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Spatial applications of topological data analysis: Cities, snowflakes, random structures, and spiders spinning under the influence
Physical Review Research Pub Date : 2020-09-16 , DOI: 10.1103/physrevresearch.2.033426
Michelle Feng , Mason A. Porter

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.

中文翻译:

拓扑数据分析的空间应用:城市,雪花,随机结构和蜘蛛在影响下旋转

空间网络在社会,地理,物理和生物应用中无处不在。要了解网络的大规模结构,开发允许人们直接探测空间对结构和动力学影响的方法非常重要。从历史上看,代数拓扑为严格和定量地描述空间的整体结构提供了一个框架,并且拓扑数据分析的最新进展为学者提供了一种分析网络数据的新方法。在本文中,我们使用最近开发的用于分析空间系统的拓扑方法研究了各种空间网络(包括合成的和自然的)。我们证明了我们的方法能够捕获有意义的数量,具体取决于上下文,在空间网络中的应用,从而为这些网络的结构提供有用的见解。我们以合成网络及其动力学,城市中的街道网络,雪花以及在各种精神药物的影响下被蜘蛛纺成的网幅为例来说明这些想法。
更新日期:2020-09-16
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