1,135 research outputs found
Power Laws and the Cosmic Ray Energy Spectrum
Two separate statistical tests are applied to the AGASA and preliminary Auger
Cosmic Ray Energy spectra in an attempt to find deviation from a pure
power-law. The first test is constructed from the probability distribution for
the maximum event of a sample drawn from a power-law. The second employs the
TP-statistic, a function defined to deviate from zero when the sample deviates
from the power-law form, regardless of the value of the power index. The AGASA
data show no significant deviation from a power-law when subjected to both
tests. Applying these tests to the Auger spectrum suggests deviation from a
power-law. However, potentially large systematics on the relative energy scale
prevent us from drawing definite conclusions at this time.Comment: 21 pages, 18 figures, submitted to Astro. Part. Phy
The Irreducible Spine(s) of Undirected Networks
Using closure concepts, we show that within every undirected network, or
graph, there is a unique irreducible subgraph which we call its "spine". The
chordless cycles which comprise this irreducible core effectively characterize
the connectivity structure of the network as a whole. In particular, it is
shown that the center of the network, whether defined by distance or
betweenness centrality, is effectively contained in this spine. By counting the
number of cycles of length 3 <= k <= max_length, we can also create a kind of
signature that can be used to identify the network. Performance is analyzed,
and the concepts we develop are illurstrated by means of a relatively small
running sample network of about 400 nodes.Comment: Submitted to WISE 201
A systematic review of cognitive distortions in online child sexual exploitation material offenders
Black String Perturbations in RS1 Model
We present a general formalism for black string perturbations in
Randall-Sundrum 1 model (RS1). First, we derive the master equation for the
electric part of the Weyl tensor . Solving the master equation
using the gradient expansion method, we give the effective Teukolsky equation
on the brane at low energy. It is useful to estimate gravitational waves
emitted by perturbed rotating black strings. We also argue the effect of the
Gregory-Laflamme instability on the brane using our formalism.Comment: 14 pages, Based on a talk presented at ACRGR4, the 4th Australasian
Conference on General Relativity and Gravitation, Monash University,
Melbourne, January 2004. To appear in the proceedings, in General Relativity
and Gravitatio
Water wave propagation and scattering over topographical bottoms
Here I present a general formulation of water wave propagation and scattering
over topographical bottoms. A simple equation is found and is compared with
existing theories. As an application, the theory is extended to the case of
water waves in a column with many cylindrical steps
Lyapunov exponents for products of complex Gaussian random matrices
The exact value of the Lyapunov exponents for the random matrix product with each , where
is a fixed positive definite matrix and a complex Gaussian matrix with entries standard complex normals, are
calculated. Also obtained is an exact expression for the sum of the Lyapunov
exponents in both the complex and real cases, and the Lyapunov exponents for
diffusing complex matrices.Comment: 15 page
The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states
The nature of the zero temperature ordering transition in the 3D Gaussian
random field Ising magnet is studied numerically, aided by scaling analyses. In
the ferromagnetic phase the scaling of the roughness of the domain walls,
, is consistent with the theoretical prediction .
As the randomness is increased through the transition, the probability
distribution of the interfacial tension of domain walls scales as for a single
second order transition. At the critical point, the fractal dimensions of
domain walls and the fractal dimension of the outer surface of spin clusters
are investigated: there are at least two distinct physically important fractal
dimensions. These dimensions are argued to be related to combinations of the
energy scaling exponent, , which determines the violation of
hyperscaling, the correlation length exponent , and the magnetization
exponent . The value is derived from the
magnetization: this estimate is supported by the study of the spin cluster size
distribution at criticality. The variation of configurations in the interior of
a sample with boundary conditions is consistent with the hypothesis that there
is a single transition separating the disordered phase with one ground state
from the ordered phase with two ground states. The array of results are shown
to be consistent with a scaling picture and a geometric description of the
influence of boundary conditions on the spins. The details of the algorithm
used and its implementation are also described.Comment: 32 pp., 2 columns, 32 figure
Line Graphs of Weighted Networks for Overlapping Communities
In this paper, we develop the idea to partition the edges of a weighted graph
in order to uncover overlapping communities of its nodes. Our approach is based
on the construction of different types of weighted line graphs, i.e. graphs
whose nodes are the links of the original graph, that encapsulate differently
the relations between the edges. Weighted line graphs are argued to provide an
alternative, valuable representation of the system's topology, and are shown to
have important applications in community detection, as the usual node partition
of a line graph naturally leads to an edge partition of the original graph.
This identification allows us to use traditional partitioning methods in order
to address the long-standing problem of the detection of overlapping
communities. We apply it to the analysis of different social and geographical
networks.Comment: 8 Pages. New title and text revisions to emphasise differences from
earlier paper
Hierarchical Organization in Complex Networks
Many real networks in nature and society share two generic properties: they
are scale-free and they display a high degree of clustering. We show that these
two features are the consequence of a hierarchical organization, implying that
small groups of nodes organize in a hierarchical manner into increasingly large
groups, while maintaining a scale-free topology. In hierarchical networks the
degree of clustering characterizing the different groups follows a strict
scaling law, which can be used to identify the presence of a hierarchical
organization in real networks. We find that several real networks, such as the
World Wide Web, actor network, the Internet at the domain level and the
semantic web obey this scaling law, indicating that hierarchy is a fundamental
characteristic of many complex systems
Dynamics in online social networks
An increasing number of today's social interactions occurs using online
social media as communication channels. Some online social networks have become
extremely popular in the last decade. They differ among themselves in the
character of the service they provide to online users. For instance, Facebook
can be seen mainly as a platform for keeping in touch with close friends and
relatives, Twitter is used to propagate and receive news, LinkedIn facilitates
the maintenance of professional contacts, Flickr gathers amateurs and
professionals of photography, etc. Albeit different, all these online platforms
share an ingredient that pervades all their applications. There exists an
underlying social network that allows their users to keep in touch with each
other and helps to engage them in common activities or interactions leading to
a better fulfillment of the service's purposes. This is the reason why these
platforms share a good number of functionalities, e.g., personal communication
channels, broadcasted status updates, easy one-step information sharing, news
feeds exposing broadcasted content, etc. As a result, online social networks
are an interesting field to study an online social behavior that seems to be
generic among the different online services. Since at the bottom of these
services lays a network of declared relations and the basic interactions in
these platforms tend to be pairwise, a natural methodology for studying these
systems is provided by network science. In this chapter we describe some of the
results of research studies on the structure, dynamics and social activity in
online social networks. We present them in the interdisciplinary context of
network science, sociological studies and computer science.Comment: 17 pages, 4 figures, book chapte
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