Gi-Ren Liu
girenliu@gmail.com
Department of Mathematics, National Cheng Kung University, Taiwan
RESEARCH INTERESTS
Stochastic modeling for medical signals, Time-frequency analysis, Probabilistic models in machine learning, Central limit theorems
EMPLOYMENT
Started in 2020 National Cheng Kung University, Tainan
Department of Mathematics
Associate Professor
2016–2020 National Cheng Kung University, Tainan
Department of Mathematics
Assistant Professor
2015–2016 National Tsing Hua University, Hsinchu
Department of Mathematics
Specially Appointed Assistant Professor
2014–2015 University of California, Davis, USA
Department of Mathematics
Postdoctoral Fellow
2013–2014 National Yang Ming Chiao Tung University, Hsinchu
Department of Computer Science
Postdoctoral Fellow
EDUCATION
2008–2013 National Taiwan University, Taipei, Ph.D. in Mathematics.
GRANTS FROM NATIONAL SCIENCE AND TECHNOLOGY COUNCIL (NSTC)
2021 - 2024 Neural Activation Scattering Transform and its Applications on Medical Signal Processing
2019 - 2021 Heterogeneous Sensor Data Fusion based on Hidden Markov Models
2017 - 2019 Diffusion Map with Application to Sleep Stage Assessment
2015 - 2017 Performance Analysis of Phase Retrieval Algorithms
HONORS
2023/08 - 2025/08 National Center for Theoretical Science (NCTS) Center Scientists
2021/08 - 2024/07 Outstanding Young Scholars Research Project sponsored by NSTC
2020/08 - 2022/08 National Center for Theoretical Science (NCTS) Center Scientists
Publications
Preprint:
Gi-Ren Liu, Yuan-Chung Sheu and Hau-Tieng Wu. (2023+). Gaussian approximation for the moving averaged modulus wavelet transform and its variants. arXiv e-prints, 36 pages. arXiv: 2301.01540
Su, Yan-Wei, Gi-Ren Liu, Yuan-Chung Sheu, and Hau-Tieng Wu. (2023+). Ridge detection for nonstationary multicomponent signals with time-varying wave-shape functions and its applications. arXiv e-prints arXiv:2309.06673
Gi-Ren Liu. (2023+). Convergence rate analysis in limit theorems for nonlinear functionals of the second Wiener chaos. arXiv e-prints arXiv:2312.05882
Published/To appear:
[19] Gi-Ren Liu, Yuan-Chung Sheu and Hau-Tieng Wu. (2023). When scattering transform meets non-Gaussian random processes, a double scaling limit result. (Accepted by Bernoulli). arXiv: 2112.13475
[18] Xin-Xue Lin, Phone Lin, En-Hau Yeh, Gi-Ren Liu, Wan-Ching Lien and Yuguang Fang. (2022). RAPIDEST: A Framework for Obstructive Sleep Apnea Detection. IEEE Transactions on Neural Systems and Rehabilitation Engineering 31, 387-397. Link
[17] Gi-Ren Liu, Yuan-Chung Sheu and Hau-Tieng Wu. (2023). Central and non-central limit theorems arising from the scattering transform and its neural activation generalization. SIAM Journal on Mathematical Analysis 55(2), 1170-1213 Link (early version, 53 pages, arXiv:2011.10801).
[16] Gi-Ren Liu, Yuan-Chung Sheu and Hau-Tieng Wu. (2022). Asymptotic Analysis of Higher-order Scattering Transform of Gaussian Processes. Electronic Journal of Probability 27, 1-27. Link
[15] Gi-Ren Liu, Ting-Yu Lin, Hau-Tieng Wu, Yuan-Chung Sheu, Ching-Lung Liu, Wen-Te Liu, Mei-Chen Yang, Yung-Lun Ni, Kun-Ta Chou, Chao-Hsien Chen, Dean Wu, Chou-Chin Lan, Kuo-Liang Chiu, Hwa-Yen Chiu, Yu-Lun Lo. (2021). Large Scale Assessment of Consistency in Sleep Stage Scoring Rules among Multiple Sleep Centers Using an Interpretable Machine Learning Algorithm. Journal of Clinical Sleep Medicine 17, 159-166. Link
[14] Gi-Ren Liu, Caroline Lustenberger, Yu-Lun Lo, Wen-Te Liu, Yuan-Chung Sheu and Hau-Tieng Wu. (2020). Save Muscle Information – Unfiltered EEG Signal Helps Distinguish Sleep Stages. Sensors 20, 1-12. Link
[13] Gi-Ren Liu, Yu-Lun Lo, John Malik, Yuan-Chung Sheu and Hau-Tieng Wu. (2020). Diffuse to fuse EEG spectra - intrinsic geometry of sleep dynamics for classification. Biomedical Signal Processing and Control 55, 1-13. Link
[12] Gi-Ren Liu, Phone Lin and Mohamad Khattar Awad. (2018). Modeling Energy Saving Mechanism for Green Routers. IEEE Transactions on Green Communications and Networking 2(3), 817-829. Link
[11] Pengwen Chen, Albert Fannjiang and Gi-Ren Liu. (2018). Phase retrieval with one or two diffraction patterns by alternating projection with null initialization. Journal of Fourier Analysis and Applications 24, 719-758. Link
[10] Pengwen Chen, Albert Fannjiang and Gi-Ren Liu. (2017) Phase retrieval by linear algebra. SIAM Journal on Matrix Analysis and Applications 38, 854-868. Link
[9] Mohamad Khattar Awad, Phone Lin and Gi-Ren Liu. (2017). Distributed and Load Adaptive Energy Management Algorithm for Ethernet Green Routers. Journal of Internet Technology 19(3), 781-794. Link
[8] Gi-Ren Liu and Narn-Rueih Shieh. (2017). Multi-Scaling Limits for Time-Fractional Relativistic Diffusion Equations with Random Initial Data. Theory of Probability and Mathematical Statistics 95, 109-130. Link
[7] Gi-Ren Liu, Phone Lin and Yi-Bing Lin. (2016). Modeling Mobile Ticket Dispenser System with Impatient Clerk. IEEE Transactions on Vehicular Technology 65, 9931-9941. Link
[6] Gi-Ren Liu. (2015). Stochastic Wave Propagation in Maxwell’s Equations. Journal of Statistical Physics 158, 1126-1146. Link
[5] Gi-Ren Liu, Phone Lin, Yuguang Fang and Yi-Bing Lin. (2015) Optimal threshold policy for in-home smart grid with renewable generation integration. IEEE Transactions on Parallel and Distributed Systems 26, 1096-1105. Link
[4] Gi-Ren Liu and Narn-Rueih Shieh. (2015). Multi-scaling limits for relativistic diffusion equations with random initial data. Transactions of the American Mathematical Society 367, 3423-3446. Link
[3] Gi-Ren Liu and Narn-Rueih Shieh. (2011). Homogenization of fractional kinetic equations with random initial data. Electronic Journal of Probability 16, 962-980. Link
[2] Gi-Ren Liu and Narn-Rueih Shieh. (2010). Scaling limits for time-fractional diffusion-wave systems with random initial data. Stochastics and Dynamics 10, 1-35. Link
[1] Gi-Ren Liu and Narn-Rueih Shieh. (2010). Scaling limits for some P.D.E. systems with random initial conditions. Stochastic Analysis and Applications 28, 505-522. Link
Book/Chapter:
[3] Gi-Ren Liu, Yu-Lun Lo, Yuan-Chung Sheu and Hau-Tieng Wu. (2020). Explore intrinsic geometry of sleep dynamics and predict sleep stage by unsupervised learning techniques. Harmonic Analysis and Applications, Springer, 279-324. Link
[2] Tal Shnitzer, Roy R. Lederman, Gi-Ren Liu, Ronen Talmon and Hau-Tieng Wu. (2019) Diffusion Operators for Multimodal Data Analysis. Handbook of Numerical Analysis: Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2, Volume 20, 1-39. Link
[1] Gi-Ren Liu. (2014). Partial Differential Equations with Random Initial Data. Scholar’s Press, 148 pages. Link
SELECTED TALKS
2023 10th International Congress on Industrial and Applied Mathematics (ICIAM) at Waseda University, Tokyo, Japan.
2023 Mathematics for Signal Processing and Applications in Geophysics and Other Fields in Rome, Italy.
2022 Chung Hsing Workshop in Probability and Related Fields.
2022 Taiwan Mathematical Society Annual Meeting in Hsinchu.
2021 Dong Hwa Workshop in Probability and Related Fields.
2019 Taiwan Mathematical Society Annual Meeting in Taichung.
2019 The 12th Mathematical Society of Japan, Seasonal Institute (MSJ-SI).
Topic: Stochastic Analysis, Random Fields and Integrable Probability.
2018 Symposium on Molecular Imaging, Biorhythms, and Quantitative Science in Biomedicine and Public Health in Institute of Statistical Science, Academia Sinica.
2018 年統計學術研討會暨中央大學統計所 40 週年國際學術研討會
2017 Taiwan-Japan Joint Workshop on Inverse Problems in Kanazawa.
2017 Taiwan Mathematical Society Annual Meeting in Chiayi.
2016 NCTS Workshop on Computational Mathematics for Young Researchers in Taipei.
2016 Spring Probability Workshop at the Institute of Mathematics, Academica Sinica, Taipei.
2015 Japan-Taiwan Joint Workshop on Inverse Problem in Taipei.
2015 International Mathematical Meeting and Annual Meeting of the Taiwanese Mathematical Society in Kaohsiung.
TEACHING
National Cheng Kung University, Tainan
Introduction of Probability: 2016, 2017, 2018, 2019, 2020.
Probability: 2018, 2023.
Stochastic Processes: 2018, 2021.
Multiscale Analysis of Random Processes: 2020.
Calculus: 2016, 2017, 2019, 2021, 2022.
National Tsing Hua University, Hsinchu
Stochastic Calculus: 2015, Fall.
Financial Mathematics: 2016, Spring.
National Center for Theoretical Sciences, Taipei
Central Limit Theorems and Stein’s Method for Gaussian Approximations, 2023/07/03-2023/08/11.
Data Science with Medical Applications, 2021/10-2022/07.
Random Walk and Discrete Heat Equation, 2021/7/22-2021/8/5.
Scattering Transform and its Applications, 2020/07/20~2020/08/28.
Hidden Markov Models and its Applications, 2019/07/01~2019/08/09.
Diffusion Map and its Applications in the Automatic Sleep Stage Scoring, 2018/07/23~2018/08/24.
Performance Evaluation of Phase Retrieval Algorithm, 2017/07/12~2017/08/20.
DEPARTMENT SERVICE
National Cheng Kung University, Tainan
Design of the Qualification Test: 2016, 2020, 2021.
Bachelor's Degree-Admission Committee: 2017.
Master's Degree-Admission Committee: 2020.
Advisor of Graduated Students: 2018 – present.
National Tsing Hua University, Hsinchu
Chair of Departmental Colloquium, 2015, Fall.
CONFERENCE ORGANIZATIONAL COMMITTEE
2022 Winter Workshop on Probability and Related Fields, NCTS.
2021 Japan-Taiwan Joint Online Workshop on Numerical Analysis and Inverse Problems
Go to the PDF file of my curriculum vitae.