Sentence examples for derived below from inspiring English sources

The estimators derived below and later in "Ratio with tours estimator (RT-estimator)" section exploit the independence of the tours and the result that expected sum of functions of nodes visited in a tour is proportional to (sum _{u in V} g u)) [4, Lemma 3].

Trajectories generated using exactly these values, except with the Hill coefficient changed from 1 to 2 to reflect cooperative binding of transcription factors as dimers, are similar whether from the analytical approximate solutions to Eq. 5 derived below, the continuous-time ODE solution, or the corresponding stochastic dynamics for discrete particle numbers (Fig. 2).

The expression of the estimator is derived below.

The parameters β and δ depend on t and are derived below.

Here, an alternative solution proposed is to use its an upper bound, which is derived below.

The probability of error is derived below based on the probabilities in Eqs.

However, as we derive below, the variance of eigenvalues depends both on experimental sample size and effective population size, and so these parameters affect the sampling variance of heritability.

This decision critically depends on the creditor's conditional expected payoffs for both alternatives, which we derive below.

In principle, most of the results we derive below should therefore be readily applicable to more complex bottleneck scenarios by mapping the real bottleneck onto an effective single-generation bottleneck, provided that the real bottleneck is not long enough that beneficial mutations appear during the bottleneck.

If ultrasensitivity is helpful to MFMS, then increasing n and m should increase S X, S Y, F X and F Y. (See section 4 of Additional file 1 for derivation. This same approach can be taken on the steady states of x2 and y2 directly with the same result we derive below).

Assuming that all the carriers diffuse along the radial direction, namely, minority-carrier diffusion in the vertical direction is negligible [17], the steady-state Eq. (1) can be then derived as below, {D}_hfrac{partial^2varDelta h(r)}{partial {r}^2}-frac{varDelta h}{tau_h}+{g}_h=0, (2).