419 citations · 802 across the 23 of their papers we have counts for
23 papers
Large deviation principle for persistence diagrams of random cubical filtrations
Yasuaki Hiraoka, Shu Kanazawa, Jun Miyanaga +1
The objective of this article is to investigate the asymptotic behavior of the persistence diagrams of a random cubical filtration as the window size tends to infinity. Here, a ran…
Persistent Homology Analysis for Materials Research and Persistent Homology Software: HomCloud
Ippei Obayashi, Takenobu Nakamura, Yasuaki Hiraoka
This paper introduces persistent homology, which is a powerful tool to characterize the shape of data using the mathematical concept of topology. We explain the fundamental idea of…
Girth, magnitude homology, and phase transition of diagonality
Yasuhiko Asao, Yasuaki Hiraoka, Shu Kanazawa
This paper studies the magnitude homology of graphs focusing mainly on the relationship between its diagonality and the girth. Magnitude and magnitude homology are formulations of…
Algebraic stability theorem for derived categories of zigzag persistence modules
Yasuaki Hiraoka, Yuichi Ike, Michio Yoshiwaki
We study distances on zigzag persistence modules from the viewpoint of derived categories and Auslander--Reiten quivers. The derived category of ordinary persistence modules is der…
Zeta functions of periodic cubical lattices and cyclotomic-like polynomials
Yasuaki Hiraoka, Hiroyuki Ochiai, Tomoyuki Shirai
Zeta functions of periodic cubical lattices are explicitly derived by computing all the eigenvalues of the adjacency operators and their characteristic polynomials. We introduce cy…
Mapping Firms' Locations in Technological Space: A Topological Analysis of Patent Statistics
Emerson G. Escolar, Yasuaki Hiraoka, Mitsuru Igami +1
Where do firms innovate? Mapping their locations and directions in technological space is challenging due to its high dimensionality. We propose a new method to characterize firms'…