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Fractal fluctuations and quantum-like chaos in the brain by analysis of variability of brain waves: A new method based on a fractal variance function and random matrix theory: A link with El Naschie fractal Cantorian space–time and V. Weiss and H. Weiss golden ratio in brain

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  • Conte, Elio
  • Khrennikov, Andrei
  • Federici, Antonio
  • Zbilut, Joseph P.

Abstract

We develop a new method for analysis of fundamental brain waves as recorded by the EEG. To this purpose we introduce a Fractal Variance Function that is based on the calculation of the variogram. The method is completed by using Random Matrix Theory. Some examples are given. We also discuss the link of such formulation with H. Weiss and V. Weiss golden ratio found in the brain, and with El Naschie fractal Cantorian space–time theory.

Suggested Citation

  • Conte, Elio & Khrennikov, Andrei & Federici, Antonio & Zbilut, Joseph P., 2009. "Fractal fluctuations and quantum-like chaos in the brain by analysis of variability of brain waves: A new method based on a fractal variance function and random matrix theory: A link with El Naschie f," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2790-2800.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2790-2800
    DOI: 10.1016/j.chaos.2008.10.016
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    References listed on IDEAS

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    1. Di Matteo, T. & Aste, T. & Dacorogna, M.M., 2003. "Scaling behaviors in differently developed markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 183-188.
    2. Conte, Elio & Todarello, Orlando & Federici, Antonio & Vitiello, Francesco & Lopane, Michele & Khrennikov, Andrei & Zbilut, Joseph P., 2007. "Some remarks on an experiment suggesting quantum-like behavior of cognitive entities and formulation of an abstract quantum mechanical formalism to describe cognitive entity and its dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1076-1088.
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    1. Karkare, Siddharth & Saha, Goutam & Bhattacharya, Joydeep, 2009. "Investigating long-range correlation properties in EEG during complex cognitive tasks," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2067-2073.
    2. Bhaduri, Anirban & Bhaduri, Susmita & Ghosh, Dipak, 2017. "Visibility graph analysis of heart rate time series and bio-marker of congestive heart failure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 786-795.

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