2 citations · 5 across the 8 of their papers we have counts for
8 papers
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…
Fibers of point cloud persistence
David Beers, Heather A Harrington, Jacob Leygonie +2
Persistent homology (PH) studies the topology of data across multiple scales by building nested collections of topological spaces called filtrations, computing homology and returni…
The fiber of persistent homology for trees
David Beers, Jacob Leygonie
Consider the space of continuous functions on a geometric tree whose persistent homology gives rise to a finite generic barcode . We show that there are exactly as many path…
Stability and Inference of the Euler Characteristic Transform
Lewis Marsh, David Beers
The Euler characteristic transform (ECT) is a signature from topological data analysis (TDA) which summarises shapes embedded in Euclidean space. Compared with other TDA methods, t…
Stability of topological descriptors for neuronal morphology
David Beers, Heather A. Harrington, Alain Goriely
The topological morphology descriptor of a neuron is a multiset of intervals associated to the shape of the neuron represented as a tree. In practice, topological morphology descri…
Brain Chains as Topological Signatures for Alzheimer's Disease
Christian Goodbrake, David Beers, Travis B. Thompson +2
We propose a topological framework to study the evolution of Alzheimer's disease, the most common neurodegenerative disease. The modeling of this disease starts with the representa…
Fiber of Persistent Homology on Morse functions
Jacob Leygonie, David Beers
Let be a Morse function on a smooth compact manifold with boundary. The path component containing of the space of Morse functions giving rise to…
Split Grothendieck rings of rooted trees and skew shapes via monoid representations
David Beers, Matt Szczesny
We study commutative ring structures on the integral span of rooted trees and -dimensional skew shapes. The multiplication in these rings arises from the smash product operation…