Sentence examples for using the approximations described from inspiring English sources

In this appendix, we map Eq. (1) to Eq. (5) using the approximations described in Sect.

To test significance of effects, we calculated degrees of freedom using the approximation described by Kenward and Roger (1997).

For comparisons of EN and IN (reproductive assurance) and of ISB and IX (self-compatibility), we performed a Tukey test on treatment least squares means, using the approximation described in [ 95] to adjust for multiple comparisons ("Tukey-Kramer test" performed with PROC GLIMMIX).

Instead of using shuffling, which is computationally inefficient, we pre-calculate the mean and the variance for any pattern of amino acids in an arbitrary column using an approximation described below.

(11) The approximations of the BS and FMLS models are carried out by using the LWOM, described in the next section.

Using the bisection method described in Remark 2.3, we can get a better approximation for such a b.

Therefore, slightly overestimating the FDR, we used the approximation π0=1.

TP is computed from SINR using the Shannon approximation similarly as described in[30].

Integration of material balances along with the equations obtained from the sensitivity method is carried out using the linear approximation integration schema described in the Methods section.

Using the polynomial approximations for the functions describing the matrix entries a ij x) presented in Efficient construction of the design matrix A x), it would be possible to derive analytical formulas for the Jacobian and Hessian of the objective function.

Estimate the mean m of the pdf of m s → v ( k ) using either mean-matched or mode-matched approximations described above.