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[45] Rui Liu#, Jiayuan Zhong#, Renhao Hong, Ely Chen, Kazuyuki Aihara, Pei Chen*, Luonan Chen*. Predicting local COVID-19 outbreaks and infectious disease epidemics based on landscape network entropy. Science Bulletin, 2021. DOI:10.1016/j.scib.2021.03.0222021ScienceBulletin.pdf
[44] Jiayuan Zhong, Chongyin Han, Xuhang Zhang, Pei Chen*, Rui Liu*. SGE: Predicting cell fate commitment during early embryonic development by single-cell graph entropy. Genomics, Proteomics & Bioinformatics, 2021, in press.
[43] Rui Liu, Kazuyuki Aihara*, Luonan Chen*. Collective fluctuation implies imminent state transition -- Comment on “Dynamic and thermodynamic models of adaptation” by A.N. Gorban et al. Physics of Life Reviews, 2021, 37(2021):103–107. DOI:10.1016/j.plrev.2021.04.002 2021PLREV.pdf
[42] Kazuyuki Aihara*, Rui Liu, Keiichi Koizumi, Xiaoping Liu, Luonan Chen*. Dynamical network biomarkers: theory and applications. Gene, 2021, in press.
[41] Xuhang Zhang, Rong Xie, Zhengrong Liu, Yucong Pan, Rui Liu*, Pei Chen*. Identifying pre-outbreak signals of hand, foot and mouth disease based on landscape dynamic network marker. BMC Infectious Diseases, 2021, 21:6. DOI:10.1186/s12879-020-05709-w 2021BMC Infect Dis.pdf
[40] Pei Chen, Rui Liu*, Kazuyuki Aihara, Luonan Chen*. Autoreservoir computing for multistep ahead prediction based on the spatiotemporal information transformation. Nature Communications, 2020, 11:4568. DOI: 10.1038/s41467-020-18381-0. 2020Nat. Commun.pdf
[39] Rui Liu, Pei Chen*, Luonan Chen*. Single-sample landscape entropy reveals the imminent phase transition during disease progression. Bioinformatics, 2020, 36(5): 1522-1532. DOI:10.1093/bioinformatics/btz758 2020Bioinformatics.pdf
[38] Chongyin Han#, Jiayuan Zhong#, Jiaqi Hu, Huisheng Liu, Rui Liu*, Fei Ling*. Single-sample node entropy for molecular transition in pre-deterioration stage of cancer. Frontiers in Bioengineering and Biotechnology, 2020, 8:809. DOI:10.3389/fbioe.2020.00809 2020_Front Bioeng Biotechnol.pdf
[37] Jiayuan Zhong, Rui Liu*, Pei Chen*. Identifying critical state of complex diseases by single-sample Kullback–Leibler divergence, BMC Genomics, 2020, 21(1):87. DOI:10.1186/s12864-020-6490-7 2020BMCgenomics.pdf
[36] Pei Chen#, Shuo Li#, Wenyuan Li, Jie Ren, Fengzhu Sun, Rui Liu*, Xianghong Jasmine Zhou*. Rapid diagnosis and comprehensive bacteria profiling of sepsis based on cell-free DNA. Journal of Translational Medicine, 2020, 18:5. DOI:10.1186/s12967-019-02186-x 2020JTM.pdf
[35] Tianlong Liu, Hongyan Wen, Hao Li, Haochen Xu, Ning Xiao, Rui Liu, Luonan Chen et al. Oleic acid attenuates Ang II (Angiotensin II)-induced cardiac remodeling by inhibiting FGF23 (fibroblast growth factor 23) expression in mice. Hypertension, 2020, 75(3): 680-692. DOI:10.1161/HYPERTENSIONAHA.119.14167 2020Hypertension.pdf
[34] Jiaopeng Yang, Rui Liu, Yiren Chen. Bifurcations of solitary waves of a simple equation. International Journal of Bifurcation and Chaos, 2020, 30(09), 2050138. DOI: 10.1142/S0218127420501382 2020IJBC.pdf
[33] Zongguang Li, Rui Liu*. Blow-up solutions for a case of b-family equations. Acta Mathematica Scientia, 2020, 40B(4): 1-11. DOI:10.1007/s10473-020 2020Acta Mathematica Scientia.pdf
[32] Yingqi Chen, Kun Yang, Jialiu Xie, Rong Xie, Zhengrong Liu, Rui Liu*, Pei Chen*. Detecting the outbreak of influenza based on the shortest path of dynamic city network. PeerJ, 2020, 8: e9432. DOI:10.7717/peerj.9432 2020PeerJ.pdf
[31] Kun Yang, Jialiu Xie, Rong Xie, Yucong Pan, Rui Liu*, Pei Chen*. (2020). Real-time forecast of influenza outbreak using dynamic network marker based on minimum spanning tree. BioMed Research International, 2020, 2020:7351398, 1-11. DOI:10.1155/2020/7351398 2020BioMed Research International.pdf
[30] Zongguang Li, Rui Liu*. Bifurcations and exact solutions in a nonlinear wave equation. International Journal of Bifurcation and Chaos, 2019, 29(7):1950098. DOI:10.1142/S0218127419500986 2019IJBC.pdf
[29] Rui Liu#, Jinzeng Wang#, Masao Ukai#, Ki Sewon, Pei Chen, Yutaka Suzuki, Haiyun Wang*, Kazuyuki Aihara*, Mariko Okada-Hatakeyama*, Luonan Chen*. Hunt for the tipping point during endocrine resistance process in breast cancer by dynamic network biomarkers. Journal of Molecular Cell Biology, 2019, 11(8): 649-664. DOI:10.1093/jmcb/mjy059 2019JMCB.pdf
[28] Pei Chen#, Ely Chen#, Luonan Chen, Xianghong Jasmine Zhou*, Rui Liu*. Detecting early-warning signals of influenza outbreak based on dynamic network marker. Journal of Cellular and Molecular Medicine, 2019, 23(1): 395-404. DOI:10.1111/jcmm.13943 2019JCMM.pdf
[27] Rui Liu, Jiayuan Zhong, Xiangtian Yu, Yongjun Li, Pei Chen*. Identifying critical state of complex diseases by single-sample-based hidden Markov model. Frontiers in Genetics, 2019, 10:285. DOI: 10.3389/fgene.2019.00285 2019FrontiersGenetics.pdf
[26] Pei Chen, Yongjun Li, Xiaoping Liu, Rui Liu*, Luonan Chen*. Detecting the tipping points in a three-state model of complex diseases by temporal differential networks. Journal of Translational Medicine, 2017, 15:217. DOI:10.1186/s12967-017-1320-7 2017JTM.pdf
[25] Xiaoping Liu, Xiao Chang, Rui Liu, Xiangtian Yu, Luonan Chen, Kazuyuki Aihara. Quantifying critical states of complex diseases using single-sample dynamic network biomarkers. PLoS Computational Biology, 2017, 13(7): e1005633. DOI:10.1371/journal.pcbi.1005633 2017PLOS CB.pdf
[24] Bo Jin#, Rui Liu#, Shiying Hao, et al. Defining and characterizing the critical transition state prior to the type 2 diabetes disease. PLoS ONE, 2017, 12(7): e0180937. DOI:10.1371/journal.pone.0180937 2017PLOS ONE.pdf
[23] Pei Chen, Rui Liu, Yongjun Li, Luonan Chen. Detecting critical state before phase transition of complex biological systems by hidden Markov model. Bioinformatics, 2016, 32(14): 2143-2150. DOI:10.1093/bioinformatics/btw154 2016Bioinformatics.pdf
[22] Yiren Chen, Weibo Ye, Rui Liu*. The explicit periodic wave solutions and their limit forms for a generalized b-equation. Acta Mathematicae Applicatae Sinica, 2016, 32(2): 513-528. DOI:10.1007/s10255-016-0581-x 2016AMAS.pdf
[21] Pei Chen, Rui Liu, Kazuyuki Aihara, Luonan Chen. Identifying critical differentiation state of MCF-7 cells for breast cancer by dynamical network biomarkers. Frontiers in Genetics, 2015, 6:252. DOI:10.3389/fgene.2015.00252 2015FrontiersGenetics.pdf
[20] Rui Liu, Pei Chen, Kazuyuki Aihara, Luonan Chen. Identifying early-warning signals of critical transitions with strong noise by dynamical network markers. Scientific Reports, 2015, 5:17501. DOI:10.1038/srep17501 2015Srep.pdf
[19] Zhou Tan#, Rui Liu#, Le Zheng, et al. Cerebrospinal fluid protein dynamic driver network: At the crossroads of brain tumorigenesis. Methods, 2015, 83: 36-43. DOI:10.1016/j. ymeth.2015.05.004 2015Methods.pdf
[18] Yiren Chen, Rui Liu*. Some new nonlinear wave solutions for two (3+1)-dimensional equations. Applied Mathematics and Computation, 2015, 260: 397-411. DOI:10.1016/j.amc.2015.03.098 2015AMC.pdf
[17] Weifang Yan, Rui Liu. Traveling wave solutions in n-dimensional delayed nonlocal diffusion system with mixed quasimonotonicity. Analysis and Applications, 2015, 13(1): 23-43. DOI:10.1142/S0219530514500055 2015A&A.pdf
[16] Yue Wang, Jin Luo, Shiying Hao, Haihua Xu, Andrew Young Shin, Bo Jin, Rui Liu et al. NLP based congestive heart failure case finding: A prospective analysis on statewide electronic medical records. International journal of medical informatics, 2015, 84(12): 1039-1047. DOI:10.1016/j.ijmedinf.2015.06.007 2015InternationalJournalofMedicalInformatics.pdf
[15] Rui Liu, Xiangtian Yu, Xiaoping Liu, Dong Xu, Kazuyuki Aihara, Luonan Chen. Identifying critical transitions of complex diseases based on a single sample. Bioinformatics, 2014, 30(11): 1579-1586. DOI:10.1093/bioinformatics/btu084 2014Bioinformatics.pdf
[14] Rui Liu, Xiangdong Wang, Kazuyuki Aihara, Luonan Chen. Early diagnosis of complex diseases by molecular biomarkers, network biomarkers, and dynamical network biomarkers. Medicinal Research Reviews, 2014, 34(3): 455-478. DOI:10.1002/med.21293 2014MRR.pdf
[13] Meiyi Li, Tao Zeng, Rui Liu, 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. Briefings in Bioinformatics, 2014, 15(2): 229-243. DOI:10.1093/bib/bbt027 2014BIB.pdf
[12] Tao Zeng, Wanwei Zhang, Xiangtian Yu, Xiaoping Liu, Meiyi Li, Rui Liu, Luonan Chen. Edge biomarkers for classification and prediction of phenotypes. Science China Life Sciences, 2014, 57(11): 1103-1114. DOI:10.1007/s11427-014-4757-4 2014ScienceChina.pdf
[11] Tao Zeng, Chuanchao Zhang, Wanwei Zhang, Rui Liu, Juan Liu, Luonan Chen. Deciphering early development of complex diseases by progressive module network. Methods, 2014, 67(3): 334-343. DOI:10.1016/j.ymeth.2014.01.021 2014Methods.pdf
[10] Xiaoping Liu#, Rui Liu#, Xingming Zhao, Luonan Chen. Detecting early-warning signals of type 1 diabetes and its leading biomolecular networks by dynamical network biomarkers. BMC Medical Genomics, 2013, S6. DOI:10.1186/1755-8794-6-S2-S8 2013BMC Medic.pdf
[9] Rui Liu, Weifang Yan. Some common expressions and new bifurcation phenomena for nonlinear waves in a generalized mKdV equation. International Journal of Bifurcation and Chaos, 2013, 23(3): 13330007. DOI:10.1142/S0218127413300073 2013IJBC.pdf
[8] Rui Liu. The explicit nonlinear wave solutions of the generalized b-equation. Communications on Pure and Applied Analysis, 2013, 12(2): 1029-1047. DOI:10.3934/cpaa.2013.12.1029 2013CPAA.pdf
[7] Rui Liu, Kazuyuki Aihara, Luonan Chen. Dynamical network biomarkers for identifying critical transitions and their driving networks of biologic processes. Quantitative Biology, 2013, 1(2):105-14. DOI:10.1007/s40484-013-0008-0 2013QB.pdf
[6] Weifang Yan, Rui Liu. Existence and critical speed of traveling wave fronts in a modified vector disease model with distributed delay. Journal of Dynamical and Control Systems, 2012, 18(3): 355–378. DOI:10.1007/s10883-012-9148-1 2012JDCS.pdf
[5] Luonan Chen, Rui Liu, Zhi-Ping Liu, Meiyi Li, Kazuyuki Aihara. Detecting early-warning signals for sudden deterioration of complex diseases by dynamical network biomarkers. Scientific Reports, 2012, 2:342. DOI:10.1038/srep00342 2012Srep.pdf
[4] Rui Liu, Meiyi Li, Zhi-Ping Liu, Jiarui Wu, Luonan Chen, Kazuyuki Aihara. Identifying critical transitions and their leading biomolecular networks in complex diseases. Scientific Reports, 2012, 2:813. DOI:10.1038/srep00813 2012Srep_L.pdf
[3] Rui Liu. Coexistence of multifarious exact nonlinear wave solutions for generalized b-equation. International Journal of Bifurcation and Chaos, 2010, 20(10): 3193-3208. DOI:10.1142/S0218127410027623 2010IJBC.pdf
[2] Rui Liu. Some new results on explicit traveling wave solutions of k(m, n) equation. Discrete and Continuous Dynamical Systems-Series B, 2010, 13(3): 633-646. DOI:10.3934/dcdsb.2010.13.633 2010DCDS-B.pdf
[1] Rui Liu. Several new types of solitary wave solutions for the generalized Camassa- Holm-Degasperis-Procesi equation. Communications on Pure and Applied Analysis, 2010, 9(1): 77-90. DOI:10.3934/cpaa.2010.9.77 2010CPAA.pdf