Modeling the effects of signal gain and position tuning narrowing. **A)** We obtained a BOLD response curve for use in subsequent simulations by measuring the BOLD signal along slices on each subject’s inflated cortex (see Supplemental Experimental Procedures). Data from all subjects were plotted together and normalized by peak amplitude to generate a prototypical BOLD response profile for use in modeling. These data were fit with a difference-of-Gaussians function (black curve), and 200 points were sampled evenly along this curve for use in subsequent simulations. B) Using the resulting BOLD response curve, we produced a simulated position discrimination plot (like those in ), sampling on a continuous range of stimulus separations (green curve). To produce this plot, in a Monte Carlo simulation, we added realistic noise (SNR = 15.33; see Supplemental Experimental Procedures) to two copies of the prototype BOLD response curve, and varied the offset between them, computing the correlation at each separation. To model the effects of gain and narrowing on the position discrimination plot, we repeated the same Montecarlo simulation after adding a 10% amplitude gain (red curve) and, separately, a 10% width narrowing (blue curve) to the BOLD response profiles. The application of signal gain increased the correlation between the simulated BOLD response patterns at every separation along the abscissa, while narrowing the BOLD response profiles decreased the correlation at every separation; both gain and tuning narrowing made the slope of the curve steeper. **C)** Simultaneously applying both gain and narrowing to the simulated BOLD response profiles produced the purple curve. This curve crosses the baseline (green) curve in the same fashion that the attended and unattended regression lines cross in the position discrimination data presented in . **D)** To model the effects across a broad range of signal gain strengths and levels of position tuning narrowing, we performed a similar Monte Carlo simulation as above, this time holding the separation between the two simulated BOLD response curves constant, and instead varying the gain level (left plot in red) or the curve width (right plot in blue) over a wide range of values. We separately tested the effects of response gain, activity gain, and additive gain (see ): response gain and activity gain yielded the same monotonically increasing curve (solid red), while additive gain left the correlations unchanged at all levels (dashed red). Narrowing the curve widths always decreased their correlation (blue curve).

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