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Here we overview the key steps: For simplicity, suppose the case of prediction of 2 subclasses, A and B. The signature genes consist of nA (marker.A) and nB (marker.B) over-expressed marker genes in subclass A and B, respectively.
Suppose the case of prediction of 2 subclasses, A and B, and the signature to be tested includes nA and nB over-expressed marker genes in subclass A and B, respectively.
Suppose the case with NL comparison and let X i,j,k be the logarithm taken the ith probe expression of jth sample in the kth group (i=1,…, p, j=1,…, n, k∈ N, L, H).
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I suppose the best case you can make here is that raising rates on the top 2 percent was never going to be enough anyway, so Obama getting less from that than he should have isn't that big a deal.
Suppose the latter case holds.
In fact, suppose the contrary case.
"I suppose the worst-case scenario is that it's a niche brand," said Ms. Maneaty of BMO Capital.
Suppose the number of cases in the training data is M ; sample M cases randomly with replacement from the original data to keep the size of the original data not changing.
I suppose in the case of nutrition there are physical effects that can be measured, though; isn't this more intangible?
I suppose, in the case of Piccadilly, the artist is trying to uncover some awful truth about the "special relationship", rendering it as a kind of secret, mutually abusive bond.
Suppose that the case n is valid.
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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