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There is a widespread intuitive sense that different kinds of information spread differently on-line, but it has been difficult to evaluate this question quantitatively since it requires a setting where many different kinds of information spread in a shared environment. Here we study this issue on Twitter, analyzing the ways in which tokens known as hashtags spread on a network defined by the interactions among Twitter users. We find significant variation in the ways that widely-used hashtags on different topics spread. Our results show that this variation is not attributable simply to differences in "stickiness," the probability of adoption based on one or more exposures, but also to a quantity that could be viewed as a kind of "persistence" - the relative extent to which repeated exposures to a hashtag continue to have significant marginal effects. We find that hashtags on politically controversial topics are particularly persistent, with repeated exposures continuing to have unusually large marginal effects on adoption; this provides, to our knowledge, the first large-scale validation of the "complex contagion" principle from sociology, which posits that repeated exposures to an idea are particularly crucial when the idea is in some way controversial or contentious. Among other findings, we discover that hashtags representing the natural analogues of Twitter idioms and neologisms are particularly non-persistent, with the effect of multiple exposures decaying rapidly relative to the first exposure. We also study the subgraph structure of the initial adopters for different widely-adopted hashtags, again finding structural differences across topics. We develop simulation-based and generative models to analyze how the adoption dynamics interact with the network structure of the early adopters on which a hashtag spreads.