嵌套信道函数的证书复杂度与对称性

Certificate complexity and symmetry of nested canalizing functions

Boolean nested canalizing functions (NCFs) have important applications in molecular regulatory networks, engineering and computer science. In this paper, we study their certificate complexity. For both Boolean values $b\in\{0,1\}$, we obtain a formula for $b$-certificate complexity and consequently, we develop a direct proof of the certificate complexity formula of an NCF. Symmetry is another interesting property of Boolean functions and we significantly simplify the proofs of some recent theorems about partial symmetry of NCFs. We also describe the algebraic normal form of $s$-symmetric NCFs.…

Stratification and enumeration of Boolean functions by canalizing depth

Boolean network models have gained popularity in computational systems biology over the last dozen years. Many of these networks use canalizing Boolean functions, which has led to increased interest in the study of these functions. The canalizing depth of a function describes how many canalizing variables can be recursively picked off, until a non-canalizing function remains. In this paper, we show how every Boolean function has a unique algebraic form involving extended monomial layers and a well-defined core polynomial. This generalizes recent work on the algebraic structure of nested canali…

关于非退化渠化布尔函数的数量

On the number of non-degenerate canalizing Boolean functions

本文推导了计算具有特定本质变量数及渠化特性的布尔函数的递归公式，确定了非退化渠化布尔函数的数量，为量化随机布尔函数中渠化频率及其在生物网络模型中的过表达提供了严格基础。