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FIGURE 20.1 Migration on retrieval is associated with violation of the scalar property, while slowed encoding follows the scalar rule. Estimate distributions from training and testing sessions in real time (left panels) and time relative to the median time (right panels). The smooth curves are Gaussian fits to the data. The ON-ON group (top row) shows veridical estimates in both training and testing sessions ON DA supplementation. Migration occurs in the OFF state during both training (OFF-ON group, bottom row, black) and testing (ON-OFF group, middle row, black) sessions. The ON testing data from the OFF-ON group are right shifted (bottom row, gray). In the right panels all four estimation distributions of each group are shown in relative time. Functions in the ON-ON group (upper right panel) superpose (scalar property). This is not the case for the functions in the ON-OFF and OFF-ON groups, where in both cases increased variability (broader functions) is seen OFF L-Dopa (black distributions) as compared to the ON state (gray distributions). Increased variability in the OFF state was found to violate the scalar property (Malapani et al., 2002a).

response-times that are longer than the target interval. However, animal data suggest that dopamine depletion slows the clock (Meck, 1996), rather than speeding it up. Moreover, those results indicating a slowing of the clock with dopamine depletion are easier to reconcile with the findings of overall cognitive slowness known as "bradyphrenia" in dopamine-depleted PD patients (Malapani et al., 1994), than are suggestions of a speeded clock. Consequently, a clock-speed account of the lengthened estimates seems unlikely. A "slowed encoding" process was instead suggested to accommodate the double overestimates, such that veridical accumulations get translated into exaggerated (slowed) memory values (Gibbon and Malapani, 2002). The most likely SET implementation of this effect involves changes to the K* parameter, however, there is no corroborating data to indicate that DA modulates this parameter. While great difficulty remains in attributing specific neuromodulator action to specific SET parameters, SET itself has several information-processing components with parameters that can give rise to the "slowed encode" effect seen in PD.

The migration effect, however, cannot be reconciled with the scalar expectancy theory or other theories that posit a monotonic relationship between changes in the subjective experience of time and changes to model parameters that effect linear transformations of represented time. A great strength of SET is that cognitive sources of timing accuracy and variability are stated in time-independent terms. This formulation allows the scalar property of timing variability to emerge, but also makes modeling of duration-dependent effects, such as migration, difficult. As a result, new theories are necessary to further research a phenomenon that is emerging as central to understanding the internal clock.

Toward this end, we present a simple neural network model of a pacemaker-accumulator system developed by Miall (1996). This model can produce migration in mean time values by simultaneous adjustment of the model's two free parameters, as well as unidirectional effects of the sort exemplified by slowed encoding. Of special interest are the general properties of the model that can be abstracted from the overly simple network architecture and used to modify SET to account for the migration effect. In addition, this model has several other interesting features that suggest analogy to PD neuropathology and experimental tests of timing behavior in both healthy and pathological populations (Malapani et al., 2002a; in press).

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