9,152 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
Diffusion-Based Adaptive Distributed Detection: Steady-State Performance in the Slow Adaptation Regime
This work examines the close interplay between cooperation and adaptation for
distributed detection schemes over fully decentralized networks. The combined
attributes of cooperation and adaptation are necessary to enable networks of
detectors to continually learn from streaming data and to continually track
drifts in the state of nature when deciding in favor of one hypothesis or
another. The results in the paper establish a fundamental scaling law for the
steady-state probabilities of miss-detection and false-alarm in the slow
adaptation regime, when the agents interact with each other according to
distributed strategies that employ small constant step-sizes. The latter are
critical to enable continuous adaptation and learning. The work establishes
three key results. First, it is shown that the output of the collaborative
process at each agent has a steady-state distribution. Second, it is shown that
this distribution is asymptotically Gaussian in the slow adaptation regime of
small step-sizes. And third, by carrying out a detailed large deviations
analysis, closed-form expressions are derived for the decaying rates of the
false-alarm and miss-detection probabilities. Interesting insights are gained.
In particular, it is verified that as the step-size decreases, the error
probabilities are driven to zero exponentially fast as functions of ,
and that the error exponents increase linearly in the number of agents. It is
also verified that the scaling laws governing errors of detection and errors of
estimation over networks behave very differently, with the former having an
exponential decay proportional to , while the latter scales linearly
with decay proportional to . It is shown that the cooperative strategy
allows each agent to reach the same detection performance, in terms of
detection error exponents, of a centralized stochastic-gradient solution.Comment: The paper will appear in IEEE Trans. Inf. Theor
Languages cool as they expand: Allometric scaling and the decreasing need for new words
We analyze the occurrence frequencies of over 15 million words recorded in millions of books published during the past two centuries in seven different languages. For all languages and chronological subsets of the data we confirm that two scaling regimes characterize the word frequency distributions, with only the more common words obeying the classic Zipf law. Using corpora of unprecedented size, we test the allometric scaling relation between the corpus size and the vocabulary size of growing languages to demonstrate a decreasing marginal need for new words, a feature that is likely related to the underlying correlations between words. We calculate the annual growth fluctuations of word use which has a decreasing trend as the corpus size increases, indicating a slowdown in linguistic evolution following language expansion. This ââcooling patternââ forms the basis of a third statistical regularity, which unlike the Zipf and the Heaps law, is dynamical in nature
Scaling Laws for Infrastructure Single and Multihop Wireless Networks in Wideband Regimes
With millimeter wave bands emerging as a strong candidate for 5G cellular
networks, next-generation systems may be in a unique position where spectrum is
plentiful. To assess the potential value of this spectrum, this paper derives
scaling laws on the per mobile downlink feasible rate with large bandwidth and
number of nodes, for both Infrastructure Single Hop (ISH) and Infrastructure
Multi-Hop (IMH) architectures. It is shown that, for both cases, there exist
\emph{critical bandwidth scalings} above which increasing the bandwidth no
longer increases the feasible rate per node. These critical thresholds coincide
exactly with the bandwidths where, for each architecture, the network
transitions from being degrees-of-freedom-limited to power-limited. For ISH,
this critical bandwidth threshold is lower than IMH when the number of users
per base station grows with network size. This result suggests that multi-hop
transmissions may be necessary to fully exploit large bandwidth degrees of
freedom in deployments with growing number of users per cell.Comment: 5 pages, 3 figure
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