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where Z i is the normalized vector obtained by normalizing the values of X j (j = 1, 2, 3…, k) z ij = X ij − X ¯ j S j, Open image in new window (2) X ¯ j = ∑ i = 1 n X ij n i, Open image in new window (3).
In its basic form, CMN consists of subtracting the mean feature vector μ x from each vector x t and normalizing by variance σ x to obtain the normalized vector x ^ t. x ^ t = x t - μ x σ x (7).
(boolean, optional) Indicates whether to use a normalized vector basis.
We denote the normalized vector of by (Equation 25, page 6.3.1 ).
If this argument is not provided, use of a normalized vector basis is enabled.
The considered laser pulse has a wavelength λ = 1 μm and a peak normalized vector potential a0 ~ 9, following the experimental parameters.
Similar(7)
The coordinate axes were set to the Frenet vectors of the curve at this position; specifically, the x-axis was set to the normalized binormal vector b, the y-axis to the negated normalized normal vector − n, and the z-axis to the normalized tangent vector t.
The first is how to normalize similarity vectors, so that the normalized vectors are more suitable to be processed by other methods, while preserving the information granted by similarity vectors.
(4.18) (ii) For (u(cdot)inmathcal{H}), u(x)=sum_{n=-infty}^{infty}bigllangle u(cdot),psi_{n}(cdot) bigrrangle _{mathcal{H}} psi_{n}(x), (4.19) where (psi_{n}(cdot)=frac{varphi(cdot,lambda_{n})}{|varphi (cdot,lambda_{n})|_{mathcal{H}}}) is the normalized vector-valued eigenfunction of the problem (2.1 - 2.4 2.1 - 2.4
The generated null space vectors are normalized vectors, which could avoid the noise amplification problem efficiently.
It is noted that the cosine similarity measurement is also equivalent to the euclidean distance measurement for normalized vectors.
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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