419 citations · 448 across the 27 of their papers we have counts for
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math-ph2015
Quantum walks on simplicial complexes
Kaname Matsue, Osamu Ogurisu, Etsuo Segawa
We construct a new type of quantum walks on simplicial complexes as a natural extension of the well-known Szegedy walk on graphs. One can numerically observe that our proposing qua…
math.DS2015★ 6 cited
Rigorous numerics for fast-slow systems with one-dimensional slow variable: topological shadowing approach
Kaname Matsue
We provide a rigorous numerical computation method to validate periodic, homoclinic and heteroclinic orbits as the continuation of singular limit orbits for the fast-slow system $x…
cond-mat.soft2015★ 419 cited
Hierarchical structures of amorphous solids characterized by persistent homology
Yasuaki Hiraoka, Takenobu Nakamura, Akihiko Hirata +3
This article proposes a topological method that extracts hierarchical structures of various amorphous solids. The method is based on the persistence diagram (PD), a mathematical to…