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The algorithm is outlined in Algorithm 1, where K is a predefined maximal number of iterations, ε is a predefined small constant, and the iterative error ε k is defined as ε k = γ ̂ k − γ ̂ k − 1 γ ̂ k 2, k = 1, 2, ⋯. (21).
where is a predefined threshold.
where δ is a predefined threshold.
({delta _{E}^{b}}) is a predefined threshold reflecting the energy requirement, and ({delta _{R}^{b}}) is a predefined threshold reflecting the data rate requirement.
The condition (14) must be satisfied, where θ is a predefined threshold value.
where Th is a predefined threshold that needs to be decided upon.
where is a predefined threshold; the inverse expanding function is described in the following.
where is a block, is a predefined threshold,,,, and are pixel values in, is the "AND" operator.
For a specific cascade c, node (i in C_j^c), if and only if (| tau (i, c) - tau (j, c) | <= theta ), where (theta ) is a predefined threshold.
In Algorithm 1, the interval [ λ min, λ max ] is selected to contain λ∗, and ϵ is a predefined small constant.
where Ls is the length of a synchronization code, and T is a predefined threshold to make-decision for presence of a synchronization code.
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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