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Peak Shift

FIGURE 2.18 Peak-interval gap procedure, peak time distributions. This figure demonstrates the differing predictions of the stop-reset and decay hypotheses. If subjects' accumulated subjective time decays smoothly over the course of a gap, one would expect that the amount of peak shift would be normally distributed. If the subjective time is either held or reset, one would expect a bimodal distribution, with some trials showing no loss of subjective time and some showing complete resetting.

short gap, producing something similar to a stop result. In a longer gap, the stored duration would have had time to decay almost completely, producing something like a reset result. The model described here uses a decay system.

These two hypotheses could be tested by looking at the sizes of peak shifts for individual gap trials. If the stop-reset concept was correct, one would expect to see a bimodal distribution of peak shifts, with stop results clustered at one end of the distribution and resets clustered at the other. If the decay hypothesis is correct, the distribution should be relatively normal, as illustrated in Figure 2.18. So far, this analysis has not been done due to the complexity of determining peak times for individual gap trials. Individual trials tend to be noisy, and the methods for determining the peak time of an individual trial are complex and not universally accepted (Church et al., 1994).

A parametric study of the gap procedure done by Cabeza de Vaca et al. (1994) provided three distinct patterns of data. These results, taken together, represent the best opportunity available for comparing the performance of a timing model to animal data in a quantitative fashion. The results of this experiment were very clean and precisely in accord with the predictions of a decay process. In the following simulations, all simulation data represent the peak shift on the very first gap presentation after 100 trials of the PI procedure training.

In the fixed onset series, the subjects were presented with gaps of varying lengths that always started at a fixed point 6 sec into the trial, as shown in Figure 2.19, bottom panel. As described above, the mean peak shifts were almost always somewhere between a stop result and a reset result. The subjects showed a nonlinear pattern of peak shifts, with the peak shifts starting very close to a stop result in the

Gap Length

Peak trial -

Gap at 3 sec

Gap at 6 sec

Gap at 9 sec

Gap at 12 sec

### Gap at 15 sec

FIGURE 2.19 Peak-interval gap procedure, fixed onset simulations. These data present the amount of peak shift resulting from gaps of different durations but with the same onset time. The lower panel graphically shows the six locations of the gaps within the interval. The animal data presented are taken from Cabeza de Vaca et al. (1994).

short gap trials and asymptotically approaching a reset result in the longer gap trials, as illustrated in Figure 2.19, top panel. The model matches these data extremely well, with a correlation of .9994 (P < .0001).

In the fixed offset series, gaps of various lengths were presented that always ended at a fixed point 21 sec into the trial, as shown in the bottom panel of Figure 2.20. The peak shifts produced were again nonlinear, starting close to a stop result and approaching a reset result asymptotically, as shown in Figure 2.20, top panel. The model again matches these data very well, with a correlation of .998 (P < .0001).

In the location series, 6-sec gaps were presented at various times within the interval, as shown in Figure 2.21, bottom panel. Subjects produced peak shifts that

Peak trial

Gap of 6 sec

Gap of 9 sec

Gap of 12 sec

Gap of 15 sec

### Gap at 15 sec

FIGURE 2.20 Peak-interval gap procedure, fixed offset simulations. These data present the amount of peak shift resulting from gaps of different durations but with the same offset time. The lower panel graphically shows the six locations of the gaps within the interval. The animal data presented are taken from Cabeza de Vaca et al. (1994).

increased linearly with the location of the gap, approximately midway between a stop and a reset result, as illustrated in Figure 2.21, top panel. Once again, the model matches the animal data very well, with a correlation of .995 (P < .0005).

The excellence of these fits is not unique. Hopson (1999) found that adding a decay mechanism to the spectral timing model allowed it to model these data nearly as well. The success of these fits is most likely due to the fact that the data conform so perfectly to the predictions of a decay process.

### 2.4.3.2 Filled-Gap Timing

One of the most interesting aspects of the gap procedure is the lack of learning that goes on. Gaps occur only during probe trials; therefore, one might expect that the

Peak trial

Gap of 3 sec Gap of 6 sec Gap of 9 sec

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