Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Computing Linking Numbers of a Filtration

  • Conference paper
  • First Online:
Algorithms in Bioinformatics (WABI 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2149))

Included in the following conference series:

Abstract

We develop fast algorithms for computing the linking number of a simplicial complex within a filtration. We give experimental results in applying our work toward the detection of non-trivial tangling in biomolecules, modeled as alpha complexes.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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.

Similar content being viewed by others

References

  1. Colin C. Adams. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. W. H. Freeman and Company, New York, NY, 1994.

    MATH  Google Scholar 

  2. Richard A. Bissell, Emilio Cordova, Angel E. Kaifer, and J. Fraser Stoddart. A checmically and electrochemically switchable molecular shuttle. Nature, 369:133–137, 1994.

    Article  Google Scholar 

  3. C. P. Collier, E. W. Wong, Belohradský, F. M. Raymo, J. F Stoddart, P. J. Kuekes, R. S. Williams, and J. R. Heath. Electronically configurable moleculear-based logic gates. Science, 285:391–394, 1999.

    Article  Google Scholar 

  4. Thomas H. Cormen, Charles E. Leiserson, and Ronald L. Rivest. Introduction to Algorithms. The MIT Press, Cambridge, MA, 1994.

    Google Scholar 

  5. C. J.Ã. Delfinado and H. Edelsbrunner. An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere. Comput. Aided Geom. Design, 12:771–784, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  6. H. Edelsbrunner, D. Letscher, and A. Zomorodian. Topological persistence and simplification. In Proc. 41st Ann. IEEESympos. Found. Comput. Sci., pages 454–463, 2000.

    Google Scholar 

  7. H. Edelsbrunner and E. P. Mücke. Three-dimensional alpha shapes. ACM Trans. Graphics, 13:43–72, 1994.

    Article  MATH  Google Scholar 

  8. Erica Flapan. When Topology Meets Chemistry: A Topological Look at Molecular Chirality. Cambridge University Press, New York, NY, 2000.

    MATH  Google Scholar 

  9. P. J. Giblin. Graphs, Surfaces, and Homology. Chapman and Hall, New York, NY, second edition, 1981.

    MATH  Google Scholar 

  10. Wolfgang Haken. Theorie der Normalflächen. Acta Math., 105:245–375, 1961.

    Article  MATH  MathSciNet  Google Scholar 

  11. Dov Harel and Robert Endre Tarjan. Fast algorithms for finding nearest common ancestors. SIAMJ. Comput., 13:338–355, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  12. Joel Hass, Jeffrey C. Lagarias, and Nicholas Pippenger. The computational complexity of knot and link problems. J. ACM, 46:185–211, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  13. William Jaco and Jeffrey L. Tollefson. Algorithms for the complete decomposition of a closed 3-manifold. Illinois J. Math., 39:358–406, 1995.

    MATH  MathSciNet  Google Scholar 

  14. Andrew R. Leach. Molecular Modeling, Principles and Applications. Pearson Education Limited, Harlow, England, 1996.

    Google Scholar 

  15. J.R. Munkres. Elements of Algebraic Topology. Addison-Wesley, Redwood City, California, 1984.

    MATH  Google Scholar 

  16. RCSB. Protein data bank. http://www.rcsb.org/pdb/.

  17. Dale Rolfsen. Knots and Links. Publish or Perish, Inc., Houston, Texas, 1990.

    MATH  Google Scholar 

  18. H. Seifert. Über das Geschlecht von Knoten. Math. Annalen, 110:571–592, 1935.

    Article  MATH  MathSciNet  Google Scholar 

  19. William R. Taylor. A deeply knotted protein structure and how it might fold. Nature, 406:916–919, 2000.

    Article  Google Scholar 

  20. Jan van Leeuwen. Finding lowest common ancestors in less than logarithmic time. Unpublished report.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Edelsbrunner, H., Zomorodian, A. (2001). Computing Linking Numbers of a Filtration. In: Gascuel, O., Moret, B.M.E. (eds) Algorithms in Bioinformatics. WABI 2001. Lecture Notes in Computer Science, vol 2149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44696-6_9

Download citation

  • DOI: https://doi.org/10.1007/3-540-44696-6_9

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42516-8

  • Online ISBN: 978-3-540-44696-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics