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The potential dispute over whether there is a single precise notion of randomness that answers perfectly to our intuitive conception of random sequence can be largely sidestepped for present purposes.
So no Borel normal sequence, and hence no random sequence, can model the sequence of outcomes of a Markov chain, even though each outcome happens by chance.
Wold-Cramer representation [9], of a nonstationary random sequence can be expressed as an infinite sum of sinusoids with random and time-dependent amplitudes and phases, or (1).
Random sequence can be chosen from 2 N R possible permutation and combination of "0" and "1," where R is the number of the sequences, and N is the length of a sequence.
There is no way of predicting a genuinely random sequence in advance because no random sequence can be effectively produced, yet every predictable sequence of outcomes can (intuitively) be generated by specifying the way in which future outcomes can be predicted on the basis of prior outcomes.
As with wtRepD, a random sequence can be used here, albeit with a lower affinity for RepD.
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Therefore, their output random sequences can be used without the conditioning component in Section 3.1.
Though deep (or random) sequencing can generate genome-wide transcriptome information, it does not discriminate strand-specific transcription.
Random sequences can dilute the position-specific amino acid exchange characteristics of native alignments.
We have recently found that the addition of a large number of computer-generating random sequences can classify the metagenomic sequences according to phylotypes [ 42].
According to Karlin and Altschul [ 28] also the sum statistics of the k-best alignment scores for random sequences can be derived analytically for asymptotically long sequences.
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