10 papers
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…
On the maximum likelihood degree for Gaussian graphical models
Carlos Améndola, Rodica Andreea Dinu, Mateusz Michałek +1
In this paper we revisit the likelihood geometry of Gaussian graphical models. We give a detailed proof that the ML-degree behaves monotonically on induced subgraphs. Furthermore,…
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…
Gorenstein property for phylogenetic trivalent trees
Rodica Dinu, Martin Vodička
We study the Gorenstein property for phylogenetic group-based models. We prove that for the groups and and trivalent trees the associa…
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…
The Finite Embedding Property for IP Loops and Local Embeddability of Groups into Finite IP Loops
Martin Vodička, Pavol Zlatoš
We prove that the class of all loops with the inverse property (IP loops) has the Finite Embedding Property (FEP). As a consequence, every group is locally embeddable into finite I…
A uniform stability principle for dual lattices
Martin Vodička, Pavol Zlatoš
We prove a highly uniform stability or "almost-near" theorem for dual lattices of lattices . More precisely, we show that, for a vector from the linear sp…