Office: Room 385 in the Zhihua Building (New Math Building), Peking University.
伊人直播
智华楼(新数学楼)385室
Tel: 86-10-62757592
Fax: 86-10-62751801
Email: tieli{at} math {dot} pku {dot} edu {dot} cn
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Algorithmic and Theoretical Studies for scRNA-seq Data Analysis: scRNA-seq data analysis provides a great
platform for applied mathematicians, in which the stochastic dynamics, statistical data analysis and machine learning can be integrated to boost
the understanding of cell developments. In this field, we collaborate with the biologists like Prof. Fuchou Tang (PKU), and the applied mathematicians
like Prof. Luonan Chen (CAS), Qing Nie (UC Irvine), and Xiaojie Qiu (MIT) et al.
- Energy landscape decomposition for cell differentiation with proliferation effect, with Jifan Shi, Kazuyuki Aihara, and Luonan Chen, National Science Review, 9 (2022), nwac116.
- Integrating single-cell datasets with ambiguous batch information by incorporating molecular network features, with Ji Dong, Peijie Zhou, Yichong Wu, Wendong Wang, Yidong Chen, Xin Zhou, Haoling Xie, Jiansen Lu, Xiannian Zhang, Lu Wen, Wei Fu, and Fuchou Tang, Briefings in Bioinformatics, 23 (2022), bbab366.
- On the mathematics of RNA velocity I: theoretical analysis, with Jifan Shi, Yichong Wu, and Peijie Zhou, CSIAM Trans. Appl. Math. 2 (2021), 1-55.
- Dissecting transition cells from single-cell transcriptome data through multiscale stochastic dynamics, with Peijie Zhou, Shuxiong Wang, Qing Nie, Nature Comm., 12 (2021), 5609.
- Quantifying pluripotency landscape of cell differentiation from scRNA-seq data by continuous birth-death process, with Jifan Shi, Luonan Chen, and Aihara, PLoS Comp. Biol. 15 (2019), e1007488.
- Quantifying Waddington’s epigenetic landscape: a comparison of single-cell potency measures, with Jifan Shi, Andrew E. Teschendorff, Weiyan Chen, and Luonan Chen, Briefings in Bioinformatics 21 (2020), 248-261.
Stochastic Dynamics and Data Analysis in Life Sciences: We are also trying to develop theory and
algorithms for the stochastic problems in life sciences, especially the chemical reaction kinetics and genetic interactions in the cellular level. It is
surprising that the stochastics can play so important role in life sciences. In this field, we collaborate with the physicists like Prof. Qi Ouyang,
Fangting Li (PKU), and the applied mathematicians like Prof. Luonan Chen (CAS) et al.
- Uncovering the cell fate decision in lysis-lysogeny transition and stem cell development via Markov state modeling, with Xiaoguang Li, Tongkai Li, and Chunhe Li, J. Chem. Phys., 155 (2021), 245101.
- Stochasticity triggers activation of the S-phase checkpoint pathway in budding yeast, with Peijie Zhou, Xin Gao, Xiaoli Li, Linxi Li, Caoyuan Niu, Qi Ouyang, Huiqiang Lou, and Fangting Li, Phys. Rev. X 11 (2021), 011004.
- No-oscillation theorem for the transient dynamics of the linear signal transduction pathway and beyond, with Tongkai Li and Shaoying Lu, Discret. Contin. Dyn. Syst. B 25 (2020), 2749-2774.
- Differential network inference via the fused D-trace loss with cross variables, with Yichong Wu, Xiaoping Liu, and Luonan Chen, Electr. J. Stat. 14 (2020), 1269-1301.
- Quantifying direct dependencies in biological network by multiscale association analysis, with Jifan Shi, Juan Zhao, and Luonan Chen, IEEE Trans. Comput. Biol. Bioinform. 17 (2020), 449-458.
- Detecting direct associations in a network by information theoretic approaches, with Jifan Shi, Juan Zhao, and Luonan Chen, Sci. China Math. 62 (2019), 823-838.
- Large deviations for two-scale chemical kinetic processes, with Feng Lin, Comm. Math. Sci. 15 (2017), 123-163.
- Two-scale large deviations for chemical reaction kinetics through second quantization path integral, with Feng Lin, J. Phys. A: Math. Theor. 49 (2016), 135204.
- Construction of the landscape for multi-stable systems: Potential landscape, quasi-potential, A-type integral and beyond, with Peijie Zhou, J. Chem. Phys. 144 (2016), 094109.
- Energy landscape reveals that the budding yeast cell cycle is a robust and adaptive multi-stage process, with Cheng Lv, Xiaoguang Li and Fangting Li, PLoS Comp. Biol. 11 (2015), e1004156. SI
- Constructing the energy landscape for genetic switching system driven by intrinsic noise, with Cheng Lv, Xiaoguang Li and Fangting Li, PLoS One 9 (2014), e88167. SI
- Highly accurate tau-leaping methods for simulating chemically
reacting systems, with Yucheng Hu, J. Chem. Phys 130 (2009), 124109.
- Analysis of explicit tau-leaping schemes for simulating chemically
reacting systems, SIAM Multi. Mod. Simul. 6 (2007), 417-436.
Other Selected Publications
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Below are some unsorted selected publications from my research. It is a bit diverse. You can feel my taste, and find my growth path from these papers.
- Transition path theory for Langevin dynamics on manifolds: optimal control and data-driven solver, with Yuan Gao, Xiaoguang Li, and Jianguo Liu, SIAM Multi. Model. Simul. 21 (2023), 1-33.
- Gamma-Limit of the Onsager-Machlup Functional on the Space of Curves, with Xiaoguang Li, SIAM J. Math. Anal. 53 (2021), 1-31.
- The graph limit of the minimizer of the Onsager-Machlup functional and its computation, with Qiang Du, Xiaoguang Li and Weiqing Ren, Sci. China Math. 64 (2021), 239-280.
- Analysis of the closure approximation for a class of stochastic differential equations, with Yunfeng Cai, Jiushu Shao and Zhiming Wang, Numer. Math. Theor. Meth. Appl. 10 (2017), 299-330.
- Finding transition pathways on manifolds, with Xiaoguang Li and Xiang Zhou, SIAM Multi. Model. Simul. 14 (2016), 173-206.
- Towards a critical transition theory under different temporal scales and noise strengths, with Jifan Shi and Luonan Chen, Phys. Rev. E 93 (2016), 032137.
- Adiabatic elimination for systems with inertia driven by compound Poisson colored noise, with Bin Min and Zhiming Wang, Phys. Rev. E 89 (2014), 022144.
- Marcus canonical integral for non-Gaussian processes and its computation: Pathwise simulation and tau-leaping algorithm, with Bin Min and Zhiming Wang, J. Chem. Phys. 138 (2013), 104118.
- Nucleation rate calculations for the phase transition of diblock copolymers under stochastic Cahn-Hilliard dynamics, with Wei Zhang and Pingwen Zhang, SIAM Multi. Model. Simul. 11 (2013), 385-409.
- Transport in weak dynamic disorder: a unified theory, with Bin Min, Phys. Rev. E 88 (2013), 052140.
- Numerical study for the nucleation of one-dimensional stochastic Cahn-Hilliard dynamics, with Wei Zhang and Pingwen Zhang, Comm. Math. Sci. 10 (2012), 1105-1132.
- Subdiffusive spreading of a Bose-Einstein condensate in random potentials, with Weizhu Bao, Bin Min, and M. Rosenkranz, Phys. Rev. A 86 (2012), 053612.
- Localized basis of eigen-subspaces and operator compression, with Weinan E and Jianfeng Lu, Proc. Nat. Acad. Sci. USA, 107 (2010), 1273.
- Probabilistic framework for network partition, with Weinan E and Jian Liu, Phys. Rev. E 80 (2009), 026106.
- Optimal partition and effective dynamics of complex networks, with Weinan E and Eric Vanden-Eijnden, Proc. Nat. Acad. Sci. USA, 105 (2008), 7907-7912. SI
- S-ROCK methods for stiff Ito SDEs,
with Assyr Abdulle, Comm. Math. Sci. 6 (2008), 845-868.
- Mathematical analysis of multiscale models of complex fluids, with Pingwen Zhang, Comm. Math. Sci. 5 (2007), 1-51.
- On the Poisson approximation for photon distribution for
faint lasers, with Yucheng Hu, Xiang Peng and Hong Guo, Phys. Lett. A, 367 (2007), 173-176.
- Local existence for the dumbbell model of
polymeric fluids, with Hui Zhang and Pingwen Zhang, Comm. PDE, 29 (2004), 903-923.
- Well-posedness for the dumbbell model of polymeric fluids, with Weinan E and Pingwen Zhang, Comm. Math. Phys. 248 (2004), 409-427.
- Stochastic models of polymeric liquids at small Deborah number, with Eric Vanden-Eijnden, Pingwen Zhang, and Weinan E, J. Non-Newtonian Fluid Mech. 121 (2004), 117-125.
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Postdocs: Wanted!!!
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We have funding for postdoc positions. If you have interests to perform research in stochastic modeling and computations, e.g. mathematical life sciences, machine learning, numerical methods for SDEs, applications in rare events, etc. Please send your CV and application letter to me directly.
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Grants
- NSFC, grant 10401004, 2005.1-2007.12
- NSFC, grant 20490222, 2005.1-2008.12
- MST, grant 2005CB321704, 2005.11-2010.11
- NSFC, grant 10871010, 2009.1-2011.12
- NSFC, grant 11171009, 2012.1-2015.12
- Major Program of NNSFC, grant 91130005, 2012.1-2015.12
- NSFC, grant 11222114, 2013.1-2015.12
- NSFC, grant 11421101, Creative group
- Major Program of NNSFC, grant 91530322, 2016.1-2018.12
- NSFC, grant 11825102, 2019.01-2023.12
- National Key R&D Program of China, grant 2021YFA1003301, 2022.05-2026.04
- NSFC, grant 12288101, 2023.01-2027.12
Current Members
- Yue Zhao, PhD student
- Yi Zeng, PhD student
- Mingguang Han, PhD student
- Qiangwei Peng, PhD student
- Zichen Liu, PhD student
- Zhaoqi Liu, PhD student
- Zhenyi Zhang, PhD student
- Xu Zhu, PhD student
- Yizhuo Wang, Master student
Former Students
- Xiang Zhou, Master (co-supervise with Professor Pingwen Zhang), currently Associate Professor in City University of Hongkong
- Yan Ding, Ph.D (co-supervise with Professor Pingwen Zhang), currently
in China Everbright Bank
- Yibiao Wu, Master (co-supervise with Professor Pingwen Zhang), currently
in Ping An Insurance Company of China
- Jing Huang, Master 2009 (co-supervise with Professor Pingwen Zhang), currently
in Baidu
- Dajiang Tao, Master 2009, currently in IBM
- Yucheng Hu, Ph.D 2010, currently Associate Professor in Capital Normal University
- Jinlong Wu, Ph.D 2010 (co-supervise
with Professor Weinan E), currently in Shiji Jiayuan
- Rensheng Zhu, Master 2010
- Jian Liu, PhD 2011 (co-supervise with Professor Weinan E), currently in PICC
- Wei Zhang, PhD 2012 (co-supervise with Professor Pingwen Zhang), currently PostDoc in Freie University of Berlin
- Bin Min, Ph.D 2013, currently PI in National Lab at Lingang, Shanghai
- Ping Qin, Master 2013, currently in Douban
- Sisi Wang, Master 2015, currently in Renda Fuzhong
- Xiaoguang Li, Ph.D 2016, currently Assistant Professor in Hunan Normal University
- Ye Chen, Ph.D 2016, currently in Huatai Securities
- Zhiming Wang, Ph.D 2016, currently in JPMorgan Chase & Co.
- Feng Lin, Ph.D 2016, currently in Huawei
- Fan Yao, Master 2016, currently in Talking Data
- Chongning Liao, Master 2016
- Jifan Shi, PhD 2018, currently Assistant Professor in Fudan University
- Peijie Zhou, PhD 2019, currently PostDoc in UC Irvine
- Haijiao Feng, Master 2019, currently in Tsinghua Fuzhong
- Ziyu Tian, Master 2020, currently in Meituan
- Jingjing Liu, PostDoc 2021, Currently in Huadian University
- Yichong Wu, PhD 2021, Currently in Huawei
- Tongkai Li, PhD 2021, Currently in Huawei
- Siqi Zheng, Master 2021, Currently in Tencent
- Yang Han, Master 2022, Currently China Telecomm Institute at Beijing
- Tiannan Xiao, PhD 2023, currently in Huawei
Last modified: Feb. 14th, 2023.
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