Scaling laws in the dynamics of crime growth rate

Alves, Luiz G. A.; Ribeiro, Haroldo V.; Mendes, Renio dos Santos

doi:10.1016/j.physa.2013.02.002

Cited by 52 publications

(35 citation statements)

References 41 publications

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“…Hence, it is not surprising that Pr{Y = k} does not approximate a normal distribution (or a binomial, if we keep Y discrete). This is consistent with the fact that total output in cities has been found to be lognormally distributed [3][4][5][6][7][8] .…”

Section: A04 Probability Distribution Of Total Outputsupporting

confidence: 87%

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Explaining the prevalence, scaling and variance of urban phenomena

2016

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The prevalence of many urban phenomena changes systematically with population size 1 . We propose a theory that unifies models of economic complexity 2, 3 and cultural evolution 10 to derive urban scaling. The theory accounts for the difference in scaling exponents and average prevalence across phenomena, as well as the difference in the variance within phenomena across cities of similar size. The central ideas are that a number of necessary complementary factors must be simultaneously present for a phenomenon to occur, and that the diversity of factors is logarithmically related to population size. The model reveals that phenomena that require more factors will be less prevalent, scale more superlinearly and show larger variance across cities of similar size. The theory applies to data on education, employment, innovation, disease and crime, and it entails the ability to predict the prevalence of a phenomenon across cities, given information about the prevalence in a single city.Scaling is ubiquitous across many phenomena 5 , including physical 6 and biological 7 systems, plus a wide range of human 8,9 and urban activities 1,10 . Figure 1 shows, for US Metropolitan Statistical Areas, ten different phenomena classified in five broad types: employment, innovation, crime, educational attainment, and infectious disease. We observe scaling in the sense that the counts of people in each phenomenon scale as a power of population size. This relation takes the form E{Y |N } = Y 0 N β , where E{·|N } is the expectation operator conditional on population size N , Y is the random variable representing the output of a phenomenon in a city, Y 0 is a measure of general prevalence of the activity in the country, and β is the scaling exponent, i.e., the relative rate of change of Y with respect to N . From Fig. 1 we can also observe notable differences in the average prevalence, the slopes of the regression lines and the variance across all ten phenomena. Hence, we seek to explain four empirical facts: Prevalence follows a power-law scaling with population size, different phenomena have different general prevalence, different scaling exponents, and variance for cities of similar size. Remarkably, these observations appear to be pervasive across phenomena as we find them to be present in more than forty different urban activities. In this paper we propose a mechanism to explain them simultaneously.Scaling laws are important in science because they constrain the development of new theories: any theory that attempts to explain a phenomenon should be compatible with the empirical 3 scaling relationships that the data exhibit. A number of mechanisms have been proposed to explain the origins of scaling. Most theories are based on a network description of the underlying phenomena and derive the scaling properties from the way the number of links grow with the number of nodes in the network, under some energy or budget constraints [11][12][13][15][16][17] . Other scaling relationships are the result of how lines relate to surfaces, and...

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Section: A04 Probability Distribution Of Total Outputsupporting

confidence: 87%

“…Scaling is ubiquitous across many phenomena 5 , including physical 6 and biological 7 systems, plus a wide range of human 8,9 and urban activities 1,10 . Figure 1 shows, for US Metropolitan Statistical Areas, ten different phenomena classified in five broad types: employment, innovation, crime, educational attainment, and infectious disease.…”

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confidence: 99%

Explaining the prevalence, scaling and variance of urban phenomena

2016

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“…An additional relevant model for generating power-law distributions is the class of random multiplicative processes, often used to model growth of entities, such as business firms, cities, and biological populations [18][19][20][21][22][23][24][25]. The common starting point to explain the mechanisms of power-law formation in those growth phenomena is the Gibrat's law of proportional growth, stating that an entity grows proportionally to its current size but with a growth rate independent of it [26].…”

Section: Introductionmentioning

confidence: 99%

Power-Law Distributions from Sigma-Pi Structure of Sums of Random Multiplicative Processes

Sousa

Takayasu

Sornette

et al. 2017

Entropy

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Abstract:We introduce a simple growth model in which the sizes of entities evolve as multiplicative random processes that start at different times. A novel aspect we examine is the dependence among entities. For this, we consider three classes of dependence between growth factors governing the evolution of sizes: independence, Kesten dependence and mixed dependence. We take the sum X of the sizes of the entities as the representative quantity of the system, which has the structure of a sum of product terms (Sigma-Pi), whose asymptotic distribution function has a power-law tail behavior. We present evidence that the dependence type does not alter the asymptotic power-law tail behavior, nor the value of the tail exponent. However, the structure of the large values of the sum X is found to vary with the dependence between the growth factors (and thus the entities). In particular, for the independence case, we find that the large values of X are contributed by a single maximum size entity: the asymptotic power-law tail is the result of such single contribution to the sum, with this maximum contributing entity changing stochastically with time and with realizations.

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“…On one hand, population [11,12], building sizes [12], personal fortunes [13], firm sizes [14], number of patents [15], and other indicators have been found to asymptotically follow power-law distributions. On the other hand, allometries with the population size have been reported for crime [16,17,18], suicide [19], several urban metrics including patents, gasoline stations, gross domestic product [20,21,22], number of election candidates [23], party memberships [24], among others. These allometries were recently modeled by Bettencourt [25] via a small set of simple and locally-based principles.…”

Section: Introductionmentioning

confidence: 99%

Empirical analysis on the connection between power-law distributions and allometries for urban indicators

Alves

Ribeiro

Lenzi

et al. 2014

Physica A: Statistical Mechanics and its Applications

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We report on the existing connection between power-law distributions and allometries. As it was first reported in [PLoS ONE 7, e40393 (2012)] for the relationship between homicides and population, when these urban indicators present asymptotic power-law distributions, they can also display specific allometries among themselves. Here, we present an extensive characterization of this connection when considering all possible pairs of relationships from twelve urban indicators of Brazilian cities (such as child labor, illiteracy, income, sanitation and unemployment). Our analysis reveals that all our urban indicators are asymptotically distributed as power laws and that the proposed connection also holds for our data when the allometric relationship displays enough correlations. We have also found that not all allometric relationships are independent and that they can be understood as a consequence of the allometric relationship between the urban indicator and the population size. We further show that the residuals fluctuations surrounding the allometries are characterized by an almost constant variance and log-normal distributions.

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Scaling laws in the dynamics of crime growth rate

Cited by 52 publications

References 41 publications

Explaining the prevalence, scaling and variance of urban phenomena

Explaining the prevalence, scaling and variance of urban phenomena

Power-Law Distributions from Sigma-Pi Structure of Sums of Random Multiplicative Processes

Empirical analysis on the connection between power-law distributions and allometries for urban indicators

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