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The low-frequency coefficients (LL components) represent the approximation of the original image.
Instead of storing a fully dense (n times n) approximation, L-BFGS stores just m vectors ((m ll n)) of length n that implicitly represent the approximation.
As the coefficients in the coarsest scale subband represent the approximation component of the source image, the simplest way is to use the conventional averaging method to produce the composite coefficients.
We represent the approximation top-k teams generated by the framework as {(g_1^a,dots,g_k^a)}, and the exact top-k teams is denoted as {(g_1^mathrm{ex},dots,g_k^mathrm{ex})}.
For convenience, we use an ((N+1))-dimensional vector U_{n}= bigl( U^{0}_{n},U^{1}_{n}, ldots,U^{N}_{n} bigr) ^{T} to represent the approximation T, W, I, or V at time (t_{n}), the notation ((cdot )^{T}) for the transposition of a vector, and the notation (Ugeq 0), meaning that all components of a vector U are nonnegative.
Q-values represent the approximation of maximal false-positive rate among the proteins supposed to be significant.
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where 휖 i u ∈ R d is a Gaussian noise representing the approximation error.
We have used low-level image, where LL1 represents the approximation of original image and is further decomposed to second-level approximation and details of image.
Because these Hessian kernels represented the approximation of the diagonal elements in the Hessian matrix, the Hessian kernel acted like a normalization factor within the sensitive area.
The lower part of Fig. 11 represents the approximation of the crack length after repair.
Although no IPSC-derived cell is likely to be phenotypically identical to the parental input cell, we believe that TER cells represent the best approximation possible.
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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