标题： 有向环作为复杂网络中信息处理的高阶单元 显示英文标题

标题： Directed Cycles as Higher-Order Units of Information Processing in Complex Networks

摘要： 定向环是在自然、社会和人工网络中的基本模块，但它们不同的计算作用仍缺乏深入研究，尤其是在高阶结构和功能的背景下。 在本工作中，我们研究了两种类型的定向环——前馈环和反馈环——如何作为高阶结构来促进稀疏随机网络中信息的流动和整合，以及这些作用如何依赖于环的环境。 使用信息论度量，我们表明网络大小、稀疏性和相对方向性对定向环的信息处理能力有关键影响。 在一个没有首选全局方向的网络中，前馈环促进了更大的信息流动，而反馈环则允许更高的信息整合。 前馈环的相对方向及其引起的结构不一致性决定了其生成高阶行为的能力。 最后，我们证明，在原本为前馈结构的网络中引入反馈环会增加网络活动模式的多样性。 这些发现表明，定向环作为具有局部信息处理能力的计算模块，其能力取决于其所嵌入的结构。 通过定向环，我们强调了高阶结构与其在网络动态中可能引发的高阶行为之间的相互依赖关系。 显示英文摘要

摘要： Directed cycles form the fundamental motifs in natural, social and artificial networks, yet their distinct computational roles remain under-explored, particularly in the context of higher-order structure and function. In this work, we investigate how two types of directed cycles - feedforward and feedback - can act as higher-order structures to facilitate the flow and integration of information in sparse random networks, and how these roles depend on the environment of the cycles. Using information-theoretic measures, we show that network size, sparsity and relative directionality critically impact the information-processing capacities of directed cycles. In a network with no-preferred global direction, a feedforward cycle enables greater information flow and a feedback cycle allows for increased information integration. The relative direction of a feedforward cycle as well as the structural incoherence it induces, determines its capacity to generate higher-order behaviour. Finally, we demonstrate that introducing feedback loops into otherwise feedforward architectures increases the diversity of network activity patterns. These findings suggest that directed cycles serve as computational motifs with local information processing capabilities that depend on the structure they are embedded. Using directed cycles, we highlight the interdependence between higher-order structures and the higher-order order behaviour they can induce in the network dynamics.