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The maximum number of read mismatches and read gap length were set to 2. Multiple mappings of single reads was set to 10 (default: 20) to decrease the bias for genes with more multimapping reads.
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The plug-in linux_proc_maps returns the memory mappings of a single process.
The Banach contraction principle has been extended in different directions either by using generalized contractions for multivalued mappings and hybrid pairs of single and multivalued mappings, or by using more general spaces.
Naturally, many authors have started to investigate the existence of a fixed point theorem via α-admissible mappings for single valued and multivalued mappings (see [31 38]).
A special case of Single Mappings occurs when one or both reads of a mapping pair also map to other regions of the reference, but they cannot be associated with a Perfect or Distorted read pair.
In 2008, Suzuki [1] introduced a class of single valued mappings 1 2 ∥ x − T x ∥ ≤ ∥ x − y ∥ implies ∥ T x − T y ∥ ≤ ∥ x − y ∥ (C).
As an application, a common fixed point result for a hybrid pair of single and multivalued mappings is obtained.
While some WGA methods have reported the generation of chimeric DNA molecules in bacteria [ 44], these artifacts would mainly affect paired-end mappings of structural rearrangements, not single-end read copy number measurements that rely on sequence read depth.
If the sequence { S n } (resp. { T n } ) of averaged mappings consists of a single mapping S (resp. T), then { S n } and { T n } obviously verify conditions (3.1) and (3.2), and hence from Lemma 3.3 we have the following corollary.
Fixed point problems for multivalued mappings are more difficult than those of single-valued mappings and play very important role in applied science and economics.
We consider the equivalence of the existence of fixed points of single-valued mappings and multivalued mappings for some classes of mappings by proving some equivalence theorems for the completeness of metric spaces.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com