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Self-inverse linear subspaces of matrices
Rodica Andreea Dinu, Martin Vodička
We study linear subspaces of matrices whose inverse spaces are also linear. Based on the fact that any linear space containing the identity matrix and whose inverse space is linear…
Proof of a Conjecture of Drton, Sturmfels and Sullivant on the maximum likelihood degree of the Gaussian graphical model of a cycle
Rodica Andreea Dinu, Martin Vodička
In this article, we compute the precise value of the maximum likelihood degree of the Gaussian graphical model of a cycle, confirming a conjecture due to Drton, Sturmfels and Sulli…
Phylogenetic degrees for Jukes-Cantor model
Rodica Andreea Dinu, Martin Vodička
Jukes-Cantor model is one of the most meaningful statistical models from a biological perspective. We are interested in computing the algebraic degrees for phylogenetic varieties,…
Classification of normal phylogenetic varieties for tripods
Rodica Andreea Dinu, Martin Vodička
We provide a complete classification of normal phylogenetic varieties coming from tripods, and more generally, from trivalent trees. Let be an abelian group. We prove that the…
Phylogenetic degrees for claw trees
Rodica Andreea Dinu, Martin Vodička
Group-based models appear in algebraic statistics as mathematical models coming from evolutionary biology, respectively the study of mutations of organisms. Both theoretically and…
Geometry of the Gaussian graphical model of the cycle
Rodica Andreea Dinu, Mateusz Michałek, Martin Vodička
We prove a conjecture due to Sturmfels and Uhler concerning the degree of the projective variety associated to the Gaussian graphical model of the cycle. We involve new methods bas…