About the Authors

Juntao Liu

Contributed equally to this work with: Juntao Liu, Guojun Li

Affiliation School of Mathematics, Shandong University, Jinan, China

Guojun Li

Contributed equally to this work with: Juntao Liu, Guojun Li

guojunsdu@gmail.com (GL); xhuang@astate.edu (XH)

Affiliation School of Mathematics, Shandong University, Jinan, China

Zheng Chang

Affiliation School of Mathematics, Shandong University, Jinan, China

Ting Yu

Affiliation School of Mathematics, Shandong University, Jinan, China

Bingqiang Liu

Affiliation School of Mathematics, Shandong University, Jinan, China

Rick McMullen

Affiliation High Performance Computing Center, University of Arkansas, Fayetteville, Arkansas, United States of America

Pengyin Chen

Affiliation Crop, Soil, and Environmental Sciences, University of Arkansas, Fayetteville, Arkansas, United States of America

Xiuzhen Huang

guojunsdu@gmail.com (GL); xhuang@astate.edu (XH)

Affiliation Department of Computer Science, Arkansas State University, Jonesboro, Arkansas, United States of America

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Conceived and designed the experiments: GL. Performed the experiments: JL. Analyzed the data: JL TY BL. Contributed reagents/materials/analysis tools: JL ZC. Wrote the paper: JL GL XH. Designed the software used in analysis: JL TY RM PC. Oversaw the project: GL XH.