103 research outputs found
Pareto's Law of Income Distribution: Evidence for Germany, the United Kingdom, and the United States
We analyze three sets of income data: the US Panel Study of Income Dynamics
PSID), the British Household Panel Survey (BHPS), and the German Socio-Economic
Panel (GSOEP). It is shown that the empirical income distribution is consistent
with a two-parameter lognormal function for the low-middle income group
(97%-99% of the population), and with a Pareto or power law function for the
high income group (1%-3% of the population). This mixture of two qualitatively
different analytical distributions seems stable over the years covered by our
data sets, although their parameters significantly change in time. It is also
found that the probability density of income growth rates almost has the form
of an exponential function.Comment: Latex2e v1.6; 16 pages with 5 figure
Topological Properties of Citation and Metabolic Networks
Topological properties of "scale-free" networks are investigated by
determining their spectral dimensions , which reflect a diffusion process
in the corresponding graphs. Data bases for citation networks and metabolic
networks together with simulation results from the growing network model
\cite{barab} are probed. For completeness and comparisons lattice, random,
small-world models are also investigated. We find that is around 3 for
citation and metabolic networks, which is significantly different from the
growing network model, for which is approximately 7.5. This signals a
substantial difference in network topology despite the observed similarities in
vertex order distributions. In addition, the diffusion analysis indicates that
whereas the citation networks are tree-like in structure, the metabolic
networks contain many loops.Comment: 11 pages, 3 figure
Interface Depinning in the Absence of External Driving Force
We study the pinning-depinning phase transition of interfaces in the quenched
Kardar-Parisi-Zhang model as the external driving force goes towards zero.
For a fixed value of the driving force we induce depinning by increasing the
nonlinear term coefficient , which is related to lateral growth, up to
a critical threshold. We focus on the case in which there is no external force
applied (F=0) and find that, contrary to a simple scaling prediction, there is
a finite value of that makes the interface to become depinned. The
critical exponents at the transition are consistent with directed percolation
depinning. Our results are relevant for paper wetting experiments, in which an
interface gets moving with no external driving force.Comment: 4 pages, 3 figures included, uses epsf. Submitted to PR
The depinning transition of a driven interface in the random-field Ising model around the upper critical dimension
We investigate the depinning transition for driven interfaces in the
random-field Ising model for various dimensions. We consider the order
parameter as a function of the control parameter (driving field) and examine
the effect of thermal fluctuations. Although thermal fluctuations drive the
system away from criticality the order parameter obeys a certain scaling law
for sufficiently low temperatures and the corresponding exponents are
determined. Our results suggest that the so-called upper critical dimension of
the depinning transition is five and that the systems belongs to the
universality class of the quenched Edward-Wilkinson equation.Comment: accepted for publication in Phys. Rev.
Growing Scale-Free Networks with Small World Behavior
In the context of growing networks, we introduce a simple dynamical model
that unifies the generic features of real networks: scale-free distribution of
degree and the small world effect. While the average shortest path length
increases logartihmically as in random networks, the clustering coefficient
assumes a large value independent of system size. We derive expressions for the
clustering coefficient in two limiting cases: random (C ~ (ln N)^2 / N) and
highly clustered (C = 5/6) scale-free networks.Comment: 4 pages, 4 figure
Effect of the accelerating growth of communications networks on their structure
Motivated by data on the evolution of the Internet and World Wide Web we
consider scenarios of self-organization of the nonlinearly growing networks
into free-scale structures. We find that the accelerating growth of the
networks establishes their structure. For the growing networks with
preferential linking and increasing density of links, two scenarios are
possible. In one of them, the value of the exponent of the
connectivity distribution is between 3/2 and 2. In the other, and
the distribution is necessarily non-stationary.Comment: 4 pages revtex, 3 figure
Highly clustered scale-free networks
We propose a model for growing networks based on a finite memory of the
nodes. The model shows stylized features of real-world networks: power law
distribution of degree, linear preferential attachment of new links and a
negative correlation between the age of a node and its link attachment rate.
Notably, the degree distribution is conserved even though only the most
recently grown part of the network is considered. This feature is relevant
because real-world networks truncated in the same way exhibit a power-law
distribution in the degree. As the network grows, the clustering reaches an
asymptotic value larger than for regular lattices of the same average
connectivity. These high-clustering scale-free networks indicate that memory
effects could be crucial for a correct description of the dynamics of growing
networks.Comment: 6 pages, 4 figure
Simple models of small world networks with directed links
We investigate the effect of directed short and long range connections in a
simple model of small world network. Our model is such that we can determine
many quantities of interest by an exact analytical method. We calculate the
function , defined as the number of sites affected up to time when a
naive spreading process starts in the network. As opposed to shortcuts, the
presence of un-favorable bonds has a negative effect on this quantity. Hence
the spreading process may not be able to affect all the network. We define and
calculate a quantity named the average size of accessible world in our model.
The interplay of shortcuts, and un-favorable bonds on the small world
properties is studied.Comment: 15 pages, 9 figures, published versio
Large-scale structural organization of social networks
The characterization of large-scale structural organization of social
networks is an important interdisciplinary problem. We show, by using scaling
analysis and numerical computation, that the following factors are relevant for
models of social networks: the correlation between friendship ties among people
and the position of their social groups, as well as the correlation between the
positions of different social groups to which a person belongs.Comment: 5 pages, 3 figures, Revte
Evolving networks with disadvantaged long-range connections
We consider a growing network, whose growth algorithm is based on the
preferential attachment typical for scale-free constructions, but where the
long-range bonds are disadvantaged. Thus, the probability to get connected to a
site at distance is proportional to , where is a
tunable parameter of the model. We show that the properties of the networks
grown with are close to those of the genuine scale-free
construction, while for the structure of the network is vastly
different. Thus, in this regime, the node degree distribution is no more a
power law, and it is well-represented by a stretched exponential. On the other
hand, the small-world property of the growing networks is preserved at all
values of .Comment: REVTeX, 6 pages, 5 figure
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