5 papers
Distance Optimization in the Grassmannian of Lines
Hannah Friedman, Andrea Rosana, Bernd Sturmfels
The square of a skew-symmetric matrix is a symmetric matrix whose eigenvalues have even multiplicities. When the matrices have rank two, they represent the Grassmannian of lines, a…
The Likelihood Correspondence
Thomas Kahle, Hal Schenck, Bernd Sturmfels +1
An arrangement of hypersurfaces in projective space is strict normal crossing (SNC) if and only if its Euler discriminant is nonzero. We study the critical loci of arbitrary Lauren…
Varieties of Lines in 3-Space
Benjamin Hollering, Elia Mazzucchelli, Matteo Parisi +1
We consider configurations of lines in 3-space with incidences prescribed by a graph. This defines a subvariety in a product of Grassmannians. Leveraging a connection with rigidity…
Squared Linear Models
Hannah Friedman, Bernd Sturmfels, Maximilian Wiesmann
We study statistical models that are parametrized by squares of linear forms. All critical points of the likelihood function are real and positive. There is one critical point in e…
Arrangements and Likelihood
Thomas Kahle, Lukas Kühne, Leonie Mühlherr +2
We develop novel tools for computing the likelihood correspondence of an arrangement of hypersurfaces in a projective space. This uses the module of logarithmic derivations. This o…