Rapidly stopping action engages a network in the brain including the right presupplementary motor area (preSMA), the right inferior frontal gyrus, and the basal ganglia. Yet the functional role of these different regions within the overall network still remains unclear. Here we focused on the role of the right preSMA in behavioral stopping. We hypothesized that the underlying neurocognitive fun...

Let (Sn)n≥0 be a correlated random walk on the integers, let M0 ≥ S0 be an arbitrary integer, and let Mn = max{M0, S1, . . . , Sn}. An optimal stopping rule is derived for the sequence Mn − nc, where c > 0 is a fixed cost. The optimal rule is shown to be of threshold type: stop the first time that Mn−Sn ≥ ∆, where ∆ is a certain nonnegative integer. An explicit expression for this optimal thres...

We consider two distinct centers which arise in measuring how quickly a random walk on a tree mixes. Lovász and Winkler [8] point out that stopping rules which “look where they are going” (rather than simply walking a fixed number of steps) can achieve a desired distribution exactly and efficiently. Considering an optimal stopping rule that reflects some aspect of mixing, we can use the expecte...