论文标题
简单复合物：高阶光谱维度和动力学
Simplicial complexes: higher-order spectral dimension and dynamics
论文作者
论文摘要
简单络合物构成了相互作用的复杂系统的基本拓扑，包括其他大脑和社交互动网络。它们是通用的网络结构，可以超越成对相互作用的框架，并捕获两个或多个节点之间强烈影响动态过程的多体相互作用。实际上，简单复合物拓扑允许将动态变量分配给相互作用的复杂系统的节点，还可以将链接，三角形等分配给。在这里，我们显示的证据表明，即使我们比较属于同一简单复合物的简单动力学，在不同维度的简单上定义的动力学也可能有显着不同。通过研究称为“带有风味的网络几何形状”的简单复杂模型的光谱特性，我们提供了向上和向下的高阶laplacians可以具有有限的频谱维度，其值随着拉普拉斯人的增加而增加。最后，我们讨论了该结果对在简单复合物上定义的高阶扩散的含义。
Simplicial complexes constitute the underlying topology of interacting complex systems including among the others brain and social interaction networks. They are generalized network structures that allow to go beyond the framework of pairwise interactions and to capture the many-body interactions between two or more nodes strongly affecting dynamical processes. In fact, the simplicial complexes topology allows to assign a dynamical variable not only to the nodes of the interacting complex systems but also to links, triangles, and so on. Here we show evidence that the dynamics defined on simplices of different dimensions can be significantly different even if we compare dynamics of simplices belonging to the same simplicial complex. By investigating the spectral properties of the simplicial complex model called "Network Geometry with Flavor" we provide evidence that the up and down higher-order Laplacians can have a finite spectral dimension whose value increases as the order of the Laplacian increases. Finally we discuss the implications of this result for higher-order diffusion defined on simplicial complexes.
