480,857 research outputs found
Bounding the Bias of Tree-Like Sampling in IP Topologies
It is widely believed that the Internet's AS-graph degree distribution obeys
a power-law form. Most of the evidence showing the power-law distribution is
based on BGP data. However, it was recently argued that since BGP collects data
in a tree-like fashion, it only produces a sample of the degree distribution,
and this sample may be biased. This argument was backed by simulation data and
mathematical analysis, which demonstrated that under certain conditions a tree
sampling procedure can produce an artificail power-law in the degree
distribution. Thus, although the observed degree distribution of the AS-graph
follows a power-law, this phenomenon may be an artifact of the sampling
process. In this work we provide some evidence to the contrary. We show, by
analysis and simulation, that when the underlying graph degree distribution
obeys a power-law with an exponent larger than 2, a tree-like sampling process
produces a negligible bias in the sampled degree distribution. Furthermore,
recent data collected from the DIMES project, which is not based on BGP
sampling, indicates that the underlying AS-graph indeed obeys a power-law
degree distribution with an exponent larger than 2. By combining this empirical
data with our analysis, we conclude that the bias in the degree distribution
calculated from BGP data is negligible.Comment: 12 pages, 1 figur
Azimuthal Anisotropy in High Energy Nuclear Collision - An Approach based on Complex Network Analysis
Recently, a complex network based method of Visibility Graph has been applied
to confirm the scale-freeness and presence of fractal properties in the process
of multiplicity fluctuation. Analysis of data obtained from experiments on
hadron-nucleus and nucleus-nucleus interactions results in values of
Power-of-Scale-freeness-of-Visibility-Graph-(PSVG) parameter extracted from the
visibility graphs. Here, the relativistic nucleus-nucleus interaction data have
been analysed to detect azimuthal-anisotropy by extending the Visibility Graph
method and extracting the average clustering coefficient, one of the important
topological parameters, from the graph. Azimuthal-distributions corresponding
to different pseudorapidity-regions around the central-pseudorapidity value are
analysed utilising the parameter. Here we attempt to correlate the conventional
physical significance of this coefficient with respect to complex-network
systems, with some basic notions of particle production phenomenology, like
clustering and correlation. Earlier methods for detecting anisotropy in
azimuthal distribution, were mostly based on the analysis of statistical
fluctuation. In this work, we have attempted to find deterministic information
on the anisotropy in azimuthal distribution by means of precise determination
of topological parameter from a complex network perspective
Markov processes on the path space of the Gelfand-Tsetlin graph and on its boundary
We construct a four-parameter family of Markov processes on infinite
Gelfand-Tsetlin schemes that preserve the class of central (Gibbs) measures.
Any process in the family induces a Feller Markov process on the
infinite-dimensional boundary of the Gelfand-Tsetlin graph or, equivalently,
the space of extreme characters of the infinite-dimensional unitary group
U(infinity). The process has a unique invariant distribution which arises as
the decomposing measure in a natural problem of harmonic analysis on
U(infinity) posed in arXiv:math/0109193. As was shown in arXiv:math/0109194,
this measure can also be described as a determinantal point process with a
correlation kernel expressed through the Gauss hypergeometric function
- …