41,651 research outputs found
Paradoxical Interpretations of Urban Scaling Laws
Scaling laws are powerful summaries of the variations of urban attributes
with city size. However, the validity of their universal meaning for cities is
hampered by the observation that different scaling regimes can be encountered
for the same territory, time and attribute, depending on the criteria used to
delineate cities. The aim of this paper is to present new insights concerning
this variation, coupled with a sensitivity analysis of urban scaling in France,
for several socio-economic and infrastructural attributes from data collected
exhaustively at the local level. The sensitivity analysis considers different
aggregations of local units for which data are given by the Population Census.
We produce a large variety of definitions of cities (approximatively 5000) by
aggregating local Census units corresponding to the systematic combination of
three definitional criteria: density, commuting flows and population cutoffs.
We then measure the magnitude of scaling estimations and their sensitivity to
city definitions for several urban indicators, showing for example that simple
population cutoffs impact dramatically on the results obtained for a given
system and attribute. Variations are interpreted with respect to the meaning of
the attributes (socio-economic descriptors as well as infrastructure) and the
urban definitions used (understood as the combination of the three criteria).
Because of the Modifiable Areal Unit Problem and of the heterogeneous
morphologies and social landscapes in the cities internal space, scaling
estimations are subject to large variations, distorting many of the conclusions
on which generative models are based. We conclude that examining scaling
variations might be an opportunity to understand better the inner composition
of cities with regard to their size, i.e. to link the scales of the city-system
with the system of cities
Reducing the number of inputs in nonlocal games
In this work we show how a vector-valued version of Schechtman's empirical
method can be used to reduce the number of inputs in a nonlocal game while
preserving the quotient of the quantum over the classical
bias. We apply our method to the Khot-Vishnoi game, with exponentially many
questions per player, to produce another game with polynomially many () questions so that the quantum over the classical bias is
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