论文标题
拓扑数据分析的空间应用：在影响下旋转的城市，雪花，随机结构和蜘蛛
Spatial Applications of Topological Data Analysis: Cities, Snowflakes, Random Structures, and Spiders Spinning Under the Influence
论文作者
论文摘要
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（TDA）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，我们使用用于分析空间网络的新型拓扑方法研究了各种空间网络，包括合成和天然网络。我们证明，我们的方法能够捕获有意义的数量，并具有取决于上下文，在空间网络中的细节，从而为这些网络的结构提供了有用的见解，包括一种基于其拓扑结构来表征它们的新方法。我们以合成网络的示例及其上的动态，城市，雪花和网络在各种精神物质的影响下旋转的街道网络来说明这些想法。
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 (TDA) 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 novel topological methods that we recently developed for analyzing spatial networks. 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, including a novel approach for characterizing them based on their topological structures. We illustrate these ideas with examples of synthetic networks and dynamics on them, street networks in cities, snowflakes, and webs spun by spiders under the influence of various psychotropic substances.
