For dealing with plant nonlinearities and external disturbances, a nonlinear transformation is performed on the accessible variables such that the transformed system behaves as an integrator, to which linear control techniques are then applied.
Distortions caused by gradient nonlinearities were corrected by applying a predefined, scanner-specific, nonlinear transformation (Jovicich et al. 2006).
It has been shown that the prediction performance of an LN model can be increased by using a nonlinear transformation of the stimulus (e.g., a transformation may capture nonlinearities at earlier stages of processing) that precedes the linear filtering stage [25], [47], [48].
Without the nonlinear transformation from non-normal variables to normal variables as required by the first order reliability method (FORM), MVFOSA is also more accurate than FORM in certain circumstances, especially when the transformation significantly increases the nonlinearity of a performance function.
To introduce a nonlinear generalization of CCA based on a kernel formulation to take account the nonlinearity of transformation between the profile face image and frontal one, KPCA is used instead of PCA.
Due to the nonlinearity of the transformation between the frontal and the profile pose, we were constrained to not represent the global face but to restrict to its main components (eyes, nose, mouth, chin) and to use kernel functions.
Therefore, we use a kernel-PCA [16] followed by a CCA, resulting in a kernel canonical correlation analysis (KCCA) [36] which allows us to consider the nonlinearity of the transformation between the components of frontal and profile faces.
For systems with a single nonlinearity, an affine transformation that retains the original steady-state and eigenvalue structure brings the system to a much simpler form, the companion normal form, which in the cases of two- and three-dimensional systems is shown to coincide with the classical F1 and G1 bifurcation normal forms that are based on Jordan block structure.
Gaussian white noise is often used in reverse-correlation studies, but would have involved intensity modulation over time, which would have added another nonlinearity in the transformation between optogenetic illumination and behavioral response.
Although these criteria are somewhat arbitrary, they provide a starting point for understanding how the biochemical epistasis we observed, along with a simple nonlinearity in the transformation of affinity into function, might affect the mutational paths available to the evolving TF-RE complex.
