A deviation function is chosen to reshape the originally generated curve.
It is well known [21] that a deviation mean generated by a continuous deviation function (Ecolon mathbb {R}_^{2}to mathbb {R}) is homogeneous if and only if E is of the form (E x,y)=g y)f( frac{x}{y})) for some continuous functions (f,gcolon mathbb {R}_to mathbb {R}) such that f vanishes at 1 and g is positive.
The average deviations between the two intraoral scans at all points on the surfaces were computed by using the "shell/shell deviation" function in the program.
Z-sections were then projected on a single plane by using the ImageJ standard deviation function under Z-project.
We demonstrated plausibility of the two-component representation of the standard deviation and showed equivalence of the consecutive sampling method and gene-by-gene evaluation of the standard deviation function.
The estimator of the characteristic standard deviation function SD is then determined by fitting the linear function SD = a + bY mean to the experimental points at the logarithmic scale; (Eq. (1), Y m is the sample mean).
The standard deviation function is then determined by fitting the logarithmically transformed values to the logarithm of the linear function of the mean expression (see the Methods section).
Approximation of the standard deviation across array, provided by the characteristic function derived from the consecutive sampling, was compared to the standard deviation function, derived from the individual genes: the difference for the coefficients a and b in two independent tests was in the range -3% to -12% and -8% to -14%, respectively.
Each release scenario is described by an initiating event (i.e., a deviation), the barrier functions introduced to prevent the initiating event from developing into a release, and how the barrier functions are implemented in terms of barrier systems.
Local road unevenness is described by a deterministic function that represents the deviation of the travelled surface from a true planar surface.
