12,739 research outputs found
Distance to the scaling law: a useful approach for unveiling relationships between crime and urban metrics
We report on a quantitative analysis of relationships between the number of
homicides, population size and other ten 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.
This approach have proved to be robust and useful for unveiling
relationships/behaviors that were not properly carried out by the regression
analysis, such as i) the non-explanatory potential of the elderly population
when the number of homicides is much above or much below the scaling law, ii)
the fact that unemployment has explanatory potential only when the number of
homicides is considerably larger than the expected by the power law, and iii) a
gender difference in number of homicides, where cities with female population
below the scaling law are characterized by a number of homicides above the
power law.Comment: Accepted for publication in PLoS ON
Scale-adjusted metrics for predicting the evolution of urban indicators and quantifying the performance of cities
More than a half of world population is now living in cities and this number
is expected to be two-thirds by 2050. Fostered by the relevancy of a scientific
characterization of cities and for the availability of an unprecedented amount
of data, academics have recently immersed in this topic and one of the most
striking and universal finding was the discovery of robust allometric scaling
laws between several urban indicators and the population size. Despite that,
most governmental reports and several academic works still ignore these
nonlinearities by often analyzing the raw or the per capita value of urban
indicators, a practice that actually makes the urban metrics biased towards
small or large cities depending on whether we have super or sublinear
allometries. By following the ideas of Bettencourt et al., we account for this
bias by evaluating the difference between the actual value of an urban
indicator and the value expected by the allometry with the population size. We
show that this scale-adjusted metric provides a more appropriate/informative
summary of the evolution of urban indicators and reveals patterns that do not
appear in the evolution of per capita values of indicators obtained from
Brazilian cities. We also show that these scale-adjusted metrics are strongly
correlated with their past values by a linear correspondence and that they also
display crosscorrelations among themselves. Simple linear models account for
31%-97% of the observed variance in data and correctly reproduce the average of
the scale-adjusted metric when grouping the cities in above and below the
allometric laws. We further employ these models to forecast future values of
urban indicators and, by visualizing the predicted changes, we verify the
emergence of spatial clusters characterized by regions of the Brazilian
territory where we expect an increase or a decrease in the values of urban
indicators.Comment: Accepted for publication in PLoS ON
Magnetocaloric effect in integrable spin-s chains
We study the magnetocaloric effect for the integrable antiferromagnetic
high-spin chain. We present an exact computation of the Gr\"uneisen parameter,
which is closely related to the magnetocaloric effect, for the quantum spin-s
chain on the thermodynamical limit by means of Bethe ansatz techniques and the
quantum transfer matrix approach. We have also calculated the entropy S and the
isentropes in the (H,T) plane. We have been able to identify the quantum
critical points H_c^{(s)}=2/(s+1/2) looking at the isentropes and/or the
characteristic behaviour of the Gr\"uneisen parameter.Comment: 6 pages, 3 figure
The thermal conductivity of alternating spin chains
We study a class of integrable alternating (S1,S2) quantum spin chains with
critical ground state properties. Our main result is the description of the
thermal Drude weight of the one-dimensional alternating spin chain as a
function of temperature. We have identified the thermal current of the model
with alternating spins as one of the conserved currents underlying the
integrability. This allows for the derivation of a finite set of non-linear
integral equations for the thermal conductivity. Numerical solutions to the
integral equations are presented for specific cases of the spins S1 and S2. In
the low-temperature limit a universal picture evolves where the thermal Drude
weight is proportional to temperature T and central charge c.Comment: 15 pages, 1 figur
Symbolic Sequences and Tsallis Entropy
We address this work to investigate symbolic sequences with long-range
correlations by using computational simulation. We analyze sequences with two,
three and four symbols that could be repeated times, with the probability
distribution . For these sequences, we verified that
the usual entropy increases more slowly when the symbols are correlated and the
Tsallis entropy exhibits, for a suitable choice of , a linear behavior. We
also study the chain as a random walk-like process and observe a nonusual
diffusive behavior depending on the values of the parameter .Comment: Published in the Brazilian Journal of Physic
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