We reformulate the Landau analysis of Feynman integrals with the aim of advancing the
state of the art in modern particle-physics computations. We contribute new algorithms for …

Maximum likelihood estimation (MLE) is a fundamental computational problem in statistics,
and it has recently been studied with some success from the perspective of algebraic …

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

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 …

We study the maximum likelihood (ML) degree of linear concentration models in algebraic
statistics. We relate it to an intersection problem on the variety of complete quadrics. This …

We showcase applications of nonlinear algebra in the sciences and engineering. Our review
is organized into eight themes: polynomial optimization, partial differential equations …

We study multivariate Gaussian statistical models whose maximum likelihood estimator
(MLE) is a rational function of the observed data. We establish a one-to-one correspondence …

In this paper we study the role of planarity in generalized scattering amplitudes, through
several closely interacting structures in combinatorics, algebraic and tropical geometry. The …