198 citations · 732 across the 46 of their papers we have counts for
7 papers · 1 filter
Voronoi Cells of Varieties
Diego Cifuentes, Kristian Ranestad, Bernd Sturmfels +1
Every real algebraic variety determines a Voronoi decomposition of its ambient Euclidean space. Each Voronoi cell is a convex semialgebraic set in the normal space of the variety a…
Moment Varieties of Measures on Polytopes
Kathlén Kohn, Boris Shapiro, Bernd Sturmfels
The uniform probability measure on a convex polytope induces piecewise polynomial densities on its projections. For a fixed combinatorial type of simplicial polytopes, the moments…
Maximum Likelihood Estimation for Totally Positive Log-Concave Densities
Elina Robeva, Bernd Sturmfels, Ngoc Tran +1
We study nonparametric maximum likelihood estimation for two classes of multivariate distributions that imply strong forms of positive dependence; namely log-supermodular (MTP)…
K3 Polytopes and their Quartic Surfaces
Gabriele Balletti, Marta Panizzut, Bernd Sturmfels
K3 polytopes appear in complements of tropical quartic surfaces. They are dual to regular unimodular central triangulations of reflexive polytopes in the fourth dilation of the sta…
Varieties of Signature Tensors
Carlos Améndola, Peter Friz, Bernd Sturmfels
The signature of a parametric curve is a sequence of tensors whose entries are iterated integrals. This construction is central to the theory of rough paths in stochastic analysis.…
The Geometry of SDP-Exactness in Quadratic Optimization
Diego Cifuentes, Corey Harris, Bernd Sturmfels
Consider the problem of minimizing a quadratic objective subject to quadratic equations. We study the semialgebraic region of objective functions for which this problem is solved b…