8 papers
The K-theory of uniform Roe algebras for coarse structures generated by finite-rank free abelian subgroups
Charles Fanning, Mehmet Emin Aktas
For a uniformly locally finite coarse space , the uniform Roe algebra is the operator norm closure of the controlled operators on . The -theory of unifo…
On the Spectral Synthesis of Lipschitz Vectorizations of Persistence Diagrams
Charles Fanning, Mehmet Emin Aktas
Persistence diagrams are fundamental descriptors in topological data analysis. Many statistical and machine learning methods require persistence diagrams to be mapped into vector s…
Square Metric Spaces
Charles Fanning, Mehmet Aktas
Product decompositions of metric spaces are built from coordinate maps, but these maps are not part of the resulting metric space. We recover this missing coordinate structure thro…
Higher-order Persistence Diagrams
Charles Fanning, Mehmet Aktas
Persistent homology tracks when topological features appear and disappear across filtered data and represents the lifetime of each feature by a persistence interval. In multiple in…
Random Walks on Virtual Persistence Diagrams
Charles Fanning, Mehmet Aktas
In the uniformly discrete case of virtual persistence diagram groups , we construct a translation-invariant heat semigroup. The kernels are supported on a countable subgrou…
Reproducing Kernel Hilbert Spaces on Banach Completions of Virtual Persistence Diagram Groups
Charles Fanning, Mehmet Aktas
Persistent homology maps a simplicial complex filtered by elements in to finite formal sums of elements of $\mathbb R_{\leq}^{2} = \{ (b,d) \in \mathbb R^2 \cup \{ \inf…
Topological Conditioning for Mammography Models via a Stable Wavelet-Persistence Vectorization
Charles Fanning, Mehmet Emin Aktas
Breast cancer is the most commonly diagnosed cancer in women and a leading cause of cancer death worldwide. Screening mammography reduces mortality, yet interpretation still suffer…
Reproducing Kernel Hilbert Spaces for Virtual Persistence Diagrams
Charles Fanning, Mehmet Aktas
A persistence diagram is a finite multiset of birth-death pairs representing the lifetimes of topological features across a filtration. Existing functional and kernel representatio…