Sharing

On My Supervision

From My Postgraduate Students

On Postgraduate Study

My Brief Bio. and Research Summary

Ching is a Professor at the Department of Mathematics at the University of Hong Kong. Doing mathematical research is one of his hobbies and he enjoys listening to pop music. His favorite singers are Miyuki Nakajima and Teresa Teng. He was told that people can feel the meanings of their songs even though they don't understand their languages. His favorite bands are Anzen-chitai and Beyond . One can find different tastes of life from their songs. Ching was the Head of Department from 2014 to 2017. Under his leadership, the Department ranked 9th in Best Global Universities for Mathematics by U.S. News, 2014 and 20th in QS World University Rankings by Subject, 2015. He was the departmental RAE 2020 Champion from 2017 to 2019, the departments (MATH and SAAS) ranked No. 1 in overall 4* performance in Mathematics and Statistics Panel .

He finished his high school study at St. Paul's College. He got his HKCEE and HKAL. In his study at the college, he developed his interest in Mathematics. He was also encouraged to further his study in Mathematics. He then obtained his B. Sc. and M. Phil. degrees in Mathematics and applied Mathematics from the University of Hong Kong. His M. Phil. supervisor is Prof. Raymond H. CHAN. He obtained his Ph.D. degree in Systems Engineering and Engineering Management from the Chinese University of Hong Kong. His Ph.D. supervisor is Prof. Xun Yu ZHOU. He then obtained the Postgraduate Certificate in Academic Practice , a professional qualification from the University of Southampton. This is a very useful course for a new University teacher.

He has previously taught at the department of applied mathematics of Hong Kong Polytechnic University and also the department of mathematics of Hong Kong University of Science and Technology . He was a Statistician in the Census and Statistics Department of the Hong Kong SAR Government , where he worked with the shipping and cargo statistics. He learned a lot in human resource management in this post. He was a visiting post-doc fellow at the Judge Business School of the Cambridge University . He worked with Prof. Stefan SCHOLTES on traffic demand estimation problems. Before joining his Alma Mater, he was a lecturer at the Faculty of Mathematical Studies of the University of Southampton, where he taught both graduate and undergraduate courses in operations research.

Ching was awarded the Best Student Paper Prize (2nd Prize) in the Copper Mountain Conference (Colorado University and SIAM) U.S.A. (1998), the Outstanding PhD Thesis Prize in the Engineering Faculty, the Chinese University of Hong Kong, Hong Kong (1998), the Certificate of Merit in the IEEE (Hong Kong Section) Postgraduate Student Paper Contest, Hong Kong (1998), the Croucher Foundation Fellowship, Hong Kong (1999), Doris Zimmern HKU-Cambridge Hughes Hall Fellowship (2011), Doris Zimmern HKU-Cambridge Hughes Hall Visiting Fellow (2012-), HKU Overseas Fellowship Award (2013) and 2013 Higher Education Outstanding Scientific Research Output Awards (Second Prize) from the Ministry of Education in China (2014), Visiting professor of Beijing University of Chemical Technology (2016), Distinguished Alumni Award, Faculty of Engineering, The Chinese University of Hong Kong, (2017), Long Service award (15-year) (2017), Outstanding Reviewer for International Journal of Production Economics (2017), Outstanding Reviewer for Journal of Economics Dynamics and Control (2018), 2019 Higher Education Outstanding Scientific Research Output (Team Member) Awards (Second Prize), Hunan Province, China (2019), 2018-19 Outstanding Research Student Supervisor Award, the University of Hong Kong (2020), World's Top 2% Most-cited Scientists (2021,2022,2023).

His students won the following awards: [1] the Excellent Student Paper Award in the 36th International Conference on C & IE, Taiwan, (06/2006), [2] the Outstanding Research Postgraduate Student Award, HKU, (2007,2011,2012), [3] DAAD Summer School Travel Award, China, (2007), [4] Award of Postgraduate Fellowships, HKU (2009,2010,2011,2013), [5] Hong Kong Fellowship, HKSAR (2015) [6] Best Student Paper Award in the International Conference of Applied and Engineering Mathematics, The World Congress on Engineering (2009), London, U.K., [7] APBC2010 Conference Travel Award (2010), [8] Best paper award in the 4th International Joint Conference on Computational Science and Optimization, Kunming, China, (2011), [9] The IMS Workshop Travel Award, Columbia University, New York, U.S. (2011), [10] IEOR Faculty Fellowship (2011), UC Berkeley, [11] Marshall-Oliver-Rosenberger Fellowship (2012), UC Berkeley, [12] Best paper award in the 5th International Joint Conference on Computational Science and Optimization, Heilongjiang, China, (2012), [13] Best paper award in the 5th International Conference on Business Intelligence and Financial Engineering, Lanzhou, China, (2012), [14] The best paper award in the 6th IEEE International Conference on Systems Biology (ISB 2012), Xian, China, (2012), [15] Best paper award in the 7th International Joint Conference on Computational Science and Optimization, Beijing, China, (2014), [16] PIMS Student Awards (2016) [17] SIAM Student Travel Awards (2016, 2017) [18] Outstanding Paper Award in the World Conference on Business and Management (WCBM2018), Jeju Island, (2018), [19] Best Paper Award in the International Conference on Digital Health and Medical Analytics (DHA2019), Zhengzhou, China, (2019). [20] Japan Society for the Promotion of Science Fellowship (2023).

He is an author/editor of over 400 publications including over 250 journal papers, 5 edited journal special issues, 6 books and over 110 book chapters and conference proceedings. He has been served as a referee for more than 100 journals and book series . He is a committee member of Curriculum Development Council (2019-) Curriculum Development Council on Mathematics Education (2017-2023), Education Bureau, HKSAR government, the Public Examinations Board (2017-2023), Standards Committee (2017-2023), Examination Authority, the High-level Advisory Panel of Chief Executive's Award for Teaching Excellence, HKSAR government, (2016, 2021) and International Consortium for Optimization and Modelling in Science and Industry (iCOMSI). He is also an assessor of the Chang Jiang Scholars Program, Ministry of Education, P.R. China government, (2015).

Highlights of Some Projects and Contributions

(I) Numerical Algorithms for Queueing and Manufacturing Systems: Continuous time Markov chains are popular models for modeling and analyzing queueing and manufacturing systems. For the purpose of performance analysis, one requires the solution of the steady-state probability distribution of a large and complex Markov chain. Typical examples can be found in Flexible Manufacturing Systems (FMSs) and queueing systems with batch arrivals. Classical iterative methods such as Gauss-Seidel (GS) and Successive Over-Relaxation (SOR) method are common solvers for these problems. However, their convergence rates are slow in general when the problem size is getting large. To speed up the computations, we consider Preconditioned Conjugate Gradient (PCG) methods. Preconditioners are designed by exploiting the near-Toeplitz and block structure of the underlying generator matrices. The idea can be extended to Stochastic Automata Networks (SANs), a general class of stochastic networks. We proved that the preconditioned systems have singular values clustered around one and therefore CG type methods will converge very fast when apply to solving the preconditioned systems. Numerical examples of practical problems are also given to demonstrate the efficiency of our proposed methods.

Related Publications

1. R. Chan and W. Ching, Toeplitz-circulant Preconditioners for Toeplitz Systems and Their Applications to Queueing Networks with Batch Arrivals, SIAM Journal on Scientific Computing, 17 (1996) 762-772.
2. W. Ching, R. Chan and X. Zhou, Circulant Preconditioners for Markov Modulated Poisson Processes and Their Applications to Manufacturing Systems, SIAM Journal on Matrix Analysis and Applications, 18 (1997) 464-481.
3. R. Chan and W. Ching, Circulant Preconditioners for Stochastic Automata Networks, Numerische Mathematik, 87 (2000) 35-57.
4. W. Ching, Iterative Methods for Queuing and Manufacturing Systems. Springer Monographs in Mathematics, Springer, London, 2001.
5. W. Ching, Iterative Methods for Queuing Systems with Batch Arrivals and Negative Customers, BIT, 43 (2003) 285-296.

(II) Iterative Solvers for Toeplitz Systems and Imaging Processing Problems: A square matrix is called a Toeplitz matrix if it is constant along its diagonals. Toeplitz and Toeplitz-like matrices appear in many real world applications such as signal processing, image processing and queueing systems etc. Preconidtioned Conjugate Gradient (PCG) method is an efficient iterative solver for solving such as a linear system. Circulant matrix is a classical candidate for preconditioner. We exploited the off-diagonal decay property of the inverse of a Toeplitz matrix and construct a factorized banded inverse preconditioner. Using the constructed preconditioner, we proved that the spectra of the preconditioned matrices clustered around one and PCG method converges very fast in solving a class of image restoration problems. Numerical results indicate that it is even better than the circulant type preconditioner. We also proposed iterative algorithms for solving the image restoration problems. The algorithms are based on the decoupling of deblurring and denoising steps in the restoration process. The algorithms make use of the Fast Fourier Transform (FFT) and take advantage of the Toeplitz-like structure of the concerned matrix. We proved that the algorithms are convergent. Numerical examples show that the proposed algorithms are both efficient and effective for the captured problem.

Related Publications

1. F. Lin and M. Ng and W. Ching, Factorized Banded Inverse Preconditioners for Matrices with Toeplitz Structure, SIAM Journal on Scientific Computing, 26 (2005) 1852-1870.
2. W. Ching, M. Ng, K. Sze and C. Yau, Super-Resolution Image Reconstruction Using Multisensor, Numerical Linear Algebra with Applications, 12 (2005) 2-3, 271-281.
3. W. Ching, M. Ng and Y. Wen, Block Diagonal and Schur Complement Preconditioners for Block-Toeplitz Systems with Small Size Blocks, SIAM Journal on Matrix Analysis and Applications, 29 (2007) 1101-1119.
4. Y. Wen, M. Ng and W. Ching, Iterative Algorithms Based on Decoupling of Deblurring and Denoising for Image Restoration, SIAM Journal on Scientific Computing, 30 (2008) 2655-2675.
5. M. Nikolova, M. Ng, S. Zhang and W. Ching, Efficient Reconstruction of Piecewise Constant Images Using Nonsmooth Nonconvex Minimization, SIAM Journal on Imaging Sciences, 1 (2008) 2-25.

(III) High-dimensional Markov Chains with Applications in Management Sciences: High-dimensional Markov chains are popular stochastic models for many practical problems in management sciences such as inventory systems, categorical time series and financial credit risk. Given an aperiodic and irreducible Markov chain, it is well-known that the Perron-Frobenius theorem is important for studying the existence of the system stationary distribution. In many applications, one has to employ a multivariate Markov chain so as to capture the positive correlations among different chains. In a conventional multivariate Markov chain model of s chains and each chain has m states, the total number of states is of O(m^s), therefore it grows exponentially with respect to s. We proposed an approximate first-order model (O(m^2^s^2) parameters) for this problem. To capture the long-range dependence of a categorical data time series, one has to employ a Markov chain of order n. The number of model parameters grows exponentially with respect to the order n. We proposed a parsimonious model (O(nm^2) parameters) for this problem. We then extended the above models to the case of high-order multivariate Markov chains. We generalized the classical Perron-Frobenius theorem to all the above high-dimensional Markov chain models. Based on the theorems, efficient algorithms are then developed for solving the parameters of the proposed models. Finally the models are also extended to the case of negative correlations and they have been applied successfully in the captured real world problems.

Related Publications

1. W. Ching, E. Fung and M. Ng, Higher-order Markov Chain Models for Categorical Data Sequences, Naval Research Logistics, 51 (2004) 557-574.
2. T. Siu, W. Ching, M. Ng and E. Fung, On a Multivariate Markov Chain Model for Credit Risk Measurement, Quantitative Finance, 5 (2005) 543-556.
3. W. Ching, M. Ng and E. Fung, Higher-order Multivariate Markov Chains and their Applications, Linear Algebra and Its Applications, 428 (2-3) (2008) 492-507.
4. W. Ching, T. Siu, L. Li, H. Jiang, T. Li and W. Li, An Improved Parsimonious Multivariate Markov Chain Model for Credit Risk, The Journal of Credit Risk, 5 (2009) 1-25.
5. W. Ching, X. Huang, M. Ng and T. Siu, Markov Chains : Models, Algorithms and Applications, International Series on Operations Research and Management Science, (2nd Edition) Springer, New York, 2013.

(IV) Boolean Networks and Probabilistic Boolean Networks: Mathematical and computational models are important for studying genetic regulatory networks. Boolean Networks (BNs) and its extension Probabilistic Boolean Networks (PBNs) are effective mathematical models for studying genetic regulatory interactions. For a BN, finding a control strategy leading to the desired global state is a NP-hard problem in general. We proved that a polynomial time algorithm exists if the network has a tree structure. A PBN is essentially a collection of BNs driven by a Markov chain process and therefore can be studied by using the Markov chain theory. The steady-state distribution of a PBN gives useful information about the desirable states (attractor cycles) of the underlying genetic network where the attractor cycles have important biological interpretations. Controls (interventions) can be applied to a genetic network to avoid undesirable states associated with diseases like cancer. The optimal control problem can be formulated mathematically by using the principle of stochastic dynamic programming. The size of the transition probability matrix of a PBN is 2^n-by-2^n where n is the number of genes in the network and the problem size grows exponentially with respect to n. By employing a matrix approximation technique, we obtain approximations for both the steady-state distribution of a PBN and also a near-optimal policy for the captured control problem. The approximation method can reduce the computational cost significantly and yet still retain the important information of the network. We established some theoretical bounds for the errors by using matrix perturbation theory. Numerical examples and simulation results are given to demonstrate both the efficiency and effectiveness of our proposed methods.

Related Publications

1. T. Akutsu, M. Hayasida, W. Ching and M. Ng, Control of Boolean Networks: Hardness Results and Algorithms for Tree Structured Networks, Journal of Theoretical Biology, 244 (2007) 670-679.
2. W. Ching, S. Zhang, M. Ng and T. Akutsu, An Approximation Method for Solving the Steady-state Probability Distribution of Probabilistic Boolean Networks, Bioinformatics, 23 (2007) 1511-1518.
3. S. Zhang, W. Ching, M. Ng and T. Akutsu, Simulation Study in Probabilistic Boolean Network Models for Genetic Regulatory Networks, International Journal of Data Mining and Bioinformatics, 1 (2007) 217-240.
4. W. Ching, S. Zhang, Y. Jiao, T. Akutsu, N. Tsing and A. Wong, Optimal Control Policy for Probabilistic Boolean Networks with Hard Constraints, IET Systems Biology, 3 (2009) 90-99.
5. Y. Cong, W. Ching, N. Tsing and H. Leung, On Finite-Horizon Control of Genetic Regulatory Networks with Multiple Hard-Constraints, BMC Systems Biology (2010), 4(Suppl 2).

Mottoes