1. Statistics: For function estimation and functional data analysis, we have extended the fundamental Gauss-Markov theorem for nonparametric mixed-effects models, which leads to the best linear unbiased prediction (BLUP) and a nonlinear estimator for wavelet shrinkage with generalized cross validation (GCV). In survival analysis, we have developed an inference method for Q-Q plots for right censored data by bootstrap and transformation models for interval scale grouped data. For reliability studies, we have studied the Bayesian analysis of fault location and system performance. We also apply these skills to the analysis of medical data that often contain censoyvvred or grouped data. We will analyze and integrate different types of data by developing statistical models and methodologies for advanced data mining and machine learning with the power of statistical inference and computation algorithms.
2. Biomedical image analysis: We have investigated the reconstruction and correction problems in positron emission tomography (PET) with the related but incomplete information by fast iterative methods and statistical analysis with research groups in this field. This had boosted our further interdisciplinary studies on ultrasound and dynamic images in a series of studies. In the studies of echo textures in ultrasound images, an early vision model by Gabor filter banks that mimics human vision was proposed. Different segmentation and dimension reduction methods are proposed studied and compared for static and dynamic images. Computer assistant diagnosis (CAD) for liver diseases by ultrasound images is investigated as well. These techniques of image analysis are further developed to analyze microarray images and the other types of images.
3. Bioinformatics: We have studied the associated analysis problems on the biological data generated by international and local research groups. The research studies involve the statistical and network analysis of high throughput data for sequence data, microarray data, protein-protein interaction, pathway reconstruction, molecular evolution and medical data. Further studies related to these research topics are under intensive developments with collaborators in a wide spectrum of interdisciplinary studies and ongoing projects.
1. Proposed a method to maximum likelihood estimation of continuous time stochastic volatility models with partially observed GARCH.
2. Proposed a network based approach for measuring the collective correlation of a large number of stocks. With a sample of S&P 500 components the index is closely related to the CBOE VIX and can be used as an alternative risk measure.
1. Derive a correspondence relationship between image segmentation problem and network community detection problem and design an efficient framework based on spectral matting to realize the modularity optimization.
2. Propose an automatic framework to deal with the neuroimages segmentation and crosstalk problem for Brainbow/Flybow images.
3. Propose an analytical model for evaluating the transmission performance of wireless radio resource allocation algorithms.
4. Propose an opportunity indicator for wireless packet scheduling controls.
5. Propose a handover control method to UMTS radio access system and file a patent with MediaTek incorporation.
1. Developed a generalized Green’s theorem-based theory using Kramers-Kronig relations to trace and predict the electron transport phenomena within on-chip polygonal spiral micromachining inductors in views of solid theory.
2. Developed a multiple energy coupled theory and a Green’s theorem-based algorithm that were established for thermal analysis and can well predict the most probable path of thermal flow of 3D optical stacking structures and 3D-nanoelectronic circuit systems.
3. To study the proximity effect of localized ELF-EMF (Extremely Low Frequency Electromagnetic Field) on the growth of in-vitro Cells, a lab-on-a-chip scheme and associated dynamical model are established for the observation and prediction of interference of cellular signal transduction processes. A mechanism of cell growth prohibition was then proposed and verified experimentally.
4. Fully elucidated and developed a corresponding physical response model considering with squeeze air damping effects for clarifying auditory dynamical behaviors of the conventional central-supported diaphragm and then a new hybridizing biomimetic microphone using a clover-stem-like gimbal floating support and fly-ear was presented theoretically and experimentally.