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Paulus MP, Geyer MA. 
“A temporal and spatial scaling hypothesis for the behavioral effects of psychostimulants”. 
Psychopharmacology (Berl). 1991;104(1):6-16.
A variety of psychoactive substances (amphetamine, nicotine, scopolamine, apomorphine, lisuride, and MDMA) were tested to examine whether a proposed scaling hypothesis is appropriate for the description of the amount and the structure of rat locomotor paths recorded in the Behavioral Pattern Monitor (BPM). The analytical approach was based on the assumption that the scaling behavior of a few collective variables may characterize sufficiently changes in the animal's behavior induced by different drugs. The temporal scaling exponent alpha, describing the ratio of fast to slow responses in the BPM, sensitively reflected the different stimulant properties of the substances. The spatial scaling exponent d, which relates the average path length to the resolution used to measure consecutive responses, was found to discriminate substances that had been separated previously via qualitative descriptions. Several behavioral response categories emerged from comparisons of the locations of different drugs on a two-dimensional d-a plane. Scopolamine, MDMA, lisuride, and high doses of apomorphine increased a while decreasing d, whereas amphetamine, nicotine, and caffeine produced an increased a with no change or an increase in d. Stereotypies could be identified on the opposite ends of the spatial scaling exponent scale and were interpreted as reflecting two kinds of perseveration. These results suggest that scaling approaches can be used to assess quantitatively the state of the animal based on its locomotor behavior and that the exponents can serve as collective variables providing a macroscopic description based on the microscopic elements of behavior.
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