6 citations · 14 across the 14 of their papers we have counts for
16 papers
Magnitude, path and coarse homology
Yasuhiko Asao
In this article, we introduce Borel--Moore and uniformly finite versions of magnitude homology and path homology for locally finite graphs by allowing possibly infinite chains subj…
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…
Magnitude and magnitude homology of filtered set enriched categories
Yasuhiko Asao
In this article, we give a framework for studying the Euler characteristic and its categorification of objects across several areas of geometry, topology and combinatorics. That is…
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…
Magnitude homology and Path homology
Yasuhiko Asao
In this article, we show that magnitude homology and path homology are closely related, and we give some applications. We define differentials ${\mathrm MH}^{\ell}_k(G) \longrighta…
Image recognition via Vietoris-Rips complex
Yasuhiko Asao, Jumpei Nagase, Ryotaro Sakamoto +1
Extracting informative features from images has been of capital importance in computer vision. In this paper, we propose a way to extract such features from images by a method base…
Curvature of point clouds through principal component analysis
Yasuhiko Asao, Yuichi Ike
In this article, we study curvature-like feature value of data sets in Euclidean spaces. First, we formulate such curvature functions with desirable properties under the manifold h…
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…
Geometric approach to graph magnitude homology
Yasuhiko Asao, Kengo Izumihara
In this paper, we introduce a new method to compute magnitude homology of general graphs. To each direct sum component of magnitude chain complexes, we assign a pair of simplicial…
Magnitude homology of geodesic metric spaces with an upper curvature bound
Yasuhiko Asao
In this article, we study the magnitude homology of geodesic metric spaces of curvature , especially spaces. We will show that the magnitude homology $MH^{l}…
The loop homology algebra of discrete torsion
Yasuhiko Asao
We show that Lupercio-Uribe-Xicoténcatl's orbifold loop product and coproduct can be described by a group cohomology class in some cases. By computing this cohomology class, we sho…
Loop homology of some global quotient orbifolds
Yasuhiko Asao
We determine the ring structure of the loop homology of some global quotient orbifolds. We can compute by our theorem the loop homology ring with suitable coefficients of the globa…