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We assessed the linearity of the PAF and O3 association by replacing the linear air pollution term with a penalized spline (3 df) in the conditional logistic regression model.
Moreover, we test the performance of the self-organizing map by replacing the linear Least Mean Squares adaptation rule with the marginal median.
The NCT controller is designed by replacing the linear PD in the conventional CT controller with the nonlinear PD (NPD) algorithm.
The SCMAI model improves the committee machine artificial intelligence (CMAI) model by replacing the linear combination in the CMAI with a nonlinear supervised ANN framework.
Formally, it is obtained by replacing the linear term b ( m t + n t ) by the function h t = h ( m t + n t ), where h ( x ) = { κ 1 + e − λ ( x − ν ), x ≤ ϕ 0 N, b x, x > ϕ 0 N (14).
By replacing the linear term appearing in the formulation of variational inequalities by a vector-valued term, Parida et al. [5] and Yang and Chen [6] independently introduced and studied a class of variational inequalities known as variational-like inequalities or pre-variational inequalities which is an important extension of the variational inequalities.
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The extension to separate trial effects can be achieved by simply replacing the linear β0 j and λ k terms with the interaction of them, i.e. Model B. Fixed effect Models A and B can be implemented using any GLM software package, such as glm within Stata [ 29].
In the future, even smaller resolution distances could be achieved by replacing the final linear filling process of incorporating filtered markers with a more flexible method (e.g., an additional HMM model).
It is shown that the non-linear wave equations (partly new), can be written in a form similar to the linear acoustics ones (mostly known), by taking into account the self-convection of sound by sound; this implies replacing the linear local and material derivatives, byself-convected and non-linear extensions of these (Table 2), which also affect the sound speed.
The circular economy is replacing the linear one.
By replacing the lower level linear programs with their KKT conditions, we transform the bilevel MINLP into a single-level nonconvex MINLP, which is further globally optimized using an improved branch-and-refine algorithm.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com