The phrase "applied to refinement" is correct and usable in written English.
It can be used in contexts where you are discussing the application of certain principles, methods, or processes to the act of refining something.
Example: "The techniques we developed were specifically applied to refinement of the manufacturing process to enhance efficiency."
Alternatives: "utilized for improvement" or "implemented for enhancement".
Finally, a multi-stage refinement procedure is applied to refine the initial peak lists.
Therefore, it can be easily applied to any refinement ratio.
As the nodes of R corresponding to the leaves of a given speciation subtree of H are pairwise joined by speciation edges, they form a clique in R S (in Fig. 1 the cliques in red are selected and the corresponding joins are applied to compute refinement H).
We believe that many of our algorithmic approaches, including applications of scan statistics, abnormal chromosome detection using k-means clustering and the jump method, CUSUM applied to boundary refinement following region detection, and error rate estimation, may be novel applications for abnormality detection in SNP array data.
As shown in [1] and [2], the above results can be applied to obtain refinements of the Jensen, Hölder, Minkowski and Schwarz inequalities for weights satisfying certain conditions.
Thus we use the slope as the stop criterion for refinement, which can be easily applied to real-case refinement in the future.
The resultant CHOCIP data will be a rich information source that can be applied to the development or refinement of patient classification systems and associated resource allocation models for community health and outpatient care services.
Nevertheless, some refinement processes applied to genome-scale models involve finding additional biological evidence that supports the refinement, thereby breaking the circular reasoning.
It is worth to mention that the Padé approximation method has also been applied to dealing with the refinements of certain inequalities for trigonometric functions and hyperbolic functions in our recent papers [20] and [21].
