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Using Assumption 1, we know that sequence ({ x_{k} }) is bounded, and there is a positive constant η such that (Vert x_{k} Vert le eta) for all (k ge 1).
Based on the theory underlying modern phylogenetic models, we know that sequence similarity is only one component that indirectly affects the model selection tests [ 31, 101, 102].
By condition (3.5), we know that sequence { θ j n } is monotone decreasing and θ j n → θ j as n → ∞.
In the developing world, we seek to emulate the same goals and trajectory but we know that sequence cannot be repeated.
You know that sequence in 12 Monkeys when the creepy fellow brings some tubes filled with fluid onto an airplane, passing them through security and even wafting one of them under the nose of a security agent with total impunity?
Given that we now know that sequence insertions and deletions are common, and considering that around 80% of the reference genome is derived from a single individual [ 9, 10], it is reasonable to expect that many common sequences, i.e. those present in at least 1% of the population, may be absent in the reference data due to missing copies in the few individuals that were studied.
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This is important as it is known that sequence alignments often fail at pairwise sequence identities below ~60%.
Because it is known that sequence coverage will not be uniform on all the exons, we only analysed the common variant alleles that were detected in three samples.
Indeed it is well known that sequences with functional activity – such as coding sequences or regulatory regions – are subject to selective pressures that prevent the fixation of mutations and conserve sequences during evolution.
Although many of the endogenous viral sequences are of different lengths in alignments, it is now well known that sequences of very different lengths can be accurately placed on phylogenies [ 58].
Although many of the sequences are of different lengths in the NP alignment (Additional file 2: Fig. S2), it is now well known that sequences of very different lengths can be accurately placed on phylogenies [ 21].
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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