6 papers · 1 filter
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,…
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…
Complete quadrics: Schubert calculus for Gaussian models and semidefinite programming
Laurent Manivel, Mateusz Michałek, Leonid Monin +2
We establish connections between: the maximum likelihood degree (ML-degree) for linear concentration models, the algebraic degree of semidefinite programming (SDP), and Schubert ca…
Normality of the Kimura 3-parameter model
Martin Vodička
The Kimura 3-parameter model is one of the most fundamental phylogenetic models in algebraic statistics. We prove that all algebraic varieties associated to this model are projecti…