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Finally, if the problem has multiple solutions, all of them can be found.
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It is quite possible that Algorithm 1 returns multiple network coding solutions all of which have the same objective value.
The clever thing is that the many people in need all have multiple solutions to their woes: a cat stuck in a tree might be saved by a ladder, but it might also be saved by a flying carpet, say.
Then a numerical technique is proposed to find all possible multiple solutions.
This is so as "real-world" problems are inherently ill-structured and seldom have a single, best solution; they typically possess multiple solutions or no solution at all (Kitchner 1983).
The maximum entropy method states that if there are multiple solutions to a problem and all available information has been used to narrow the selection, the best solution is the one with the highest entropy.
In other words, HC outcomes contain only the functions which are assigned to complexes and proteins, in all the multiple solutions.
EEEP, LatTrans, HorizStory and PhyloNet all have options to report multiple solutions if there are more than one minimal RSPR path.
The risk in using this is that if a puzzle does have multiple solutions, this assumption may lead you to miss all of them.
If multiple solutions occur the false transient method is not capable of calculating all profiles.
Finally, whatever the fuzzy system under consideration, there is no need to study its invertibility beforehand since the algorithm is able to handle all possible situations (no solution, one unique solution, multiple solutions, an infinity of solutions).
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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