Wang Xu, Sipahi Rifat, Porfiri Maurizio
Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA.
Center for Urban Science and Progress, Tandon School of Engineering, New York University, Brooklyn, New York 11201, USA.
Chaos. 2022 Jul;32(7):073115. doi: 10.1063/5.0096773.
This study develops mathematical tools and approaches to investigate spatiotemporal patterns of firearm acquisition in the U.S. complemented by hypothesis testing and statistical analysis. First, state-level and nation-level instant background check (BC) data are employed as proxy of firearm acquisition corresponding to 1999-2021. The relative-phase time-series of BC in each U.S. state is recovered and utilized to calculate the time-series of the U.S. states' synchronization degree. We reveal that U.S. states present a high-level degree of synchronization except in 2010-2011 and after 2018. Comparing these results with respect to a sitting U.S. president provides additional information: specifically, any two presidential terms are characterized by statistically different synchronization degrees except G. W. Bush's first term and B. H. Obama's second term. Next, to detail variations of BC, short-time Fourier transform, dimensionality reduction techniques, and diffusion maps are implemented within a time-frequency representation. Firearm acquisition in the high frequency band is described by a low-dimensional embedding, in the form of a plane with two embedding coordinates. Data points on the embedding plane identify separate clusters that signify state transitions in the original BC data with respect to different time windows. Through this analysis, we reveal that the frequency content of the BC data has a time-dependent characteristic. By comparing the diffusion map at hand with respect to a presidential term, we find that at least one of the embedding coordinates presents statistically significant variations between any two presidential terms except B. H. Obama's first term and D. J. Trump's pre-COVID term. The results point at a possible interplay between firearm acquisition in the U.S. and a presidential term.
本研究开发了数学工具和方法，通过假设检验和统计分析来研究美国枪支获取的时空模式。首先，使用州级和国家级即时背景调查（BC）数据作为1999 - 2021年期间枪支获取情况的代理指标。恢复并利用美国各州BC的相对相位时间序列来计算美国各州同步程度的时间序列。我们发现，除了2010 - 2011年以及2018年之后，美国各州呈现出高度的同步性。将这些结果与在任美国总统的情况进行比较可提供更多信息：具体而言，除了乔治·W·布什的第一个任期和巴拉克·H·奥巴马的第二个任期外，任何两个总统任期的同步程度在统计上都存在差异。接下来，为了详细说明BC的变化情况，在时频表示中采用了短时傅里叶变换、降维技术和扩散映射。高频带内的枪支获取情况通过二维嵌入来描述，即一个具有两个嵌入坐标的平面。嵌入平面上的数据点标识出不同的聚类，这些聚类表示原始BC数据在不同时间窗口下的状态转变。通过这种分析，我们揭示了BC数据的频率内容具有时间依赖性特征。通过比较与总统任期相关的现有扩散映射，我们发现除了巴拉克·H·奥巴马的第一个任期和唐纳德·J·特朗普在新冠疫情前的任期外，任何两个总统任期之间至少有一个嵌入坐标存在统计上的显著差异。研究结果表明美国枪支获取情况与总统任期之间可能存在相互作用。
