Skip to main content
SpringerLink
Log in

Reachability Analysis of Delta-Notch Lateral Inhibition Using Predicate Abstraction

  • Conference paper
  • First Online:
High Performance Computing — HiPC 2002 (HiPC 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2552))

Included in the following conference series:

Abstract

This paper examines the feasibility of predicate abstraction as a method for the reachability analysis of hybrid systems. A hybrid system can be abstracted into a purely discrete system by mapping the continuous state space into an equivalent finite discrete state space using a set of Boolean predicates and a decision procedure in the theory of real closed fields. It is then possible to find the feasible transitions between these states. In this paper, we propose new conditions for predicate abstraction which greatly reduce the number of transitions in the abstract discrete system. We also develop a computational technique for reachability analysis and apply it to a biological system of interest (the Delta-Notch lateral inhibition problem).

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

Access this chapter

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Alur, T. Dang, and F. Ivančić. Reachability analysis of hybrid sytems via predicate abstraction. In C. Tomlin and M. Greenstreet, eds., 5th International Workshop, Hybrid Systems: Computation and Control, volume LNCS 2289, pages 35–48, Stanford, CA, USA, 2002. Springer. 715

    Chapter  Google Scholar 

  2. Spyros Artavanis-Tsakonas, Matthew D. Rand, and Robert J. Lake. Notch signaling: cell fate control and signal integration in development. Science, 284:770–776, April 1999. 716

    Google Scholar 

  3. S. Das, D. Dill, and S. Park. Experience with predicate abstraction. In Computer Aided Verification, 11th international Conference, volume LNCS 1633, 1999. 715

    Chapter  Google Scholar 

  4. Manolis Fanto and Marek Mlodzik. Asymmetric notch activation specifies photoreceptors R3 and R4 and planar polarity in the Drosophila eye. Nature, 397:523–526, February 1999. 716

    Google Scholar 

  5. R. Ghosh and C. Tomlin. Lateral inhibition through delta-notch signaling: A piecewise affine hybrid model. In 4th International Workshop, Hybrid Systems: Computation and Control, volume LNCS 2034, pages 232–246, Rome, Italy, 2001. 715, 718, 721, 722, 723

    Chapter  Google Scholar 

  6. S. Graf and H. Saidi. Construction of abstract state graphs with pvs. In Computer Aided Verification, 9th International Conference, volume LNCS 1254, 1997. 715

    Google Scholar 

  7. H. Hong. An improvement of the projection operator in cylindrical algebraic decomposition. In Proceedings of ISAAC 90, pages 261–264, 1990. 719

    Google Scholar 

  8. G. Lafferriere, G.J. Pappas, and S. Yovine. Symbolic reachability computation for families of linear vector fields. Journal of Symbolic Computation, 32(3):231–253, September 2001. 715

    Article  MATH  MathSciNet  Google Scholar 

  9. Julian Lewis. Notch signalling and the control of cell fate choices in vertebrates. Seminars in Cell & Developmental Biology, 9:583–589, 1998. 716

    Article  Google Scholar 

  10. G. Marnellos, G. A. Deblandre, E. Mjolsness, and C. Kintner. Delta-notch lateral inhibitory patterning in the emergence of ciliated cells in Xenopus: experimental observations and a gene network model. In Pacific Symposium on Biocomputing, pages 5:326–337, 2000. 716

    Google Scholar 

  11. O. Sokolsky and H. Hong. Qualitative modeling of hybrid systems. In Proceedings of the Monterey Workshop, June 2001. 715

    Google Scholar 

  12. A. Tiwari and G. Khanna. Series of abstractions for hybrid automata. In C. Tomlin and M. Greenstreet, eds., 5th International Workshop, Hybrid Systems: Computation and Control, volume LNCS 2289, pages 465–478, Stanford, CA, USA, 2002. 715, 718, 720

    Chapter  Google Scholar 

  13. A. Tiwari and P. Lincoln. Automated techniques for stability analysis of delta notch lateral inhibition mechanism. 2002. 715

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Hybrid Systems Laboratory, Department of Aeronautics and Astronautics, Stanford University, 94305, Stanford, CA

    Inseok Hwang, Hamsa Balakrishnan, Ronojoy Ghosh & Claire Tomlin

Authors
  1. Inseok Hwang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hamsa Balakrishnan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ronojoy Ghosh
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Claire Tomlin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. CISE Department, University of Florida, 32611, FL, Gainesville, USA

    Sartaj Sahni

  2. Department of Electrical Engineering, EEB 200C, University of Southern California, 3740 McClintok Ave., 90089-2562, CA, Los Angeles, USA

    Viktor K. Prasanna

  3. India Software Lab, IBM Global Services India Exports, Golden Enclave, TISL Tower, Airport Road, 560 017, Bangalore, India

    Uday Shukla

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hwang, I., Balakrishnan, H., Ghosh, R., Tomlin, C. (2002). Reachability Analysis of Delta-Notch Lateral Inhibition Using Predicate Abstraction. In: Sahni, S., Prasanna, V.K., Shukla, U. (eds) High Performance Computing — HiPC 2002. HiPC 2002. Lecture Notes in Computer Science, vol 2552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36265-7_69

Download citation

  • DOI: https://doi.org/10.1007/3-540-36265-7_69

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00303-8

  • Online ISBN: 978-3-540-36265-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation