DHB: Mathematical and Simulation Modeling of Crime Hot Spots

该项目将重点发展犯罪热点形成、持续和消散的分析和计算模型。犯罪热点是指在一定的时间间隔内，犯罪活动集中发生的地理区域。热点地区可能由一系列财产犯罪（如入室盗窃或汽车盗窃）或暴力犯罪（如杀人）组成，这些犯罪的发生时间从几小时到几个月不等。绘制犯罪热点在当前理解犯罪行为的方法中非常重要，并且越来越多地被警察部门和政策制定者用于战略预防犯罪。然而，尽管有复杂的数字地图和分析工具，但在理解罪犯的低水平行为如何导致包括犯罪热点在内的总体犯罪模式方面仍存在很大差距。因此，例如，不可能确切地说明为什么警察在犯罪热点采取的定向行动有时会导致犯罪在空间上的转移，但令人惊讶的是，这往往也会导致热点消散和犯罪发生率的真正减少。利用统计物理的分析方法、群体数学和基于主体的计算建模的新技术，将开发罪犯运动和目标选择的正式模型，并在不同的环境中进行模拟。这些基线模型将扩展到考虑抽象城市街道网络中的罪犯行为，然后通过探索模拟犯罪地图的空间特性将这两种模型类型与地理信息系统（GIS）相结合。最后，在模型开发的每个阶段，将对洛杉矶、圣地亚哥和长滩警察局提供的空间犯罪数据进行实证检验。该项目将有助于澄清犯罪行为、犯罪机会和警务之间的定量关系，并可能为如何设计更好的预防犯罪战略提供见解，有助于就国土安全问题展开更广泛的对话。同时开发数学和模拟模型，以及持续的实证测试，将为这些工具在社会科学中的实验使用提供指导，而该项目广泛的跨学科基础将为数学家和社会科学家之间的合作提供模型。

This project will concentrate on the development of analytical and computational models of crime hot spot formation, persistence and dissipation. Crime hot spots are geographical areas with clusters of criminal offenses occurring within a specified interval of time. Hot spots may consist of clusters of property crimes such as burglaries or auto thefts, or violent crimes such as homicides, which occur on time scales ranging from hours to months. Mapping of crime hot spots is important in current approaches to understanding criminal offender behavior and is a tool used increasingly by police departments and policy makers for strategic crime prevention. However, despite the availability of sophisticated digital mapping and analysis tools there is a substantial gap in the understanding of how low-level behaviors of offenders lead to aggregate crime patterns including crime hot spots. Thus, for example, it is not possible to specify exactly why directed police action at crime hot spots sometimes leads to displacement of crime in space but, surprisingly, often can also lead to hot spot dissipation and a real reduction in crime incidences. Drawing on analytical methods in statistical physics, the mathematics of swarms, and new techniques in agent-based computational modeling, formal models of offender movement and target selection will be developed and simulated in different environments. These baseline models will be extended to consider offender behavior on abstract urban street networks and then integrate both model types with Geographic Information Systems (GIS) by exploring the spatial properties of simulated crime maps. Finally, at each stage of model development, empirical tests will be conducted against spatial crime data provided by the Los Angeles, San Diego and Long Beach Police Departments. The project will help clarify the quantitative relationships between criminal behavior, criminal opportunities and policing and may provide insight into how to design better crime prevention strategies, contributing to a broader dialog on homeland security. Simultaneous development of mathematical and simulation models, as well as continuous empirical testing, will provide a guide for the experimental use of these tools in the social sciences, while the broad interdisciplinary foundation of the project will provide a model for collaboration between mathematicians and social scientists.