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The entire computational procedure is implemented using a program written in MATLAB computer language.
Nonlinear regression analysis method using a program written on MicroMath Scientist software (Salt Lake City, Utah) was used to obtain the least square fit for all the models.
In Example 1, the results are computed by using a program written in Mathematica 11.0 and are compared with the computed solutions of another well-known method.
All data were analysed with non-linear regression analysis method using a program written on MicroMath Scientist software (Salt Lake City, UT).
Non-linear regression analysis method using a program written on Micro Math Scientist software (Salt Lake City, Utah) was used to obtain the least square fit for all the models.
This section presents several numerical examples to demonstrate the high accuracy and applicability of the present method, and all of them were performed on the computer using a program written in Mathematica 8.0.
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Randomisation used a program written in R (version 2.14.2) by a statistician not otherwise involved in the study.
In all ORFs in the genome of M. tuberculosis we used a program written in PERL to determine the occurrences of the four amino acids that can be encoded by a homogeneous codon (i.e., a codon that consists of three identical nucleotides) as well as one or more non-homogeneous codons (codons that do not consist of three identical nucleotides).
The stem profiles from "Autostem" were then processed using "Sweep Extractor", a program written specifically for this task, to obtain the maximum curvature of a log according to a predetermined length and a predetermined position in the tree.
For the annotation of mutations found in interspecies comparisons, we used MitoPositions, a program written in Perl that is available on request.
Axial ratios were determined from the LM micrographs, with the use of a program written in the C# programming language.
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