2009
DOI: 10.1142/s1793005709001271
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Coherent States, Fractals and Brain Waves

Abstract: 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.

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Cited by 66 publications
(87 citation statements)
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References 57 publications
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“…Moreover, a fundamental role is played by the (fractal-like) self-similarity (Figure 2) of the EMS emitted by the DNA-{water dipole wave} interaction vertex, which has been shown [20][21][22][23] to be the manifestation of coherent microscopic dynamics, as indeed our discussion in this paper has suggested. These (fractal-like) self-similarity properties of the EMS in turn induce self-similar organization in the irradiated water.…”
Section: Discussion and Concluding Remarkssupporting
confidence: 64%
See 1 more Smart Citation
“…Moreover, a fundamental role is played by the (fractal-like) self-similarity (Figure 2) of the EMS emitted by the DNA-{water dipole wave} interaction vertex, which has been shown [20][21][22][23] to be the manifestation of coherent microscopic dynamics, as indeed our discussion in this paper has suggested. These (fractal-like) self-similarity properties of the EMS in turn induce self-similar organization in the irradiated water.…”
Section: Discussion and Concluding Remarkssupporting
confidence: 64%
“…The decimal dilutions of original concentration of 2 ng/ml HIV-1 emitting EMS are between 10 −6 and 10 −10 (the first of the serial dilutions do not emit detectable signals) [3][4][5][6]. In the range between about 100 and 2000 Hz the signal shows fluctuations densely distributed around the linear fit with negative slope coefficient d = 0.80794, thus exhibiting scale-free, self-similar behavior in that frequency range with self-similarity (fractal) dimension d. It is known [20][21][22][23] that such a fractal-like self-similarity structure is the manifestation of coherent dynamics active at a microscopic level, as we indeed find in the following sections. This first step can be followed in different conditions of space and time by a second step, consisting in transformation of the signal into an analog form and sending its electric vector to a solenoid which will generate a magnetic field in a test tube of water.…”
Section: The Taq-dna Interaction and Open Questionsmentioning
confidence: 99%
“…3 and 6) belong to different dynamical regimes (phases) [24]. It is interesting to observe that the linear behavior in log-log PDS/frequency plots in specific intervals of frequencies found in the present system, also appears in brain studies where assemblies (clusters) of large number of neurons with phase locked amplitude modulated oscillations and self-similarity properties are observed as well [25,26,27,28,29,30,21]. Our expectation is that, in addition to its specific biochemical and cellular composition, coherent dynamics and self-similarity properties would play a crucial role in the evolution of a biological system through non-equilibrium processes driven by external inputs and boundary conditions.…”
Section: Discussionsupporting
confidence: 66%
“…In other words, memory is embodied as an ordered pattern supported by long-range correlations. This leads to the following apparent paradox: if neural information is transmitted via well-defined pulses and dendritic currents through specific synapses, then how can neural fields exist, transmissions maintained and being organized in large-scale patterns of activity without apparent regard to specific pathways in the cortical tissue (Vitiello 2009). Pribram addressed similar questions using his holographic theory of brain operation (Pribram 2013).…”
Section: Phase Transitions In Cortical Dynamicsmentioning
confidence: 99%