We use the formulae developed by Shkolnikov, Andreev, and Begun (DR 8(11):305–358, 2003) to decompose the differences between Gini coefficients by age and cause of death.
If I use the formulae for the time constants for growth and decay of seismicity, a threshold value of (C_{text{RST}} = 100,{text{kPa}}) provides 43 h until RST seismicity density grows to half the CPT level and 4 h to drop after 111 h.
Since the Hopf point of the layer problem is ( 0, 0 ; 0, μ ^ 0, 0 ), it is straightforward to use the formulae in Section 3.1 to compute the first Lyapunov coefficient (13) for the Hopf bifurcation in the layer problem for (17), i.e. for the system x ′ = f 1 ( x, y ; z, μ, 0 ), y ′ = f 2 ( x, y ; z, μ, 0 ).
Thus, we can use the formulae derived in this reference to obtain, e.g., for the mean the system of differential equations d d t E n Θ t n = − 1 τ E n Θ t n + 1 τ ∑ k = 1 P l ( k, n ) E n f ( ∑ j = 1 P W ¯ k j n Θ t k, n ) e k. (B.1).
Therefore, it is safe to use the formulae for end-to-end extension/fluctuation to estimate the internal properties of the confined DNA in our experiments.
An investigator can use the formulae presented in this paper to conduct a sensitivity analysis of their estimates of the diagnostic accuracy of Test 2. For the trial conducted by Lehman et al. [ 5], an example of this sort of sensitivity analysis is given in the immediately preceding paragraph.
