Spatial applications of topological data analysis: Cities, snowflakes, random structures, and spiders spinning under the influence
Spatial applications of topological data analysis: Cities, snowflakes, random structures, and spiders spinning under the influence
复制标题
DOI：
10.1103/physrevresearch.2.033426
复制
发表时间：
2020-09-16
影响因子：
4.2
通讯作者：
Porter, Mason A.
中科院分区：
文献类型：
--
作者：
Feng, Michelle;Porter, Mason A.
空间网络在社会，地理，物理和生物学应用中无处不在。要了解网络的大规模结构，重要的是开发允许人们直接探测空间对结构和动态的影响的方法。从历史上看，代数拓扑为严格和定量描述空间的全球结构提供了一个框架，拓扑数据分析的最新进展为学者提供了一个新的镜头，用于分析网络数据。在本文中，我们研究了各种空间网络，包括我们最近开发的用于分析空间系统的合成和自然拓扑方法。我们证明，我们的方法能够捕获有意义的数量，并在空间网络中取决于上下文，从而为这些网络的结构提供了有用的见解。我们以合成网络及其动态的示例，城市的街道网络，雪花和网络的范围为例来说明这些想法，这些网络在各种精神物质的影响下被蜘蛛旋转。
Spatial networks are ubiquitous in social, geographical, physical, and biological applications. To understand the large-scale structure of networks, it is important to develop methods that allow one to directly probe the effects of space on structure and dynamics. Historically, algebraic topology has provided one framework for rigorously and quantitatively describing the global structure of a space, and recent advances in topological data analysis have given scholars a new lens for analyzing network data. In this paper, we study a variety of spatial networks-including both synthetic and natural ones-using topological methods that we developed recently for analyzing spatial systems. We demonstrate that our methods are able to capture meaningful quantities, with specifics that depend on context, in spatial networks and thereby provide useful insights into the structure of those networks. We illustrate these ideas with examples of synthetic networks and dynamics on them, street networks in cities, snowflakes, and webs that were spun by spiders under the influence of various psychotropic substances.