Abstract
In the preceding two chapters, the challenge has been to understand the transition from sensation to perception. The problem and the solution could be remarkably similar in all sense modalities. The stimuli are microscopic forms of diverse energies in the form of molecules, photons, vibrations, and phonons, which are captured by molecular structures embedded in cilia of neurons in the eye, ear, nose, and skin. Cilia are macromolecular threads that extend from or through the individual receptor neurons. The cilia selectively transduce and amplify the incident energies by supplying their own metabolic energies and expressing them in ionic currents. The receptor cells convert the currents to pulse trains and transmit the microscopic information by pulse frequency modulation in proportion to transmembrane current density.
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- 1.
The question whether episodic synchronization occurred among channels was addressed with an index of synchrony between pairs of signals that was developed by Pikovsky et al. (2001) and applied by Tass et al. (1999) to evaluate coupling between a magnetoencephalographic (MEG) signal and an electromyographic (EMG) signal in subjects with Parkinsonian tremor. The index was based on normalized Shannon entropy and was modified to give zero for a uniform distribution of phase differences in a moving window and unity for global phase locking. Here the index was generalized to the nearly 2,000 channel pairs by combining them into a t-value at each step of the window (Freeman and Rogers 2002). The validity of the algorithm was first tested on 64-channel data by replicating the intermittent synchrony of bursts in the several rabbit neocortices. Then it was applied to the data from the multicortical ECoGs of cats (Freeman and Rogers 2003). All values were significantly above chance levels, but the salient features were four spikes in synchrony adjacent to the times of the peaks in correct classification (Fig. 10.3d, arrows in c).
- 2.
The dynamics of Gestalt formation has been modeled using K-sets (Sect. 8.2; Freeman and Erwin 2008) to implement the action–perception cycle in intentional robots (Kozma et al. 2003, 2008). The modeling was simplified by the linearity of the four operations: concatenation of macroscopic input feature vectors, spatiotemporal integration following a phase transition, transmission with the Gabor transform, down-sampling by local integration over the global AM pattern, and partitioning of the output to multiple targets. The operations were simulated with matrix algebra. Owing to linearity, the operations were commutative. The weights of the connections were expressed in matrices and adapted by learning in updating the memory bank of limit cycle attractors (Fig. 6.14).
- 3.
Measuring spatial phase gradients is an arduous task, requiring identification of an ECoG segment with a prominent spectral peak, band-pass filtering, calculation of a phase surface with respect to the frequency of the ensemble average, and fitting a conic surface by nonlinear regression (Freeman and Barrie 2000). A simpler assay could facilitate preliminary explorations (Ruiz et al. 2009). The analytic phase difference in rad was calculated between each pair of signals and grouped in accord with the distance between them in mm for the duration of an epoch of stable carrier frequency. The group averages in rad were plotted with distance in mm and fitted with a straight line, giving the gradient in rad/mm. This with the carrier frequency gave the phase velocity and half-power radius. The presence of a cone might be detected by grouping the phase differences with direction as well as distance.
- 4.
Stephen O. Rice (Sect. 9.5) proved (Rice 1944) that the modal recurrence rate in Hz of beats in white noise passed through an ideal filter was proportional solely to the width of the pass band in Hz and was independent of the center frequency. We demonstrated that this proportionality held for brown and black noise as well. The constant was 0.641, which the pass band of 7 H predicted a burst rate of 4.5 Hz.
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Freeman, W.J., Quiroga, R.Q. (2013). ECoG and EEG Images in Higher Cognition. In: Imaging Brain Function With EEG. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4984-3_10
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