Fig 7. Markov chain describing the state transition that detectors undergo during training considering the immunological model.

In this representation, n describes the number of top positions to be corrected in a list of size N, W_m the waiting states, that represent a list with m correctly ranked items on the top n positions and E the education state. The probability of transition from the list education state E to the waiting states, W_m, is $q_m=\left(\begin{array}{c}\begin{array}{c}n\\ m\end{array}\end{array}\right){(1/2)}^{n-m}{(1/2)}^m$. The transition probability from a waiting state, W_m, to the education state, E, is q_educ = (n − m)/N.