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.

- Block probabilities
- Kolmogorov conditions in matrix form
- Probabilistic de Bruijn matrix
- Some properties of n-block probabilities
- Some simple examples
- Determinant and inverse
- Characteristic equation
- Correlations

E-mail:mcintosh@servidor.unam.mx