3 citations · 5 across the 7 of their papers we have counts for
9 papers
Using Persistent Homology to Analyze Access to Heterogeneous-Quality Resources and Heterogeneous-Severity Nuisances
Sarah Tymochko, Gillian Grindstaff, Abigail Hickok +2
We develop a framework to use multiparameter persistent homology (PH) to examine access to heterogeneous-quality resources and exposure to heterogeneous-severity nuisances in a geo…
Nested tree space: a geometric framework for co-phylogeny
G. Grindstaff, R. S. Hoekzema
Nested (or reconciled) phylogenetic trees model co-evolutionary systems in which one evolutionary history is embedded within another. We introduce a geometric framework for such sy…
Intrinsic Bottleneck Distance for Merge Trees
David Beers, Gillian Grindstaff
Merge trees are a topological descriptor of a filtered space that enriches the degree zero barcode with its merge structure. The space of merge trees comes equipped with an interle…
Tropical Bisectors and Carlini-Wagner Attacks
Gillian Grindstaff, Julia Lindberg, Daniela Schkoda +2
Pasque et al. showed that using a tropical symmetric metric as an activation function in the last layer can improve the robustness of convolutional neural networks (CNNs) against s…
Topological classification of tumour-immune interactions and dynamics
Jingjie Yang, Heidi Fang, Jagdeep Dhesi +5
The complex and dynamic crosstalk between tumour and immune cells results in tumours that can exhibit distinct qualitative behaviours - elimination, equilibrium, and escape - and i…
Topological Data Analysis Detects Percolation Thresholds in Arctic Melt-Pond Evolution
Wilfred Offord, Michael Coughlan, Ian J. Hewitt +2
During the summer melt period, ponds form on the surface of Arctic sea ice as it melts, with important consequences for ice evolution and marine ecology. Due to the ice-albedo feed…
The isometry group of phylogenetic tree space is
Gillian Grindstaff
A phylogenetic tree is an acyclic graph with distinctly labeled leaves, whose internal edges have a positive weight. Given a set of n leaves, the collection of all phylogenetic tre…
Geometric comparison of phylogenetic trees with different leaf sets
Gillian Grindstaff, Megan Owen
The metric space of phylogenetic trees defined by Billera, Holmes, and Vogtmann, which we refer to as BHV space, provides a natural geometric setting for describing collections of…
Lie Ideal Enhancements of Counting Invariants
Gillian Roxanne Grindstaff, Sam Nelson
We define enhancements of the quandle counting invariant for knots and links with a finite labeling quandle Q embedded in the quandle of units of a Lie algebra \mathfrak{a} using L…