Publications

(Link: the official websites of journals)

[20] Yan-Wei Su, Chia-Cheng Hao, Gi-Ren Liu, Yuan-Chung Sheu and Hau-Tieng Wu. (2024). Reconsider photoplethysmogram signal quality assessment in the free living environment. Physiological Measurement 45(6), 06NT01. Link

[19] Gi-Ren Liu, Yuan-Chung Sheu and Hau-Tieng Wu. (2024). When scattering transform meets non-Gaussian random processes, a double scaling limit result. Bernoulli 30, 2346-2371. Link

[18] Xin-Xue Lin, Phone Lin, En-Hau Yeh, Gi-Ren Liu, Wan-Ching Lien and Yuguang Fang. (2023). 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 Link2

[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 Link2

[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 Link2

[1] Gi-Ren Liu. (2014). Partial Differential Equations with Random Initial Data. Scholar’s Press, 148 pages. Link