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end{aligned}The inequality is obtained by letting the summands in the left-hand side assume the minimal possible values.
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This ensures that the genus can be computed and it is not artificially increased (by "artificially" introduced crossings), and it has a well defined minimal possible value.
The set of possible vertices (discretized offset values) for each parameter depends on the parameter's range, the discretization base b, and the maximal precision of the parameters ϵ, which defines the minimal possible offset value.
A multi-criteria optimization based on maximal possible values of WL and WR and minimal value of SG was achieved.
The minimal difference between two possible values of a variable is inversely proportional to the granularity of the variable.
We tried 5 possible values for the minimal number of cases in a group parameter (from 1 to 5) and 7 possible values for post-pruning confidence (1, 5, 10, 25, 50, 75, and 99%), which lead to 5×× 7 = 35 possible parameter settings.
0 is minimal possible score.
This value is an element of the [0, 1] interval, and is obtained by calculating all possible pair-wise co-expression relationships among members of the module (all possible values of r), and identifying the weakest co-expression relationship between any two module members (i.e., the minimal value of |r|).
The ratio of the maximal and minimal concentration for gradient detection ρmax/ρmin can be used together with the diffusion constant d to find an upper bound on the possible values of the absorption parameter k j.
Possible values: right, left, center.
Solve both possible values of the problem.
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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