Skip to main content
SpringerLink
Log in
Book cover

International Conference on Information Computing and Applications

ICICA 2012: Information Computing and Applications pp 242–248Cite as

Improved Calculation Scheme of Structure Matrix of Boolean Network Using Semi-tensor Product

  • Conference paper

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 307))

Abstract

Semi-tensor product is an efficient tool for analyzing the characteristics of a Boolean network. Using it, the number of fixed points and numbers of all possible circles of different lengths are determined by the structure matrix of a Boolean network. But the conventional method to obtain the structure matrix is very complex. In this paper, a novel method is proposed to get the structure matrix. Unlike existing methods, our approach gets the structure matrix of a Boolean network not through the complex matrix operations but through the truth table which reflects the state transformation of the Boolean network. Comparing our solutions with the conventional method shows the advantage of our new approach through an example of a Boolean Network.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Kauffman, S.A.: Metabolic stability and epigenesist in randomly constructed genetic nets. Journal of Theoretical Biology 22, 437–467 (1969)

    Article  MathSciNet  Google Scholar 

  2. Akustsu, T., Miyano, S., Kuhara, S.: Inferring qualitative relations in genetic networks and metabolic pathways. Bioinformatics 16, 727–773 (2000)

    Article  Google Scholar 

  3. Albert, R., Barabasi, A.L.: Dynamics of complex systems: scaling laws or the period of Boolean networks. Phys. Rev. Lett. 84, 5660–5663 (2000)

    Article  Google Scholar 

  4. Shumlevich, I., Dougherty, R., Kim, S., Zhang, W.: Probabilistic Boolean network: a rule-based uncertainty model for gene regulatory networks. Bioinformatics 18(2), 261–274 (2002)

    Article  Google Scholar 

  5. Harris, S.E., Sawhill, B.K., Wuensche, A., Kauffman, S.: A model of transcriptional regulatory networks based on biases in the observed regulation rules. Complexity 7, 23–40 (2002)

    Article  Google Scholar 

  6. Aldana, M.: Boolean dynamics of networks with scale-free topology. Physica D 185, 45–66 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Samuelsson, B., Troein, C.: Superpolynomial growth in the number of attractors in kayffman networks. Phys. Rev. Lett. 90, 90098701 (2003)

    Article  MathSciNet  Google Scholar 

  8. Drossel, B., Mihaljev, T., Greil, F.: Number and length of attractors in a critical Kauffman model with connectivity one. Phys. Rev. Lett. 94, 088701 (2005)

    Article  Google Scholar 

  9. Albert, R., Othmer, H.G.: The topology and signature of the regulatory interactions predict the expression pattern of the segment polarity genes in Drospphila melanogaster. Journal of Theory Biology 223(1), 1–18 (2003)

    Article  MathSciNet  Google Scholar 

  10. Huang, S.: Regulation of cellular states in mammalian cells from a genomewide view. In: Collado-Vodes, J., Hofestadt, R. (eds.) Gene Regulation and Metabolism, pp. 181–220. MIT Press, Cambridge (2002)

    Google Scholar 

  11. Heidel, J., Maloney, J., Farrow, J., Rogers, J.: Finding cycles in synchronous Boolean networks with applications to biochemical systems. Int. J. Bifurcat. Chaos 13(3), 535–552 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  12. Farrow, C., Heidel, J., Maloney, H., Rogers, J.: Scalar equations for synchronous Boolean networks with biological applications. IEEE Trans. Neural Networks 15(2), 348–354 (2004)

    Article  Google Scholar 

  13. Zhao, Q.: A remark on Scalar Equations for synchronous Boolean Networks with biologicapplications by C.Farrow, J.Heidel, J.Maloney, and J.Rogers. IEEE Trans. Neural Networks 16(6), 1715–1716 (2005)

    Article  Google Scholar 

  14. Cheng, D., Qi, H.: Semi-tensor Product of Matrices-Theory and Application, 2nd edn. Science Press, Beijing (2011)

    Google Scholar 

  15. Cheng, D., Qi, H., Li, Z.: Analysis and Control of Boolean Networks: A Semi-tensor Product Approach. Springer Press, London (2011)

    Book  Google Scholar 

  16. Cheng, D.: Matrix and Polynomial Approach to Dynamic Control Systems. Science Press, Beijing (2002)

    Google Scholar 

  17. Cheng, D.: Semi-tensor product of matrices and its applications - A survey. In: ICCM 2007, vol. 3, pp. 641–668 (2007)

    Google Scholar 

  18. Cheng, D., Qi, H., Zhao, Y.: Analysis and control of Boolean networks: a semi-tensor product approach. Acta Automatica Sinica 37(5), 529–539 (2011)

    MATH  MathSciNet  Google Scholar 

  19. Cheng, D., Qi, H., Li, Z.: Model construction of Boolean network via observed data. IEEE Transactions on Neural Networks 22(4), 525–536 (2011)

    Article  Google Scholar 

  20. Cheng, D., Qi, H.: A linear representation of dynamics of boolean networks. IEEE Transactions on Automatic Control 55(10), 2251–2258 (2011)

    Article  MathSciNet  Google Scholar 

  21. Cheng, D., Qi, H.: State-space analysis of Boolean networks. IEEE Transaction on Neural Networks 21(4), 584–594 (2010)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, China

    Jinyu Zhan, Shan Lu & Guowu Yang

Authors
  1. Jinyu Zhan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shan Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guowu Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. College of Sciences, Hebei United University, 063000, Tangshan, Hebei, China

    Chunfeng Liu  & Aimin Yang  & 

  2. Northeastern University at Qinhuangdao, Hebei, China

    Leizhen Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zhan, J., Lu, S., Yang, G. (2012). Improved Calculation Scheme of Structure Matrix of Boolean Network Using Semi-tensor Product. In: Liu, C., Wang, L., Yang, A. (eds) Information Computing and Applications. ICICA 2012. Communications in Computer and Information Science, vol 307. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34038-3_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-34038-3_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34037-6

  • Online ISBN: 978-3-642-34038-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation