Figure 5. Predicting the shape of the RP as a function of waiting time. A, Average stochastic input to the accumulator, time aligned to first crossing times in the output, separately for trials with a long wait (upper 33rd percentile; black line) and for trials with a short wait (lower 33rd percentile; gray line). B, Same as A but for the output of the accumulator. The early tail of the output on “short wait” trials is noisier than the rest because of missing data: on trials with a short wait, often the climb to the threshold was shorter than the epoch length. C, Schematic depiction of the input and output for constant input, time aligned to the beginning of the trial. On trials with a short wait, the input is greater and the output rises more quickly to the threshold. D, Same as C, but time aligned to the threshold crossing. Notice that when time is aligned to the threshold crossing the relationship between input and output becomes reversed. This helps to intuitively explain the reversal in the relationship between the predicted shape of the RP for long- and short-wait time trials. Parameters used for A, B: β = 1.4, I = 0.1, k = 0.6, and threshold = 0.1256. However, the relationship between predicted RPs for short versus long wait times (reversal of amplitude relationship for input versus output) remained qualitatively the same regardless of the specific parameters used, as long as β was >∼0.5. Regarding A, B, note that, because the epochs are time locked to threshold crossings in the output, only the outputs (B) are guaranteed to reach the same amplitude at t(0). The two curves in A do not necessarily have to reach the same amplitude at t(0), because these are the average inputs to the accumulator. The inputs for long and short waits in C, D are set to 1 and 2, respectively, for illustrative purposes, so that the slope of their respective outputs will be 1 and 2. Note that this overly simplified schematic is only intended to describe the relationship between the input and output but not their shape.