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The constitutive relations for electrostrictors are developed in terms of the standard quadratic function and the hyperbolic tangent squared function of the applied electric field.
Open image in new window Fig. 9 Piecewise linearization of squared function.
The major contribution of LTSNE is the simultaneous enhancement and compression of dark and bright pixels using a nonlinear sine squared function with image-dependent parameters.
We chose here a squared function having a slow start followed by a rapid growth which makes our model resemblant to TCP to some extent [16, 17].
Under this assumption the minimization of ∥w∥2 is replaced by the minimization of the squared function norm ∥ f ∥ H 2 in Hilbert space, and Equation 4 can be reformulated as: min f ∥ f ∥ H 2 + C ∑ i = 1 m l ε 2 f x i - y i. (5).
where the integration of the sinc squared function is computed by int^{infty}_{-infty}frac{1}{M}frac{ipi}{2}left(frac{ipi}{M}right)}{left(frac{ipi}{M}right)^{2}}di =frac{M}{pi}int^{infty}_{-infty}frac{1}{M}frac{ipi}{2}left(frac{ipi}{M}right)}{left(frac{ipi}{M}right)^{2}}dfrac{ipi}{M} =1 (39).
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More generally, a similar computation shows that the derivative of the squaring function at is.
Hence the slope of the graph of the squaring function at the point (3, 9) is 6, and so its derivative at is.
Many loss functions can be chosen (e.g. logit function, squared loss function, misclassification rate, entropy, Gini index,...).
To define our GP prior, we choose a zero mean function and the squared exponential function of Equation (8).
The squared loss function is popular for continuous response variables, and the logit function for categorical responses.
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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