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We also found that recovery from errors follows a long-tailed distribution with an exponential cut-off.
Jensen [28] claims that finite-size systems often show an exponential cut-off below the system size.
In this case, the matter power spectrum has an exponential cut-off at ({simeq}0.05mbox { Mpc}), which corresponds to a mass of ({simeq}5times10^{6}mbox { M}_{odot}).
The authors further find that the rank-ordered ingredient distribution (i.e., ingredients are ranked by the number of recipes in which they appear) follows a power law with an exponential cut-off to capture finite size effects.
The popularity of YouTube videos, commonly expressed by the number of views in research studies, follows a heavy-tailed distribution that, depending on the data set and the method used to fit the distribution, can be described by power-law with exponential cut-off [28], Weibull [41], log-normal [42], or Gamma distributions [43].
(a) The recency-based rank of D1 has exponents (alpha_{K_{s}} approx 1.644) and exponential cut-off (kappa_{K_{s}}approx40.94), whereas the frequency-based rank distribution has a better fit for (alpha_{K_{f}}approx1.56) with (kappa_{K_{f}} approx23.6).
On the other hand, the weight distribution is heterogeneous and decays approximately as a power law, with an exponential cut-off, as shown in Figure 5, panel B. Figure 4 Network of contacts between household members aggregated over the whole study duration.
Under these circumstances they have often been modified by the inclusion of one or more additional parameters, e.g. Gaussian or exponential cut-offs.
We therefore also tried to fit an integrated (cumulative) distribution of the exact waiting-time probability distribution derived from the Barabási's model with two tasks [24] and a power-law distribution plus exponential cut-off, in addition to the stretched exponential form, to active period durations (Appendix S1; Table S5, Table S6 and Table S7; Figure S1).
Although there is a discrepancy between the model networks and the yeast PIN for a large k (see Discussion), the results showed that both models can reproduce the degree distribution of the yeast PIN that follows a power law with an exponential cut-off.
(In the case of PINs, it is known that P(k) better fits a power law with an exponential cut-off, i.e., P k)∼ k0+k)−γ e−k/kc [7], [10].) Therefore, a scale-free network is highly heterogeneous and is characterized by the presence of a large number of nodes having only a few links and a small number of nodes (hubs) that have numerous links.
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Justyna Jupowicz-Kozak
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