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Seeger et al. [17] suggested that a student's t distribution can be approximated in terms of a Gaussian distribution, we therefore use a zero-mean multivariate Gaussian distribution to approximate the sparse prior of q t, where (q_tsim prod _1^N{mathcal {N}(0,c)}.) The constant value c is determined by the level of variations q t.
Therefore, Lg phases have been used to magnitude estimates of shallow events (m b (Lg), see, e.g., Nuttli 1973; Herrmann and Nuttli 1982) and to map crustal heterogeneities by estimating Lg attenuation variations (Q Lg ; e.g., Phillips et al. 2000; Xie et al. 2006; Chung et al. 2007; Hong et al. 2008).
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When the index of regular variation q is zero, we say that the function is slowly varying.
Each element q ti of the variation q t is randomly sampled from a zero-mean Gaussian distribution (N q_{ti}|0,alpha _i^{-1}),) the variance α t of which is randomly sampled from a Gamma (varGamma (alpha _i|a,b).) That is, p(q_t|a,b) = prod_{i=1}^{N_t}{int_0^infty{mathcal{N}(q_{ti}|0,alpha_i^{-1})Gamma alpha_i|a,b mathrm{d}alpha_i}}.
The O-PLS models are here described with the statistical parameters explained by variation (R) and predicted variation (Q).
In order to evaluate the fit of a model, values of explained variation, R, and predicted variation, Q, were computed as in [ 51].
Predicted variation (Q) values obtained as in equation (1) were calculated for the MAF of the six polymorphisms included in the PLSR model.
Eleven proteins with the most highly significant variation (q-values <3.5×10−7) are highlighted in Figure 12 and shown in Table 4. Nine out of eleven are relatively small proteins (<25 kDa).
Variation of q means variations in the temperature rise, which one can measure.
The results show marked variations in Q p −1 with depth (Fig. 4a).
Figure 2 Temporal variations in Q C -1 at five frequency bands.
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