\subsection{Temporal analysis of delay and span}
In Figure 6, we plot the distributions of $\Theta_{\text{ax}}(a_i)$, $\Delta_{\text{ax}}(a_i)$, $\Theta_{\text{tw}}(a_i)$, and $\Delta_{\text{tw}}(a_i)$ following article submission. We can see that the distributions of $\Theta_{\text{ax}}(a_i)$, $\Delta_{\text{ax}}(a_i)$, $\Theta_{\text{tw}}(a_i)$, and $\Delta_{\text{tw}}(a_i)$ are highly skewed towards very low values, with very few cases characterized by extensive delays or time spans. In Figure 6(a), the distribution of  $\Theta_{\text{ax}}(a_i)$ curve shows that nearly all articles take at least 5 days to reach the peak of arXiv downloads ($x<=4: y=1$), i.e., all articles take more than 4 days to reach peak downloads. In addition, the distribution of $\Delta_{\text{ax}}(a_i)$ curve shows that most of the articles are downloaded persistently for over 100 days ($x<=100: y>0.6$). 

From Figure 6(b), it emerges that nearly 80\% of the articles in the corpus reach the peak of Twitter mention just one day after they are submitted, as is shown on the distribution of $\Theta_{\text{tw}}(a_i)$ curve ($x=2:y \simeq0.8$). Over 70\% articles reach the peak of Twitter mention within 5 days of submission ($x=5: y < 0.3$). However, the distribution of  $\Delta_{\text{tw}}(a_i)$ curve shows that over 80\% of arXiv.org articles are mentioned one and one day only ($x=2: y<0.2$), i.e., one or multiple tweets about an article are posted within the time range of 24 hours and then are never mentioned again. Overall, compared with arXiv downloads, the Twitter response to scientific articles is typically swift, yet highly ephemeral, a pattern indicative of a process in which the news of a publication is quickly passed around and very little in-depth discussion taking place afterward.
