2,657 research outputs found
Tipping the balances of a small world
Recent progress in the large scale mapping of social networks is opening new
quantitative windows into the structure of human societies. These networks are
largely the result of how we access and utilize information. Here I show that a
universal decision mechanism, where we base our choices upon the actions of
others, can explain much of their structure. Such collective social
arrangements emerge from successful strategies to handle information flow at
the individual level. They include the formation of closely-knit communities
and the emergence of well-connected individuals. The latter can command the
following of others while only exercising ordinary judgement.Comment: 10 pages, 4 figures, uses RevTe
Multiple-Scale Analysis of Quantum Systems
Conventional weak-coupling Rayleigh-Schr\"odinger perturbation theory suffers
from problems that arise from resonant coupling of successive orders in the
perturbation series. Multiple-scale analysis, a powerful and sophisticated
perturbative method that quantitatively analyzes characteristic physical
behaviors occurring on various length or time scales, avoids such problems by
implicitly performing an infinite resummation of the conventional perturbation
series. Multiple-scale perturbation theory provides a good description of the
classical anharmonic oscillator. Here, it is extended to study (1) the
Heisenberg operator equations of motion and (2) the Schr\"odinger equation for
the quantum anharmonic oscillator. In the former case, it leads to a system of
coupled operator differential equations, which is solved exactly. The solution
provides an operator mass renormalization of the theory. In the latter case,
multiple-scale analysis elucidates the connection between weak-coupling
perturbative and semiclassical nonperturbative aspects of the wave function.Comment: 30 pages, LaTeX/RevTeX, no figures. Available through anonymous ftp
from ftp://euclid.tp.ph.ic.ac.uk/papers/ or on WWW at
http://euclid.tp.ph.ic.ac.uk/Papers
Urban Scaling in Europe
Over the last decades, in disciplines as diverse as economics, geography, and
complex systems, a perspective has arisen proposing that many properties of
cities are quantitatively predictable due to agglomeration or scaling effects.
Using new harmonized definitions for functional urban areas, we examine to what
extent these ideas apply to European cities. We show that while most large
urban systems in Western Europe (France, Germany, Italy, Spain, UK)
approximately agree with theoretical expectations, the small number of cities
in each nation and their natural variability preclude drawing strong
conclusions. We demonstrate how this problem can be overcome so that cities
from different urban systems can be pooled together to construct larger
datasets. This leads to a simple statistical procedure to identify urban
scaling relations, which then clearly emerge as a property of European cities.
We compare the predictions of urban scaling to Zipf's law for the size
distribution of cities and show that while the former holds well the latter is
a poor descriptor of European cities. We conclude with scenarios for the size
and properties of future pan-European megacities and their implications for the
economic productivity, technological sophistication and regional inequalities
of an integrated European urban system.Comment: 35 pages, 7 Figures, 1 Tabl
Urban Geography and Scaling of Contemporary Indian Cities
This paper attempts to create a first comprehensive analysis of the
integrated characteristics of contemporary Indian cities, using scaling and
geographic analysis over a set of diverse indicators. We use data at the level
of Urban Agglomerations in India from the Census 2011 and from a few other
sources to characterize patterns of urban population density, infrastructure,
urban services, economic performance, crime and innovation. Many of the results
are in line with expectations from urban theory and with the behaviour of
analogous quantities in other urban systems in both high and middle-income
nations. India is a continental scale, fast developing urban system, and
consequently there are also a number of interesting exceptions and surprises
related to both specific quantities and strong regional patterns of variation.
We characterize these patterns in detail for crime and innovation and connect
them to the existing literature on their determinants in a specifically Indian
context. The paucity of data at the urban level and the absence of official
definitions for functional cities in India create a number of limitations and
caveats to any present analysis. We discuss these shortcomings and spell out
the challenge for a systematic statistical data collection relevant to cities
and urban development in India.Comment: 20 pages, 11 figure
Visually-salient contour detection using a V1 neural model with horizontal connections
A convolution model which accounts for neural activity dynamics in the
primary visual cortex is derived and used to detect visually salient contours
in images. Image inputs to the model are modulated by long-range horizontal
connections, allowing contextual effects in the image to determine visual
saliency, i.e. line segments arranged in a closed contour elicit a larger
neural response than line segments forming background clutter. The model is
tested on 3 types of contour, including a line, a circular closed contour, and
a non-circular closed contour. Using a modified association field to describe
horizontal connections the model is found to perform well for different
parameter values. For each type of contour a different facilitation mechanism
is found. Operating as a feed-forward network, the model assigns saliency by
increasing the neural activity of line segments facilitated by the horizontal
connections. Alternatively, operating as a feedback network, the model can
achieve further improvement over several iterations through cooperative
interactions. This model has no dynamical stability issues, and is suitable for
use in biologically-inspired neural networks
Formation of Scientific Fields as a Universal Topological Transition
Scientific fields differ in terms of their subject matter, research
techniques, collaboration sizes, rates of growth, and so on. We investigate
whether common dynamics might lurk beneath these differences, affecting how
scientific fields form and evolve over time. Particularly important in any
field's history is the moment at which shared concepts and techniques allow
widespread exchange of ideas and collaboration. At that moment, co-authorship
networks show the analog of a percolation phenomenon, developing a giant
connected component containing most authors. We develop a general theoretical
framework for analyzing finite, evolving networks in which each scientific
field is an instantiation of the same large-scale topological critical
phenomenon. We estimate critical exponents associated with the transition and
find evidence for universality near criticality implying that, as various
fields approach the topological transition, they do so with the same set of
critical exponents consistent with an effective dimensionality .
These results indicate that a common dynamics is at play in all scientific
fields, which in turn may hold policy implications for ways to encourage and
accelerate the creation of scientific and technological knowledge.Comment: 8 pages, including 5 figure
When is social computation better than the sum of its parts?
Social computation, whether in the form of searches performed by swarms of
agents or collective predictions of markets, often supplies remarkably good
solutions to complex problems. In many examples, individuals trying to solve a
problem locally can aggregate their information and work together to arrive at
a superior global solution. This suggests that there may be general principles
of information aggregation and coordination that can transcend particular
applications. Here we show that the general structure of this problem can be
cast in terms of information theory and derive mathematical conditions that
lead to optimal multi-agent searches. Specifically, we illustrate the problem
in terms of local search algorithms for autonomous agents looking for the
spatial location of a stochastic source. We explore the types of search
problems, defined in terms of the statistical properties of the source and the
nature of measurements at each agent, for which coordination among multiple
searchers yields an advantage beyond that gained by having the same number of
independent searchers. We show that effective coordination corresponds to
synergy and that ineffective coordination corresponds to independence as
defined using information theory. We classify explicit types of sources in
terms of their potential for synergy. We show that sources that emit
uncorrelated signals provide no opportunity for synergetic coordination while
sources that emit signals that are correlated in some way, do allow for strong
synergy between searchers. These general considerations are crucial for
designing optimal algorithms for particular search problems in real world
settings.Comment: 5 pages, 1 figure; In H. Liu, J. J. Salerno, and M. J. Young,
editors, Social Computing, Behavior Modeling, and Prediction, 200
Urban Skylines: building heights and shapes as measures of city size
The shape of buildings plays a critical role in the energy efficiency,
lifestyles, land use and infrastructure systems of cities. Thus, as most of the
world's cities continue to grow and develop, understanding the interplay
between the characteristics of urban environments and the built form of cities
is essential to achieve local and global sustainability goals. Here, we compile
and analyze the most extensive data set of building shapes to date, covering
more than 4.8 million individual buildings across several major cities in North
America. We show that average building height increases systematically with
city size and follows theoretical predictions derived from urban scaling
theory. We also study the allometric relationship between surface area and
volume of buildings in terms of characteristic shape parameters. This allows us
to demonstrate that the reported trend towards higher (and more voluminous)
buildings effectively decreases the average surface-to-volume ratio, suggesting
potentially significant energy savings with growing city size. At the same
time, however, the surface-to-volume ratio increases in the downtown cores of
large cities, due to shape effects and specifically to the proliferation of
tall, needlelike buildings. Thus, the issue of changes in building shapes with
city size and associated energy management problem is highly heterogeneous. It
requires a systematic approach that includes the factors that drive the form of
built environments, entangling physical, infrastructural and socioeconomic
aspects of cities
The hypothesis of urban scaling: formalization, implications and challenges
There is strong expectation that cities, across time, culture and level of
development, share much in common in terms of their form and function.
Recently, attempts to formalize mathematically these expectations have led to
the hypothesis of urban scaling, namely that certain properties of all cities
change, on average, with their size in predictable scale-invariant ways. The
emergence of these scaling relations depends on a few general properties of
cities as social networks, co-located in space and time, that conceivably apply
to a wide range of human settlements. Here, we discuss the present evidence for
the hypothesis of urban scaling, some of the methodological issues dealing with
proxy measurements and units of analysis and place these findings in the
context of other theories of cities and urban systems. We show that a large
body of evidence about the scaling properties of cities indicates, in analogy
to other complex systems, that they cannot be treated as extensive systems and
discuss the consequences of these results for an emerging statistical theory of
cities.Comment: 37 pages, 6 figure
Thermal vortex dynamics in a two-dimensional condensate
We carry out an analytical and numerical study of the motion of an isolated
vortex in thermal equilibrium, the vortex being defined as the point
singularity of a complex scalar field obeying a nonlinear
stochastic Schr\"odinger equation. Because hydrodynamic fluctuations are
included in this description, the dynamical picture of the vortex emerges as
that of both a massive particle in contact with a heat bath, and as a passive
scalar advected to a background random flow. We show that the vortex does not
execute a simple random walk and that the probability distribution of vortex
flights has non-Gaussian (exponential) tails.Comment: RevTex, 9 pages, 3 figures, To appear in Phys. Rev.
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