Layered mixed matrices and reaction networks
Abstract
The purpose of this work is twofold. In the first part, we consider layered mixed matrices introduced by Murota, relate them to existing notions in combinatorial commutative algebra, and investigate the irreducibility of their determinants. Furthermore, for a layered mixed matrix in combinatorial canonical form, we determine the sparsity structure of its inverse. That is, we characterize which entries of the inverse are nonzero. In the second part, we establish for the first time a formal connection between these algebraic results and the theory of buffering structures for reaction networks developed by Mochizuki and Okada. We identify the lattice of buffering structures with the lattice of order ideals of the block poset of the combinatorial canonical form of the associated layered mixed matrix. This allows us to characterize the reducibility of the symbolic Jacobian determinant as a polynomial in the reaction-rate derivatives, as well as the nonzero sensitivity responses of species concentrations to reaction-rate perturbations.
Related
- Persistence of bounded trajectories in positively transverse reaction networks
- Implementation of Linear Regression and Linear Interpolation using Reaction Networks
- Simulation-free approximate Bayesian computation for stochastic reaction networks
- Simulation-free approximate Bayesian computation for stochastic reaction networks
- Lumping of reaction networks: Generic and critical parameters
BibTeX
@misc{kuhrs2026layered,
title = {{Layered mixed matrices and reaction networks}},
author = {Arne Kuhrs and Máté L. Telek and Nicola Vassena},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05100},
eprint = {2609.05100},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05100},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Layered mixed matrices and reaction networks
AU - Arne Kuhrs
AU - Máté L. Telek
AU - Nicola Vassena
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05100
UR - https://arxiv.org/abs/2609.05100
AB - The purpose of this work is twofold. In the first part, we consider layered mixed matrices introduced by Murota, relate them to existing notions in combinatorial commutative algebra, and investigate the irreducibility of their determinants. Furthermore, for a layered mixed matrix in combinatorial canonical form, we determine the sparsity structure of its inverse. That is, we characterize which entries of the inverse are nonzero. In the second part, we establish for the first time a formal connection between these algebraic results and the theory of buffering structures for reaction networks developed by Mochizuki and Okada. We identify the lattice of buffering structures with the lattice of order ideals of the block poset of the combinatorial canonical form of the associated layered mixed matrix. This allows us to characterize the reducibility of the symbolic Jacobian determinant as a polynomial in the reaction-rate derivatives, as well as the nonzero sensitivity responses of species concentrations to reaction-rate perturbations.
ER -