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© 2011

Analysis and Control of Boolean Networks

A Semi-tensor Product Approach

Benefits

  • Shows the reader methods of dealing with biologically-derived networks mathematically using well-known and proven techniques MATLAB® toolbox allows the reader to simulate the results of algorithms easily Demonstrates how logical functions can be translated into matrices for arithmetic treatment.

Book

Part of the Communications and Control Engineering book series (CCE)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 1-18
  3. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 19-53
  4. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 55-65
  5. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 67-101
  6. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 103-140
  7. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 141-161
  8. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 163-187
  9. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 189-212
  10. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 213-231
  11. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 233-248
  12. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 249-273
  13. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 275-296
  14. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 297-311
  15. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 313-345
  16. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 347-369
  17. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 371-388
  18. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 389-407
  19. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 409-429
  20. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 431-450

About this book

Introduction

The Boolean network has become a powerful tool for describing and simulating cellular networks in which the elements behave in an on–off fashion. Analysis and Control of Boolean Networks presents a systematic new approach to the investigation of Boolean control networks. The fundamental tool in this approach is a novel matrix product called the semi-tensor product (STP). Using the STP, a logical function can be expressed as a conventional discrete-time linear system. In the light of this linear expression, certain major issues concerning Boolean network topology – fixed points, cycles, transient times and basins of attractors – can be easily revealed by a set of formulae. This framework renders the state-space approach to dynamic control systems applicable to Boolean control networks. The bilinear-systemic representation of a Boolean control network makes it possible to investigate basic control problems including controllability, observability, stabilization, disturbance decoupling, identification, optimal control, etc.

The book is self-contained, requiring only knowledge of linear algebra and the basics of the control theory of linear systems. It begins with a short introduction to prepositional logic and the concepts and properties of the STP and progressing via the (bi)linear expression of Boolean (control) networks to disturbance decoupling and decomposition of Boolean control systems. Finally multi-valued logic is considered as a more precise way of describing real networks and stochastic Boolean networks are touched upon. Relevant numerical calculations are explained in an appendix and a MATLAB® toolbox for the algorithms in the book can be downloaded from http://lsc.amss.ac.cn/~dcheng/.

Analysis and Control of Boolean Networks will be a fundamental reference for researchers in systems biology, control, systems science and physics. The book was developed for a short course for graduate students and is suitable for that purpose. Computer scientists and logicians may also find this book to be of interest.

Keywords

Boolean network Control Logic Semi-tensor product of matricies Topological structure

Authors and affiliations

  1. 1.Academy of Mathematics & Systems Science, Institute of Systems ScienceChinese Academy of SciencesBeijingChina, People's Republic
  2. 2., Institute of Systems, AMSSChinese Academy of SciencesBeijingChina, People's Republic
  3. 3., Institute of Systems, AMSSChinese Academy of SciencesBeijingChina, People's Republic

About the authors

Daizhan Cheng received the Ph.D. degree in systems science from Washington University, St. Louis, in 1985. Currently, he is a Professor with the Institute of Systems Science, Chinese Academy of Sciences, Beijing, China. His research interests include nonlinear systems, numerical method, complex systems, etc. Dr. Cheng is Chairman of the Technical Committee on Control Theory (since 2003), Chinese Association of Automation, a Fellow of the IEEE, and a Fellow of the International Federation of Automatic Control. Hongsheng Qi received the Ph.D. degree in systems theory from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences in 2008. He is currently a post-doctoral fellow at the Key Laboratory of Systems and Control, Chinese Academy of Sciences. His research interests include nonlinear systems control, complex systems, etc. Zhiqiang Li received the M.S. degree from Zhengzhou University in 2007. He is currently a Ph.D. student in the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. His research interests include nonlinear systems control, complex systems, etc.

Bibliographic information

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Reviews

From the reviews:

“The aim of the book is to provide a new framework for the study of Boolean control networks. … The book is self-contained and contains many examples which illustrate the concepts and the proposed techniques. … the book represents a fundamental reference for researchers in systems biology, systems science and physics.” (Valeriu Prepeliţă, Zentralblatt MATH, Vol. 1209, 2011)