论文标题
高式谐波分析，用于研究高阶信息理论信号
Hyperharmonic analysis for the study of high-order information-theoretic signals
论文作者
论文摘要
网络表示通常无法充分说明跨越多个组织的复杂系统的结构丰富性。最近提出的高阶信息理论信号非常适合捕获超越成对相互作用的协同现象。但是，其基数的指数增长极大地阻碍了其适用性。在这项工作中，我们将谐波分析和组合拓扑结合的方法结合在一起，以构建高阶信息理论信号的有效表示。我们方法的核心是Laplace-DE RHAM操作员的离散版本的对角线化，该laplace-de operator几何编码系统的结构属性。我们通过开发一个完整的工作流程来构建高阶信号的超谐音表示，这使这些想法利用了这些想法，这适用于广泛的场景。
Network representations often cannot fully account for the structural richness of complex systems spanning multiple levels of organisation. Recently proposed high-order information-theoretic signals are well-suited to capture synergistic phenomena that transcend pairwise interactions; however, the exponential-growth of their cardinality severely hinders their applicability. In this work, we combine methods from harmonic analysis and combinatorial topology to construct efficient representations of high-order information-theoretic signals. The core of our method is the diagonalisation of a discrete version of the Laplace-de Rham operator, that geometrically encodes structural properties of the system. We capitalise on these ideas by developing a complete workflow for the construction of hyperharmonic representations of high-order signals, which is applicable to a wide range of scenarios.
