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Some of the resultant integrals are evaluated by using the Gauss Chebyshev integration rules after moving the series coefficients to the outside of the integral sign; others are evaluated exactly, including the modified hypersingular integral.
That's why we are forced to spend half our lives (almost exactly, including the time most people spend sleeping) coding (writing computer programs using c++), which is an activity that at least 50% of physicists find abhorrently difficult, at first anyway.
In the limit of weak coupling, as in Fig. 8 left), both the neural model and the derived phase model agree almost exactly, including the type of bifurcation that occurs when entrainment is lost.
However, using our model to simulate their data we can reproduce their graphical data almost exactly including the scattering around the linear fit (cf Fig. 5 with Fig. 3 in [10]).
Estimates of the standard errors for absolute mean quarterly changes in number of prescriptions or deaths were determined exactly, including the covariance of level and slope terms.
The procedure in the present study mirrored the Amir study exactly including the same faces, number and spacing of the trials, and the location and duration of the stimuli.
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The surveys do not have exactly include the same questions, making comparisons limited.
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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