论文标题
一种用于检测可逆化学反应网络稳态理想的二项式的线性代数方法
A Linear Algebra Approach for Detecting Binomiality of Steady State Ideals of Reversible Chemical Reaction Networks
论文作者
论文摘要
由化学反应网络理论的问题引起的，我们研究了可逆反应网络的稳态理想是由二项式产生的。我们采用一种代数方法，考虑到物种浓度，也将常数评为不确定。这使我们达到了无条件二项式的概念，这意味着所有速率常数值的二项式。当给出速率常数或关系常数之间的速率常数值或关系时，该概念与条件二元性不同。我们首先表示稳态理想的发电机作为二项式总和，该二项式总和产生相应的系数矩阵。从这些理由上讲，我们提出了一种有效的算法来检测无条件的二项式。该算法在系数矩阵上使用独家基本列和行操作。我们证明了算法的时间复杂性上的渐近性最差情况。此外，我们通过实验将其性能与其他现有方法进行比较。
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.
