Also, Becker-Stark's inequality (2.5) has various applications, extensions and refinements, see [13 16] and [17 19].
Later refinements (see, e.g., [12, 13, 19]) show that the knowing eigenvalues associated with a number of different boundary conditions can also determine the potential uniquely.
A third, less extreme, option is to insist that objects of different kinds, e.g., a clay statue and the piece of clay it is composed of, can occupy the same space at the same time, but objects of the same kind, e.g., two statues, cannot (Wiggins 1968; for refinements, see Oderberg 1996).
An initial difference in branch phenotype can be observed at 60 hr APF and subsequently at 72 hr APF, the typical refinement seen in wild type is largely absent in the EGFRDN background.
Taking L k ∗, 3 ( x ) = ( L k ∗, 0 ( x ) + L k ∗, 1 ( x ) + L k ∗, 2 ( x ) ) / 3 as input, we further invoke local refinement (see Section 4.1) to optimize object segmentation.
Interface post-predictions were made on all docking runs (CPORT-driven and ab-initio) that were subjected to refinement (see above), except for complexes with internal symmetry.
Table 1 lists the Gene Ontology categories in this taxonomy that show significant enrichment of diet-related genes after the refinement (hypergeometric test; for details about refinement see [24]).
During subsequent refinement (see below), we also estimated particle rotations by aligning 3-frame sums (see below).
For detailed crystallisation, freezing and measurement conditions and for details on structure solution and refinement, see Supplementary Information.
Genome-scale metabolic network was reconstructed using an automated procedure in combination with the manual refinement (see Methods section).
