198 citations · 732 across the 46 of their papers we have counts for
10 papers · 1 filter
Twenty-Seven Questions about the Cubic Surface
Kristian Ranestad, Bernd Sturmfels
We present a collection of research questions on cubic surfaces in 3-space. These questions inspired a collection of papers to be published in a special issue of the journal Le Mat…
Algebraic Analysis of Rotation Data
Michael F. Adamer, András C. Lőrincz, Anna-Laura Sattelberger +1
We develop algebraic tools for statistical inference from samples of rotation matrices. This rests on the theory of D-modules in algebraic analysis. Noncommutative Gröbner bases ar…
D-Modules and Holonomic Functions
Anna-Laura Sattelberger, Bernd Sturmfels
In algebraic geometry, one studies the solutions to polynomial equations, or, equivalently, to linear partial differential equations with constant coefficients. These lecture notes…
Estimating linear covariance models with numerical nonlinear algebra
Bernd Sturmfels, Sascha Timme, Piotr Zwiernik
Numerical nonlinear algebra is applied to maximum likelihood estimation for Gaussian models defined by linear constraints on the covariance matrix. We examine the generic case as w…
Optimal Transport to a Variety
T. Ö. Çelik, A. Jamneshan, G. Montúfar +2
We study the problem of minimizing the Wasserstein distance between a probability distribution and an algebraic variety. We consider the setting of finite state spaces and describe…
Positivity Certificates via Integral Representations
Khazhgali Kozhasov, Mateusz Michałek, Bernd Sturmfels
Complete monotonicity is a strong positivity property for real-valued functions on convex cones. It is certified by the kernel of the inverse Laplace transform. We study this for n…