About the Authors

Douglas Zhou

zdz@sjtu.edu.cn (DZ); cai@cims.nyu.edu (DC)

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

Yanyang Xiao

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

Yaoyu Zhang

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

Zhiqin Xu

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

David Cai

zdz@sjtu.edu.cn (DZ); cai@cims.nyu.edu (DC)

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, NYUAD Institute, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

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