About the Authors

Mo Deng

Contributed equally to this work with: Mo Deng, Chenglong Yu

Affiliation Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, Illinois, United States of America

Chenglong Yu

Contributed equally to this work with: Mo Deng, Chenglong Yu

Affiliation The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin, Hong Kong, People's Republic of China

Qian Liang

Affiliation Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, Illinois, United States of America

Rong L. He

Affiliation Department of Biological Sciences, Chicago State University, Chicago, Illinois, United States of America

Stephen S.-T. Yau

yau@uic.edu

Affiliation Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, Illinois, United States of America

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Performed the experiments: MD CY RLH. Analyzed the data: MD CY RLH. Wrote the paper: MD CY. Conceived and designed method: SSTY. Normalizations of method: MD. Programming: MD QL. Helped write the paper: RLH SSTY.