Duality in mass-action networks

TL;DR

This paper explores the duality relationships in mass-action networks, proposing new concepts like maximal invariant polyhedral supports and conjecturing dualities between siphons and preclusters.

Contribution

It introduces the concept of maximal invariant polyhedral supports and hypothesizes duality relations between key network structures.

Findings

Conserved quantities are dual to internal cycles.

Maximal invariant polyhedral supports are a key new concept.

Siphons and preclusters are conjectured to be dual objects.

Abstract

Mass-action networks are special cases of chemical reaction networks. For these systems, we argue that conserved quantities are dual to internal cycles. We introduce maximal invariant polyhedral supports, and we conjecture that there is a duality relation between preclusters and maximal invariant polyhedral supports. Given the close relation between maximal invariant polyhedral supports and siphons, we also conjecture that siphons and preclusters are dual objects.