Boundary
Boundary
The boundary of an application is an empirical measurement of its performance, validated under trial conditions. The trial requires a total perspective.
Boundary delivers a realistic assessment of the depth of ancestry at which a particular implementation of meiosis, is likely to cease yielding useful akin, for a given breadth.
This is important because applications do not attain optimum theoretical performance. Boundary therefore can provide a way to compare performance between applications.
comprehensive ancestral set
A comprehensive ancestral set is the set of all ancestors of a single descendent, up to a particular depth. The set is comprehensive because it is artificially constructed so as to have no gaps in the ancestry. Every ancestral line is complete down to the required depth. The most ancient ancestors are all synthetic cTags.
Thus one cTag has exactly 2depth -2 kin relations and zero affinity relations within the CAS. Other cTags in the CAS has varying numbers of kin / affinity relations.
Result
Boundary's result takes into account all cTags in the CAS equally. Since we are interested in signal/noise, boundary needs to compare both false negative and false positive with both true positive and true negative.
Probabilistic
Boundary's results are statistical. Different runs using different original synthetic cTags will produce varialbe results. The greater the breadth, the less variation.
For a depth of trial (d) over a single, comprehensive ancestral set whose original ancestors are all synthetic.
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(d) boundary(b), is the greatest dissimilarity value of an actually unrelated pair to be recorded by akin as having less dissimilarity than some, in fact, meiotically related pair, at breadth (b).
Boundary score may reflect the average outcome of numerous trials.
Turbulence
Turbulence specifies the region beyond the lowest dissimilarity value at which a pair of cTags related meiotically by g generations produces a greater dissimilarity value than a different meiotic pair of g +x generation, for a positive integer value of x. Trial conditions and parameters to turbulence are identical to those of boundary.
This is of particular significance to bread-crumb following operations, which may be considered unreliable in the region of turbulence.