373 citations · 422 across the 24 of their papers we have counts for
6 papers · 1 filter
Mixed volumes of networks with binomial steady-states
Jane Ivy Coons, Mark Curiel, Elizabeth Gross
The steady-state degree of a chemical reaction network is the number of complex steady-states for generic rate constants and initial conditions. One way to bound the steady-state d…
Broken Bracelets and Kostant's Partition Function
Mark Curiel, Elizabeth Gross, Pamela E. Harris
Inspired by the work of Amdeberhan, Can, and Moll on broken necklaces, we define a broken bracelet as a linear arrangement of marked and unmarked vertices and introduce a generaliz…
When do two networks have the same steady-state ideal?
Mark Curiel, Elizabeth Gross, Carlos Munoz
Chemical reaction networks are often used to model and understand biological processes such as cell signaling. Under the framework of chemical reaction network theory, a process is…
Binomial ideals of domino tilings
Elizabeth Gross, Nicole Yamzon
In this paper, we consider the set of all domino tilings of a cubiculated region. The primary question we explore is: How can we move from one tiling to another? Tiling spaces can…
The steady-state degree and mixed volume of a chemical reaction network
Elizabeth Gross, Cvetelina Hill
The steady-state degree of a chemical reaction network is the number of complex steady-states, which is a measure of the algebraic complexity of solving the steady-state system. In…
The Maximum Likelihood Threshold of a Graph
Elizabeth Gross, Seth Sullivant
The maximum likelihood threshold of a graph is the smallest number of data points that guarantees that maximum likelihood estimates exist almost surely in the Gaussian graphical mo…