Graph-theoretic characterizations of monotonicity of chemical networks in reaction coordinates.

Graph-theoretic Analysis of Multistability and Monotonicity for Biochemical Reaction Networks

Mathematical models of biochemical reaction networks are usually high dimensional, nonlinear, and have many unknown parameters, such as reaction rate constants, or unspecified types of chemical kinetics (such as mass-action, Michaelis-Menten, or Hill kinetics). On the other hand, important properties of these dynamical systems are often determined by the network structure, and do not depend on ...

Alternative Axiomatic Characterizations of the Grey Shapley Value

The Shapley value, one of the most common solution concepts of cooperative game theory is defined and axiomatically characterized in different game-theoretic models. Certainly, the Shapley value can be used in interesting sharing cost/reward problems in the Operations Research area such as connection, routing, scheduling, production and inventory situations. In this paper, we focus on the Shapl...

Graph-theoretic Approaches to Injectivity and Multiple Equilibria in Systems of Interacting Elements∗

We extend previous work on injectivity in chemical reaction networks to general interaction networks. Matrixand graph-theoretic conditions for injectivity of these systems are presented. A particular signed, directed, labelled, bipartite multigraph, termed the “DSR graph”, is shown to be a useful representation of an interaction network when discussing questions of injectivity. A graph-theoreti...

Omega and PIv Polynomial in Dyck Graph-like Z(8)-Unit Networks

Design of crystal-like lattices can be achieved by using some net operations. Hypothetical networks, thus obtained, can be characterized in their topology by various counting polynomials and topological indices derived from them. The networks herein presented are related to the Dyck graph and described in terms of Omega polynomial and PIv polynomials.

A GRAPH-THEORETIC ANALYSIS OF CHEMICAL REACTION NETWORKS I. Invariants, Network Equivalence and Nonexistence of Various Types of Steady States