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Probabilistic de Bruijn matrix

The reduced evolutionary matrix and the de Bruijn diagram have probabilistic versions, in which the zeroes and ones which enable links in the diagram are replaced by probabilities that the links are to be used. This does more than express the likelihood that one thing or another will occur; it allows some quantitative comparisons to be made.

Since the reduced evolution matrix enumerates the numbers of -block ancestors of n-blocks, the probabilistic evolution matrix can be used estimate the likelihood that the ancestors actually occur, and thus to develop self-consistent estimates for their probabilities. Probabilistic de Bruijn matrices are useful for studying correlations between cells or strings of cells situated at a distance from one another because its matrix elements could describe the probability that one n-block will overlap the next; powers of the matrix would relate blocks through a chain of overlaps.

Harold V. McIntosh