46 citations · 224 across the 37 of their papers we have counts for
38 papers
Mathematical analysis of one-layer neural network with fixed biases, a new activation function and other observations
Fabricio Macià, Shu Nakamura
We analyze a simple one-hidden-layer neural network with ReLU activation functions and fixed biases, with one-dimensional input and output. We study both continuous and discrete ve…
Continuum limit of resonances for discrete Schrödinger operators
Kentaro Kameoka, Shu Nakamura
We consider complex resonances for discrete and continuous Schrödinger operators, and we show that the resonances of discrete models converge to resonances of continuous models in…
Equivalence of the staggered fermion Hamiltonan and the discrete Hodge-Dirac operator on square lattices
Shu Nakamura
We show that the free massless staggered fermion (or the KS-fermion) Hamiltonian is equivalent to a discrete Hodge-Dirac operator on the -dimensional square lattice $h\mathbb{Z}…
Continuum limit for Laplace and Elliptic operators on lattices
Keita Mikami, Shu Nakamura, Yukihide Tadano
Continuum limits of Laplace operators on general lattices are considered, and it is shown that these operators converge to elliptic operators on the Euclidean space in the sense of…
Remarks on discrete Dirac operators and their continuum limits
Shu Nakamura
We discuss possible definitions of discrete Dirac operators, and discuss their continuum limits. It is well-known in the lattice field theory that the straightforward discretizatio…
Essential self-adjointness for the Klein-Gordon type operators on asymptotically static spacetime
Shu Nakamura, Kouichi Taira
Let be the spacetime, where is a closed manifold equipped with a Riemannian metric , and we consider a symmetric Klein-Gordon type operator on …