arXiv subjects
Publications and source records attributed to Kazushi Ahara.
In this paper, we address the dynamic construction problem for Malfatti circles with respect to a fixed triangle, using the LC and CC modules. We show that the configuration of the Malfatti circles constitutes a stable fixed point and provide lower bounds for the main parameters of the LC and CC modules. We now remark that all mathematical proofs in this paper were generated by ChatGPT.
We introduce Cubical Ripser for computing persistent homology of image and volume data (more precisely, weighted cubical complexes). To our best knowledge, Cubical Ripser is currently the fastest and the most memory-efficient program for computing persistent homology of weighted cubical complexes. We demonstrate our software with an example of image analysis in which persistent homology and convolutional neural networks are successfully combined. Our open-source implementation is available online.
For a given tiling of the euclidean plane ${\bf E}^2$, we call the degree of freedom of perturbed edges of prototiles {\it escher degree}. In this paper we consider non-periodic L-tilings by 2 prototiles and obtain the escher degree of them.
In this paper we propose {\it a region choice problem} for a knot projection. This problem is an integral extension of Shimizu's 'region crossing change unknotting operation.' We show that there exists a solution of the region choice problem for all knot projections.