A flux pattern is called an elementary flux pattern if it cannot be generated by combination of two or more different flux patterns.
Very recently, the concept of elementary flux patterns was introduced, where an elementary flux pattern is defined as a set of reactions within a subsystem of a larger network that represents the basic routes of each steady-state flux of the larger network through the sub-network [ 81].
We say that a periodic pattern (langle mathcal {T}), (U), (b), (p), (erangle ) is an elementary periodic pattern when a sequence of multisets (mathcal {T}) consists of one multiset that consists only of (k) identical elements, i.e. (mathcal {T} = T^k).
If an elementary periodic pattern (langle T_i^k), (U), (b), (p), (erangle ) is valid in (A) then for any syntax tree (T_j) such that (T_j sqsubseteq T_i) and (k' le k) an elementary periodic pattern (langle T_j^{k'}), (U), (b), (p), (erangle ) is valid in (A). 2.
If an elementary periodic pattern (langle T_i^k), (U), (b), (p), (erangle ) is not valid in (A) then for any syntax tree (T_j) such that (T_i sqsubseteq T_j) and (k le k') an elementary periodic pattern (langle T_j^{k'}), (U), (b), (p), (erangle ) is not valid in (A). 4.
If an elementary periodic pattern (langle T_i^k), (U), (b), (p), (erangle ) is not valid in (A) then for any syntax tree (T_j) such that (T_j sqsubseteq T_i) and (lnot exists T_{n} ne T_{i}) such that (T_{j} sqsubseteq T_{n}) an elementary periodic pattern (langle T_j^{k'}), (U), (b), (p), (erangle ) where (k le k') is not valid in (A).
If an elementary periodic pattern (langle T_i^k), (U), (b), (p), (erangle ) is valid in (A) then for any syntax tree (T_j) such that (T_i sqsubseteq T_j) and (lnot exists T_{n} ne T_{j}) such that (T_{i} sqsubseteq T_{n}) an elementary periodic pattern (langle T_j^{k'}), (U), (b), (p), (erangle ) where (k' le k) is valid in (A). 3.
Discovering an elementary periodic pattern (langle T^k), (U), (b), (p), (erangle ) for a given set of time units (U), and a given value of support parameter (0<sigma le 1) is performed through the nested iterations over the syntax trees included in a reduced syntax tree table and the iterations over the positional parameters (b), (p), and (e).
This elementary pattern was much elaborated during the reign of James I, when Jones provided increasingly magnificent costumes and scenic effects for masques at court.
