11 citations · 33 across the 7 of their papers we have counts for
8 papers
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…
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…
-Selmer group and Modular symbols
Ryotaro Sakamoto
In this paper, we prove that the dimension of the -Selmer group for an elliptic curve is controlled by certain analytic quantities associated with modular symbols, which is conj…
Euler Systems for
Chi-Yun Hsu, Zhaorong Jin, Ryotaro Sakamoto
For a non-endoscopic cohomological cuspidal automorphic representation of , assumed to be -ordinary, we construct an Euler system for the Ga…
A higher rank Euler system for the multiplicative group over a totally real field
Ryotaro Sakamoto
In this paper, we construct a higher rank Euler system for the multiplicative group over a totally real field by using the Iwasawa main conjecture proved by Wiles. A key ingredient…
On the theory of higher rank Euler, Kolyvagin and Stark systems, IV: the multiplicative group
David Burns, Ryotaro Sakamoto, Takamichi Sano
We describe a refinement of the general theory of higher rank Euler, Kolyvagin and Stark systems in the setting of the multiplicative group over arbitrary number fields. We use the…