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Fig. 5 Mapping to ( k 1, k 2 ) -plane.
(a) If (T_{1} : X rightrightarrows X^) is the normal mapping to K and (T_{2}: Xrightarrow X^) is a single-valued monotone operator such that (operatorname {int}Kcap operatorname {dom}(T_{2})neq emptyset) and (T_{2}) is continuous on K, then (T_{1}+T_{2}) is a maximal monotone operator.
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In the same way that Chen and Storey relax the single-trait mapping threshold by controlling the probability that a trait falsely maps to k or more genomic locations, we relax the conservative threshold by controlling the probability that ≥ n traits falsely map to a common genomic location.
The first run uses a first sample; then, any reads mapping to k-mer contigs belonging to repeats ("inchworm" contigs; see Trinity manual) are added to a second independent sample, and Trinity is performed one more time.
All negative values of κ are mapped to K = 0, making this a type of mass-at-chance (MAC) transformation (Morey, Rouder, & Speckman, 2009; Rouder et al. 2007).
Here, z ∈ ℝ3 m are current moment vectors of unknown sources at m locations in the brain and F ∈ ℝ k × 3 m describes the mapping from sources to k sensors, which is determined by the shape of the head and the conductivities of brain, skull and skin tissues.
We define the occlusion map from k 1 to k 2 as follows: O k 1, k 2 ( m, n ) = u ( R k 1, k 2 ( m, n ) - τ ) (4).
Additional file 10: Number of paired-reads, reads mapping to OCV3-91 k, mapped contigs and "tissue-specific" contigs.
Remark 3.1 Theorems 3.1-3.3 3.1-3.3 the maimproveltheof [7, 10, 12, 13] fromainnonexpansive mapping to a k-stresultspseudofontractive mapping, respectively.
Since T maps K to K, T is weakly inward.
end{cases} Similarly to the proof of Theorem 3.1, we can easily verify that (A_{n}) is well defined and maps E to K.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com