Research Directions & Main Achievements

2013-05-17

      The research activities in the laboratory focus on 3 directions: (1) High-performance scientific computing; (2) Information Computing; (3) Biological Computing and Control. All three research directions are under developing and already got some significant achievements:

1. High-performance scientific computing:
      As a prominent expert in Fast Calculation of Integral Equation, Professor Yuesheng Xu with together his cooperators has made outstanding works in the areas of Wavelet analysis on the invariant set, Fast Numerical Solution of Integral Equation and Differential Equations, Numerical Approximation, Adaptive signal analysis method, Super Fast Fourier analysis about the Precision of High dimensional data and High-precision image processing based on Integral Equation.
      Professor Zhongying Chen has obtained significant achievements in the area of Generalized Difference Methods for Differential Equations (Finite volume method), Approximate Solutions of Operator Equations Theory, and Wavelet Analysis and Applications. Professor Zhimin Zhang is internationally well known by his contribution on the research of Finite element superconvergence.
      Currently, the High Performance Computing Research Group in the laboratory is developing a User-friendly high-performance parallel programming platform in order to parallel implement the Numerical Methods of scientific computing.

2. Information Computing:
      Led by Professor Daren Huang and Professor Lihua Yang, our laboratory has achieved a series of characteristic research results in mathematical theory , algorithms and applications of information processing, time-frequency invariants of signals, features detection and identification, representation theory and identification algorithms of character information, digital watermarks, digital media information security methods, signal empirical patterns analysis, and the mathematical theory of Hilbert-Huang transformation.
      Professor Lixin Yan has made some notable researches in singular integral operators, theory of function spaces, functional calculus of differential operators, thermal kernel estimation and elliptic boundary value problems in nonsmooth domains; Professor Daoqing Dai has got significant progress in vision based wavelet basis construction, nonlinear face feature extraction and face recognition, and is exploring transforming computational technique which uses the quasiconformal mapping method from discrete geometry and complex analysis for providing resolution to the display of three dimensional medical images; Professor Ning Bi has obtained remarkable results in vibration response signal understanding and analysis, especially in the bridge health monitoring and diagnosis system. Working with Professor Yuesheng Xu, Haizhang Zhang who is the youngest professor in our lab has got unique achievements in the field of machine learning, especially in the area of reproducing kernel with the property of uniformly convergence, kernel theory of scaler refinement, sampling theory in reproducing kernel Hilbert spaces and reproducing kernel Banach spaces.

3. Biological Computing and Control:
      Professor Tianshou Zhou has got significant achievements in System Biology, network reconfiguration based on experimental data, and network modeling and analyzing; the project which he as one of the participants, “Anti-control of chaos, theory of Lorenz system family and its application”, was awarded the second prize of National Prize for Natural in Sciences. Professor Guo Xianping established an average optimal equation for disperse time stationary Markov decision process; this equation is considered to have solved the technological problem of status and moving process which was put forward by Kitaev and Rykov (1995), and provided optimality conditions. Professor Xueqin Wang is well known by his unique researches in Mathematical Statistics, Statistical Genetics, Biological and Computing Science and Bioinformatics, especially in Data Mining and GWA analyzing.