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We have applied an algorithmic methodology which provably decomposes any complex network into a complete family of principal subcircuits to study the minimal circuits that describe the Krebs cycle. Every operational behavior that the network is capable of exhibiting can be represented by some combination of these principal subcircuits and this computational… (More)

We construct an algebraic-combinatorial model of the SOS compartment of the EGFR biochemical network. A Petri net is used to construct an initial representation of the biochemical decision making network, which in turn defines a hyperdigraph. We observe that the linear algebraic structure of each hyperdigraph admits a canonical set of… (More)

In this paper we derive and present an application of hypergraphic oriented matroids for the purpose of enumerating the variable inter-dependencies that define the chemical complexes associated with the kinetics of non-linear dynamical system representations of chemical kinetic reaction flow networks. The derivation of a hypergraphic oriented matroid is… (More)

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