About the Authors

Douglas Zhou

Affiliation Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China

Songting Li

Affiliation Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China

Xiao-hui Zhang

Affiliation Institute of Neuroscience and State Key Laboratory of Neuroscience, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, Shanghai, China

David Cai

sdcai@sjtu.edu.cn

Affiliations Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China, Courant Institute of Mathematical Sciences and Center for Neural Science, New York University, New York, New York, United States of America

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Conceived and designed the experiments: DZ SL XhZ DC. Performed the experiments: DZ SL XhZ DC. Analyzed the data: DZ SL XhZ DC. Contributed reagents/materials/analysis tools: DZ SL XhZ DC. Wrote the paper: DZ SL XhZ DC.