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In practice, the unwrapped phase can be obtained recursively by adding a multiple of 2π to the wrapped phase until the absolute difference between neighboring phases becomes less than or equal to π. Denote by φ ^ k the wrapped MLE of the phase and φ ̃ k the unwrapped MLE.
Adding a multiple of any row to another row, or a multiple of any column to another column, does not change the determinant.
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This happens when the unwrap procedure should not add a multiple of 2π to the next phase, but does it because the absolute difference between the neighboring noisy phases is greater than π.
This happens when the unwrap procedure should add a multiple of 2π to the next phase (for instance at k = - 3 in Figure 1b), but does not do it because the absolute difference between the neighboring noisy phases is less than π ( | φ ^ - 3 - φ ^ - 4 | ≤ π ).
In the revised manuscript, we also add a multiple alignment of the WD domains as Additional file 1 : Figure S2.
The chemical and genomic similarity matrices S c and S g were not all positive semi-definite, so those that were not were made so by symmetrizing (adding the transpose and dividing by 2), then adding a small multiple of the identity matrix to their diagonal until all eigenvalues became non-negative.
When, is added by a multiple of 8 to become a positive value smaller than 8. Hence, "1", "9", and " 7" denote the same directions.
The solutions to the equation ez = 1 are the integer multiples of 2πi: :\{ z : e^z = 1 \} = \{ 2k\pi i : k \in \mathbb{Z} \} More generally, if ev = w, then every solution to ez = w can be obtained by adding an integer multiple of 2πi to v: :\{ z : e^z = w \} = \{ v + 2k\pi i : k \in \mathbb{Z} \} Thus the complex exponential function is a periodic function with period 2πi.
The number of repeats, below or above this value were assigned to amplicons' lengths, calculated by adding or subtracting a multiple of the repeat size, at a given locus, from the amplicon size, determined for the M. kansasii ATCC 12478 reference strain.
Muggins is a game of dominoes where points are scored every time a play makes the total of both open ends add up to a multiple of 5.
has the property that its digits will always add up to a multiple of 9.
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