Distance to the Scaling Law: A Useful Approach for Unveiling Relationships between Crime and Urban Metrics

Alves, Luiz G. A.; Ribeiro, Haroldo V.; Lenzi, E. K.; Mendes, R. S.

doi:10.1371/journal.pone.0069580

Cited by 81 publications

(113 citation statements)

References 34 publications

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“…Table I lists values (or forms) of β at the limiting values of the four parameters calculated by Eq. (31). From the value of β at m = 0, we see that superlinear or sublinear urban scaling is realized depending on the sign of η even for networks formed by a nongeographical mechanism.…”

Section: Urban Scalingmentioning

confidence: 80%

“…Statistical properties of such fluctuations of Y (N ) have been extensively studied in recent works [28][29][30][31]. In the present work, no analysis of fluctuations is performed, nor is any methodology to compute them given.…”

Section: Discussionmentioning

confidence: 99%

“…These include many creative productivities and infrastructure volumes [14][15][16][17] such as the gross domestic product (GDP), the number of patents, human online activities [18], prosocial behaviors [19], quantities related to highway systems [20], the number of crimes [21], the number of supply stations [22], and emissions of CO 2 [23] and NO 2 [24]. There exist several models explaining such allometric scaling behavior [25][26][27][28] and fluctuations around average power-law relations [29][30][31]. These findings allow us to write an urban indicator Y as a function of the population size N as…”

Section: Introductionmentioning

confidence: 99%

“…Bettencourt et al [14][15][16] found that an urban indicator representing a creative productivity, such as the number of new patents, the GDP, the number of * yakubo@eng.hokudai.ac.jp † dean.korosak@um.si crimes, etc., obeys a superlinear scaling law (β > 1), while an indicator related to the degree of infrastructure development, such as the total length of electrical cables, the number of gas stations, the total road surface, etc., scales sublinearly with the population size (β < 1). Due to the nonlinear scaling (1), a meaningful comparison between characteristics of individual cities requires evaluation of deviations from this average scaling behavior, instead of considering per capita quantity Y (N )/N [28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Superlinear and sublinear urban scaling in geographical networks modeling cities

Yakubo

Saijo²,

Korošak

2014

Phys. Rev. E

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Using a geographical scale-free network to describe relations between people in a city, we explain both superlinear and sublinear allometric scaling of urban indicators that quantify activities or performances of the city. The urban indicator Y (N ) of a city with the population size N is analytically calculated by summing up all individual activities produced by person-to-person relationships. Our results show that the urban indicator scales superlinearly with the population, namely, Y (N ) ∝ N β with β > 1, if Y (N ) represents a creative productivity and the indicator scales sublinearly (β < 1) if Y (N ) is related to the degree of infrastructure development. These results coincide with allometric scaling observed in real-world urban indicators. We also show how the scaling exponent β depends on the strength of the geographical constraint in the network formation.

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Section: Urban Scalingmentioning

confidence: 80%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Superlinear and sublinear urban scaling in geographical networks modeling cities

Yakubo

Saijo²,

Korošak

2014

Phys. Rev. E

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“…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.…”

mentioning

confidence: 99%

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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An Efficient Critical Incident Propagation Model for Social Networks Based on Trust Factor

Yuan

Liu

et al. 2018

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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Distance to the Scaling Law: A Useful Approach for Unveiling Relationships between Crime and Urban Metrics

Cited by 81 publications

References 34 publications

Superlinear and sublinear urban scaling in geographical networks modeling cities

Superlinear and sublinear urban scaling in geographical networks modeling cities

Explaining the prevalence, scaling and variance of urban phenomena

An Efficient Critical Incident Propagation Model for Social Networks Based on Trust Factor

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