Referee 2's review:

The authors examined a "memory" phenomenon in perceptual bistability. Previous research demonstrated that the same percept of an ambiguous visual stimulus persisted when the stimulus was presented briefly and intermittently. Presumably, brief and intermittent presentations do not substantially engage the inhibitory interactions and negative adaptation processes that generate spontaneous perceptual switches that occur during prolonged and continuous viewing of an ambiguous stimulus. The technique of briefly and intermittently presenting an ambiguous stimulus may thus reveal a memory process where each activation of a dominant percept leaves a "memory trace" that facilitates dominance of the same percept in subsequent brief presentations. The authors investigated a temporal aspect of this memory effect. Specifically, they determined whether the memory effect arising from each percept accumulated over time, or the effect reset following each percept. The authors nicely demonstrated that the memory effect was a combination of a short-term and long-term effect. The currently dominant percept had a relatively strong but short-lasting (several seconds) effect on the immediately following percepts. In addition, a long-term history of perceptual dominance (based on the relative proportion of dominance of the competing percepts during the preceding period of up to at least one minute) produced a long-lasting (> 16 seconds) effect. Importantly, the effect based on long-term history recovered after the short-lasting effect from the immediately preceding percept wore off, suggesting that the long-term and short-term effects are independent. The authors successfully fit these results by adding separate positive-adaptation terms, one with a short time constant and the other with a long time constant, to a standard dynamic model of perceptual switching. I think the results are clear, interesting, and the paper is well written.

Suggestions:
When presenting Spearman's correlation results, please provide the values of r in addition to the p values.
Figure S3 seems to be a duplication of Figure 3. Please provide Figure S3.
The authors might want to briefly discuss Wilson's model (Vision Research, 2007) which also incorporates the memory effect.

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N.B. These are the comments made by the referee when reviewing an earlier version of this paper. Prior to publication the manuscript has been revised in light of these comments and to address other editorial requirements.