A document by Takuma Yoshimura . Click on the document to view its contents.

The Map-Airy distribution describes the probability distribution of the area under a Brownian excursion over a unit interval. In this paper, an approximate formula with 16-digit relative error, which is accurate enough for double type of IEEE754, and an approximate formula with 34-digit relative error for float128 are obtained. In addition to the approximation, numerical evaluation of Map-Airy distribution and random number generation method are also presented.

The Landau distribution is an important distribution in physical sciences that describes the statistical property of the energy loss by charged particles as they traversing a thin layer of matter. However, this distribution is difficult to treat analytically and requires integration for numerical evaluation. The CERNLIB-G110 approximation, which is currently widely used, is accurate to within 8-9 digits of the relative error. In this paper, an approximate formula with 16-digit relative error, which is accurate enough for double type of IEEE754, and an approximate formula with 34-digit relative error for float128 are obtained. In addition to the approximation, numerical evaluation of Landau distribution and random number generation method are also presented.

A document by Takuma Yoshimura . Click on the document to view its contents.

In this research, I propose a two-variable activation function “Yamatani” that satisfies the first-degree homogeneity, and realize a super-resolution convolutional neural network that is independent of the dynamic range and symmetrical about the luminance inversion.