When using this pulse encoding method, M = 3, N = 19, then 286 cases can be represented, which are 30 more than that the binary encoding method can provide, and each case only three pulses need to be activated.
Hence, although a binary phenotype can be regarded as a special case of the ordinal model considered here, a binary model is not readily expandable to several categories.
Now there are several thresholds at unknown positions, but otherwise the binary model can be seen as a special case of the ordinal model.
A larger order binary BIJT can be generated by the following recursive relation, otherwise, the non-binary case is proved in Section 6.
In the cases of three-gene networks, six kinds of binary relations can be considered; X1-> X2, X1-> X3, X2-> X1, X2-> X3, X3-> X1, X3-> X2.
Proof: The above derivation for binary alphabet can be generalized for any alphabet cardinality; for simplicity, we focus on the quaternary case.
The score value of each binary relations included in network structure, S k (k = 1, 2,...; the number of binary relations), can be defined as follows: (i = 1, 2, …; the number of possible network structures) (for cases when the binary relation k is not included in the ith network structure, B i, r = 1; for the case when binary relation k is included in the network structure, B i, r = 2).
