11 citations · 23 across the 13 of their papers we have counts for
14 papers
Which Vertical Graphs are Non VPHT Reconstructible?
Jette Gutzeit, Kalani Kistler, Tim Ophelders +1
The verbose persistent homology transform (VPHT) is a topological summary of shapes in Euclidean space. Assuming general position, the VPHT is injective, meaning shapes can be reco…
Counting Triangulations of Fixed Cardinal Degrees
Erin Chambers, Tim Ophelders, Anna Schenfisch +1
A fixed set of vertices in the plane may have multiple planar straight-line triangulations in which the degree of each vertex is the same. As such, the degree information does not…
Sweeping Orders for Simplicial Complex Reconstruction
Tim Ophelders, Anna Schenfisch
Standard sweep algorithms require an order of discrete points in Euclidean space, and rely on the property that, at a given point, all points in the halfspace below come earlier in…
Outerplanar graphs with positive Lin-Lu-Yau curvature
George Brooks, Fadekemi Osaye, Anna Schenfisch +2
In this paper, we show that all simple outerplanar graphs with minimum degree at least and positive Lin-Lu-Yau Ricci curvature on every edge have maximum degree at most …
How Small Can Faithful Sets Be? Ordering Topological Descriptors
Brittany Terese Fasy, David L. Millman, Anna Schenfisch
Recent developments in shape reconstruction and comparison call for the use of many different (topological) descriptor types, such as persistence diagrams and Euler characteristic…
K-Theory of Multi-parameter Persistence Modules: Additivity
Ryan E. Grady, Anna Schenfisch
Persistence modules stratify their underlying parameter space, a quality that make persistence modules amenable to study via invariants of stratified spaces. In this article, we ex…
Efficient Graph Reconstruction and Representation Using Augmented Persistence Diagrams
Brittany Terese Fasy, Samuel Micka, David L. Millman +2
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in , the (augmented)…
Catching Polygons
Bradley McCoy, Eli Quist, Anna Schenfisch
Consider an arrangement of lines intersecting the unit square. There is some minimum scaling factor so that any placement of a rectangle with aspect ratio with $p\…
Zig-Zag Modules: Cosheaves and K-Theory
Ryan E. Grady, Anna Schenfisch
Persistence modules have a natural home in the setting of stratified spaces and constructible cosheaves. In this article, we first give explicit constructible cosheaves for common…
Regularity via Links and Stein Factorization
Ryan E. Grady, Anna Schenfisch
Here, we introduce a new definition of regular point for piecewise-linear (PL) functions on combinatorial (PL triangulated) manifolds. This definition is given in terms of the rest…
A Faithful Discretization of Verbose Directional Transforms
Brittany Terese Fasy, Samuel Micka, David L. Millman +2
The persistent homology transform, Betti function transform, and Euler characteristic transform represent a shape with a multiset of persistence diagrams, Betti functions, or Euler…
Reconstructing Embedded Graphs from Persistence Diagrams
Robin Lynne Belton, Brittany Terese Fasy, Rostik Mertz +6
The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides impor…
Challenges in Reconstructing Shapes from Euler Characteristic Curves
Brittany Terese Fasy, Samuel Micka, David L. Millman +2
Shape recognition and classification is a problem with a wide variety of applications. Several recent works have demonstrated that topological descriptors can be used as summaries…
Learning Simplicial Complexes from Persistence Diagrams
Robin Lynne Belton, Brittany Terese Fasy, Rostik Mertz +6
Topological Data Analysis (TDA) studies the shape of data. A common topological descriptor is the persistence diagram, which encodes topological features in a topological space at…