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Planar Symmetry Detection and Quantification using the Extended Persistent Homology Transform
Nicholas Bermingham, Vanessa Robins, Katharine Turner
Symmetry is ubiquitous throughout nature and can often give great insights into the formation, structure and stability of objects studied by mathematicians, physicists, chemists an…
Computation of degree-1 persistent homology on larger point-clouds using the Reduced Vietoris-Rips filtration
Musashi Ayrton Koyama, Facundo Mémoli, Vanessa Robins +1
Computing Persistent Homology for large point clouds remains a bottleneck for the wider adoption of persistent homology by the scientific community. We present an algorithm which c…
Graph Pseudometrics from a Topological Point of View
Ana Lucia Garcia-Pulido, Kathryn Hess, Jane Tan +3
We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful…
Notes on an Elementary Proof for the Stability of Persistence Diagrams
Primoz Skraba, Katharine Turner
These notes are a self-contained short proof of the stability of persistence diagrams.
Stratified Space Learning: Reconstructing Embedded Graphs
Yossi Bokor, Daniel Grixti-Cheng, Markus Hegland +2
Many data-rich industries are interested in the efficient discovery and modelling of structures underlying large data sets, as it allows for the fast triage and dimension reduction…
Same But Different: Distance Correlations Between Topological Summaries
Katharine Turner, Gard Spreemann
Persistent homology allows us to create topological summaries of complex data. In order to analyse these statistically, we need to choose a topological summary and a relevant metri…