shift from hyperactivity to motor stereotypy (Paulus et al, 1991). Studies that

shift from hyperactivity to motor stereotypy (Paulus et al, 1991). Studies that followed demonstrated that “q-moment” distributions of heterogeneous scaling exponents and their relative statistical weightings were useful in making subtle discriminations between effects of psychopharmacological agents and behavioral (isolation) influences on animal behavior as well as patterns of simple psychomotor behavior in normal subjects and schizophrenic patients (Paulus et al, 1994; 1996; 1998; Krebs-Thomson et al, 1998a; 1998b). Fractal Scaling Measures on Reconstructed Time Series from Biological Dynamics Publications involving the applications of various D measures, particularly Dz, to brain-relevant times series number in the hundreds and are growing exponentially. The following constitutes a brief review of a representative set of empirical findings. In doing so, for the reasons discussed below, we ignore what some might consider the rather abstract and philosophical issue of “determinism” versus “randomness” or “error” (Sugihara and May, 1990; Casdagli, 1991; Wayland et al, 1993; Kaplan and Glass, 1992; Kaplan, 1994) since this question is relatively unproductive with respect to generating new neurobiological insights, novel experiments or new quantitative approaches to brain dynamics. In addition, as noted in the final section, this discrimination may not even have definitive theoretical meaning in that the conduct of much of the rigorous mathematics about “deterministic dynamical systems” involve Markoff partitions and matrices which are also the generic operators of formal probability theory (Sullivan, 1979; Kolmogorov, 1950). For example, N-dimensional non-linear Markoff processes can be shown to capture the dynamics of multidimensional neurobiological processes such as the EEG (Silipo et al, 1998). We have also ignored the related issue of the presence or absence of “low dimensional structure” (Theiler and Rapp, 1996; Rapp, 1995) which, from the authors’ point of view, resulted from an unfortunately concrete interpretation of the word “dimensions.” With respect to experimental brain data, dimensions are defined 232 HOUSE_OVERSIGHT_013732