对称布尔函数多项式展开式的组合方法

A combinatorial problem about binary necklaces and attractors of Boolean automata networks

It is known that there are no more Lyndon words of length n than there are periodic necklaces of same length. This paper considers a similar problem where, additionally, the necklaces must be without some forbidden factors. This problem relates to a different context, concerned with the behaviours of particular discrete dynamical systems, namely, Boolean automata networks. A formal argument supporting the following idea is provided: addition of cycle intersections in network structures causes exponential reduction of the networks' number of attractors.

Combinatorial and Algorithmic Properties of One Matrix Structure at Monotone Boolean Functions

One matrix structure in the area of monotone Boolean functions is defined here. Some of its combinatorial, algebraic and algorithmic properties are derived. On the base of these properties, three algorithms are built. First of them generates all monotone Boolean functions of $n$ variables in lexicographic order. The second one determines the first (resp. the last) lexicographically minimal true (resp. maximal false) vector of an unknown monotone function $f$ of $n$ variables. The algorithm uses at most $n$ membership queries and its running time is $Θ(n)$. It serves the third algorithm, which …

布尔函数的本质间隔

Essential arity gap of Boolean functions

研究了本质元间隔为2的布尔函数.我们使用全合取范式代替Zhegalkin多项式，这使我们能够简化证明，并获得几个组合的结果，有关布尔函数与一个给定的arity间隙。

图的布尔组合

Boolean combinations of graphs

本文首次系统研究图的布尔组合，重点分析其对χ-有界性等组合与结构性质的影响，并刻画了各类图的布尔组合的结构特征。

A Boolean Functions Theoretic Approach to Quantum Hypergraph States and Entanglement

The hypergraph states are pure multipartite quantum states corresponding to a hypergraph. It is an equal superposition of the states belonging to the computational basis. Given any hypergraph, we can construct a hypergraph state determined by a Boolean function. In contrast, we can find a hypergraph, corresponding to a Boolean function. This investigation develops a number of combinatorial structures concerned with the hypergraph states. For instance, the elements of the computational basis generate a lattice. The chains and antichains in this lattice assist us to find the equation of the Bool…

用于揭示非小细胞肺癌化疗耐药性的布尔网络简化与规则拟合

Boolean-network simplification and rule fitting to unravel chemotherapy resistance in non-small cell lung cancer

针对布尔网络组合爆炸难以穷尽分析的问题，提出将31节点非小细胞肺癌化疗耐药布尔模型约简为9节点核心模型的方法，保留原吸引子景观与临床相关稳态，缩小状态空间四个数量级，为耐药机制研究与药物发现提供支撑。