RESUMEN
Self-organization of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of biological intuition. Discrete models provide straightforward interpretations by tracking each individual yet can be computationally expensive. Alternatively, continuous models supply a large-scale perspective by representing the 'effective' dynamics of infinite agents, but their results are often difficult to translate into experimentally relevant insights. We address this challenge by quantitatively linking spatio-temporal dynamics of continuous models and individual-based data in settings with biologically realistic, time-varying cell numbers. Specifically, we introduce and fit scaling parameters in continuous models to account for discrepancies that can arise from low cell numbers and localized interactions. We illustrate our approach on an example motivated by zebrafish-skin pattern formation, in which we create a continuous framework describing the movement and proliferation of a single cell population by upscaling rules from a discrete model. Our resulting continuous models accurately depict ensemble average agent-based solutions when migration or proliferation act alone. Interestingly, the same parameters are not optimal when both processes act simultaneously, highlighting a rich difference in how combining migration and proliferation affects discrete and continuous dynamics.
RESUMEN
We examine patterns of reported crime in Santa Monica, California before and after the passage of Proposition 47, a 2014 initiative that reclassified some non-violent felonies as misdemeanors. We also investigate impacts of the opening of four new light rail stations in 2016 and of increased community-based policing starting in late 2018. Our statistical analyses of reclassified crimes-larceny, fraud, possession of narcotics, forgery, receiving/possessing stolen property-and non-reclassified ones are based on publicly available reported crime data from 2006 to 2019. These analyses examine reported crime at various levels: city-wide, within eight neighborhoods, and within a 450-meter radius of the new transit stations. Monthly reported reclassified crimes increased city-wide by approximately 15% after enactment of Proposition 47, with a significant drop observed in late 2018. Downtown exhibited the largest overall surge. Reported non-reclassified crimes fell overall by approximately 9%. Areas surrounding two new train stations, including Downtown, saw significant increases in reported crime after train service began. While reported reclassified crimes increased after passage of Proposition 47, non-reclassified crimes, for the most part, decreased or stayed constant, suggesting that Proposition 47 may have impacted reported crime in Santa Monica. Reported crimes decreased in late 2018 concurrent with the adoption of new community-based policing measures. Follow-up studies needed to confirm long-term trends may be challenging due to the COVID-19 pandemic that drastically changed societal conditions. While our research detects changes in reported crime, it does not provide causative explanations. Our work, along with other considerations relevant to public utility, respect for human rights, and existence of socioeconomic disparities, may be useful to law enforcement and policymakers to assess the overall effect of Proposition 47.