Communications and Control Engineering

Analysis and Control of Boolean Networks

A Semi-tensor Product Approach

Authors: Cheng, Daizhan, Qi, Hongsheng, Li, Zhiqiang

  • Presents well-known and proven mathematical techniques for dealing with biologically-derived networks
  • Demonstrates how logical functions can be translated into matrices for arithmetic treatment
  • MATLAB® toolbox allows the reader to simulate the results of algorithms easily
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About this book

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.

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.

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)

Table of contents (19 chapters)

  • Propositional Logic

    Cheng, Daizhan (et al.)

    Pages 1-18

  • Semi-tensor Product of Matrices

    Cheng, Daizhan (et al.)

    Pages 19-53

  • Matrix Expression of Logic

    Cheng, Daizhan (et al.)

    Pages 55-65

  • Logical Equations

    Cheng, Daizhan (et al.)

    Pages 67-101

  • Topological Structure of a Boolean Network

    Cheng, Daizhan (et al.)

    Pages 103-140

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-0-85729-097-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-0-85729-096-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-1-4471-2611-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Analysis and Control of Boolean Networks
Book Subtitle
A Semi-tensor Product Approach
Authors
Series Title
Communications and Control Engineering
Copyright
2011
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Limited
eBook ISBN
978-0-85729-097-7
DOI
10.1007/978-0-85729-097-7
Hardcover ISBN
978-0-85729-096-0
Softcover ISBN
978-1-4471-2611-9
Series ISSN
0178-5354
Edition Number
1
Number of Pages
XVI, 472
Topics