About the Authors

Wei Zheng

Affiliation School of Mathematical Sciences and LPMC, Nankai University, Tianjin, People’s Republic of China

Jishou Ruan

Affiliations School of Mathematical Sciences and LPMC, Nankai University, Tianjin, People’s Republic of China, State Key Laboratory of Medicinal Chemical Biology, Nankai University, Tianjin, People’s Republic of China

Gang Hu

Affiliation School of Mathematical Sciences and LPMC, Nankai University, Tianjin, People’s Republic of China

Kui Wang

Affiliation School of Mathematical Sciences and LPMC, Nankai University, Tianjin, People’s Republic of China

Michelle Hanlon

Affiliation Department of Physical Sciences, Grant MacEwan University, Alberta, Canada

Jianzhao Gao

gaojz@nankai.edu.cn

Affiliation School of Mathematical Sciences and LPMC, Nankai University, Tianjin, People’s Republic of China

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Conceived and designed the experiments: JG. Performed the experiments: WZ. Analyzed the data: JG WZ JR GH KW MH. Contributed reagents/materials/analysis tools: JG WZ JR GH KW. Wrote the paper: JG WZ JR GH KW MH. Designed the software used in analysis: ZW JG.