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For each read, the number of mappings on the reference is counted along with the lowest number of mismatches found among the various mappings of that read.
Next, Stage D processes the batch, skipping the reads that were previously mapped in stage B. For each unmapped read in the batch, this stage uses the seeds produced by stage C to obtain a list of candidate alignment locations (CALs) or regions, which define potential mappings of that read.
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Let be a subset of a real Banach space, and let be a family of mappings of such that.
Let be a countable family of nonexpansive mappings of such that and an operator which is -Lipschitzian and -strong monotone on.
To deal with a family of mappings, the following conditions are introduced: let be a subset of a real Hilbert space, and let be a family of mappings of such that.
If μ n = 0 and l n = 0 for all n ≥ 1, we obtain from (1.5) the class of mappings that includes the class of nonexpansive mappings.
If (u_{n}equiv0) and (v_{n}equiv0) for all (ngeq1), we obtain from (1.6) the class of mappings that includes the class of Bregman quasi-nonexpansive mappings.
Let be a nonempty subset of a metric space and let be self-mappings of Assume that is nonempty,, is complete, and is an -contraction.
Let be a nonempty subset of a metric space and let be self-mappings of Assume that is nonempty,, is complete, and is an -weak contraction.
Therefore, we restrict the solution space to a set of mappings that are plausible, that is, mappings that have been observed experimentally (Fig. 2B ).
Let be two self-mappings of such that there exist and such that is a -nondecreasing mapping and (3.2). for all for which and all.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com