单纯复形上的最优导航
Optimal Navigation on Simplicial Complexes
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中文总结 AI 辅助
本研究将二分图的导航与搜索策略扩展至含高阶相互作用的单纯复形，通过引入长程随机传送项并提出微扰近似方案，分析其可探索性与最优导航相关拓扑测度。
中文摘要 AI 辅助
网络科学领域已广泛探索和分析了二分图上随机动力学过程产生的导航时间与最优搜索策略。本研究将这类拓扑测度扩展至单纯复形——一种包含高阶相互作用的几何与代数结构，针对节点（即0阶单形）间的平均首达时间开展单纯复形的可探索性分析，引入了受各维度局部随机游走跳跃调制的长程随机传送项，还提供了一种微扰近似方案，以纯随机游走与传送模式（高阶场景）间的调制参数作为展开参数，实现对该参数的有效恢复。
英文摘要
The navigation time and optimal search strategies deriving from random dynamical processes on binary graphs have been extensively explored and analyzed, being of prominent interest in the network science field. In this work, we study an extension of these topological measures for simplicial complexes: a specific type of geometric and algebraic structures that encapsulates higher-order interactions. Here, the explorability analysis of simplicial complexes has been conducted in terms of the mean first passage times between nodes, i.e. the 0th-order simplices, with the inclusion of a long-range stochastic teleportation term modulated with respect to the local random walk hopping across the various dimensions. We also provide a perturbative approximation scheme recovering the modulation parameter between pure random walk and teleportation mode (for higher-order setting) acting as the expansion parameter.
