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In any given sequence he may rise up on his back wheels, rearing like a bronco and spinning in a tight, furious circle, a wheelchair pirouette; or tilt forward to balance on the tiny front wheels as if en pointe; or spill the chair sideways and overboard, balancing on one rim with a hand on the floor.
Furthermore, when present, they were usually located at unique positions in any given sequence.
In other words, the probability of any of the hidden variables being one in any given sequence is the same.
As the best matches to each of the PWM can potentially overlap in any given sequence, this sequence score is not necessarily equal to the weighted sum of these two best matches.
The partition function based P ij, which captures the probability of the i t h residue pairing up with the j t h residue in any given sequence is used to capture an informative prior on the structures.
The program UVWORD, which determines the types and frequencies of overlapping words of DNA in any given sequence, was used to generate oligonucleotide profiles of the sequences described in Table 1 (see Methods).
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Unlike genomes where most sequences should be approximately equally represented, coverage of any given sequence in a transcriptome can vary over several orders of magnitude due to expression differences [ 4].
Next, a similarity threshold was selected to determine how similar any given sequence in a promoter region must be to the PWM to be considered an actual instance of the putative regulatory element.
Based on the assumption that, for any given sequence and in the absence of altering factors, the relation between mean of the peak height of two nucleotides, namely C and T, should be relatively constant, we calculated the ratio between C and T within the tail of the primers and used this ratio to normalize the overscaled C signals of the sequence (see Methods).
Then for any given sequence { x n } in H, any given sequence { λ n } n = 1 ∞ of positive numbers with ∑ n = 1 ∞ λ n = 1 and for any positive integer i, j with i < j, ∥ ∑ n = 1 ∞ λ n x n ∥ 2 ≤ ∑ n = 1 ∞ λ n ∥ x n ∥ 2 − λ i λ j ∥ x i − x j ∥ 2. Lemma 2.3 Let H be a Hilbert space.
Second, the method that is used, called diagonalisation was already present in the work of du Bois-Reymond for building real functions growing faster than any function in a given sequence of functions.
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