Speaker
Description
Biochemical and environmental modeling utilizes reaction networks to represent complex transformations, yet the standard Linkage Class Decomposition (LCD), which is based purely on visual connectivity, frequently fails to capture the algebraic properties that govern long-term system dynamics. This work introduces a structural classification based on the finest decompositions of chemical reaction networks, which bridges this gap by mapping the hierarchical relationships between the LCD and two critical algebraic structures: the Finest Independent Decomposition (FID) and the Finest Incidence-Independent Decomposition (FIID). They act as the fundamental building blocks for characterizing general and complex-balanced equilibria, respectively. By the partial order of "coarsens to," between such decompositions, we categorize reaction networks into six distinct classes, three subclasses of Independent Linkage Classes (ILC) and three subclasses of Dependent Linkage Classes (DLC). To facilitate this classification, we introduce two discriminants: the Deficiency Difference, measuring the variance between total and subnetwork deficiencies, and Common Complexes Cardinality. We further establish the properties of these subclasses and provide illustrative examples. By separating ILC and DLC networks, the framework reveals alignment between structural connectivity and kinetic attributes that could offer insights in the steady state analysis of biochemical and environmental systems.
