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第二届最优化与系统生物学国际研讨会

作者： Wai-Ki Ching Ho-Yin Leung Nam-Kiu Tsing Shu-Qin Zhang Advanced Modeling and Applied Computing Laboratory Department of Mathematics The University of Hong Kong Faculty of Mathematical Sciences Fudan University

We study the problem of finding optimal control policies for Probabilistic Boolean Networks (PBNs). Boolean Networks (BNs) and PBNs are effective tools for modeling genetic regulatory networks. A PBN is a collection of BNs driven by a Markov chain process. It is well-known that the control/intervention of a genetic regulatory network is useful for avoiding undesirable states associated with diseases like cancer. The optimal control problem can be formulated as a probabilistic dynamic programming problem. However, due to the curse of dimensionality, the complexity of the problem is huge. The main objective of this paper is to introduce a Genetic Algorithm (GA) approach for the optimal control problem. Numerical results are given to demonstrate the efficiency of our proposed GA method.

关键词： Boolean Networks Dynamic Programming Genetic Algorithm Intervention Opti- mal Control Policy Probabilistic Boolean Networks.

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On Distribution and Enumeration of Attractors in Probabilistic Boolean Networks

On Distribution and Enumeration of Attractors in Probabilist...

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第二届最优化与系统生物学国际研讨会

作者： Morihiro Hayashida Takeyuki Tamura Tatsuya Akutsu Wai-Ki Ching Advanced Modelling and Applied Computing Laboratory Department of Mathematics The University of Hong Kong

In this paper, we study attractors in Probabilistic Boolean Networks (PBNs). We study the expected number of singleton attractors in a PBN and show that it is 1.5 n if the number of Boolean functions assigned to each node is 2, where n is the number of nodes in a PBN. Then, we present algorithms for identifying singleton and small attractors and perform both theoretical and computational analyses on their average case time complexities. The results of computational experiments suggest that these algorithms are much more efficient than the naive algorithm that examines all possible 2n states. We also show a simple and interesting relation between the distribution of attractors in a BN and the steady-state distribution in a corresponding variant of a PBN.

关键词： Probabilistic Boolean Network Attractor Algorithm

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Construction and Control of Genetic Regulatory Networks:A Multivariate Markov Chain Approach

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Journal of Biomedical Science and Engineering 2008年第1期1卷 15-21页

作者： Shu-Qin Zhang Ling-Yun Wu Wai-Ki Ching Yue Jiao Raymond, H. Chan Advanced Modeling and Applied Computing Laboratory Department of Mathematics The University of Hong Kong Pokfulam Road Hong Kong Department of Mathematics The Chinese University of Hong Kong Shatin N.T. Hong Kong Institute of Applied Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences School of Mathematical Sciences Fudan University Shanghai200433 China

In the post-genomic era, the construction and control of genetic regulatory networks using gene expression data is a hot research topic. Boolean networks (BNs) and its extension Probabilistic Boolean Networks (PBNs) have been served as an effective tool for this purpose. However, PBNs are difficult to be used in practice when the number of genes is large because of the huge computational cost. In this paper, we propose a simplified multivariate Markov model for approximating a PBN The new model can preserve the strength of PBNs, the ability to capture the inter-dependence of the genes in the network, qnd at the same time reduce the complexity of the network and therefore the computational cost. We then present an optimal control model with hard constraints for the purpose of control/intervention of a genetic regulatory network. Numerical experimental examples based on the yeast data are given to demonstrate the effectiveness of our proposed model and control policy.

关键词： Gene Expression Sequences Multivariate Markov Chain Optimal Control Policy Probabilistic Boolean Networks.

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A Simplified Multivariate Markov Chain Model for the Construction and Control of Genetic Regulatory Networks

A Simplified Multivariate Markov Chain Model for the Constru...

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International Conference on Bioinformatics and Biomedical Engineering (ICBBE)

作者： Shu-Qin Zhang Wai-Ki Ching Yue Jiao Ling-Yun Wu Raymond H. Chan School of Mathematical Sciences Fudan University Shanghai China Advanced Modeling and Applied Computing Laboratory Department of Mathematics University of Hong Kong Hong Kong China Institute of Applied Mathematics Academy of Mathematics and System Sciences Chinese Academy and Sciences China Department of Mathematics Chinese University of Hong Kong New Territories Hong Kong China

The construction and control of genetic regulatory networks using gene expression data is an important research topic in bioinformatics. Probabilistic Boolean Networks (PBNs) have been served as an effective tool for this purpose. However, PBNs are difficult to be used in practice when the number of genes is large because of the huge computational cost. In this paper, we propose a simplified multivariate Markov model for approximating a PBN. The new model can preserve the strength of PBNs and at the same time reduce the complexity of the network and therefore the computational cost. We then present an optimal control model with hard constraints for the purpose of control/intervention of a genetic regulatory network. Numerical experimental examples based on the yeast data are then given to demonstrate the effectiveness of our proposed model and control policy.

关键词： Genetics Mathematical model mathematics Gene expression Optimal control Electronic mail Biological system modeling Computational efficiency Fungi Diseases

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A Multiple Regression Approach for Building Genetic Networks

A Multiple Regression Approach for Building Genetic Networks

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International Conference on BioMedical Engineering and Informatics (BMEI)

作者： Shu-Qin Zhang Wai-Ki Ching Nam-Kiu Tsing Ho-Yin Leung Diane D. Guo School of Mathematical Sciences Fudan University Shanghai China Advanced Modeling and Applied Computing Laboratory Department of Mathematics University of Hong Kong Hong Kong China Department of Biology Chinese University of Hong Kong Hong Kong China

The construction of genetic regulatory networks from time series gene expression data is an important research topic in bioinformatics as large amounts of quantitative gene expression data can be routinely generated nowadays. One of the main difficulties in building such genetic networks is that the data set has huge number of genes but small number of time points. In this paper, we propose a linear regression model for uncovering the relations among the genes by using multiple regression method with filtering. The model takes into account of the fact that real biological networks have the scale-free property. Based on this property and the statistical tests, a filter can be constructed and the interactions among the genes can be inferred by minimizing the distance between the observed data and the predicted data. Numerical examples based on yeast gene expression data are given to demonstrate our method.

关键词： Genetics Gene expression Buildings Biological system modeling Bioinformatics Linear regression Nonlinear filters Filtering Testing Fungi

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Optimal Finite-Horizon Control for Probabilistic Boolean Networks with Hard Constraints

Optimal Finite-Horizon Control for Probabilistic Boolean Net...

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第一届最优化与系统生物学国际研讨会

作者： Wai-Ki Ching Shu-Qin Zhang Yue Jiao Tatsuya Akutsu Alice S. Wong Advanced Modeling and Applied Computing Laboratory Department of MathematicsThe University of Hong Kong School of Mathematical Sciences Fudan University Advanced Modeling and Applied Computing Laboratory Department of ZoologyThe University of Hong Kong

In this paper, we study optimal control policies for Probabilistic Boolean Networks （PBNs） with hard constraints. Boolean Networks （BNs） and PBNs are useful and effective tools for modelling genetic regulatory networks. A PBN is essentially a collection of BNs driven by a Markov chain process. It is well-known that the control/intervention of a genetic regulatory network is useful for avoiding undesirable states associated with diseases like cancer. Therefore both optimal finite-horizon control and infinite-horizon control policies have been proposed to achieve the purpose. Actually the optimal control problem can be formulated as a probabilistic dynamic programming problem. In many studies, the optimal control problems did not consider the case of hard constraints, i.e., to include a maximum upper bound for the number of controls that can be applied to the PBN. The main objective of this paper is to introduce a new formulation for the optimal finite-horizon control problem with hard constraints. Experimental results are given to demonstrate the efficiency of our proposed formulation.

关键词： Boolean Networks Dynamic Programming Finite-Horizon Intervention Markov Chain Optimal Control Probabilistic Boolean Networks.

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Interactive hidden Markov models and their applications

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IMA Journal of Management mathematics 2007年第1期18卷 85-97页

作者： Ching, W.K. Fung, E. Ng, M. Siu, T.K. Li, W.K. Advanced Modeling and Applied Computing Laboratory Department of Mathematics University of Hong Kong Pokfulam Road Hong Kong Hong Kong Department of Mathematics Hong Kong Baptist University Kowloon Tong Hong Kong Department of Actuarial Mathematics and Statistics School of Mathematical and Computer Sciences Heriot-Watt University Edinburgh EH14 4AS United Kingdom Department of Statistics and Actuarial Science University of Hong Kong Pokfulam Road Hong Kong Hong Kong

In this paper, we propose an Interactive hidden Markov model (IHMM). In a traditional HMM, the observable states are affected directly by the hidden states, but not vice versa. In the proposed IHMM, the transitions of hidden states depend on the observable states. We also develop an efficient estimation method for the model parameters. Numerical examples on the sales demand data and economic data are given to demonstrate the applicability of the model.

关键词： Categorical time series Hidden Markov model Prediction of demand Steady-state probability distribution

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Weighted Local Least Squares Imputation Method for Missing Value Estimation

Weighted Local Least Squares Imputation Method for Missing V...

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第一届最优化与系统生物学国际研讨会

作者： Wai-Ki Ching Kwai-Wa Cheng Li-Min Li Nam-Kiu Tsing Alice S. Wong Advanced Modeling and Applied Computing Laboratory Department of MathematicsThe University of Hong Kong Anderson Cancer Center The University of Texas Department of Zoology The University of Hong Kong

Missing values often exist in the data of gene expression microarray experiments. A number of methods such as the Row Average (RA) method, KNNimpute algorithm and SVDimpute algorithm have been proposed to estimate the missing values. Recently, Kim et al. proposed a Local Least Squares Imputation (LLSI) method for estimating the missing values. In this paper, we propose a Weighted Local Least Square Imputation (WLLSI) method for missing values estimation. WLLSI allows training on the weighting and therefore can take advantage of both the LLSI method and the RA method. Numerical results on both synthetic data and real microarray data are given to demonstrate the effectiveness of our proposed method. The imputation methods are then applied to a breast cancer dataset.

关键词： Missing values microarray data row average method local least squares imputation method weighted local least squares imputation method.

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Hidden markov model for the detection of machine failure

Hidden markov model for the detection of machine failure

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36th International Conference on Computers and Industrial Engineering, ICC and IE 2006

作者： Tai, Allen H. Ching, Wai-Ki Chan, L.Y. Department of Mathematics Advanced Modeling and Applied Computing Laboratory Hong Kong Hong Kong Department of Industrial and Manufacturing Systems Engineering University of Hong Kong Pokfulam Road Hong Kong Hong Kong

Hidden Markov Models (HMMs) are widely used in applied sciences and engineering. The potential applications in manufacturing industries have not yet been fully explored. In this paper, we propose to apply HMM to the detection of machine failure in a process control problem. We propose models for both cases of indistinguishable production units and distinguishable production units. Numerical examples are given to illustrate the effectiveness of the proposed models.

关键词： Hidden Markov models

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Fast solvers for queueing systems with negative customers 06

Fast solvers for queueing systems with negative customers

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VALUETOOLS: 1st International Conference on Performance Evaluation Methodologies and Tools

作者： Wen, You-Wei Ching, Wai-Ki Ng, Michael K. Department of Mathematics University of Hong Kong Pokfulam Road Hong Kong Hong Kong Advanced Modeling and Applied Computing Laboratory Department of Mathematics University of Hong Kong Pokfulam Road Hong Kong Hong Kong Department of Mathematics Hong Kong Baptist University Kowloon Tong Kowloon Hong Kong

ISBN: (纸本)1595935045

In this paper, we are interested in solving queueing systems having Poisson batch arrivals, exponential servers and negative customers. Preconditioned Conjugate Gradient (PCG) method is applied to solving the steady-state probability distribution of the queueing system. Preconditioners are constructed by exploiting near-Toeplitz structure of the generator matrix and the Gohberg-Semumcul formula. We proved that the preconditioned system has singular values clustered around one. Therefore Conjugate Gradient (CG) methods when applied to solving the preconditioned system, we expect fast convergence rate. Numerical examples are given to demonstrate our claim. Copyright 2006 ACM.

关键词： Queueing theory

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