35,964 research outputs found
Community structure in directed networks
We consider the problem of finding communities or modules in directed
networks. The most common approach to this problem in the previous literature
has been simply to ignore edge direction and apply methods developed for
community discovery in undirected networks, but this approach discards
potentially useful information contained in the edge directions. Here we show
how the widely used benefit function known as modularity can be generalized in
a principled fashion to incorporate the information contained in edge
directions. This in turn allows us to find communities by maximizing the
modularity over possible divisions of a network, which we do using an algorithm
based on the eigenvectors of the corresponding modularity matrix. This method
is shown to give demonstrably better results than previous methods on a variety
of test networks, both real and computer-generated.Comment: 5 pages, 3 figure
Large-scale structure of time evolving citation networks
In this paper we examine a number of methods for probing and understanding
the large-scale structure of networks that evolve over time. We focus in
particular on citation networks, networks of references between documents such
as papers, patents, or court cases. We describe three different methods of
analysis, one based on an expectation-maximization algorithm, one based on
modularity optimization, and one based on eigenvector centrality. Using the
network of citations between opinions of the United States Supreme Court as an
example, we demonstrate how each of these methods can reveal significant
structural divisions in the network, and how, ultimately, the combination of
all three can help us develop a coherent overall picture of the network's
shape.Comment: 10 pages, 6 figures; journal names for 4 references fixe
Mixture models and exploratory analysis in networks
Networks are widely used in the biological, physical, and social sciences as
a concise mathematical representation of the topology of systems of interacting
components. Understanding the structure of these networks is one of the
outstanding challenges in the study of complex systems. Here we describe a
general technique for detecting structural features in large-scale network data
which works by dividing the nodes of a network into classes such that the
members of each class have similar patterns of connection to other nodes. Using
the machinery of probabilistic mixture models and the expectation-maximization
algorithm, we show that it is possible to detect, without prior knowledge of
what we are looking for, a very broad range of types of structure in networks.
We give a number of examples demonstrating how the method can be used to shed
light on the properties of real-world networks, including social and
information networks.Comment: 8 pages, 4 figures, two new examples in this version plus minor
correction
The Universal Cut Function and Type II Metrics
In analogy with classical electromagnetic theory, where one determines the
total charge and both electric and magnetic multipole moments of a source from
certain surface integrals of the asymptotic (or far) fields, it has been known
for many years - from the work of Hermann Bondi - that energy and momentum of
gravitational sources could be determined by similar integrals of the
asymptotic Weyl tensor. Recently we observed that there were certain overlooked
structures, {defined at future null infinity,} that allowed one to determine
(or define) further properties of both electromagnetic and gravitating sources.
These structures, families of {complex} `slices' or `cuts' of Penrose's null
infinity, are referred to as Universal Cut Functions, (UCF). In particular, one
can define from these structures a (complex) center of mass (and center of
charge) and its equations of motion - with rather surprising consequences. It
appears as if these asymptotic structures contain in their imaginary part, a
well defined total spin-angular momentum of the source. We apply these ideas to
the type II algebraically special metrics, both twisting and twist-free.Comment: 32 page
Numerical design of streamlined tunnel walls for a two-dimensional transonic test
An analytical procedure is discussed for designing wall shapes for streamlined, nonporous, two-dimensional, transonic wind tunnels. It is based upon currently available 2-D inviscid transonic and boundary layer analysis computer programs. Predicted wall shapes are compared with experimental data obtained from the NASA Langley 6 by 19 inch Transonic Tunnel where the slotted walls were replaced by flexible nonporous walls. Comparisons are presented for the empty tunnel operating at a Mach number of 0.9 and for a supercritical test of an NACA 0012 airfoil at zero lift. Satisfactory agreement is obtained between the analytically and experimentally determined wall shapes
The electrical conductivity of a collisionless magnetoplasma in a weakly turbulent magnetic field
Electrical conductivity of collisionless magnetoplasma in nearly turbulent magnetic fiel
NMC stratospheric analyses during the 1987 Antarctic expedition
Stratospheric constant pressure analyses of geopotential height and temperature, produced as part of regular operations at the National Meteorological Center (NMC), were used by several participants of the Antarctic Ozone Expedition. A brief decription is given of the NMC stratospheric analyses and the data that are used to derive them. In addition, comparisons of the analysis values at the locations of radiosonde and aircraft data are presented to provide indications for assessing the representativeness of the NMC stratospheric analyses during the 1987 Antarctic winter-spring period
Particle flux associated with stochastic processes
Particle flux associated with stochastic processe
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