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We point out that the optimal architecture of Figure 10 is clearly valid for the smallest possible surface code (consisting of 13 data qubits and 12 ancillary qubits) able to detect and correct a single physical qubit error.
Although his arguments were clearly valid for weakly deleterious co-recessive mutations, we now know that a very large proportion of deleterious mutations will be perfectly recessive and that mut/WT heterozygotes will show very little, if any, reduction in fitness compared to WT homozygotes [ 29, 30].
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Some of these criticisms are clearly valid.
An argument of this form is clearly valid.
This principle is clearly valid in the set theories presented above, in which Replacement holds.
When the card came in the mail, it had my full, real name, but it also clearly stated: "Valid for work only with I.N.S. authorization".
As this condition is clearly not valid for programmes that were established during the global financial crisis, countries that did so were excluded from the IV estimations.
The results are clearly also valid for i = 1,2,..., N. We suppress the subscript N and just use the notation V, K, σ*, £ etc.
Clearly, Theorem 3.2 is valid for a nonexpansive mapping.
Since the formula ∑ j = 1 k − 1 j 2 j = ( k − 2 ) 2 k + 2 Open image in new window can easily be proved by mathematical induction, clearly, this inequality is valid for k = 1 too.
Clearly, the comparison principle is valid for the maximal solution.
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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