3 citations · 6 across the 6 of their papers we have counts for
8 papers
Restricted monodromy containing transpositions
Julianne Barnhart, Taylor Brysiewicz, Michael Burr +1
We relate the monodromy group of a branched cover to the monodromy groups of its restrictions. We show that the presence of a transposition in a restricted monodromy group signific…
Activation degree thresholds and expressiveness of polynomial neural networks
Bella Finkel, Jose Israel Rodriguez, Chenxi Wu +1
We study the expressive power of deep polynomial neural networks through the geometry of their neurovariety. We introduce the notion of the activation degree threshold of a network…
Completions to Discrete Probability Distributions in Log-linear Models
May Cai, Cecilie Olesen Recke, Thomas Yahl
Completion problems, of recovering a point from a set of observed coordinates, are abundant in applications to image reconstruction, phylogenetics, and data science. We consider a…
Real solutions to systems of polynomial equations in Macaulay2
Jordy Lopez Garcia, Kelly Maluccio, Frank Sottile +1
The Macaulay2 package RealRoots provides symbolic methods to study real solutions to systems of polynomial equations. It updates and expands an earlier package developed by Grayson…
Galois Groups in Enumerative Geometry and Applications
Frank Sottile, Thomas Yahl
As Jordan observed in 1870, just as univariate polynomials have Galois groups, so do problems in enumerative geometry. Despite this pedigree, the study of Galois groups in enumerat…
Polyhedral Homotopies in Cox Coordinates
Timothy Duff, Simon Telen, Elise Walker +1
We introduce the Cox homotopy algorithm for solving a sparse system of polynomial equations on a compact toric variety . The algorithm lends its name from a construction, desc…
Decomposable sparse polynomial systems
Taylor Brysiewicz, Jose Israel Rodriguez, Frank Sottile +1
The Macaulay2 package DecomposableSparseSystems implements methods for studying and numerically solving decomposable sparse polynomial systems. We describe the structure of decompo…
Solving Decomposable Sparse Systems
Taylor Brysiewicz, Jose Israel Rodriguez, Frank Sottile +1
Amendola et al. proposed a method for solving systems of polynomial equations lying in a family which exploits a recursive decomposition into smaller systems. A family of systems a…