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Open Physics

formerly Central European Journal of Physics

Editor-in-Chief: Feng, Jonathan

Managing Editor: Lesna-Szreter, Paulina

1 Issue per year


IMPACT FACTOR 2016 (Open Physics): 0.745
IMPACT FACTOR 2016 (Central European Journal of Physics): 0.765

CiteScore 2016: 0.82

SCImago Journal Rank (SJR) 2015: 0.458
Source Normalized Impact per Paper (SNIP) 2015: 1.142

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Online
ISSN
2391-5471
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Volume 13, Issue 1 (Jan 2015)

Issues

Novel measures based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis

Dragutin T. Mihailović
  • Corresponding author
  • Faculty of Agriculture, University of Novi Sad, Dositeja Obradovica Sq. 8, 21000 Novi Sad, Serbia
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Gordan Mimić
  • Faculty of Sciences, Department of Physics, University of Novi Sad, Dositeja Obradovica Sq. 3, 21000 Novi Sad, Serbia
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Emilija Nikolić-Djorić / Ilija Arsenić
Published Online: 2014-09-25 | DOI: https://doi.org/10.1515/phys-2015-0001

Abstract

We propose novel metrics based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis. We consider the origins of the Kolmogorov complexity and discuss its physical meaning. To get better insights into the nature of complex systems and time series analysis we introduce three novel measures based on the Kolmogorov complexity: (i) the Kolmogorov complexity spectrum, (ii) the Kolmogorov complexity spectrum highest value and (iii) the overall Kolmogorov complexity. The characteristics of these measures have been tested using a generalized logistic equation. Finally, the proposed measures have been applied to different time series originating from: a model output (the biochemical substance exchange in a multi-cell system), four different geophysical phenomena (dynamics of: river flow, long term precipitation, indoor 222Rn concentration and UV radiation dose) and the economy (stock price dynamics). The results obtained offer deeper insights into the complexity of system dynamics and time series analysis with the proposed complexity measures.

Keywords : complexity; physical complexity; Kolmogorov complexity spectrum; overall Kolmogorov complexity; time series

PACS : ; ; ; ;

References

  • [1] V. Arshinov, C. Fuchs, Causality, Emergence, Self-Organisation, (NIA-Priroda, Moscow, 2003)Google Scholar

  • [2] B. Edmonds, What is Complexity? - The Philosophy of Complexity per se with Application to Some Examples in Evolution, In: F. Heylighen, D. Aerts (Eds.) The Evolution of Complexity, (Dordrecht, Kluwer, 1999)Google Scholar

  • [3] S. Kauffman, The Origins of Order, (Oxford University Press, Oxford, 1993)Google Scholar

  • [4] F. Heylighen, The Growth of Structural and Functional Complexity during Evolution, In: F. Heylighen, D. Aerts (Eds.) The Evolution of Complexity, (Dordrecht, Kluwer, 1997)Google Scholar

  • [5] J. P. Crutchfield, Nat. Phys. 8, 17 (2012)CrossrefGoogle Scholar

  • [6] J. J. Binney, N. J. Dowrick, A. J. Fisher, M. E. J. Newman, The Theory of Critical Phenomena, (Oxford University Press, Oxford, 1992)Google Scholar

  • [7] M. C. Cross, P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993)CrossrefGoogle Scholar

  • [8] P. Manneville, Dissipative Structures and Weak Turbulence, (Academic Press, Boston, 1990)Google Scholar

  • [9] J. A. Wheeler, The Proceedings of the Workshop on Complexity, Entropy, and the Physics of Information, Held May-June, 1989, in Santa Fe, New Mexico, In:W. Zurek (Ed.) Entropy, Complexity, and the Physics of Information volume VIII, SFI Studies in the Sciences of Complexity, Addison-Wesley (1990)Google Scholar

  • [10] L. Zunino, M. C. Soriano,O. A. Rosso, Phys. Rev. E 86, 046210 (2012)CrossrefGoogle Scholar

  • [11] C. Adami, N. J. Cerf, Physica D 137, 62 (2000)Google Scholar

  • [12] M. Cover, J. A. Thomas, Elements of Information Theory, (Wiley, New York, 1991)Google Scholar

  • [13] P. Grassberger, arXiv:1208.3459 [physics.data-an] (2012)Google Scholar

  • [14] A. K. Sen, Stoch. Environ Res Risk Assess, 23, 361 (2009)Google Scholar

  • [15] D. T. Mihailovic, E. Nikolic-Djoric, N. Dreškovic N, G. Mimic, Physica A 395, 96 (2014)Google Scholar

  • [16] D. T. Mihailovic, V. Udovicic, M. Krmar, I. Arsenic, Appl. Radiat. Isotopes 84, 27 (2014)CrossrefGoogle Scholar

  • [17] D. P. Feldman, J. P. Crutchfield, Phys. Lett. A 238, 244 (1998)Google Scholar

  • [18] A. Kolmogorov, IEEE Trans. Inform. Theory IT-14, 662 (1968)CrossrefGoogle Scholar

  • [19] M. Li and P. Vitanyi, An Introduction to Kolmogorov Complexity and its Applications, Second Edition, (Springer Verlag, Berlin, 1997)Google Scholar

  • [20] A. Lempel, J. Ziv, IEEE Trans. Inform. Theory 22, 75 (1976)CrossrefGoogle Scholar

  • [21] X. S. Zhang, R. J. Roy, E.W. Jensen, IEEE Trans. Biomed. Eng. 48, 1424 (2001)CrossrefGoogle Scholar

  • [22] N. Radhakrishnan, J. D. Wilson, P. C. Loizou, Int. J. Bifurc. Chaos 10, 1773 (2000)CrossrefGoogle Scholar

  • [23] R. Ferenets, T. Lipping, A. Anier, IEEE Trans. Biomed. Eng. 53, 1067 (2006)CrossrefGoogle Scholar

  • [24] J. Hu, J. Gao, J. C. Principe, IEEE T. Bio-Eng 53, 2606 (2006)CrossrefGoogle Scholar

  • [25] D. Ruelle, Phys. Today 47, 24 (1994)CrossrefGoogle Scholar

  • [26] A. Serletis, A. Shahmoradi, D. Serletis, Chaos Soliton Fract. 33, 914 (2007)CrossrefGoogle Scholar

  • [27] A. Serletis, A. Shahmoradi, D. Serletis, Chaos Soliton Fract. 32, 883 (2007)CrossrefGoogle Scholar

  • [28] Y. Pomeau, P. Manneville, Commun. Math. Phys. 74, 189 (1980)CrossrefGoogle Scholar

  • [29] C. Adami, Bioessays 24, 1085 (2002)CrossrefGoogle Scholar

  • [30] P. Grassberger, Helv. Phys. Acta 62, 489 (1989)Google Scholar

  • [31] G. Grass, The Tin Drum, [Transl. by Ralph Manheim], (Secker & Warburg, London, 1962)Google Scholar

  • [32] D. T. Mihailovic, I. Balaž, I. Arsenic, Cent. Eur. J. Phys. 11, 40 (2013)Google Scholar

  • [33] B. van der Pol, J. van der Mark, Nature 120, 363 (1927)Google Scholar

  • [34] D. T. Mihailovic, I. Balaž, Mod. Phys. Lett. B 26, 1150031-1 (2012)CrossrefGoogle Scholar

  • [35] W. Krabs, S. Pickl, Dynamical Systems - Stability, Controllability and Chaotic Behavior, (Springer, 2010)Web of ScienceGoogle Scholar

  • [36] J. D. Salas, H. S. Kim, R. Eykholt, P. Burlando, T. R. Green, Nonlinear Proc. Geoph. 12, 557 (2005)CrossrefGoogle Scholar

  • [37] S. Hajian, M. Sadegh Movahed, Physica A 389, 4942 (2010)Google Scholar

  • [38] M. Sadegh Movahed, E. Hermanis, Physica A 387, 915 (2008)Google Scholar

  • [39] E. Hadžic, N. Dreškovic, Climate change impact on water river flow: A case study for Sarajevo Valley (Bosnia And Herzegovina), In: Mihailovic DT (Ed.) Essays on Fundamental and Applied Environmental Topics, (Nova Science Publishers, New York, pp. 307-332, 2012)Google Scholar

  • [40] N. Dreškovic, S. Djug, Applying the inverse distance weighting and kriging methods of the spatial interpolation on the mapping the annual precipitation in Bosnia and Herzegovina, International Environmental Modelling and Software Society (iEMSs) International Congress on Environmental Modelling and Software Managing Resources of a Limited Planet, Sixth Biennial Meeting, Leipzig, Germany (2012)Google Scholar

  • [41] V. Udovi˘cic et al., Radiat. Prot. Dosimetry 145, 155 (2011)Google Scholar

  • [42] S. Malinovic-Milicevic, D. T. Mihailovic, B. Lalic, N. Dreškovic, Climate Res. 57, 111 (2013)CrossrefGoogle Scholar

  • [43] S. Malinovic, D. T. Mihailovic, D. Kapor, Z. Mijatovic, I. Arsenic, J. Appl. Meteorol. Climatol. 45, 1171 (2006)CrossrefGoogle Scholar

  • [44] L. Gulko, Int. J. Theor. Appl. Finance 2, 293 (1999)CrossrefGoogle Scholar

  • [45] S. Pincus, R. E. Kalman, Proceedings of the National Academy of Sciences 101, 13709 (2004)Google Scholar

  • [46] J. Alvarez-Ramirez, E. Rodriguez, J. Alvarez, Int. Rev. Financ. Anal. 21, 64 (2012)CrossrefGoogle Scholar

  • [47] R. Giglio, R. Matsushita, A. Figueiredo, I. Gleria, S. Da Silva, Europhys. Lett. 84, 48005 (2008)CrossrefGoogle Scholar

  • [48] W. Härdle, L. Simar, Applied Multivariate Statistical Analysis, (Springer-Verlag, Berlin Heidelberg, 2007) Google Scholar

About the article

Received: 2013-03-11

Accepted: 2014-06-24

Published Online: 2014-09-25

Published in Print: 2015-01-01


Citation Information: Open Physics, ISSN (Online) 2391-5471, DOI: https://doi.org/10.1515/phys-2015-0001.

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© 2015 D. T. Mihailovic et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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