Sentence examples for obtained in appendix from inspiring English sources

Equations (24), (25), and (26) are explicitly obtained in Appendix Appendix 1: derivatives of the likelihood function f M L.

To do this, we use the estimates for some integrals involving function (H xi,eta;xi_{0},eta_{0})) obtained in Appendix B.

Thus following the steps as in the proof of Theorem 3 (whose proof is obtained in Appendix 2) one can show that the gradient of the stationary density, ∇ Θ Π Θ exists and equals zero at Θ 0 ∗.

In addition to the set of models obtained using multi-model selection procedures as described above, we used classical forward backwards selection procedures to provide complementary information and to strengthen the results obtained in this section (Appendix 1, section 1).

The predictive ability of our signature to classify colon and rectal localization obtained on this new dataset was highly in accordance with the performance obtained in our data (Appendix Fig S4A).

The conditional probabilities at the right-hand side of (13) can be obtained, as in Appendix A.1, through proper marginalization of joint conditional PMFs of the following type: (A10).

Weeks and months prior to final sample RNA analyses by one-step fluorogenic real-time RT-PCR, each primer-probe set (with the exception of the ABI pre-optimized 18S ribosomal RNA primer-probe set) first had to be evaluated with cDNA for optimal primer and probe concentrations to ensure that maximal real-time fluorogenic PCR kinetics is obtained in each case (see Appendix A-E).

This plot clearly suggests a comparatively strong dependence of the estimates of this measure on the full CV error as also observed in the results obtained in the simulation study presented in Appendix A (Additional file 2)—and thus provides evidence supporting the use of a ratio-based measure rather than a difference-based measure.

Due to the high number of missing data on income (average for all countries: 7.75%), the missing values were replaced using data on the perception of income, obtained in the same survey (Supplementary Appendix 3).

Similar results were obtained in three independent experiments (Fig 1E; Appendix Fig S1A).

A great number of formulas obtained in the course of treatment are summarized as tables in the appendix.