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Therefore, x = e t is an appropriate substitution for the variable x.
Proof Firstly, we take the solution ω ( t ) of Eq. (3) and make an appropriate substitution for the variable x.
Consider the differential equation ω ′ ( t ) = m 2 + ω ( t ) 2. Based on the theory of ordinary differential equations, we see that x = m sinh ( t ) is a solution on J = , where t ∈ J corresponds to ω ( t ) ∈ I. Therefore, one can see that x = m sinh ( t ) is an appropriate substitution for the variable x.
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With Hazan's first efforts at codifying recipes, she struggled to identify appropriate substitutions for the finer ingredients used in Italy.
Our model evaluation procedure is primarily a testbed for selecting an appropriate substitution model for stems, loops and neutrally-evolving sequence (see "Patterns of nucleotide substitution in non-coding RNA").
For the following tree reconstructions, we selected most appropriate substitution models for our data based on the Akaike Information Criterion as implemented in JMODELTEST version 0.1.1 [ 41, 42].
Appropriate substitution models for each data partition were chosen by computing likelihood scores for each partition on a MP tree for the 3-gene data set under 56 substitution models in PAUP* and comparing the scores in ModelTest.
The most appropriate substitution models for the merlin and mats datasets is LG + G, for the crumbs dataset is Blosum62 + G + I, and for dachsous, fat, hippo, and yorkie datasets is VT + G + I.
According to ProtTest [ 36], the most appropriate substitution models for the merlin and mats datasets is LG + G, for the crumbs dataset is Blosum62 + G + I, and for the dachsous, fat, hippo, and yorkie' s datasets is VT + G + I, based on the Bayesian information criterion.
We used jModelTest [21] to determine the most appropriate substitution model for each DNA region and these were used to guide model choice in LAMARC.
The appropriate substitution models for each phylogeny were determined by jModelTest [ 49] and ProtTest [ 50].
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