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(2) Pick k closest training vectors according to the above distance metric.
It is shown that the methodology allows the above distance to be (partially) reduced as the overall level of statistical fluctuations increases, no matter the initial distance of the mean model used in the simulations.
The above distance, function of the material properties, is measured along three alternative paths (a normal path, an inclined path and a principal stress oriented path) and, using such three different paths to determine the critical point location, the effectiveness of the criterion is evaluated by means of experimental data related to aluminium alloy specimens under cylindrical contacts.
Based upon the above distance, the diameter of M31 at the widest point is estimated to be.
In the second structure, the above distance becomes 4.5 Å and the E11 side chain now points towards the inner part of the cavity.
The approach for comparing the above distance matrices and calculating the significance of their correlations is taken directly from Goh et al. 2000[48], which includes a detailed protocol.
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Furthermore, missing high-frequency components of the target image are estimated in order that the reconstructed HR image minimizes the above distances.
From rich literature it follows that the above distances provide useful and powerful tools for investigating problems of fixed point theory.
We used this test in addition to the above distance-based relative rate test for several reasons.
The values of the above distances vary between populations from different cultures, ages, genders etc.
To implement the accessibility measures above, distances and car travel times were calculated along the street network.
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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