Stimulus counterbalance is critical for studies of neural habituation, bias, anticipation, and (more generally) the effect of stimulus history and context. We introduce de Bruijn cycles, a class of combinatorial objects, as the ideal source of pseudo-random stimulus sequences with arbitrary levels of counterbalance. Neuro-vascular imaging studies (such as BOLD fMRI) have an additional requirement imposed by the filtering and noise properties of the method: only some temporal frequencies of neural modulation are detectable. Extant methods of generating counterbalanced stimulus sequences yield neural modulations that are weakly (or not at all) detected by BOLD fMRI. We solve this limitation using a novel "path-guided" approach for the generation of de Bruijn cycles. The algorithm encodes a hypothesized neural modulation of specific temporal frequency within the seemingly random order of events. By positioning the modulation between the signal and noise bands of the neuro-vascular imaging method, the resulting sequence markedly improves detection power. These sequences may be used to study stimulus context and history effects in a manner not previously possible.
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