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Theorem 3 reveals that a conventional shortest path may have arbitrarily bad performance, since either (frac{rho _{max }}{rho _{mathrm{{opt}}}}) can be infinitely large or (rho _{min }) can be infinitely small.
This procedure tests for an association between 2 binary categorical variables (in this case, presence of an electrophysiological change and ROI) while controlling for a third variable (subject), which may have arbitrarily many levels.
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While in the case of Malcev algebras one may think that these good properties are a consequence of Malcev algebras being "close" to Lie algebras, nilpotent Sabinin algebras may have an arbitrarily big (though finite) number of independent operations.
Such a string may have an arbitrarily large dimensionality.
"This limits NOAEL data," Rusyn explains, "because the lowest dose may have been arbitrarily set".
In addition, we have arbitrarily selected an H-score cutoff point to determine positive and negative expression, which may not necessarily be biologically relevant.
It is beginning to interfere with foreign investment, as officials have arbitrarily revoked or renegotiated contracts.
Because you have arbitrarily accepted that something is better than something else.
I may have been kept arbitrarily on bail the longest, but I'm by no means alone.
Such a chronological boundary may have to be drawn arbitrarily between the last survivors of H. erectus and the earliest members of a succeeding species (e.g., Homo sapiens).
Until well-founded criteria emerge, effect sizes may have to be defined arbitrarily (e.g., as 5% or 10% effect levels), as is common practice in the estimation of effect doses by using regression-based methods.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com