373 citations · 422 across the 24 of their papers we have counts for
34 papers
Dimensions of Level-1 Group-Based Phylogenetic Networks
Elizabeth Gross, Robert Krone, Samuel Martin
Phylogenetic networks represent evolutionary histories of sets of taxa where horizontal evolution or hybridization has occurred. Placing a Markov model of evolution on a phylogenet…
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…
Statistical learning with phylogenetic network invariants
Travis Barton, Elizabeth Gross, Colby Long +1
Phylogenetic networks provide a means of describing the evolutionary history of sets of species believed to have undergone hybridization or gene flow during their evolution. The mu…
One-connection rule for structural equation models
Bibhas Adhikari, Elizabeth Gross, Marc Härkönen +1
Linear structural equation models are multivariate statistical models encoded by mixed graphs. In particular, the set of covariance matrices for distributions belonging to a linear…
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…
Identifiability of linear compartmental tree models and a general formula for input-output equations
Cashous Bortner, Elizabeth Gross, Nicolette Meshkat +2
A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable -- that is, whether parameter values can be infer…
What are higher-order networks?
Christian Bick, Elizabeth Gross, Heather A. Harrington +1
Network-based modeling of complex systems and data using the language of graphs has become an essential topic across a range of different disciplines. Arguably, this graph-based pe…
Goodness of fit for log-linear ERGMs
Elizabeth Gross, Sonja Petrović, Despina Stasi
Many popular models from the networks literature can be viewed through a common lens of contingency tables on network dyads, resulting in \emph{log-linear ERGMs}: exponential famil…
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…
Distinguishing level-1 phylogenetic networks on the basis of data generated by Markov processes
Elizabeth Gross, Leo van Iersel, Remie Janssen +3
Phylogenetic networks can represent evolutionary events that cannot be described by phylogenetic trees. These networks are able to incorporate reticulate evolutionary events such a…
Algebraic statistics, tables, and networks: The Fienberg advantage
Elizabeth Gross, Vishesh Karwa, Sonja Petrović
Stephen Fienberg's affinity for contingency table problems and reinterpreting models with a fresh look gave rise to a new approach for hypothesis testing of network models that are…
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…
Phylogenetic Networks
Elizabeth Gross, Colby Long, Joseph Rusinko
Phylogenetics is the study of the evolutionary relationships between organisms. One of the main challenges in the field is to take biological data for a group of organisms and to i…
Joining and decomposing reaction networks
Elizabeth Gross, Heather A Harrington, Nicolette Meshkat +1
In systems and synthetic biology, much research has focused on the behavior and design of single pathways, while, more recently, experimental efforts have focused on how cross-talk…
Linear compartmental models: input-output equations and operations that preserve identifiability
Elizabeth Gross, Heather A. Harrington, Nicolette Meshkat +1
This work focuses on the question of how identifiability of a mathematical model, that is, whether parameters can be recovered from data, is related to identifiability of its submo…
Algebraic signatures of convex and non-convex codes
Carina Curto, Elizabeth Gross, Jack Jeffries +4
A convex code is a binary code generated by the pattern of intersections of a collection of open convex sets in some Euclidean space. Convex codes are relevant to neuroscience as t…
Dimensions of Group-based Phylogenetic Mixtures
Hector Baños, Nathaniel Bushek, Ruth Davidson +6
In this paper we study group-based Markov models of evolution and their mixtures. In the algebreo-geometric setting, group-based phylogenetic tree models correspond to toric variet…
Identifiability of linear compartmental models: the singular locus
Elizabeth Gross, Nicolette Meshkat, Anne Shiu
This work addresses the problem of identifiability, that is, the question of whether parameters can be recovered from data, for linear compartmental models. Using standard differen…
Distinguishing Phylogenetic Networks
Elizabeth Gross, Colby Long
Phylogenetic networks are becoming increasingly popular in phylogenetics since they have the ability to describe a wider range of evolutionary events than their tree counterparts.…
The Multiple Roots Phenomenon in Maximum Likelihood Estimation for Factor Analysis
Elizabeth Gross, Sonja Petrović, Donald Richards +1
Multiple root estimation problems in statistical inference arise in many contexts in the literature. In the context of maximum likelihood estimation, the existence of multiple root…
Phylogenetic trees
Hector Baños, Nathaniel Bushek, Ruth Davidson +6
We introduce the package PhylogeneticTrees for Macaulay2 which allows users to compute phylogenetic invariants for group-based tree models. We provide some background information o…
Neural ideals and stimulus space visualization
Elizabeth Gross, Nida Kazi Obatake, Nora Youngs
A neural code is a collection of binary vectors of a given length n that record the co-firing patterns of a set of neurons. Our focus is on neural codes arising from…
What makes a neural code convex?
Carina Curto, Elizabeth Gross, Jack Jeffries +5
Neural codes allow the brain to represent, process, and store information about the world. Combinatorial codes, comprised of binary patterns of neural activity, encode information…