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(Russo and Mandell, 1984a; Mandell, 1984), and, more recently, to multiple simultaneously EEG leads which demonstrated focal increases in epileptic patients (Inouye et al, 1991; 1992). An entropy derived from the quantification of the failures in temporal forecasting of EEG signals increased in the fronto-temporal region with drug treatment in patients with Alzheimer’s syndrome (Pezard et al, 1998).

With respect to their implications for the clinical neurosciences, changes in dynamical entropy in behavior of brain dynamical systems has been regarded in two general ways: (1) Since representation of information requires the resolution of relevant ambiguity, a nonrelevant and global reduction in the dynamical entropy of a brain system (Stage IV sleep EEG slow waves, neuronal fixed point or regularly periodic activity, extrapyramidal motor tremor, fixed paranoid or obsessional mentation, the actions of some anxiolytics and antipsychotics ) reduces its potential for information encoding and transport. In contrast, “arousal” induced increases in the measures of entropy in brain wave and neuronal discharge patterns (pre-task warning signals, motivating conditions, stimulant drugs) are associated with improved psychophysical receptive and discrimination functions, learning rates and memory. (2) Regarding as potentially pathophysiological both of the two extremes of entropy generation, fixed point and periodic behavior as the lowest and fair coin flipping, “Bernoulli” randomness as the highest, another descriptor, “complexity” is defined as maximal (optimal) midway through the entropy range, making a new kind of parabolic entropy curve (Bennett, 1986; Crutchfield and Young, 1989a).

In analogy with an optimal amalgam of periodic rotations and coin flips, in higher dimension, the most meaningful maximum complexity of real, nonuniformly expansive processes may derive from a multiplicity of measure invariants, symmetries, of the system such as the growth rate of unstable periodic orbits, divergence of the tail of a density distribution and specifiable linguistic variables such as word length and redundancy. The more symmetries, the more potential for complicated information encoding and transport with the maximum complexity located midrange in each one. We have pursued the hypothesis that entropy is a conserved property in the healthy brain and that complementarity in other statistical measure mechanisms make that possible. For example, in uniformly expansive,

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