To treat more complicated (general) loop loop kissing complexes, as shown in the Fig. 2 of Cao et al. (2014), the stem-loop substructure's impact on loop entropy is approximated by replacing the terminal base pairs (of the stems) by single nucleotides.
Also, the axiom schema with measurable replaced by inaccessible can be approximated by allowing greater expressiveness in the formulas in the replacement axiom schema and be viewed as the natural limit of such approximations.
edgeR1 method uses LRT statistics that are approximated by a Chi-square distribution, whereas edgeR2 replaces the Chi-square approximation to the LRT statistic with a quasi-likelihood F-test [ 26].
A fundamental difference of this approach to the traditional Taylor expansion is in development of the basic equations for higher order probabilistic characteristics, where traditional linearization procedure (expectation is approximated by the zeroth order term) has been replaced by sequential (iterative) symbolic calculation of these characteristics.
Coal samples were crushed to 150 200 mesh, sandstone was replaced by glass beads, and natural gas in the formation was approximated by pure methane.
With current samples y and updated metric-vector ({{{overset smile {boldsymbol {Psi }} }}}^{left (k right)}), the residual v (i.e., the part of the metric-vector that has not been approximated) is replaced by {mathbf{v}} leftarrow {mathbf{y}} - {boldsymbol{Phi }}{{{oversetsmile{boldsymbol{Psi}} }}}^{left k right)}.
When the sack was replaced, the remainders were approximated in cm.
The region is approximated as an ensemble of L1 = L - + 1 candidate sites undergoing independent neutral evolution, i.e., the simultaneous updating of sites by one mutation is replaced by independent mutations.
