IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v390y2011i21p3732-3741.html
   My bibliography  Save this article

Physical complexity of variable length symbolic sequences

Author

Listed:
  • Briscoe, Gerard
  • De Wilde, Philippe

Abstract

A measure called physical complexity is established and calculated for a population of sequences, based on statistical physics, automata theory, and information theory. It is a measure of the quantity of information in an organism’s genome. It is based on Shannon’s entropy, measuring the information in a population evolved in its environment, by using entropy to estimate the randomness in the genome. It is calculated from the difference between the maximal entropy of the population and the actual entropy of the population when in its environment, estimated by counting the number of fixed loci in the sequences of a population. Up until now, physical complexity has only been formulated for populations of sequences with the same length. Here, we investigate an extension to support variable length populations. We then build upon this to construct a measure for the efficiency of information storage, which we later use in understanding clustering within populations. Finally, we investigate our extended physical complexity through simulations, showing it to be consistent with the original.

Suggested Citation

  • Briscoe, Gerard & De Wilde, Philippe, 2011. "Physical complexity of variable length symbolic sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3732-3741.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:21:p:3732-3741
    DOI: 10.1016/j.physa.2011.06.025
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437111004729
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2011.06.025?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lamberti, Pedro W. & Majtey, Ana P., 2003. "Non-logarithmic Jensen–Shannon divergence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 81-90.
    2. Richard E. Lenski & Charles Ofria & Robert T. Pennock & Christoph Adami, 2003. "The evolutionary origin of complex features," Nature, Nature, vol. 423(6936), pages 139-144, May.
    3. Constantino Tsallis & Celia Anteneodo & Lisa Borland & Roberto Osorio, 2003. "Nonextensive statistical mechanics and economics," Papers cond-mat/0301307, arXiv.org.
    4. Tsallis, Constantino & Anteneodo, Celia & Borland, Lisa & Osorio, Roberto, 2003. "Nonextensive statistical mechanics and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 89-100.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Diks, Cees & Hommes, Cars & Zeppini, Paolo, 2013. "More memory under evolutionary learning may lead to chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 808-812.
    2. Tapiero, Oren J., 2013. "A maximum (non-extensive) entropy approach to equity options bid–ask spread," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 3051-3060.
    3. Gu, Gao-Feng & Ren, Fei & Ni, Xiao-Hui & Chen, Wei & Zhou, Wei-Xing, 2010. "Empirical regularities of opening call auction in Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(2), pages 278-286.
    4. Devi, Sandhya, 2021. "Asymmetric Tsallis distributions for modeling financial market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    5. Zhao, Pan & Pan, Jian & Yue, Qin & Zhang, Jinbo, 2021. "Pricing of financial derivatives based on the Tsallis statistical theory," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    6. Meyer-Gohde, Alexander, 2019. "Generalized entropy and model uncertainty," Journal of Economic Theory, Elsevier, vol. 183(C), pages 312-343.
    7. Billio, Monica & Casarin, Roberto & Costola, Michele & Pasqualini, Andrea, 2016. "An entropy-based early warning indicator for systemic risk," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 45(C), pages 42-59.
    8. Zunino, L. & Pérez, D.G. & Kowalski, A. & Martín, M.T. & Garavaglia, M. & Plastino, A. & Rosso, O.A., 2008. "Fractional Brownian motion, fractional Gaussian noise, and Tsallis permutation entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6057-6068.
    9. Kozaki, M. & Sato, A.-H., 2008. "Application of the Beck model to stock markets: Value-at-Risk and portfolio risk assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1225-1246.
    10. Marcaccioli, Riccardo & Livan, Giacomo, 2020. "Maximum entropy approach to multivariate time series randomization," LSE Research Online Documents on Economics 115284, London School of Economics and Political Science, LSE Library.
    11. Deng, Xinyang & Deng, Yong, 2014. "On the axiomatic requirement of range to measure uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 163-168.
    12. Sandhya Devi & Sherman Page, 2022. "Tsallis Relative entropy from asymmetric distributions as a risk measure for financial portfolios," Papers 2205.13625, arXiv.org.
    13. Takahashi, Taiki & Hadzibeganovic, Tarik & Cannas, Sergio & Makino, Takaki & Fukui, Hiroki & Kitayama, Shinobu, 2009. "Cultural neuroeconomics of intertemporal choice," MPRA Paper 16814, University Library of Munich, Germany.
    14. Han, Ruokang & Takahashi, Taiki, 2012. "Psychophysics of time perception and valuation in temporal discounting of gain and loss," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6568-6576.
    15. Mauro Politi & Nicolas Millot & Anirban Chakraborti, 2011. "The near-extreme density of intraday log-returns," Papers 1106.0039, arXiv.org.
    16. Sandhya Devi, 2016. "Financial Market Dynamics: Superdiffusive or not?," Papers 1608.07752, arXiv.org, revised Sep 2017.
    17. Devi, Sandhya, 2016. "Financial Market Dynamics: Superdiffusive or not?," MPRA Paper 73327, University Library of Munich, Germany, revised 24 Aug 2016.
    18. Ausloos, Marcel & Cerqueti, Roy & Mir, Tariq A., 2017. "Data science for assessing possible tax income manipulation: The case of Italy," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 238-256.
    19. Marco A. S. Trindade & Sergio Floquet & Lourival M. S. Filho, 2018. "Portfolio Theory, Information Theory and Tsallis Statistics," Papers 1811.07237, arXiv.org, revised Oct 2019.
    20. Marian Gidea & Yuri Katz, 2017. "Topological Data Analysis of Financial Time Series: Landscapes of Crashes," Papers 1703.04385, arXiv.org, revised Apr 2017.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:390:y:2011:i:21:p:3732-3741. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.