COHERENT STATES, FRACTALS AND BRAIN WAVES

I show that a functional representation of self-similarity (as the one occurring in fractals) is provided by squeezed coherent states. In this way, the dissipative model of brain is shown to account for the self-similarity in brain background activity suggested by power-law distributions of power spectral densities of electrocorticograms. I also briefly discuss the action-perception cycle in the dissipative model with reference to intentionality in terms of trajectories in the memory state space.

[1]  K. Yasue,et al.  Quantum Brain Dynamics and Consciousness: An introduction , 1995 .

[2]  T. Ferrée,et al.  Fluctuation Analysis of Human Electroencephalogram , 2001, physics/0105029.

[3]  R. Glauber Coherent and incoherent states of the radiation field , 1963 .

[4]  J. Siegel,et al.  Unihemispheric slow wave sleep and the state of the eyes in a white whale , 2002, Behavioural Brain Research.

[5]  Dietmar Saupe,et al.  Chaos and fractals - new frontiers of science , 1992 .

[6]  Walter J. Freeman,et al.  Origin, structure, and role of background EEG activity. Part 4: Neural frame simulation , 2006, Clinical Neurophysiology.

[7]  W. Freeman,et al.  Nonlinear brain dynamics as macroscopic manifestation of underlying many-body field dynamics , 2005, q-bio/0511037.

[8]  Prof. Dr. Valentino Braitenberg,et al.  Anatomy of the Cortex , 1991, Studies of Brain Function.

[9]  W. Freeman Origin, structure, and role of background EEG activity. Part 2. Analytic phase , 2004, Clinical Neurophysiology.

[10]  A. Grinvald,et al.  Interaction of sensory responses with spontaneous depolarization in layer 2/3 barrel cortex , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[11]  K. Linkenkaer-Hansen,et al.  Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations , 2001, The Journal of Neuroscience.

[12]  K. Pribram,et al.  Brain and Being , 2004 .

[13]  Giuseppe Vitiello,et al.  DISSIPATION AND MEMORY CAPACITY IN THE QUANTUM BRAIN MODEL , 1995, quant-ph/9502006.

[14]  G. Vitiello Topological defects, fractals and the structure of quantum field theory , 2008, 0807.2164.

[15]  G. Vitiello The dissipative brain , 2004, q-bio/0409037.

[16]  M. A. Lohe,et al.  Quantum group symmetry and q-tensor algebras , 1995 .

[17]  Giuseppe Vitiello,et al.  Quantum noise, entanglement and chaos in the quantum field theory of mind/brain states , 2003, q-bio/0309009.

[18]  Péter Érdi,et al.  The KIV model - nonlinear spatio-temporal dynamics of the primordial vertebrate forebrain , 2003, Neurocomputing.

[19]  Giuseppe Vitiello,et al.  Quantum noise induced entanglement and chaos in the dissipative quantum model of brain , 2004, quant-ph/0406161.

[20]  W. Freeman Ndn, volume transmission, and self-organization in brain dynamics. , 2005, Journal of integrative neuroscience.

[21]  Miss A.O. Penney (b) , 1974, The New Yale Book of Quotations.

[22]  M. Rasetti,et al.  SU(1,1) SQUEEZED STATES AS DAMPED OSCILLATORS , 1989 .

[23]  H. Umezawa DEVELOPMENT IN CONCEPTS IN QUANTUM FIELD THEORY IN HALF CENTURY , 1995 .

[24]  W. CLEMENT LEY,et al.  Brain Dynamics , 1880, Nature.

[25]  D. Kusnezov,et al.  Quantum Dissipation , 1995, nucl-th/9507034.

[26]  Gyöngyi Gaál,et al.  A neurobiological theory of meaning in perception . Part 3 . Multiple cortical areas synchronize without loss of local autonomy International Journal of Bifurcation & Chaos [ 2003 ] 13 : in press , 2003 .

[27]  Walter J. Freeman,et al.  Origin, structure, and role of background EEG activity. Part 3. Neural frame classification , 2005, Clinical Neurophysiology.

[28]  Guanrong Chen,et al.  Complex networks: small-world, scale-free and beyond , 2003 .

[29]  H. Umezawa,et al.  On the stability and non-local properties of memory. , 1978, Journal of theoretical biology.

[30]  G. Vitiello My double unveiled , 2001 .

[31]  W. Freeman,et al.  How brains make chaos in order to make sense of the world , 1987, Behavioral and Brain Sciences.

[32]  R. Jindra Mass action in the nervous system W. J. Freeman, Academic Press, New York (1975), 489 pp., (hard covers). $34.50 , 1976, Neuroscience.

[33]  K. Pribram,et al.  FROM CONSCIOUS EXPERIENCE TO MEMORY STORAGE AND RETRIEVAL: THE ROLE OF QUANTUM BRAIN DYNAMICS AND BOSON CONDENSATION OF EVANESCENT PHOTONS , 1996 .

[34]  Friedrich Beck,et al.  Quantum Brain Dynamics and Consciousness , 2001 .

[35]  Giuseppe Vitiello,et al.  Vortices in brain waves , 2008, 0802.3854.

[36]  A. Opstal Dynamic Patterns: The Self-Organization of Brain and Behavior , 1995 .

[37]  E. Alfinito,et al.  Formation and life-time of memory domains in the dissipative quantum model of brain , 2000 .

[38]  Michael Creutz,et al.  Fractals and Self-Organized Criticality , 1994 .

[39]  Giuseppe Vitiello,et al.  Classical chaotic trajectories in quantum field theory , 2003, hep-th/0309197.

[40]  M. Raichle The Brain's Dark Energy , 2006, Science.

[41]  Nicolai Reshetikhin,et al.  Quantum Groups , 1993 .

[42]  I. Tsuda Toward an interpretation of dynamic neural activity in terms of chaotic dynamical systems. , 2001, The Behavioral and brain sciences.

[43]  V. Bargmann On a Hilbert space of analytic functions and an associated integral transform part I , 1961 .

[44]  Donald O. Walter,et al.  Mass action in the nervous system , 1975 .

[45]  Walter J. Freeman,et al.  A Neurobiological Theory of Meaning in Perception Part V: Multicortical Patterns of Phase Modulation in Gamma EEG , 2003, Int. J. Bifurc. Chaos.

[46]  Walter J. Freeman,et al.  A field-theoretic approach to understanding scale-free neocortical dynamics , 2005, Biological Cybernetics.

[47]  E. Alfinito,et al.  Domain formation in noninstantaneous symmetry breaking phase transitions , 2001 .

[48]  S. Doglia,et al.  A quantum field theoretical approach to the collective behaviour of biological systems , 1985 .

[49]  Stephen M. Kosslyn,et al.  The Languages of the Brain , 2002 .

[50]  M. M. Miller,et al.  Fundamentals of Quantum Optics , 1968 .

[51]  Maxim I. Stamenov The Fractal-Like Roots of Mind: A tutorial in direct access , 1996 .

[52]  H. Umezawa,et al.  Mixed-system brain dynamics: Neural memory as a macroscopic ordered state , 1979 .

[53]  G. Vitiello,et al.  On topological defect formation in the process of symmetry breaking phase transitions , 2002 .

[54]  J. Kelso,et al.  Cortical coordination dynamics and cognition , 2001, Trends in Cognitive Sciences.

[55]  Walter J. Freeman,et al.  A Neurobiological Theory of Meaning in Perception Part III: Multiple Cortical Areas Synchronize without Loss of Local Autonomy , 2003, Int. J. Bifurc. Chaos.

[56]  Michael Martin Nieto,et al.  Coherent States , 2009, Compendium of Quantum Physics.

[57]  G. Vitiello Essere nel mondo: Io e il mio Doppio , 2008 .

[58]  Hiroomi Umezawa,et al.  Advanced Field Theory: Micro, Macro, and Thermal Physics , 1993 .

[59]  E. H. Wilson Origin , 1927, Bulletin of popular information - Arnold Arboretum, Harvard University..

[60]  H. Kowarzyk Structure and Function. , 1910, Nature.

[61]  F. Wilczek Quantum Field Theory , 1998, hep-th/9803075.

[62]  D. Gabor A New Microscopic Principle , 1948, Nature.

[63]  L. Ryder,et al.  Quantum Field Theory , 2001, Foundations of Modern Physics.

[64]  Hubert L. Dreyfus,et al.  Why Heideggerian AI Failed and How Fixing it Would Require Making it More Heideggerian , 2007, Artif. Intell..

[65]  George Sugihara,et al.  Fractals in science , 1995 .

[66]  A. Perelomov Generalized Coherent States and Their Applications , 1986 .

[67]  D. GABOR,et al.  Improved Holographic Model of Temporal Recall , 1968, Nature.

[68]  S. Liberati Quantum Analogues: From Phase Transitions to Black Holes and Cosmology , 2008 .

[69]  E.Celeghini,et al.  Quantum groups, coherent states, squeezing and lattice quantum mechanics , 1993 .

[70]  E. Bullmore,et al.  Adaptive reconfiguration of fractal small-world human brain functional networks , 2006, Proceedings of the National Academy of Sciences.

[71]  Classical trajectories and quantum field theory , 2005 .

[72]  W. Freeman,et al.  Dissipation and spontaneous symmetry breaking in brain dynamics , 2007, q-bio/0701053.

[73]  D. Fivel Quasi-coherent states and the spectral resolution of the q-bose field operator , 1991 .

[74]  A. Malafosse,et al.  Genetic variation in EEG activity during sleep in inbred mice. , 1998, American journal of physiology. Regulatory, integrative and comparative physiology.

[75]  K. Lashley The mechanism of vision; effects of destroying the visual associative areas of the monkey. , 1948, Genetic psychology monographs.

[76]  H. Yuen Two-photon coherent states of the radiation field , 1976 .

[77]  W. Freeman,et al.  Spatial spectra of scalp EEG and EMG from awake humans , 2003, Clinical Neurophysiology.

[78]  W. Freeman,et al.  Bidirectional processing in the olfactory-limbic axis during olfactory behavior. , 1998, Behavioral neuroscience.

[79]  G. Vitiello Links. Relating different physical systems through the common QFT algebraic structure , 2006, hep-th/0610094.

[80]  M. Rasetti,et al.  Squeezing and quantum groups. , 1991, Physical Review Letters.

[81]  Shlomo Havlin,et al.  Fractals in Science , 1995 .

[82]  M. Yamaguti,et al.  Chaos and Fractals , 1987 .

[83]  Amruth N. Kumar,et al.  Links , 1999, INTL.

[84]  Alwyn C. Scott,et al.  Toward a Science of Consciousness II: The 1996 Tucson Discussions and Debates , 1998 .

[85]  Kenneth Lash,et al.  Borges and I , 1960 .

[86]  W. Freeman How Brains Make Up Their Minds , 1999 .

[87]  Walter J. Freeman,et al.  A neurobiological theory of meaning in perception , 2003, Proceedings of the International Joint Conference on Neural Networks, 2003..

[88]  A. Fingelkurts,et al.  Operational Architectonics of the Human Brain Biopotential Field: Towards Solving the Mind-Brain Problem , 2001 .

[89]  Walter J. Freeman,et al.  Origin, structure, and role of background EEG activity. Part 1. Analytic amplitude , 2004, Clinical Neurophysiology.

[90]  D. McCormick,et al.  Neocortical Network Activity In Vivo Is Generated through a Dynamic Balance of Excitation and Inhibition , 2006, The Journal of Neuroscience.

[91]  T. M. Mayhew,et al.  Anatomy of the Cortex: Statistics and Geometry. , 1991 .

[92]  E. Giudice,et al.  Electromagnetic field and spontaneous symmetry breaking in biological matter , 1986 .

[93]  Gavan Lintern,et al.  Dynamic patterns: The self-organization of brain and behavior , 1997, Complex.

[94]  Ichiro Tsuda,et al.  Towards an interpretation of dynamic neural activity in terms of chaotic dynamical systems , 2000 .