A similar reasoning applies to Example 2. If we find that a certain researcher finds the word YES over and over again, then we conclude that his algorithm is too efficient to be the result of averaging over all fitness functions; it is not likely that he chooses his fitness function uniformly at random over all possibilities at the start of each new search.
In probabilistic terms, therefore, the chance that a function taken at random is differentiable has probability zero.
Well, first of all, we would conclude that this person does not choose his fitness function uniformly at random at each search, since had he 5 done that, the success probability would have been 3/4.
When changing a Boolean function, (K, b)→ K, b'), a new function is selected at random among all considered Boolean functions with the same number of inputs.
Work [106], performed with a phantom, also shows that image quality in the case of therapy monitoring with an immediate PET scan can be improved by using TOF-PET and point-spread function modeling even at random fraction as high as > 95%%.
This prediction agrees with the present observation that the TFs with overlapping code-words are significantly closer in their biological function than expected at random.
Briefly, the hypothesis proposes that, following gene duplication, redundant functions will degenerate at random from the daughter copies until their joint function matches that of the parent gene.
In this scheme, the control functions are switched at random intervals, in accordance with the probabilities p11(l), p12(l).
The Boolean functions are chosen at random for every node, by assigning to each set of input values the outcome 1 with probability <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0017703.e004.PNG" class= inline-graphic"/>.
The neighborhood function N(x(n)) at random either deletes a random user from the vector x(n), adds a random unscheduled user (if possible), replaces one scheduled user with a random unscheduled one, or swaps the encoding order position of two random scheduled users.
The question now is: how large should be a T C r set to obtain an equally large T C r ∗ set if T C r has been populated without knowledge about the Purchase Function, i.e. at random by picking customers who are not already buying product p i ?
