It is interesting to note that our null model implies that categories with large exponents, such as transcription factors, should show larger fluctuations in gene family sizes than categories with small exponents.
The reason why we started from not p=2 but p=1 is that a small exponent value, p/(β+p) in (41) and (42) or p/(p+2) in (55) and (57), in the NMF update rules provides better separation as revealed in [54], where the exponent value monotonically decreases as a value of p decreases.
Increasing the looping probability and thus the average number of loops per chain results in
In the case of a small degree exponent, in contrast, nodes tend to have different degrees in the networks, suggesting that the connectivity of the network is heterogeneous, and therefore it is statistically possible to find highly connected nodes or hubs.
Scores with higher negative exponents, e.g., e-150, indicate greater sequence homology, while smaller exponents indicate weak or no homology.
As shown in Figure 6, the radius of gyration R G of the model NAs depends on MLD as 1.7 × MLD 0.43, which has a slightly smaller exponent than a theory in which only base-paired segments were accounted for (Yoffe et al., 2008).
Among the species S23, S4, S5, S8, and S9, the species number of S23is scaled with the smallest exponent, and thus noise in the limit of r N Z i N, 2 (t ) − Z i 2 (t ) is determined dominantly by the component r N Z 23 N, 2 (t ) − Z 23 2 (t ).
However, their optimal exponents are always smaller than the corresponding exponents in the whole space, leading to more stringent conditions in the applications (to blow-up estimates).
Shift the mantissa of the smaller exponent to the right by the difference in the exponents.
As the period for estimating the retention function becomes longer, the exponent becomes smaller.A smaller exponent leads to lower resulting values at younger ages and higher resulting values at older ages (because the predicted values were higher at younger ages and lower at older ages), but it had no influence on the overall shape of the distribution.
