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The gradient of the control variable corrects the convective flux in the nonlinear state equation so as to enforce mass conservation while minimizing deviations from the target state.
We present a concise proof that the deviation of the actual state from the target state is decaying exponentially with time if a certain control is applied to the nonlinear system.
If the fourth shaft is only one standard deviation from the target value, intervention is probably not worth the cost.
If you balk at spending the money, then with every standard deviation from the target, you risk spending more and more.
Maximizing the achievement function minimizes the deviation from the target value for the corresponding goal variable.
Loss increases by the square of deviation from the target value, L=D2C, where the constant is determined by the cost of the countermeasure that the factory might use to get on target.
The criterion for selecting the best variation is minimal standard deviation from the target SPD.
The experimental trend line (blue) shows significant deviation from the target line (black).
Then, many trivial deviations from the target tended to "stack up". An otherwise trivial variation in one part exacerbated a variation in another.
But for every San Diego set with a color density of 13 (three standard deviations from the target), Sony spent not $9 but $81.
Loss functions describe the economical consequences of the deviations from the target values.
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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