About the Authors

Masatoshi Nishikawa

Affiliations Department of Mathematical and Life Sciences, Hiroshima University, Higashi-Hiroshima, Hiroshima, Japan, CREST, Japan Science and Technology Agency, Suita, Osaka, Japan

Tatsuo Shibata

shibata@hiroshima-u.ac.jp

Affiliations Department of Mathematical and Life Sciences, Hiroshima University, Higashi-Hiroshima, Hiroshima, Japan, CREST, Japan Science and Technology Agency, Suita, Osaka, Japan, PRESTO, Japan Science and Technology Agency, Kawaguchi, Saitama, Japan

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Conceived and designed the experiments: MN TS. Performed the experiments: MN TS. Wrote the paper: MN TS.