Advertisement

Brain Dynamics Explained by Means of Spectral-Structural Neuronal Networks

  • Maricel Agop
  • Alina GavriluţEmail author
  • Gabriel Crumpei
  • Lucian Eva
Conference paper
  • 11 Downloads
Part of the Springer Proceedings in Complexity book series (SPCOM)

Abstract

In this chapter, we propose a mathematical-physical model, starting from the morphological-functional assumption of the fractal brain, by activating brain non-differentiable dynamics through the determinism-nondeterminism inference of the responsible mechanisms.

Keywords

Fractal brain Brain dynamics Neuronal networks Neuropsychological mechanisms Brain geodesics 

References

  1. 1.
    E. Kändel, Principles of Neural Science, 5th edn. (McGraw-Hill Companies, 2013)Google Scholar
  2. 2.
    H. Atmanspacher, Quantum Approaches to Consciousness (The Stanford Encyclopaedia of Philosophy, 2011)Google Scholar
  3. 3.
    H. Atmanspacher, W. Fach, A structural-phenomenological typology of mind-matter correlation. J. Anal. Psychol. 58, 219–244 (2013)CrossRefGoogle Scholar
  4. 4.
    F. Caserta, W.D. Eldred, E. Fernandez, R.E. Hausman, L.R. Stanford, S.V. Bulderev, S. Schwarzer, H.E. Stanley, Determination of fractal dimension of physiologically characterized neurons in two and three dimensions. J. Neurosci. Methods 56, 133–144 (1995)CrossRefGoogle Scholar
  5. 5.
    F. Caserta, H.E. Stanley, W.D. Eldred, G. Daccord, R.E. Hausman, J. Nittman, Physical mechanisms underlying neurite outgrowth: a quantitative analysis of neuronal shape. Phys. Rev. Lett. 64, 95–98 (1990)ADSCrossRefGoogle Scholar
  6. 6.
    T.A. Witten Jr., L.M. Sander, Diffusion-limited aggregation, a kinetic critical phenomenon. Phys. Rev. Lett. 47, 1400–1403 (1981)ADSCrossRefGoogle Scholar
  7. 7.
    K.D. Kniffki, M. Pawlak, C. Vahle-Hinz, Scaling behavior of the dendritic branches of thalamic neurons. Fractals 1, 171–178 (1993)CrossRefGoogle Scholar
  8. 8.
    G. Werner, Perspectives on the neuroscience of cognitions and consciousness. BioSystems 87, 82–95 (2007)ADSCrossRefGoogle Scholar
  9. 9.
    G. Werner, Consciousness related neural events viewed as brain state space transition. Cogn. Neurodyn. 3, 83–95 (2009)CrossRefGoogle Scholar
  10. 10.
    R.L. de Valois, K.K. de Valois, Spatial Vision, Oxford Psychology series No. 14, (Oxford University Press, New York, 1988)Google Scholar
  11. 11.
    R.L. de Valois, K.K. de Valois, A multi-stage color model. Vision Res. 33, 1053–1065 (1993)CrossRefGoogle Scholar
  12. 12.
    G. von Békési, Problems relating psychological and electrophysiological observations in sensory perception. Perspect. Biol. Med. 11, 179–194 (1970)CrossRefGoogle Scholar
  13. 13.
    S.B. Lowen, M.C. Teich, Fractal Auditory Nerve Firing Patterns May Derive From Fractal Switching in Sensory Hair Cell Ion Channels, in Proceedings of the AIP Conference on American Institute of Physics, vol. 285 eds. P.H. Handel, A.L. Chung (1993), pp. 745–748Google Scholar
  14. 14.
    S.B. Lowen, M.C. Teich, Fractal based Point Processes (Wiley, New York, 2005)CrossRefGoogle Scholar
  15. 15.
    N.B. Karayiannis, A.N. Venetsanopoulos, Artificial neural networks, learning algorithms, performance evaluation, and applications. Springer Int. Eng. Comput. Sci. 209 (1993)Google Scholar
  16. 16.
    A. Slavova, Cellular Neural Networks: Dynamics and Modeling, Mathematical Modeling: Theory and Applications, vol. 16, (Springer, Berlin, 2003)Google Scholar
  17. 17.
    N. Chomski, Language and the Study of Mind (Sansyusya Publishing, Tokyo, 1982)Google Scholar
  18. 18.
    T.W.S. Chow, Neural Networks and Computing. Learning Algorithms and Applications, Series in Electrical and Computer Engineering (2007)Google Scholar
  19. 19.
    M.H. Díaz, F.M. Córdova, L. Cañete, F. Palominos, F. Cifuentesa, C. Sánchez, M. Herrera, Order and chaos in the brain: fractal time series analysis of the EEG activity during a cognitive problem solving task, Proc. Comput. Sci. Inf. Technol. Quant. Manage. 55, 1410–1419 (2015)CrossRefGoogle Scholar
  20. 20.
    H. Diaz, F. Córdova, Harmonic fractals in the brain: transient tuning and synchronic coordination in the quasi-chaotic background of ongoing neural EEG activity. Proc. Comput. Sci. 17, 403–411 (2013)CrossRefGoogle Scholar
  21. 21.
    A.J. Ibáñez-Molina, S. Iglesias-Parro, Fractal characterization of internally and externally generated conscious experiences. Brain Cogn. 87, 69–75 (2014)CrossRefGoogle Scholar
  22. 22.
    A. Khodabakhsh, A. Mehran, R. Majid, A.M. Esfandiar, S. Firoozeh, Brain activity of women is more fractal than men. Neurosci. Lett. 535, 7–11 (2013)CrossRefGoogle Scholar
  23. 23.
    B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman and Company, New York, 1983)CrossRefGoogle Scholar
  24. 24.
    L. Nottale, Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity (World Scientific, Singapore, 1993)CrossRefGoogle Scholar
  25. 25.
    L. Nottale, Scale Relativity and Fractal Space-Time: A New Approach to Unifying Relativity and Quantum Mechanics (Imperial College Press, London, UK, 2011)CrossRefGoogle Scholar
  26. 26.
    L. Nottale, Scale relativity: a fractal matrix for organization in nature. Electron. J. Theor. Phys. 4, 187–274 (2007)Google Scholar
  27. 27.
    M. Agop, N. Forna, I. Casian-Botez, New theoretical approach of the physical processes in nanostructures. J. Comput. Theor. Nanosci. 5, 483–489 (2008)CrossRefGoogle Scholar
  28. 28.
    M. Agop, A. Gavriluţ, G. Crumpei, B. Doroftei, Informational non-differentiable entropy and uncertainty relations in complex systems. Entropy 16, 6042–6058 (2015)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    M. Agop, A. Gavriluţ, G. Ştefan, B. Doroftei, Implications of non-differentiable entropy on a space-time manifold. Entropy 17, 2184–2197 (2015)ADSCrossRefGoogle Scholar
  30. 30.
    A. Timofte, I. Casian-Botez, D. Scurtu, M. Agop, System dynamics control through the fractal potential. Acta Phys. Pol. A 119, 304–311 (2011)CrossRefGoogle Scholar
  31. 31.
    D. Bohm, A suggested interpretation of the quantum theory in terms of "hidden" variables. Phys. Rev. 85, 166–179 (1952)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    J. Cresson, Scale relativity theory for one dimensional non differentiable manifolds. Chaos Solitons Fractals 14, 553–562 (2002)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    V.S. Bîrlescu, M. Agop, M. Craus, Computational properties of a fractal medium. Int. J. Quantum Inf. 12, 22 (2014).  https://doi.org/10.1142/S0219749914500221MathSciNetCrossRefGoogle Scholar
  34. 34.
    P. Lévy, Theories de l’Addition Aléatoires (Gauthier-Villars, Paris, 1937)zbMATHGoogle Scholar
  35. 35.
    E.A. Jackson, Perspectives on Nonlinear Dynamics (Cambridge University Press, Cambridge, 1992)Google Scholar
  36. 36.
    J.V. Armitage, W.F. Eberlein, Elliptic Functions (Cambridge University Press, Cambridge, 2006)zbMATHGoogle Scholar
  37. 37.
    M. Chaichian, N.F. Nelipa, Introduction to Gauge Field Theories (Springer, Berlin, Heidelberg, 1984)CrossRefGoogle Scholar
  38. 38.
    M. Toda, Theory of Nonlinear Lattices (Springer, New York, Berlin, 1981)CrossRefGoogle Scholar
  39. 39.
    M. Toda, Nonlinear lattice and soliton theory. IEEE Trans. CAS 30, 542–554 (1983)ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    S. Willard, General Topology, (Addison-Wesley Pub. Co., Reading, MA, 1970) ISBN 0486434796, Retrieved 2013Google Scholar
  41. 41.
    T.A. Brown, Genomes, 2nd edn. (Wiley-Liss, Oxford, 2002). ISBN -10: 0-471-25046-5Google Scholar
  42. 42.
    J. Gardiner, R. Overall, J. Marc, The fractal nature of the brain. NeuroQuantology 8(2), 137–141 (2010)CrossRefGoogle Scholar
  43. 43.
    G. Crumpei, A. Gavriluţ, I. Crumpei Tanasă, M. Agop, New Paradigms on Information, Mind and Reality from a Transdisciplinary Perspective (Junimea Publishing House, Iaşi, 2016)Google Scholar
  44. 44.
    S. Pockett, The Nature of Consciousness: A Hypothesis, Writers Club Press (2000)Google Scholar
  45. 45.
    J. McFadden, The conscious electromagnetic information (Cemi) field theory: the hard problem made easy? J. Conscious. Stud. 9(8), 45–60 (2002)Google Scholar
  46. 46.
    J. McFadden, Synchronous firing and its influence on the brain’s electromagnetic field: evidence for an electromagnetic field theory of consciousness. J. Conscious. Stud. 9(4), 23–50 (2002)Google Scholar
  47. 47.
    J. McFadden, The CEMI Field Theory: Seven Clues to the Nature of Consciousness, ed. by J.A. Tuszynski (Springer, The Emerging Physics of Consciousness, Berlin, 2006), pp. 385–404Google Scholar
  48. 48.
    W.R. Uttal, Neural Theories of Mind: Why the Mind-Brain Problem May Never Be Solved (Erlbaum, Mahwah, NJ, 2005)Google Scholar
  49. 49.
    V.S. Ramachandran, Mirror Neurons and Imitation Learning as the Driving Force Behind the Great Leap Forward in Human Evolution. Edge Foundation. Retrieved 19 Oct 2011Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Maricel Agop
    • 1
  • Alina Gavriluţ
    • 2
    Email author
  • Gabriel Crumpei
    • 3
  • Lucian Eva
    • 4
  1. 1.Department of PhysicsGheorghe Asachi Technical University of IaşiIaşiRomania
  2. 2.Faculty of MathematicsAlexandru Ioan Cuza UniversityIaşiRomania
  3. 3.Faculty of Psychology and Education SciencesAlexandru Ioan Cuza UniversityIaşiRomania
  4. 4.“Prof. Dr. N. Oblu” Clinical Emergency Hospital IaşiIaşiRomania

Personalised recommendations