32 citations · 34 across the 3 of their papers we have counts for
6 papers
Tensor Computation of Euler Characteristic Functions and Transforms
Jessi Cisewski-Kehe, Brittany Terese Fasy, Alexander McCleary +1
The weighted Euler characteristic transform (WECT) and Euler characteristic function (ECF) have proven to be useful tools in a variety of applications. However, current methods for…
Galois Connections in Persistent Homology
Aziz Burak Gulen, Alexander McCleary
We present a new language for persistent homology in terms of Galois connections. This language has two main advantages over traditional approaches. First, it simplifies and unifie…
Edit Distance and Persistence Diagrams Over Lattices
Alexander McCleary, Amit Patel
We build a functorial pipeline for persistent homology. The input to this pipeline is a filtered simplicial complex indexed by any finite metric lattice and the output is a persist…
Positivity of Multiparameter Persistence Diagrams and Bottleneck Stability
Alex McCleary, Amit Patel
Persistent homology studies the birth and death of cycles in a parameterized family of spaces. In this paper, we study the birth and death of cycles in a multifiltration of a chain…
Bottleneck Stability for Generalized Persistence Diagrams
Alex McCleary, Amit Patel
In this paper, we extend bottleneck stability to the setting of one dimensional constructible persistences module valued in any small abelian category.
Subshifts with sparse traces
Ville Salo
We study two-dimensional subshifts whose horizontal trace (a.k.a. projective subdynamics) contains only points of finite support. Our main result is a classification result for suc…