussed. An integral model-independent method for estimation of equilibrium tissue-to-plasma partition ratios is proposed.

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