Skip to main content

On the α-Shiner–Davison–Landsberg Complexity Measure

  • Conference paper
  • 813 Accesses

Part of the book series: Springer Proceedings in Complexity ((SPCOM))

Abstract

Shannon entropy is essential for the study of complex continuous systems as it forms various complexity measures. Shiner–Davison–Landsberg (SDL) complexity is such a measure used for the characterization of complex bio-systems, especially in the study of the EEG signals on epileptic seizures. We consider a continuous system whose various states can be described by a wide range of distributions provided by the family of the γ-ordered Normal distributions. Moreover, for the construction of the SDL measure of complexity we consider the generalized Shannon entropy derived via the generalized Fisher’s entropy type measure of information J α . The obtained α-SDL complexity is evaluated and studied with regards to the absolute complexity state, which is important in bio-systems.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover 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

References

  1. Feldman DP, Crutchfield JP (1998) Measures of statistical complexity: why? Phys Lett A 238:244–252

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Kitsos CP, Toulias TL (2012) On the multivariate γ-ordered normal distribution. Far East J Theor Stat 38(1):49–73

    MathSciNet  MATH  Google Scholar 

  3. Kitsos CP, Toulias TL (2011) On the family of the γ-ordered normal distributions. Far East J Theor Stat 35(2):95–114

    MathSciNet  MATH  Google Scholar 

  4. Kitsos CP, Toulias TL (2010) New information measures for the generalized normal distribution. Information 1:13–27

    Article  Google Scholar 

  5. Kitsos CP, Tavoularis NK (2009) Logarithmic Sobolev inequalities for information measures. IEEE Trans Inf Theory 55(6):2554–2561

    Article  MathSciNet  Google Scholar 

  6. Lopez–Ruiz R, Mancini HL, Calbet X (1991) A statistical measure of complexity. Phys Lett A 209:321–326

    Article  ADS  Google Scholar 

  7. Lamberti PW, Martin MT, Plastino A, Rosso OA (2004) Intensive entropic non-triviality measure. Physica A 334:119–131

    Article  MathSciNet  ADS  Google Scholar 

  8. Martin MT, Plastino A, Rosso OA (2003) Statistical complexity and disequilibrium. Phys Lett A 311:126–132

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Rosso OA, Martin MT, Plastino A (2003) Brain electrical activity analysis using wavelet-based informational tools (II): Tsallis non-extensivity and complexity measures. Physica A 320:497–511

    Article  ADS  MATH  Google Scholar 

  10. Shiner JS, Davison M, Landsberg PT (1999) Simple measure for complexity. Phys Rev E 59(2):1459–1464

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Thomas L. Toulias .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this paper

Cite this paper

Toulias, T.L., Kitsos, C.P. (2013). On the α-Shiner–Davison–Landsberg Complexity Measure. In: Gilbert, T., Kirkilionis, M., Nicolis, G. (eds) Proceedings of the European Conference on Complex Systems 2012. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-00395-5_32

Download citation

Publish with us

Policies and ethics