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.
12th CHAOS Conference Proceedings, 18–22 June 2019, Chania, Crete, Greece.
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E. Kändel, Principles of Neural Science, 5th edn. (McGraw-Hill Companies, 2013)
H. Atmanspacher, Quantum Approaches to Consciousness (The Stanford Encyclopaedia of Philosophy, 2011)
H. Atmanspacher, W. Fach, A structural-phenomenological typology of mind-matter correlation. J. Anal. Psychol. 58, 219–244 (2013)
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)
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)
T.A. Witten Jr., L.M. Sander, Diffusion-limited aggregation, a kinetic critical phenomenon. Phys. Rev. Lett. 47, 1400–1403 (1981)
K.D. Kniffki, M. Pawlak, C. Vahle-Hinz, Scaling behavior of the dendritic branches of thalamic neurons. Fractals 1, 171–178 (1993)
G. Werner, Perspectives on the neuroscience of cognitions and consciousness. BioSystems 87, 82–95 (2007)
G. Werner, Consciousness related neural events viewed as brain state space transition. Cogn. Neurodyn. 3, 83–95 (2009)
R.L. de Valois, K.K. de Valois, Spatial Vision, Oxford Psychology series No. 14, (Oxford University Press, New York, 1988)
R.L. de Valois, K.K. de Valois, A multi-stage color model. Vision Res. 33, 1053–1065 (1993)
G. von Békési, Problems relating psychological and electrophysiological observations in sensory perception. Perspect. Biol. Med. 11, 179–194 (1970)
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. 745–748
S.B. Lowen, M.C. Teich, Fractal based Point Processes (Wiley, New York, 2005)
N.B. Karayiannis, A.N. Venetsanopoulos, Artificial neural networks, learning algorithms, performance evaluation, and applications. Springer Int. Eng. Comput. Sci. 209 (1993)
A. Slavova, Cellular Neural Networks: Dynamics and Modeling, Mathematical Modeling: Theory and Applications, vol. 16, (Springer, Berlin, 2003)
N. Chomski, Language and the Study of Mind (Sansyusya Publishing, Tokyo, 1982)
T.W.S. Chow, Neural Networks and Computing. Learning Algorithms and Applications, Series in Electrical and Computer Engineering (2007)
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)
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)
A.J. Ibáñez-Molina, S. Iglesias-Parro, Fractal characterization of internally and externally generated conscious experiences. Brain Cogn. 87, 69–75 (2014)
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)
B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman and Company, New York, 1983)
L. Nottale, Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity (World Scientific, Singapore, 1993)
L. Nottale, Scale Relativity and Fractal Space-Time: A New Approach to Unifying Relativity and Quantum Mechanics (Imperial College Press, London, UK, 2011)
L. Nottale, Scale relativity: a fractal matrix for organization in nature. Electron. J. Theor. Phys. 4, 187–274 (2007)
M. Agop, N. Forna, I. Casian-Botez, New theoretical approach of the physical processes in nanostructures. J. Comput. Theor. Nanosci. 5, 483–489 (2008)
M. Agop, A. Gavriluţ, G. Crumpei, B. Doroftei, Informational non-differentiable entropy and uncertainty relations in complex systems. Entropy 16, 6042–6058 (2015)
M. Agop, A. Gavriluţ, G. Ştefan, B. Doroftei, Implications of non-differentiable entropy on a space-time manifold. Entropy 17, 2184–2197 (2015)
A. Timofte, I. Casian-Botez, D. Scurtu, M. Agop, System dynamics control through the fractal potential. Acta Phys. Pol. A 119, 304–311 (2011)
D. Bohm, A suggested interpretation of the quantum theory in terms of "hidden" variables. Phys. Rev. 85, 166–179 (1952)
J. Cresson, Scale relativity theory for one dimensional non differentiable manifolds. Chaos Solitons Fractals 14, 553–562 (2002)
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/S0219749914500221
P. Lévy, Theories de l’Addition Aléatoires (Gauthier-Villars, Paris, 1937)
E.A. Jackson, Perspectives on Nonlinear Dynamics (Cambridge University Press, Cambridge, 1992)
J.V. Armitage, W.F. Eberlein, Elliptic Functions (Cambridge University Press, Cambridge, 2006)
M. Chaichian, N.F. Nelipa, Introduction to Gauge Field Theories (Springer, Berlin, Heidelberg, 1984)
M. Toda, Theory of Nonlinear Lattices (Springer, New York, Berlin, 1981)
M. Toda, Nonlinear lattice and soliton theory. IEEE Trans. CAS 30, 542–554 (1983)
S. Willard, General Topology, (Addison-Wesley Pub. Co., Reading, MA, 1970) ISBN 0486434796, Retrieved 2013
T.A. Brown, Genomes, 2nd edn. (Wiley-Liss, Oxford, 2002). ISBN -10: 0-471-25046-5
J. Gardiner, R. Overall, J. Marc, The fractal nature of the brain. NeuroQuantology 8(2), 137–141 (2010)
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)
S. Pockett, The Nature of Consciousness: A Hypothesis, Writers Club Press (2000)
J. McFadden, The conscious electromagnetic information (Cemi) field theory: the hard problem made easy? J. Conscious. Stud. 9(8), 45–60 (2002)
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)
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. 385–404
W.R. Uttal, Neural Theories of Mind: Why the Mind-Brain Problem May Never Be Solved (Erlbaum, Mahwah, NJ, 2005)
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 2011
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Agop, M., Gavriluţ, A., Crumpei, G., Eva, L. (2020). Brain Dynamics Explained by Means of Spectral-Structural Neuronal Networks. In: Skiadas, C., Dimotikalis, Y. (eds) 12th Chaotic Modeling and Simulation International Conference. CHAOS 2019. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-39515-5_3
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