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Lemma 8.8 below asserts that (B0)–(B1) imply the reduction axiom (A2).
The 'unmixing' model, described below, asserts that each sample m i, a column of M, is well approximated by a convex combination of a fixed set C = [ c0|…| c k ] of k+1 unobserved basis distributions over the gene measurements.
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So when Gill asserts that "M.
The fact asserts that implies.
Note that (3.29) asserts that is -periodic.
We assert that is bounded.
We assert that is strictly contractive on.
Now, we assert that is bounded.
where We assert that belongs to.
To assert that ancestors are hypothetical is to assert that evolutionary descent itself is hypothetical.
Brown asserted that separate is inherently unequal.
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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