渠化对布尔网络鲁棒性的影响
The Influence of Canalization on the Robustness of Boolean Networks
AI总结：
本文针对 k-渠化布尔网络，推导活跃度与 c-敏感性公式，并将 Derrida 值表示为加权和，从而无需仿真即可高效评估确定性及随机布尔网络的鲁棒性。
摘要：
时间和状态离散的动力系统常被用于分子网络建模。本文提供了一组用于研究布尔网络模型鲁棒性的数学与计算工具。研究重点是由 k-渠化函数支配的网络，这是近期提出的一类布尔函数，包含已被充分研究的嵌套渠化函数类。函数的活跃度和敏感性用于量化输入变化对函数输出的影响。本文将后一概念推广为 c-敏感性，并给出了一般 k-渠化函数以及具有更精确定义结构的渠化函数的活跃度和 c-敏感性公式。Derrida 值是一种常用的网络鲁棒性度量，可表示为支配渠化函数的 c-敏感性的加权和，并且也可针对布尔网络的随机扩展进行计算。这些发现为获得确定性或随机性布尔网络的 Derrida 值提供了一种无需仿真且计算高效的方法。
英文摘要：
Time- and state-discrete dynamical systems are frequently used to model molecular networks. This paper provides a collection of mathematical and computational tools for the study of robustness in Boolean network models. The focus is on networks governed by $k$-canalizing functions, a recently introduced class of Boolean functions that contains the well-studied class of nested canalizing functions. The activities and sensitivity of a function quantify the impact of input changes on the function output. This paper generalizes the latter concept to $c$-sensitivity and provides formulas for the activities and $c$-sensitivity of general $k$-canalizing functions as well as canalizing functions with more precisely defined structure. A popular measure for the robustness of a network, the Derrida value, can be expressed as a weighted sum of the $c$-sensitivities of the governing canalizing functions, and can also be calculated for a stochastic extension of Boolean networks. These findings provide a computationally efficient way to obtain Derrida values of Boolean networks, deterministic or stochastic, that does not involve simulation.
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