Extended Data Fig. 10: A phenomenological model of our hypothesis on how long-term physiological effects of single TMS pulses affect serial bias curves in event-related experimental sessions.

Our TMS results show a difference between the effects of sham stimulation at the vertex and sham stimulation over dlPFC (Fig. 6). We interpret this baseline difference as the possible effect of long-term physiological alterations by single pulses 58 (but see ref. ⁷²) that carry over from “strong-tms” trials to “no-tms” trials. We explicitly implemented this interpretation in the following way: we generated trial-by-trial responses biased depending on the sequence of stimuli according to a given baseline serial bias curve (a, “Vertex” condition where TMS is ineffective). In the “PFC” condition the serial bias strength changed depending on TMS conditions: in “weak-tms” trials the pulse had the acute effect of increasing the bias strength momentarily by an additive factor (3 times the baseline bias strength), in “strong-tms” trials the effect of the pulse was chronic: the bias changed with a negative additive component (equal in magnitude to the baseline strength), which decayed slowly through subsequent trials (10% decay/trial). When collapsing together “responses” obtained on the basis of this model through a sequence of randomly selected “no-tms”, “weak-tms” and “strong-tms” trials, serial bias curves showed the pattern observed experimentally, where sham (“no-tms”) trials show repulsion in the “PFC” condition (panel b) and not in the “Vertex” condition (panel a). The difference of serial bias curves for “weak-tms” and “no-tms” then showed the modulation clearly in “PFC” and not in “Vertex” (panel c), as seen in the data (Fig. 6).