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Our mapping pipeline retains genomic mappings with one mismatch regardless of the location on the genome, or multiple mappings (threshold of 100 locations).
Another 33% reads have multiple pseudogenome mappings with one mapping better than the rest, so they are filtered by quality score.
An instance of a chemical reaction may be represented by a set of atom mappings, with one atom mapping between each substrate and product atom.
A local result as regards (C^{0}) stability for a class of strictly monotonic mappings with one fixed point was considered in [13], as well as the global (C^{0}) stability with more than one fixed point in [14].
On the other hand, in the papers [26 33], the authors presented another technique which reduces coupled fixed point results in metric and various abstract metric spaces to the results for mappings with one variable.
By combining the mentioned techniques, we show in this paper that several coupled fixed point results in (ordered) G-metric spaces obtained in recent years and presented in the papers [11 23] simply follow from the well-known standard (ordered) metric results for mappings with one variable.
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Without loss of generality, we assume that there are total of m i discordant mappings with exactly one end mapped to ϕ i (Please note that m=∑ i =1 t m i, where total number of segments is t).
Such mappings are not further processed, with one exception.
Let, is a -quasicontraction that commutes with, one of the mappings and is continuous, and they satisfy.
PathCase-SB visualization produces interactive pathway graphs, model graphs or both with various mappings from one to the other.
The remaining 6% have multiple mappings with identical quality scores, so one was randomly chosen to be reported in the final output.
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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