可逆化学反应网络定态理想二项性的线性代数检测方法
A Linear Algebra Approach for Detecting Binomiality of Steady State Ideals of Reversible Chemical Reaction Networks
摘要：
受化学反应网络理论问题的启发，我们研究了可逆反应网络的稳态理想是否由二项式生成。我们采取代数的方法考虑，除了浓度的物种，也速率常数为indeterminates。这导致我们的概念无条件二项式，意味着二项式的所有值的速率常数。这一概念不同于当速率常数值或速率常数之间的关系给定时应用的条件二项式。我们首先将稳态理想的生成元表示为二项式的和，从而得到相应的系数矩阵。基于这些理由，我们提出了一个有效的算法检测无条件二项式。该算法只对系数矩阵使用初等列和行运算。我们证明了我们的算法的时间复杂度的渐近最坏情况的上界。此外，我们实验比较其性能与其他现有的方法。
英文摘要：
Motivated by problems from Chemical Reaction Network Theory, we investigate whether steady state ideals of reversible reaction networks are generated by binomials. We take an algebraic approach considering, besides concentrations of species, also rate constants as indeterminates. This leads us to the concept of unconditional binomiality, meaning binomiality for all values of the rate constants. This concept is different from conditional binomiality that applies when rate constant values or relations among rate constants are given. We start by representing the generators of a steady state ideal as sums of binomials, which yields a corresponding coefficient matrix. On these grounds we propose an efficient algorithm for detecting unconditional binomiality. That algorithm uses exclusively elementary column and row operations on the coefficient matrix. We prove asymptotic worst case upper bounds on the time complexity of our algorithm. Furthermore, we experimentally compare its performance with other existing methods.
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