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Intuitively, one can think about finding the optimal (maximum) score as a procedure of trying all possible sequence splitting into two subsequences (5′ end and 3′ end) and optimally aligning those subsequences.
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In that case, the indirect alignment of q and d through that reference will be the optimal alignment since d is optimally aligned with each reference in our index.
Here, we introduce the program CMAPi, a two-dimensional dynamic programming algorithm that, given a pair of protein complexes, optimally aligns the contact maps of their interfaces: it produces polynomial-time near-optimal alignments in the case of multiple complexes.
Let us use the Ω1|3 notation for the model defined by M1 optimally aligned versus M 3. We start from separate alignments of M1 and M 2 with M 3 as a reference.
Usually, business processes and infrastructure are not optimally aligned.
Two fibers are optimally aligned when the maximum possible light flows through their splice point.
The reconstructed brain image for each subject was then morphed into an average spherical surface representation that optimally aligned the sulcal and gyral features across subjects61.
"One building might shadow another, or you may have a street that is optimally aligned to channel the wave, either in a fortunate or unfortunate way".
By producing a structure from optimally aligned fibres and with a hedged bonding process, an increase of the manufacturing-rate and quality is possible.
We also simulate FHEC (Frequency Harmonizing Emphasis Control) strategies that allow policymakers to concentrate the policy thrust on tracking frequencies that are optimally aligned with policy goals under different targeting priorities.
A diversity of public and private sector actors, representing multiple sectors such as health, agriculture, urban planning, transportation, finance, broadcasting, education, and the food and pharmaceutical industries, will be required to collaborate for policies, programs, and interventions to be optimally aligned.
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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