In light of the increase in frequency of extreme heat events, there is a critical need to develop tools to identify geographic locations that are at risk of heat-related mortality. This paper aims to identify locations by assessing holes in cooling-center coverage using persistent homology (PH), a method from topological data analysis (TDA). Persistent homology has shown promising results in identifying holes in coverage of specific resources. We adapt these methods using a witness complex construction to study the coverage of cooling centers. We test our approach on four locations (central Boston, MA; central Austin, TX; Portland, OR; and Miami, FL) and use death times, a measurement of the size and scale of the gap in coverage, to identify most at risk regions. For comparison, we implement a standard technique for studying the risk of heat-related mortality called a heat vulnerability index (HVI). The HVI is a numerical score calculated for a geographic area based on demographic information. PH and the HVI identify different locations as vulnerable, thus indicating a potential value of assessing vulnerability from multiple perspectives. By using the regions identified by both persistent homology and the HVI, we provide a more holistic understanding of coverage.

翻译：鉴于极端高温事件频发，亟需开发识别热相关死亡风险地理位置的工具。本文旨在通过使用拓扑数据分析中的持久同调方法评估降温中心覆盖范围的空洞来识别风险区域。持久同调在识别特定资源覆盖空洞方面已展现出良好效果。我们采用见证复形构造改进该方法以研究降温中心覆盖情况。我们在四个地区（马萨诸塞州波士顿中心区、德克萨斯州奥斯汀中心区、俄勒冈州波特兰市及佛罗里达州迈阿密市）测试该方法，并利用死亡时间（表征覆盖缺口规模与尺度的度量）识别最高风险区域。作为对比，我们实施了研究热相关死亡风险的标准方法——热脆弱性指数。该指数是基于人口统计信息计算的地理区域数值评分。持久同调与热脆弱性指数识别出的脆弱区域存在差异，这表明从多角度评估脆弱性具有潜在价值。通过综合持久同调与热脆弱性指数识别的区域，我们提供了更全面的覆盖范围认知。