HOUSE_OVERSIGHT_013738.jpg

multiply periodic and aperiodic oscillations of thalamic and cortical cells and their recursive, feedback coupling, the brain stem manifests more than two orders of magnitude of “independent” neuronal driving frequencies ranging from serotonin discharges at 1 Hz, cortically direct dopamine and norepinephrine neurons in the 10-50Hz range and mesencephalic reticular neurons discharging as fast as 100 to 200 Hz. The “thalamocortical brain wave oscillator” as their target has been a fixture in global state neurophysiology since the 1940’s and 1950’s and is of great current interest (Fessard et al, 1961; Bazhenov et al, 1998). We have explored the relationships between strange nonchaotic dynamics and brain-stem neuronal and thalamocortical physiology from the standpoint of neuronal coding and the properties of the EEG attractor. (Mandell et al, 1991; Mandell and Kelso, 1991; Mandell and Selz, 1992; 1993;1994;1997a). We found that the EEG attractor could be characterized by the diagnostic triad identifying strange nonchaotic attractors: λ̅ = 0, D₀ and D₁ ≠ Integer, and a signatory power spectral distribution in which the number of peaks, N, with amplitudes greater than ϖ, N(ϖ ), went as ϖ⁻ᵃ, 1 < α < 2 (Romeiras et al, 1987; Mandell et al, 1991). In addition to being consistent with known multifrequency, brain stem driving of thalamocortical oscillations, the EEG as a strange, nonchaotic attractor is intuitively appealing in that it has the necessary mechanisms for the power law scaling of a wide range of characteristic times (D₀ and D₁ ≠ Integer) from picosecond fluctuations of neural membrane proteins to the decades of bipolar phenomena and since λ̅ = 0, the orbital points don’t tend to “mix”(get out of order) on the attractor, thus protecting the fidelity of sequence dependent brain information transport (Berns and Sejnowski, 1998).

Entropies, Unstable Periodic Orbits and Shadowing; Short Time Series Can Discriminate Experimental Conditions in Studies of Biological Dynamics

We avoid the temptation to deal with the deep analogy between thermodynamic entropy (Clausius, 1897) and information theoretic entropy (Shannon and Weaver, 1949), constraining our discussion to the context of an operational equivalence (in healthy systems) between gain of information and

238

HOUSE_OVERSIGHT_013738