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In this section, we establish a component wise definition of the required energy E p for a single application profile.
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The computation of ({mathcal T}textbf {p}) can be carried out by the pixel-wise definition (2) or by using the fast Fourier transform (FFT) with a zero padding.
In the case when the pixel-wise definition is used for ({mathcal T}textbf {p}), then mathbf{OC}(pixel-wise computation of {mathcal T}mathbf{p}) = left|Lambdaright| cdot left|{mathcal S}_{mathbf{k}}right|, (3).
for every a 1, a 2 ∈ A, b 1, b 2 ∈ B and c 1, c 2 ∈ C. When A, ℬ and C are algebras, then by the usual point-wise definitions for addition, scalar multiplication and product, A × B × C becomes an algebra.
Definition wise, utility functions are mathematical modeling techniques that is typically used to model the relative preferences of UE at different timestamps.
A new Word Wise feature adds definitions of difficult words to books, a boon for students and English learners.
As shown in Figure 1, the overlapped genes varied greatly among the three data sets, indicating that the gene-wise P value definition approach influenced the resultant subnetworks substantially.
Further examination of these genes showed that only a few of them were simultaneously identified by all three gene-wise P value definition methods, while many genes were uniquely identified in only one of the three scenarios (the second column in Table 3).
This is not to imply that artists are, by definition, brighter, wiser or more venturesome than anyone else.
The Vocabulary Builder software, meanwhile compiles all of the words kids look up in the reader's dictionary into a handy flashcard-style list, while Word Wise offers up automatic definitions above tough words while reading.
She sits in one velvet chair, the client sits in another, and for 50 minutes, they get the best part of her: the warm, wise and questing part whose definition of sanity is: "How am I feeling?
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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