Comparing SRNs

This repository contains the R implementation for the paper "Stochastic ordering tools for continuous-time Markov chains and applications to reaction network models" by Daniele Cappelletti, Giulio Cuniberti, and Paola Siri (https://doi.org/10.48550/arXiv.2604.00756). The code consists of two main scripts:

• Examples.R
• Functions.R

Installation and usage

After sourcing Functions.R, you can use its two main functions:

checkOrdering(source.complexes, product.complexes, preorder.matrix)

checks whether Theorem 4.1 can be applied to the reaction network defined by the first two arguments, given the preorder specified by the third argument.

findOrderings(source.complexes, product.complexes)

finds all rate inequalities and associated preorders on species counts that enable the application of Theorem 4.1 to the reaction network defined by the arguments.

Input format

• source.complexes and product.complexes are n × d matrices, where:

  • n = number of reactions
  • d = number of species
  • row r in source.complexes represents the source complex of reaction r
  • row r in product.complexes represents the product complex of the same reaction r
  • column s refers to the same species s, in both matrices

• preorder.matrix is the matrix M from Theorem 4.1

Output description

checkOrdering(source.complexes, product.complexes, preorder.matrix) returns a list of 4 objects.

• result: 1 or 0, depending on whether the hypotheses of Theorem 4.1 are satisfied or not
• rate.inequalities: vector whose component r corresponds to reaction r and can take the values
  • "=" if the rate constants are equal in X and Y
  • "+" if the rate constant of Y is greater or equal than that of X
  • "-" if the rate constant of Y is less or equal than that of X
  • "?" if the rate constants of X and Y are not compared
• species.inequalities: vector whose component s corresponds to species s and can take the values
  • "=" if the molecular counts are equal in X and Y
  • "+" if the molecular count of Y is greater or equal than that of X
  • "-" if the molecular count of Y is less or equal than that of X
  • "?" if the molecular counts of X and Y are not compared
• first.fail: when result = 0, it specifies the first hypothesis of Theorem 4.1 that failed to be satisfied

findOrderings(source.complexes, product.complexes) returns a list of 2 objects.

• preorders: list of all pairs of rate.inequalities and species.inequalities (as described for the previous function) that define an admissible preordering structure and for which at least one component of species.inequalities is either "+" or "-"
• equivalences: list of all pairs of rate.inequalities and species.inequalities (as described for the previous function) that define the remaining admissible preordering (equivalence) structures

Examples

All examples presented in the paper can be reproduced by running Examples.R. This file also serves as a practical guide for using the functions described above.