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Here, R RX = E H ̄ u, i H ̄ u, i H and R TX = E H ̄ u, i H H ̄ u, i determine the correlation between the elements of H ̄ u, i, and H ̄ ̄ u, i is and i.i.d.i.d
The correlation between the elements in the noise vector is neglected and the symbols in are demodulate individually, treating the output of the model (6) as independent scalar channels.
Figure 5 shows a correlation between the elements Li and P in the ler2 strain.
The correlation between the elements of the G IBS and G IBD matrices was 0.959, which agrees well with the differences in GW-EBV.
The significant positive correlation between the elements of surface soil grains suggests that their common source of origin is probably the agrochemicals, such as phosphate and nitrate fertilizers, broadcasted in the paddy fields [ 32].
However, when the models in Equations (8) and (9) hold, the observed Pearson's correlation will be inflated due to correlation between the elements of u 1 and u 2. Subtracting the true values of u 1 and u 2 from y 1 and y 2, will produce corrected vectors for which the observed Pearson's correlation will not be inflated.
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But, as fabulous as it is, not all correlations between the elements are captured on the classical table.
The employed Gaussian Mixture Models (GMMs) were set to have full covariance matrices for exploiting all possible correlations between the elements of each observation.
This result is quite remarkable, for we know that in many other systems the phase transition strongly depends on the network topology, and can even disappear for topologies that induce strong correlations between the elements (such as the scale-free topology, [45]).
The correlations between the elements of G LA and A are high (0.94).
The correlation between the central element and the element outside the window can be ignored without affecting the final result [22].
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com