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The Hurst exponents of Nitzschia sp. diatom trajectories observed by light microscopy

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  • Murguía, J.S.
  • Rosu, H.C.
  • Jimenez, A.
  • Gutiérrez-Medina, B.
  • García-Meza, J.V.

Abstract

We present the results of an experiment with light microscopy performed to capture the trajectories of live Nitzschia sp. diatoms. The time series corresponding to the motility of this kind of cells along ninety-five circular-like trajectories have been obtained and analyzed with the scaling statistical method of detrended fluctuation analysis optimized via a wavelet transform. In this way, we determined the Hurst parameters, in two orthogonal directions, which characterize the nature of the motion of live diatoms in light microscopy experiments. We have found mean values of these directional Hurst parameters between 0.70 and 0.63 with overall standard errors below 0.15. These numerical values give evidence that the motion of Nitzschia sp. diatoms is of persistent type and suggest an active cell motility with a kind of memory associated with long-range correlations on the path of their trajectories. For the collected statistics, we also find that the values of the Hurst exponents depend on the number of abrupt turns that occur in the diatom trajectory and on the type of wavelet, although their mean values do not change much.

Suggested Citation

  • Murguía, J.S. & Rosu, H.C. & Jimenez, A. & Gutiérrez-Medina, B. & García-Meza, J.V., 2015. "The Hurst exponents of Nitzschia sp. diatom trajectories observed by light microscopy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 176-184.
    • Handle: RePEc:eee:phsmap:v:417:y:2015:i:c:p:176-184
    DOI: 10.1016/j.physa.2014.09.046
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    References listed on IDEAS

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    1. Murguía, J.S. & Rosu, H.C., 2012. "Multifractal analyses of row sum signals of elementary cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(13), pages 3638-3649.
    2. Nagarajan, Radhakrishnan & Kavasseri, Rajesh G., 2005. "Minimizing the effect of trends on detrended fluctuation analysis of long-range correlated noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 182-198.
    3. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    4. Liang Li & Simon F Nørrelykke & Edward C Cox, 2008. "Persistent Cell Motion in the Absence of External Signals: A Search Strategy for Eukaryotic Cells," PLOS ONE, Public Library of Science, vol. 3(5), pages 1-11, May.
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    1. Vargas-Olmos, C. & Murguía, J.S. & Ramírez-Torres, M.T. & Mejía Carlos, M. & Rosu, H.C. & González-Aguilar, H., 2016. "Perceptual security of encrypted images based on wavelet scaling analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 22-30.

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