5 papers
Benchmarks in Leipzig
Andrei Balakin, Miklós Bóna, Marie-Charlotte Brandenburg +45
Between April 1 and May 15, 2026, a group of 49 mathematicians compiled a dataset of research-level mathematics questions with known answers. Most of the work was done during the 3…
Maxout Polytopes
Andrei Balakin, Shelby Cox, Georg Loho +1
Maxout polytopes are defined by feedforward neural networks with maxout activation function and non-negative weights after the first layer. We characterize the parameter spaces and…
Maximum Likelihood Degrees of Brownian Motion Tree Models: Star Trees and Root Invariance
Jane Ivy Coons, Shelby Cox, Aida Maraj +1
A Brownian motion tree (BMT) model is a Gaussian model whose associated set of covariance matrices is linearly constrained according to common ancestry in a phylogenetic tree. We s…
Tropicalizing binary geometries
Shelby Cox, Igor Makhlin
The type A cluster configuration space, commonly known as , is the very affine part of the binary geometry associated with the associahedron. The tropicalization…
Homaloidal Polynomials and Gaussian Models of Maximum Likelihood Degree One
Shelby Cox, Pratik Misra, Pardis Semnani
We study the Gaussian statistical models whose log-likelihood function has a unique complex critical point, i.e., has maximum likelihood degree one. We exploit the connection devel…