A comparison is made between the frequency of local minima in the analytic power (AP) of intracranial EEG (ECoG) from waking and unconscious human subjects and the frequency of putative frames of consciousness reported in earlier psychological literature. In ECoG from unconscious subjects, the frequency of deep minima in AP is found to be a linear function of bandwidth. In contrast, in ECoG from conscious subjects, the bandwidth/minima-frequency curve saturates or plateaus at minima frequencies similar to the frequencies of previously reported frames of consciousness. This result is consistent with the hypothesis that local minima in AP may act as the shutter in a cinematographic model of consciousness. The fact that artificially generated samples of black noise with power spectra similar to ECoG data give similar results in the analyses above suggests that the discontinuous nature of consciousness is not due to some specifically biological factor, but is simply a consequence of the physical properties of the 1/f (aka power law) oscillations that are widely found in nature.
An experiment using a vertical array to detect acoustic normal modes in shallow water is described. A high signal-to-noise ratio was achieved by the use of pseudorandom pulse sequences to modulate the projector. Wide bandwidth signals and a tunable acoustic source enabled the frequency dependence of normal modes to be measured and results are in good agreement with the theory. An improved method of extracting the signal present in a single mode is described and used to examine pulse shapes and frequency spectra of individual modes.
Several examples of the ease of application and accuracy of ray tracing resulting from the top-down approach are given to demonstrate the results obtainable with today’s small computers. One example of a more traditional approach is given to demonstrate how easy it is to lose computational accuracy to mixing instead of isolating the steps in the solution. The current level of commonly available computing power means that it is important for the ordinary researcher to be aware of powerful integration subroutines. Their extraordinary accuracy makes the payoff worth the effort expended in understanding their use.
Freeman and Baird [5; Freeman WJ, Baird B. Behav Neurosci 1987;101:393-408] recorded from the surface of the brain in waking rabbits and found spatial patterns of voltage that covaried with sensory experience. We simulate mathematically the electric fields produced by radial dipoles in cortical gyri and show that patterns with the spatial frequencies observed by Freeman and Baird could be produced by cortical dipoles spaced 3 mm apart. We further calculate that to resolve the patterns produced by such dipole arrays, it is necessary to record less than 2.5 mm above the surface of the cortex. High-pass spatial filters increase this distance to 4.5 mm. Since the human scalp is 15-16 mm above the brain, we conclude that spatial patterns of voltage covarying with sensation are unlikely to be detectable in scalp records. If such patterns do exist in humans, dural or sub-dural electrode arrays, with an inter-electrode spacing of 1 mm or less, will be necessary to record them.
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