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This might point out the more complex and therefore less valid structure of the Rome II Patient Modified Formula Questionnaire.
This triangle inequality holds by the correctness of the (unsparsified) algorithm: For all x < y < z we have W x, y)+ W y+1, z) ≤ W x, z) since the concatenation of the best structures for the ranges (x, y) and (y, z) always forms a valid structure for the range (x, z) with score W x, y)+ W y+1, z) which is hence never better than the optimal score W x, z) for that range.
In either case, the use of DCEs to define and quantify stakeholders' preferences can provide a valid structure for the decision making process.
Problem posing as sentence integration defines the arithmetic word problem structure, and posing a problem is a task to satisfy all the constraints and requirements to build a valid structure.
The results of these steps were SBGN PD maps with valid structure but incomplete layout.
A single compound can have more than one valid structure, each represented with a distinct standard InChI.
This ensemble was independent of resolution unless the structure was collected at high enough resolution to confidently locate all protons – at which point there would only be one valid structure.
MFOLD verifies each secondary structure prediction generated for valid structure [ 36].
Also, the FFM has been reproduced in a number of culturally different countries [ 16- 18], indicating a universally valid structure.
Since the computational complexity of the CSCCP is NP-complete, the search for optimal solutions (valid structures) in the CSCCP must be executed in exponential time complexity for any deterministic algorithms without a loss of generality.
The distinct, equally valid structures are usually stereoisomers.
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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