6 papers
Elimination Without Eliminating: Computing Complements of Real Hypersurfaces Using Pseudo-Witness Sets
Paul Breiding, John Cobb, Aviva K. Englander +6
Many hypersurfaces in algebraic geometry, such as discriminants, arise as the projection of another variety. The real complement of such a hypersurface partitions its ambient space…
Feature Propagation on Knowledge Graphs using Cellular Sheaves
John Cobb, Thomas Gebhart
Many inference tasks on knowledge graphs, including relation prediction, operate on knowledge graph embeddings -- vector representations of the vertices (entities) and edges (relat…
Inverse Eigenvalue Problems, Floquet Isospectrality and the Hilbert--Chow Morphism
John Cobb, Matthew Faust, Andreas Kretschmer
When can one change the diagonal of a matrix without changing its spectrum? We completely answer this question over an algebraically closed field of characteristic zero or larger t…
Semigroup Graded Stillman's Conjecture
John Cobb, Nathaniel Gallup, John Spoerl
We resolve Stillman's conjecture for families of polynomial rings that are graded by any semigroup under mild conditions. Conversely, we show that these conditions are necessary fo…
LikelihoodGeometry: Macaulay2 Package
David Barnhill, John Cobb, Matthew Faust
This note introduces the package for the computer algebra system . This package gives tools to construct the likelihood correspond…
Likelihood Correspondence of Toric Statistical Models
David Barnhill, John Cobb, Matthew Faust
Maximum likelihood estimation (MLE) is a fundamental problem in statistics. Characteristics of the MLE problem for discrete algebraic statistical models are reflected in the geomet…