2 citations · 4 across the 5 of their papers we have counts for
10 papers
Geometric interpretation of magnitude
Yasuhiko Asao, Kiyonori Gomi
For an positive definite symmetric matrix with for all , we show that there exists a set of vectors such that the radius $…
Magnitude homology and homotopy type of metric fibrations
Yasuhiko Asao, Yu Tajima, Masahiko Yoshinaga
In this article, we show that each two metric fibrations with a common base and a common fiber have isomorphic magnitude homology, and even more, the same magnitude homotopy type.…
Minimal projective resolution and magnitude homology of geodetic metric spaces
Yasuhiko Asao, Shun Wakatsuki
Asao-Ivanov showed that magnitude homology is a Tor functor, hence we can compute it by giving a projective resolution of a certain module. In this article, we compute magnitude ho…
Magnitude homology is a derived functor
Yasuhiko Asao, Sergei O. Ivanov
We prove that the magnitude (co)homology of an enriched category can, under some technical assumptions, be described in terms of derived functors between certain abelian categories…
Classification of metric fibrations
Yasuhiko Asao
In this paper, we study `a fibration of metric spaces' that was originally introduced by Leinster in the study of the magnitude and called metric fibrations. He showed that the mag…
Convergence of neural networks to Gaussian mixture distribution
Yasuhiko Asao, Ryotaro Sakamoto, Shiro Takagi
We give a proof that, under relatively mild conditions, fully-connected feed-forward deep random neural networks converge to a Gaussian mixture distribution as only the width of th…