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Let Z m 1 = (X m 1, Y m 1 ) and Z m 2 = (X m 2, Y m 2 ) be two sets of latent states at marker m, where X represents the upper-layer cluster and Y the lower-layer cluster (index i omitted).
We used the estimate σ ^ x 2 = ∑ i w i 2 (x i − x ) 2 (∑ i w i ) 2, since its expectation value is bounded by (1 − w max w sum ) 2 ≤ 〈 σ ^ x 2 〉 σ x 2 ≤ 1 + w max w sum and the estimate itself by σ ^ x 2 ≤ (1 − w max w sum ) 2 ∑ i (x i − X i ) 2, where X i is the weighted average with replicate i omitted, X i = ∑ j ≠ i w j x j /∑ j ≠ i w j.
Of course, I omitted my own story.
I don't know how I omitted mentioning that.
I omitted to mention this on the day.
I'd never met my grandfather, but I omitted that part.
I made one other crucial decision, too — I omitted the "Trump" name from the packaging.
However, with the word "lawsuit" ringing in my ears, I omitted her name from the article.
Similar(3)
Pyromania was already mentioned in DSM-I, omitted from the DSM-II, but then acknowledged again in the DSM-III [ 12].
Is omitting the publication's name a faux-nonchalant brag?
(I omit the dancers).
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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