4 papers
Central Limit Theorems for Persistent Betti Numbers
Shunsuke Tada
Various persistent invariants have been developed in recent years. In this paper, we develop a method based on homological algebra for deriving central limit theorems for persisten…
On preservation of relative resolutions for poset representations
Toshitaka Aoki, Shunsuke Tada
The concept of Galois connections (i.e., adjoint pairs between posets) is ubiquitous in mathematics. In representation theory, it is interesting because it naturally induces the ad…
Stability of Bipath Persistence Diagrams
Shunsuke Tada
Recently, bipath persistent homology has been proposed as an extension of standard persistent homology, along with its visualization (bipath persistence diagram) and computational…
Bipath Persistence
Toshitaka Aoki, Emerson G. Escolar, Shunsuke Tada
In persistent homology analysis, interval modules play a central role in describing the birth and death of topological features across a filtration. In this work, we extend this se…