I obtained the scaling parameter and decay time τ = 0.63 days.
Numerical relationship between χ and xT were calculated to obtain the scale; detail of the calculation is described in Supplementary Note B. In the abovementioned conservation rule, the velocity of the particle at the initial position, denoted v0, is assumed to be negligibly small.
To obtain the scale σ shown in Fig. 2 we chose the FitzHugh-Nagumo equations and g u,v) = (u+β)/25, where β is a threshold parameter that selects the pattern.
In this case biology, physics, and chemistry are given the same weight to obtain the scale (see HAM-Nat-BPC in Table 2).
Then, it was possible to scale "outer county" emissions to estimate total emissions from these counties, obtaining the scale factor as part of the fit to soil PAH data in the yards of study participants.
Gorenflo et al. [14] used the Laplace transform method to obtain the scale-invariant solution represented by the Wright function of the time fractional diffusion-wave equation.
By observing that (theta ^{-1/d} mathcal {P}(lambda)) has the same distribution with (mathcal {P}(lambda theta)), we obtain the scaling property of (hat beta _{k}(lambda, r)).
Using (49) and (50), after some elementary reductions, we obtain the scaled Newton system as follows: ( A ¯ ( d x ) − d s d x + d s ) = ( 0 v − 1 − v ).
In this way we obtain the scaled model ρ t + ( ρ u ) x = − A x A ρ u + c m ρ | u |, (4).
For consistency, we use the same hyperparameters to obtain the scaled PSFMs for the likelihood-based approach.
Scanned data were processed by the supplier's standard protocol for ChIP-chip analysis to obtain the scaled log2 (Cy5/Cy3 ratio).
