网络连通性突变时，信息处理能力骤升，揭示了结构与功能的临界关系。
Functional Percolation: Criticality of Form and Function
- 在随机网络的连通性临界点，输入输出映射能力突然增强。
- 功能多样性与输出熵激增，信息传递范围扩展至局部外。
- 适用于研究复杂系统中局部互动下的信息处理机制。
理解网络结构如何制约并促进信息处理，是相互作用系统统计力学的核心问题。本文研究随机网络在结构渗流相变过程中的表现，分析连通性如何决定级联动力学下的可实现输入-输出变换。以Erdos-Renyi网络为最小模型集，考察平均度变化下的结构、功能及信息论可观测量。发现巨连通分支出现时，可实现的信息处理能力发生急剧跃迁：复杂输入-输出响应函数变得可行，功能多样性迅速增加，输出熵上升，定向信息流（以转移熵衡量）扩展至局部区域之外。我们称此结构、功能与信息转变的同步为‘功能渗流’，指在渗流阈值处可实现输入-输出函数空间的急剧扩张。接近临界点时，网络表现出功能复杂性与多样性的帕累托最优权衡，提示渗流临界性可能是具有局部相互作用与传播影响系统的通用信息处理组织原则。
原文摘要 · Abstract (English)
Understanding how network structure constrains and enables information processing is a central problem in the statistical mechanics of interacting systems. Here we study random networks across the structural percolation transition and analyze how connectivity governs realizable input-output transformations under cascade dynamics. Using Erdos-Renyi networks as a minimal ensemble, we examine structural, functional, and information-theoretic observables as functions of mean degree. We find that the emergence of the giant connected component coincides with a sharp transition in realizable information processing: complex input-output response functions become accessible, functional diversity increases rapidly, output entropy rises, and directed information flow, quantified by transfer entropy, extends beyond local neighborhoods. We term this coincidence of structural, functional, and informational transitions functional percolation, referring to a sharp expansion of the space of realizable input-output functions at the percolation threshold. Near criticality, networks exhibit a Pareto-optimal tradeoff between functional complexity and diversity, suggesting that percolation criticality may provide a general organizing principle of information processing capacity in systems with local interactions and propagating influences.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。