The nearest point map of a real algebraic variety with respect to Euclidean distance is an
algebraic function. For instance, for varieties of low-rank matrices, the Eckart–Young …

We relate scattering amplitudes in particle physics to maximum likelihood estimation for
discrete models in algebraic statistics. The scattering potential plays the role of the log …

Computing all critical points of a monomial on a very affine variety is a fundamental task in
algebraic statistics, particle physics and other fields. The number of critical points is known …

Metric algebraic geometry combines concepts from algebraic geometry and differential
geometry. Building on classical foundations, it offers practical tools for the 21st century …

These lecture notes provide a self-contained introduction to Euler integrals, which are
frequently encountered in applications. In particle physics, they arise as Feynman integrals …

Algebraic tools have been used in statistical research since the very beginning of the field. In
recent years, the interaction between statistics and pure mathematics has intensified and …

In this work we investigate multipartition models, the subset of log-linear models for which
one can perform the classical iterative proportional scaling (IPS) algorithm to numerically …

A discrete statistical model is a subset of a probability simplex. Its maximum likelihood
estimator (MLE) is a retraction from that simplex onto the model. We characterize all models …

We study the maximum likelihood (ML) degree of toric varieties, known as discrete
exponential models in statistics. By introducing scaling coefficients to the monomial …

Polypols are natural generalizations of polytopes, with boundaries given by nonlinear
algebraic hypersurfaces. We describe polypols in the plane and in 3-space that admit a …