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Exact(4)
Equation (3.6) has exactly two solution classes and the fundamental solutions are 3 + 39 and 3 − 39.
The distribution of the four mechanisms over the three solution classes from Figure 2 is summarized in Additional file 8: Table S1.
For about a half of these profiles, however, the Kr and Gt patterns in the solutions exhibit defects in the anterior part of the spatial domain (solution classes II and III).
As a result, rather than enumerating individual solutions, we are able to enumerate solution classes (i.e. the set of all solutions having the same cost) and provide a characterization of the space of optimal and near-optimal solutions to an instance of the network history inference problem.
Similar(56)
Therefore, the positive solution class (mathcal{N}_{0}=varnothing).
end{gathered} Therefore, the positive solution class (mathcal{N}_{2}=varnothing).
(3.13) Then the positive solution class (mathcal{N}_{0}=varnothing).
end{aligned} (3.2) Then the positive solution class (mathcal{N}_{2}=varnothing).
end{aligned} (3.11) Then the positive solution class (mathcal{N}_{2}) of (1.1) is empty.
Notice that there is a trade-off between the regularity of the solution and the solution class for the uniqueness.
If we can establish higher regularity for the solutions (or approximate solutions), then we can prove the uniqueness within a larger solution class.
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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