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A common restriction on the encoding process is to assume that (mathcal {X}) is created by first generating a bias vector (vec {P} in (0,1)^{ell }) (by choosing each entry P i independently from a certain distribution f P ) and then generating code words (vec {X}_{j} in mathcal {X}) according to (mathbb {P}(X_{j,i} = 1) = P_{i}).
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But after three months of ineffective training I decided it would be better to focus on actually getting fit, rather than just beefing my neck up to the point where I couldn't move it independently from the rest of my body.
Assuming a prior probability distribution p(b), b = 1,…,4 on 𝔹 and each nucleotide b i sampled independently from 𝔹, we view the score as a random variable (RV) on 𝔹 n with the product probability distribution.
Similarly, when cooperative binding is present, the distribution is poisson binomial with the modification that shared targets have a mutation with probability a s i h i where h i is drawn independently from the distribution G(h).
If later Groups such as IId, IIe, and III evolved after Group I but independently from other ancestral WRKY genes – then where are these other ancestral genes?
Studies have also demonstrated that Ang II can be generated from Ang I, independently of ACE activity, and that long-term ACEi therapy subsequently leads to an increase in circulating levels of Ang II toward pretreatment values (9).
The bias vectors p(i) are drawn independently from a (truncated) Dirichlet distribution F with concentration parameter κ>0, F ( p ) = p − 1 + κ / B τ ( κ 1 q ) (2) B τ ( κ 1 q ) = ∫ τ 1 − ( q − 1 ) τ d q p δ ( 1 − | p | ) p − 1 + κ. (3).
By the age of 13, I was living independently from my parents, and had cast off the idea that I was possessed at all.
Although G i and G i +1 are inferred independently from the original network G by the proposed method, there should be some strong relationship between them.
In contrast, in the LAP 02206 and RBT 04143 matrices, although the Sr/CI ratios correlate with the amounts of Ca-rich secondary minerals, the LREE/CI ratios vary independently from the amounts of any secondary minerals.
H264/AVC intra I-I-I: Each frame is encoded independently from the neighboring frames without exploiting the spatial redundancy.
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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