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Direct computations with jets show that: where the dots indicate terms of order higher than 3. Substituting these truncated mappings into the sphere equation: yields: where the dots indicate terms of bidegree (2,4) and (4,2) and higher order.
We then set up the results for manual verification by placing the mappings into the i2b2 Mapper tool, which allows graphical editing and verification of merged ontologies [ 21].
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Clearly, the class of k-strictly pseudocontractive mappings falls into the one between classes of nonexpansive mappings and pseudocontractive mappings.
Clearly, the class of k-strictly pseudo-contractive mappings falls into the one between classes of nonexpansive mappings and pseudo-contractive mappings.
Clearly, the class of strictly pseudocontractive mappings falls into the one between the classes of nonexpansive mappings and of pseudocontractive mappings.
The class of strictly pseudocontractive mappings falls into the one between the class of nonexpansive mappings and that of pseudocontractive mappings.
If a read's mappings to two or more pseudogenomes are identical, Suspenders merges the mappings into one logical unit and tags the mapping with a bit vector to identify the origin.
The success of Textpresso in curation of GO subcellular localization (20) is also a good example of helping the curator to find evidence and to create the correct mappings into a terminology or ontology.
We loaded these pseudochromosome mappings into our own copy of the ATIDB Arabidopsis genome database [ 13] to enable a programmatic analysis.
Similarly and following the extension of the Banach contraction principle to the case of metric spaces endowed with a partial order, it was natural to try to investigate the case of nonexpansive mappings into such metric spaces.
In addition, one limitation in the analysis is that it precludes detection of previously unidentified miRNA precursors, an angle which could be addressed by feeding the deep-sequencing data mappings into a miRNA prediction program (based on parameters like mature/star sequence count distribution, folding properties, etc).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com