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Topological Data Analysis of Spatial Systems

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Higher-Order Systems

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

In this chapter, we discuss applications of topological data analysis (TDA) to spatial systems. We briefly review a recently proposed level-set construction of filtered simplicial complexes, and we then examine persistent homology in two cases studies: street networks in Shanghai and anomalies in the spread of COVID-19 infections. We then summarize our results and provide an outlook on TDA in spatial systems.

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Notes

  1. 1.

    This case study is related to an example in [14].

  2. 2.

    This part of Laoximen has been slated for redevelopment since 2017 [23]. When we obtained these street maps in 2019, residents were fighting redevelopment efforts and development had not yet begun [24]. It remains to be seen how this part of our Laoximen street map will change as a result of redevelopment.

  3. 3.

    See [33] for a study of geographic patterns in COVID-19 case rates and COVID-19 vaccination rates that uses PH in a different way.

  4. 4.

    We are concerned with local maxima. By contrast, the Centers for Disease Control and Prevention (CDC) defines COVID-19 ‘hotspots’ using an absolute threshold for the number of cases and criteria that are related to the temporal increase in the number of cases [37].

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Acknowledgements

We thank the Los Angeles County Department of Public Health for providing the LA data on COVID-19, and we thank Federico Battiston and Giovanni Petri for the invitation to write this chapter. We thank Deanna Needell for helpful comments. We acknowledge support from the National Science Foundation (grant number 1922952) through the Algorithms for Threat Detection (ATD) program. MAP also acknowledges support from the National Science Foundation (grant number DMS-2027438) through the RAPID program.

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Authors and Affiliations

  1. California Institute of Technology, Pasadena, CA, USA

    Michelle Feng

  2. University of California, Los Angeles, Los Angeles, CA, USA

    Abigail Hickok & Mason A. Porter

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  1. Michelle Feng
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  2. Abigail Hickok
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  3. Mason A. Porter
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Corresponding author

Correspondence to Mason A. Porter .

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Editors and Affiliations

  1. Department of Network and Data Science, Central European University, Vienna, Austria

    Federico Battiston

  2. ISI Foundation, Turin, Italy

    Giovanni Petri

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Feng, M., Hickok, A., Porter, M.A. (2022). Topological Data Analysis of Spatial Systems. In: Battiston, F., Petri, G. (eds) Higher-Order Systems. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-91374-8_16

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