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"This is due to the logarithmic nature of rating scales.
(The leaky LMS appears smoother than the other two algorithms, but this is due to the logarithmic scale of the y-axis in the plots).
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The slightly bent linear fit line was due to the logarithmic X- and Y-axes.
It seems that the small discrepancy between these curves above 50% values on the horizontal axis is due to the properties of logarithmic function but not to a statistical difference.
(b) is due to the concavity of the logarithmic function (Jensen's inequality).
(a) is due to the monotonicity of the logarithmic function and linearity of expectation and is tight in the high-SINR region.
This is due to the curation.
"The decline is due to the economy.
Note: the large errors bars at day 10 are due to the use of semi-logarithmic axes.
In fact the reason we were able to take the anti-logarithm (using exponential) to get back to the natural scale for the location quotients from the logarithmic scale was due to the invariance property of the maximum likelihood estimates.
The results of our investigation revealed no clear relationship, logarithmic or otherwise, which may be due to the consistently high humidity in the study area.
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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