发表机构
Max Planck Institute for Mathematics in the Sciences; Budapest University of Technology and Economics; Leipzig University（马克斯·普朗克科学促进学会数学与科学研究所; 布达佩斯技术与经济大学; 莱比锡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究关联分层混合矩阵与反应网络缓冲结构理论，刻画其逆矩阵稀疏性、行列式可约性及物种浓度敏感性，为相关领域提供形式联系。
AI 中文摘要
本研究有两个核心目标：第一部分中，我们考虑由Murota提出的分层混合矩阵，将其与组合交换代数中的现有概念关联，并研究其行列式的不可约性；此外，对于处于组合标准型的分层混合矩阵，我们确定其逆矩阵的稀疏结构，即刻画逆矩阵中哪些元素非零。第二部分中，我们首次建立这些代数结果与Mochizuki和Okada提出的反应网络缓冲结构理论之间的形式联系，将缓冲结构格与关联分层混合矩阵的组合标准型的块偏序集的序理想格等同，这使我们能刻画符号雅可比行列式作为反应速率导数多项式的可约性，以及物种浓度对反应速率扰动的非零敏感性响应。
英文摘要
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.
