Resolution:
## Figure 7.
Composition of Petri nets from controled reactions. a) The algorithm described with the help of Figure 6 provides the complete set of
possible controled reactions for each difference vector R= (r,_{c }f_{r}) d, here arrayed in a table where all possible controled reactions of subsequent difference
vectors are listed in subsequent columns. Any arbitrary sequence of controled reactions
obtained by taking one difference vector from each of the subsequent columns gives
one functional extended Petri net which is compatible with the time series data set
that originally served as input [7]. There are no combinations of controled reactions generated in the described way
that would give dysfunctional Petri nets because all invalid or contradictory reaction
vectors have been filtered out as described. Red arrows indicate one possible trajectory
of assembling a valid Petri net. Panel b) shows two reconstructed network motifs according
to sets of controled reactions computed by the algorithm for difference vector _{m}d(see Figure 6) both of which are compatible with the input data: in a molecular interpretation,
chemical reaction of B to C may depend on the absence of F (left) or the presence
of A (right). A vanishes in a separate reaction in both cases. The two network motifs
shown correspond to the decomposition _{1 }d_{1 }= r_{4 }+ r_{5 }(see Figure 6g). None of the two displays the wiring of the original Petri net (Figure
6a) which can be retrieved using the decomposition d_{1 }= r_{1}.
Durzinsky |