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The numerical examples show that the regularised models exhibit all of the desired features: mesh insensitivity, imperfection size insensitivity and description of size effects.

As a result of the regularised structure imposed by semi-landmarks, with numbers and positions which correspond across different images, variation in surface shape can again be explored using standard tools such as principal component analysis.

An approximate analytical solution to the problem is then obtained for motion in the vicinity of the main asteroid using the regularised coordinates through a linearized model.

For both the regularised logistic and linear regression the R-package glmnet [ 41] was used to establish the REGS.

The particular particle filter used was the regularised sequential importance sampling[23], p. 182.

The regularised zeta function for the Neumann operator at z = − 2 is computed.

The regularised solution of Eq. (4) is: (5a) where α2 is the so-called regularization parameter and I denotes the identity matrix.

As we shall see later, even though the analytic solution must retain the unphysical condition (20) there is very good agreement between this and the numerical solution which uses the regularised condition (21).

Differential gene expression was assessed using the regularised Bayesian unpaired t-test CyberT [ 70] and genes with p-values ≤ 0.005 were considered to be differentially expressed.

The regularised multivariate regression models provide a flexible workflow for drug resistance studies with promising potential.

The regularised logistic regression resulted in REGS classifiers utilising 73 genes for C and 32 for O and regularised linear regression resulted in REGS predictors utilising 27 genes for C and 21 for O.

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