6 papers
Scalable persistence pairing graphs on scalar fields with an application to porous media
John Rick Manzanares
We present a scalable method for computing persistence pairing graphs from large cubical filtrations and use it to test whether graph organization among persistent classes contains…
Persistence Pairing Graphs: Tracking Changes of Selected Homology Bases
John Rick Manzanares
Persistent homology summarizes a filtration by recording when homological features appear and disappear, but the resulting barcode does not determine a preferred homology basis or…
A Probabilistic Interpretation of the Ball Mapper Graph
John Rick Manzanares, Jay-Anne Bulauan
We introduce Probabilistic Ball Mapper, a formulation of Ball Mapper in which each data point is assigned a probability distribution supported only on the metric balls that contain…
Exact and Approximate Range Queries in Ball Mapper
Jay-Anne Bulauan, John Rick Manzanares
Ball Mapper summarizes a finite metric dataset by covering the sample with closed balls centered at selected landmarks and connecting landmarks whose balls share observations. Its…
Frame-invariant topological representations of trabecular bone microarchitecture for strength prediction
John Rick Manzanares, Richard Leslie Abel, Paweł Dłotko
Directional topological representations of trabecular bone should retain interpretable structural information without depending on an arbitrary transverse coordinate frame. We deve…
Stable Homology-Based Cycle Centrality Measures
John Rick D. Manzanares, Paul Samuel P. Ignacio
Network centrality measures play a crucial role in understanding graph structures, assessing the importance of nodes, paths, or cycles based on directed or reciprocal interactions…