A team of mathematicians believe they have come up with a formula that will accurately predict the number of murders in a given year for Brazil before they happen. The hope is that one day this formula will be able to predict and stop crime. The study was published in the scientific journal Plos One.
In order to be able to predict the future rate of Brazilian crime, the team uses what they have called "urban metrics." By measuring these metrics against population size the team believes it will be able to predict future crime. The study's abstract reads:
We report on a quantitative analysis of relationships between the number of homicides, population size and ten other urban metrics. By using data from Brazilian cities, we show that well-defined average scaling laws with the population size emerge when investigating the relations between population and number of homicides as well as population and urban metrics. We also show that the fluctuations around the scaling laws are log-normally distributed, which enabled us to model these scaling laws by a stochastic-like equation driven by a multiplicative and log-normally distributed noise. Because of the scaling laws, we argue that it is better to employ logarithms in order to describe the number of homicides in function of the urban metrics via regression analysis. In addition to the regression analysis, we propose an approach to correlate crime and urban metrics via the evaluation of the distance between the actual value of the number of homicides (as well as the value of the urban metrics) and the value that is expected by the scaling law with the population size.
The murder rates in Brazil are high due to the large number of gang and drug related violence. The BBC suggests that Brazilian cities are some of the most violent in the world. Analyzing data from the year 2000, the team discovered mathematical principles surface when they look at the different factors measured by urban metrics. The summary and conclusion sections of the study reads:
We have extensively characterized some relationships between crime and urban metrics. We have initially shown that urban indicators obey well defined average scaling laws with the population size and also that the fluctuations around these tendencies are log-normally distributed. Using these results, we have shown that the scaling laws can be represented by a multiplicative stochastic-like equation (Eq. 4) driven by a log-normal noise. Next, we have addressed the problem of applying regression analysis for explaining the number of homicides in terms of urban indicators . Because of the intrinsic nonlinearities, we have argued that it is better to employ the logarithms of these variables when performing linear regression analysis... We further believe that the present approach can be applied to other datasets in order to produce more robust relationships between crime indicators and urban metrics.
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