论文标题
网络中的多相关性：理论
Multivaluedness in Networks: Theory
论文作者
论文摘要
一个意外且令人惊讶的观察结果是，鉴于正确的条件，两个反对系统可以表现出从一个输出到另一个输出的多价性。此处介绍的主要结果是使用新颖的内在概念及其相反的超越性，可以通过反对系统表现出多价的必要条件。随后的推论提供了在特定条件下多价性的进一步表征。 作为我们的理论结果的应用，我们证明了这些结果如何有助于降低复杂网络的结构复杂性。
An unexpected and somewhat surprising observation is that two counter-cascaded systems, given the right conditions, can exhibit multivaluedness from one of the outputs to the other. The main result presented here is a necessary and sufficient condition for multivaluedness to be exhibited by counter-cascaded systems using the novel notions of immanence and its opposite, transcendence, introduced here. Subsequent corollaries provide further characterization of multivaluedness under specific conditions. As an application of our theoretical results, we demonstrate how these aid in the structural complexity reduction of complex networks.
