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\subsection{Temporal analysis of delay and span}  In Figure \ref{fig:delay_span}, \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~\ref{fig:delay_span_arxiv}, 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 ($x<=100: y>0.6$).