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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.
The lower part of Fig. 11 represents the approximation of the crack length after repair.
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The low-frequency coefficients (LL components) represent the approximation of the original image.
where 휖 i u ∈ R d is a Gaussian noise representing the approximation error.
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.
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.
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.
This latter represents the linear approximation of the function density φ(t) on the subinterval [t σ,tσ + 1] of the curve Γ.
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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