DNFE: Directed network flow entropy for detecting tipping points during biological processes

• Xueqing Peng,

  Roles Conceptualization, Formal analysis, Methodology, Validation, Visualization, Writing – original draft, Writing – review & editing

  Affiliations School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, China, Longmen Laboratory, Luoyang, Henan, China

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• Rui Qiao,

  Roles Conceptualization, Methodology, Software, Visualization, Writing – original draft

  Affiliations School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, China, Longmen Laboratory, Luoyang, Henan, China

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• Peiluan Li ,

  Roles Conceptualization, Funding acquisition, Methodology, Supervision, Writing – original draft, Writing – review & editing

  * E-mail: 9902639@haust.edu.cn (PL); lnchen@sjtu.edu.cn (LC)

  Affiliations School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, China, Longmen Laboratory, Luoyang, Henan, China

  https://orcid.org/0000-0001-5545-6185

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• Luonan Chen

  Roles Conceptualization, Funding acquisition, Supervision, Writing – review & editing

  * E-mail: 9902639@haust.edu.cn (PL); lnchen@sjtu.edu.cn (LC)

  Affiliations School of Mathematical Sciences and School of AI, Shanghai Jiao Tong University, Shanghai, China, Guangdong Institute of Intelligence Science and Technology, Hengqin, China, Key Laboratory of Systems Health Science of Zhejiang Province, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Hangzhou, China

  https://orcid.org/0000-0002-3960-0068

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