SPNE: sample-perturbed network entropy for revealing critical states of complex biological systems.

Rui Liu 0009 South China University of Technology, School of Mathematics, Guangzhou, China University of Tokyo, Laboratories for Mathematics, Lifesciences, and Informatics, Japan Peking University, School of Mathematical Sciences, Beijing, China https://orcid.org/0000-0002-4547-8695 https://www.wikidata.org/entity/Q59677566 Rui Liu Rui Liu 0001 University of Delaware, Department of Computer and Information Sciences, Newark, DE, USA Rui Liu 0002 刘睿 University of Chicago, Department of Computer Science, IL, USA National University of Singapore, Department of Computer Science, Singapore Chinese University of Hong Kong, Department of Information Engineering, Hong Kong Hong Kong Polytechnic University, Department of Computing, Hong Kong https://csruiliu.github.io/ https://orcid.org/0000-0001-9061-787X https://www.wikidata.org/entity/Q60662237 https://www.researcherid.com/rid/I-9830-2016 https://www.scopus.com/authid/detail.uri?authorId=56073527600 Rui Liu 0003 Colorado School of Mines, Department of Mechanical Engineering, Golden, CO, USA https://orcid.org/0000-0002-8932-1147 https://www.scopus.com/authid/detail.uri?authorId=56352132900 Rui Liu 0004 National University of Singapore Shandong Normal University, School of Information Science and Engineering, Jinan, China https://orcid.org/0000-0002-5051-4224 Rui Liu 0005 Arizona State University, School of Electrical, Computer, and Energy Engineering, Tempe, AZ, USA https://orcid.org/0000-0003-1642-3473 Rui Liu 0006 Louisiana Tech University, Ruston, LA, USA https://orcid.org/0000-0001-6602-808X https://www.wikidata.org/entity/Q103830505 Rui Liu 0007 Beihang University, School of Computer Science and Engineering, State Key Lab of Software Development Environment, Beijing, China https://orcid.org/0000-0003-1973-6168 Rui Liu 0008 Inner Mongolia University, College of Computer Science, Hohhot, China https://orcid.org/0000-0003-4524-7413 Rui Liu 0010 Technical University Munich, Germany Rui Liu 0011 University of Saskatchewan, Department of Electrical and Computer Engineering, Saskatoon, Canada Rui Liu 0012 The Second Xiangya Hospital of Central South University, Department of Oncology, Hunan, China Rui Liu 0013 University of Michigan, Ann Arbor, MI, USA https://scholar.google.com/citations?user=hMR1iP4AAAAJ Rui Liu 0014 Dartmouth College, Hanover, NH, USA University of Washington, Tacoma, WA, USA Tsinghua University, Beijing, China https://www.cs.dartmouth.edu/~rliu/ Rui Liu 0015 Dalian University, School of Software Engineering, China https://orcid.org/0000-0002-5200-640X https://www.wikidata.org/entity/Q91509716 Rui Liu 0016 Zhejiang University, College of Information Science and Electronic Engineering, Hangzhou, China https://ieeexplore.ieee.org/author/37085838872 Rui Liu 0017 University of California San Diego, Department of Physics, CA, USA Huazhong University of Science and Technology, Wuhan National Laboratory for Optoelectronics, China https://orcid.org/0000-0002-3634-0344 https://www.wikidata.org/entity/Q86075566 https://www.scopus.com/authid/detail.uri?authorId=56873521600 Rui Liu 0018 Chang'an University, School of Automobile, Xi'an, China Tongji University, School of Automotive Studies, Shanghai, China https://orcid.org/0000-0001-6071-5225 Rui Liu 0019 Chinese University of Hong Kong, Department of Electrical Engineering, CUHK-SenseTime Joint Laboratory, Hong Kong University of Electronic Science and Technology of China, Chengdu, China https://orcid.org/0000-0003-2115-8491 Rui Liu 0020 Beihang University, Sino-German Joint Software Institute, Beijing, China https://orcid.org/0000-0003-3412-8953 https://ieeexplore.ieee.org/author/37086068604 Rui Liu 0021 North China Electric Power University, Beijing, China https://orcid.org/0000-0001-7348-0365 Rui Liu 0022 Harbin Institute of Technology, Shenzhen Graduate School, China Huazhong University of Science and Technology, School of Management, Wuhan, China https://orcid.org/0000-0001-5946-676X Rui Liu 0023 Ningxia University, School of Agriculture, Yinchuan, China https://orcid.org/0000-0001-5356-2275 https://ieeexplore.ieee.org/author/37088229120 Rui Liu 0024 North University of China, MOE Key Laboratory of Instrumentation Science and Dynamic Measurement, Taiyuan, China https://orcid.org/0000-0003-0035-1858 https://ieeexplore.ieee.org/author/37088477013 Rui Liu 0025 Beihang University, School of Mechanical Engineering and Automation, Beijing, China https://orcid.org/0000-0003-3299-5463 Rui Liu 0026 Nanjing Tech University, School of Mechanical and Power Engineering, China Nanjing University of Aeronautics and Astronautics, China https://orcid.org/0000-0001-6150-1456 https://www.wikidata.org/entity/Q89861147 https://ieeexplore.ieee.org/author/37086187655 Rui Liu 0027 Space Engineering University, School of Space Information, Beijing, China https://orcid.org/0000-0003-3147-878X https://ieeexplore.ieee.org/author/37088661827 Rui Liu 0028 University of Science and Technology Beijing, School of Automation and Electrical Engineering / Institute of Artificial Intelligence, China https://orcid.org/0000-0002-8598-4736 Rui Liu 0029 Chengdu University of Technology, College of Geophysics, MOE Key Laboratory of Earth Exploration and Information Technology, China https://orcid.org/0000-0003-0310-8044 Rui Liu 0030 Boston University, Division of Systems Engineering, Quincy, MA, USA Boston University, USA https://orcid.org/0000-0001-7333-6291 Rui Liu 0031 Indiana University, Department of Computer and Information Science, IN, USA Purdue University, USA Rui Liu 0032 Chinese Academy of Sciences, Institute of Information Engineering, China University of Chinese Academy of Sciences, School of Cyber Security, China https://orcid.org/0000-0002-2967-6296 Rui Liu 0033 City University of Hong Kong, Department of Mechanical Engineering, Hong Kong https://orcid.org/0000-0003-4421-760X Rui Liu 0034 Nanyang Technological University, Singapore https://orcid.org/0000-0002-3606-0553 Rui Liu 0035 Chongqing University, College of Computer Science, Chongqing, China https://orcid.org/0009-0001-2263-8270

Jiayuan Zhong Dandan Ding Juntan Liu Rui Liu 0009 Pei Chen SPNE: sample-perturbed network entropy for revealing critical states of complex biological systems. 2023 March 24 Briefings Bioinform. 2 https://doi.org/10.1093/bib/bbad028 db/journals/bib/bib24.html#ZhongDLLC23

Jiayuan Zhong Chongyin Han Pei Chen Rui Liu 0009 SGAE: single-cell gene association entropy for revealing critical states of cell transitions during embryonic development. 2023 September 24 Briefings Bioinform. 6 https://doi.org/10.1093/bib/bbad366 db/journals/bib/bib24.html#ZhongHCL23 streams/journals/bib

Hui Tang Xiangtian Yu Rui Liu 0009 Tao Zeng 0003 Vec2image: an explainable artificial intelligence model for the feature representation and classification of high-dimensional biological data by vector-to-image conversion. 2022 23 Briefings Bioinform. 2 https://doi.org/10.1093/bib/bbab584 db/journals/bib/bib23.html#TangYLZ22

Pei Chen Jiayuan Zhong Kun Yang Xuhang Zhang Yingqi Chen Rui Liu 0009 TPD: a web tool for tipping-point detection based on dynamic network biomarker. 2022 23 Briefings Bioinform. 5 https://doi.org/10.1093/bib/bbac399 https://www.wikidata.org/entity/Q114093468 db/journals/bib/bib23.html#ChenZYZCL22

Hao Peng 0003 Jiayuan Zhong Pei Chen Rui Liu 0009 Identifying the critical states of complex diseases by the dynamic change of multivariate distribution. 2022 23 Briefings Bioinform. 5 https://doi.org/10.1093/bib/bbac177 db/journals/bib/bib23.html#PengZCL22

Jiayuan Zhong Chongyin Han Yangkai Wang Pei Chen Rui Liu 0009 Identifying the critical state of complex biological systems by the directed-network rank score method. 5398-5405 2022 December 38 Bioinform. 24 https://doi.org/10.1093/bioinformatics/btac707 db/journals/bioinformatics/bioinformatics38.html#ZhongHWCL22

Jiayuan Zhong Chongyin Han Xuhang Zhang Pei Chen Rui Liu 0009 scGET: Predicting Cell Fate Transition During Early Embryonic Development by Single-cell Graph Entropy. 461-474 2021 19 Genom. Proteom. Bioinform. 3 https://doi.org/10.1016/j.gpb.2020.11.008 db/journals/gpb/gpb19.html#ZhongHZCL21

Hao Peng 0003 Pei Chen Rui Liu 0009 Luonan Chen Spatiotemporal convolutional network for time-series prediction and causal inference. 2021 abs/2107.01353 CoRR https://arxiv.org/abs/2107.01353 db/journals/corr/corr2107.html#abs-2107-01353

Rui Liu 0009 Pei Chen Luonan Chen Single-sample landscape entropy reveals the imminent phase transition during disease progression. 1522-1532 2020 36 Bioinform. 5 https://doi.org/10.1093/bioinformatics/btz758 https://www.wikidata.org/entity/Q90621732 db/journals/bioinformatics/bioinformatics36.html#LiuCC20

Rui Liu 0009 Pei Chen Luonan Chen Corrigendum to: Single-sample landscape entropy reveals the imminent phase transition during disease progression. 2644 2020 36 Bioinform. 8 https://doi.org/10.1093/bioinformatics/btz935 https://www.wikidata.org/entity/Q92674566 db/journals/bioinformatics/bioinformatics36.html#0009CC20

Jiaopeng Yang Rui Liu 0009 Yiren Chen Bifurcations of Solitary Waves of a Simple Equation. 2050138:1-2050138:20 2020 30 Int. J. Bifurc. Chaos 9 https://doi.org/10.1142/S0218127420501382 db/journals/ijbc/ijbc30.html#Yang0C20

Hao Peng 0003 Pei Chen Rui Liu 0009 Multi-step-ahead Prediction from Short-term Data by Delay-embedding-based Forecast Machine. 2020 abs/2005.07842 CoRR https://arxiv.org/abs/2005.07842 db/journals/corr/corr2005.html#abs-2005-07842

Zongguang Li Rui Liu 0009 Bifurcations and Exact Solutions in a Nonlinear Wave Equation. 1950098:1-1950098:10 2019 29 Int. J. Bifurc. Chaos 7 https://doi.org/10.1142/S0218127419500986 db/journals/ijbc/ijbc29.html#LiL19

Xiaoping Liu 0002 Xiao Chang Rui Liu 0009 Xiangtian Yu Luonan Chen Kazuyuki Aihara Quantifying critical states of complex diseases using single-sample dynamic network biomarkers. 2017 13 PLoS Comput. Biol. 7 https://doi.org/10.1371/journal.pcbi.1005633 https://www.wikidata.org/entity/Q38662535 db/journals/ploscb/ploscb13.html#LiuCLYCA17

Pei Chen Rui Liu 0009 Yongjun Li Luonan Chen Detecting critical state before phase transition of complex biological systems by hidden Markov model. 2143-2150 2016 32 Bioinform. 14 https://doi.org/10.1093/bioinformatics/btw154 https://www.wikidata.org/entity/Q39788045 db/journals/bioinformatics/bioinformatics32.html#ChenLLC16

Yiren Chen Rui Liu 0009 Some new nonlinear wave solutions for two (3+1)-dimensional equations. 397-411 2015 260 Appl. Math. Comput. https://doi.org/10.1016/j.amc.2015.03.098 db/journals/amc/amc260.html#ChenL15

Yue Wang Jin Luo Shiying Hao Haihua Xu Andrew Young Shin Bo Jin Rui Liu 0009 Xiaohong Deng Lijuan Wang Le Zheng Yifan Zhao Chunqing Zhu Zhongkai Hu Changlin Fu Yanpeng Hao Yingzhen Zhao Yunliang Jiang Dorothy Dai Devore S. Culver Shaun T. Alfreds Todd Rogow Frank Stearns Karl G. Sylvester Eric Widen Xuefeng Bruce Ling NLP based congestive heart failure case finding: A prospective analysis on statewide electronic medical records. 1039-1047 2015 84 Int. J. Medical Informatics 12 https://doi.org/10.1016/j.ijmedinf.2015.06.007 https://www.wikidata.org/entity/Q40645542 db/journals/ijmi/ijmi84.html#WangLHXSJLDWZZZ15

Meiyi Li Tao Zeng 0003 Rui Liu 0009 Luonan Chen Detecting tissue-specific early warning signals for complex diseases based on dynamical network biomarkers: study of type 2 diabetes by cross-tissue analysis. 229-243 2014 15 Briefings Bioinform. 2 https://doi.org/10.1093/bib/bbt027 https://www.wikidata.org/entity/Q51225674 db/journals/bib/bib15.html#LiZLC14

Rui Liu 0009 Xiangtian Yu Xiaoping Liu 0002 Dong Xu 0002 Kazuyuki Aihara Luonan Chen Identifying critical transitions of complex diseases based on a single sample. 1579-1586 2014 30 Bioinform. 11 https://doi.org/10.1093/bioinformatics/btu084 https://www.wikidata.org/entity/Q87275958 db/journals/bioinformatics/bioinformatics30.html#LiuYLXAC14

Changlin Fu Zhou Tan Rui Liu 0009 Shiying Hao Zhen Li Pei Chen Taichang Jang Milton Merchant John C. Whitin Oxford Wang Minyi Guo Harvey J. Cohen Lawrence Recht Xuefeng Bruce Ling CSF protein dynamic driver network: At the crossroads of brain tumorigenesis. 168-175 2014 BIBM https://doi.org/10.1109/BIBM.2014.6999147 https://doi.ieeecomputersociety.org/10.1109/BIBM.2014.6999147 conf/bibm/2014 db/conf/bibm/bibm2014.html#FuTLHLCJMWWGCRL14

Rui Liu 0009 Weifang Yan Some Common Expressions and New bifurcation Phenomena for nonlinear Waves in a generalized mKdV equation. 2013 23 Int. J. Bifurc. Chaos 3 https://doi.org/10.1142/S0218127413300073 db/journals/ijbc/ijbc23.html#LiuY13

Rui Liu 0009 Kazuyuki Aihara Luonan Chen Dynamical network biomarkers for identifying critical transitions and their driving networks of biologic processes. 105-114 2013 1 Quant. Biol. 2 https://doi.org/10.1007/s40484-013-0008-0 db/journals/quanbio/quanbio1.html#LiuAC13

Rui Liu 0009 Coexistence of Multifarious Exact Nonlinear Wave Solutions for Generalized B-equation. 3193-3208 2010 20 Int. J. Bifurc. Chaos 10 https://doi.org/10.1142/S0218127410027623 db/journals/ijbc/ijbc20.html#Liu10

Kazuyuki Aihara Shaun T. Alfreds Xiao Chang Luonan Chen Pei Chen Yingqi Chen Yiren Chen Harvey J. Cohen Devore S. Culver Dorothy Dai Xiaohong Deng Dandan Ding Changlin Fu Minyi Guo Chongyin Han Shiying Hao Yanpeng Hao Zhongkai Hu Taichang Jang Yunliang Jiang Bo Jin Meiyi Li Yongjun Li Zhen Li Zongguang Li Xuefeng Bruce Ling Juntan Liu Xiaoping Liu 0002 Jin Luo Milton Merchant Hao Peng 0003 Lawrence Recht Todd Rogow Andrew Young Shin Frank Stearns Karl G. Sylvester Zhou Tan Hui Tang Lijuan Wang Oxford Wang Yangkai Wang Yue Wang John C. Whitin Eric Widen Dong Xu 0002 Haihua Xu Weifang Yan Jiaopeng Yang Kun Yang Xiangtian Yu Tao Zeng 0003 Xuhang Zhang Yifan Zhao Yingzhen Zhao Le Zheng Jiayuan Zhong Chunqing Zhu

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