Then, in Section 3, we make some estimates on the maximum number of solutions of (1.1), and, in Section 4, we establish some results on the minimum numbers of solutions and positive solutions of (1.1).
In this section, we consider the minimum numbers of solution and positive solutions of (1.1).
The sizes of the training and testing sets depend on the parameter <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0013803.e097.PNG" class= inline-graphic"/> (majority voting threshold), which determines the minimum number of non-dominated solutions that must agree with each other in the voting context.
It consisted of a fractional factorial design created in order to span the range of all parameters and their combinations that were found to have a clear effect in (2), by means of a minimum number of numerical simulation solutions.
Under convex/concave conditions imposed on g, some results on the exact numbers of solutions and positive solutions are established based on the discussions to the maximum and minimum numbers of (positive) solutions.
In this paper, based on the discussions to the maximum and minimum numbers of (positive) solutions, we establish some results on the exact number of (positive) solutions of (1.1) under convex/concave conditions.
The results indicate that an increase in the number of satellites is vital especially in urban areas where minimum number of satellites for a solution may not be obtained.
MOMA and ROOM are appropriate only for the simulation of mutants, since they calculate the minimum distance solution or the solution with minimum number of changes, respectively, for the mutant strain relative to the original "wild-type" solution (i. e. obtained with FBA).
Considering the Pacific Biosciences data has high error rates and generating an error-free read is unlikely, a solution with the minimum number of corrected errors is likely preferred over a solution that successfully maps more fragments without errors.
We discuss the minimum number of boundary conditions required for solution uniqueness and illustrate this with numerical examples.
