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It is much easier to manage dense mappings from one key to one value than sparse mappings from one key to multiple values.
Analytic free maps include vector-valued polynomials in free (non-commuting) variables and form a canonical class of mappings from one non-commutative domain D in say g variables to another non-commutative domain ˜D in ˜g variables.
Extend the mappings from one family of mappings to two families of mappings; Extend the mappings from the class of asymptotically nonexpansive mappings to the class of generalized asymptotically nonexpansive mappings.
(1) Extend the mappings from one family of mappings to two families of mappings; (2) Extend the mappings from the class of asymptotically nonexpansive mappings to the class of generalized asymptotically nonexpansive mappings. .
PathCase-SB visualization produces interactive pathway graphs, model graphs or both with various mappings from one to the other.
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Figure 2 Projection from a sphere to a plane: one-to-one mappings from a node on a sphere to a node in a plane.
It is different from other theories in having several parallel representations for sentences, each with its own architecture and vocabulary, subject to its own organizational constraints, and linked by principles of correspondence (mappings), not derived from one another.
The one-to-one mappings from Inparanoid was generated by selecting the mappings with the higher bootstrap score.
We have considered simple integrators as mappings from (x, ν) at one discrete time level to (x, ν) at the next.
In Figure 3, the mapping set of read 4 has two different mappings (one from maternal and one from paternal).
Our mapping pipeline retains genomic mappings with one mismatch regardless of the location on the genome, or multiple mappings (threshold of 100 locations).
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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