3,635 research outputs found
A Note on MHV Amplitudes for Gravitons
We show how the maximally helicity violating (MHV) scattering amplitudes for
gravitons can be related to current correlators and vertex operators in twistor
space. This is similar to what happens in Yang-Mills theory and raises the
possibility of a direct twistor-string-like construction for
supergravity.Comment: 14 pages, LaTe
More is less: Connectivity in fractal regions
Ad-hoc networks are often deployed in regions with complicated boundaries. We
show that if the boundary is modeled as a fractal, a network requiring line of
sight connections has the counterintuitive property that increasing the number
of nodes decreases the full connection probability. We characterise this decay
as a stretched exponential involving the fractal dimension of the boundary, and
discuss mitigation strategies. Applications of this study include the analysis
and design of sensor networks operating in rugged terrain (e.g. railway
cuttings), mm-wave networks in industrial settings and
vehicle-to-vehicle/vehicle-to-infrastructure networks in urban environments.Comment: 5 page
Connectivity of confined 3D Networks with Anisotropically Radiating Nodes
Nodes in ad hoc networks with randomly oriented directional antenna patterns
typically have fewer short links and more long links which can bridge together
otherwise isolated subnetworks. This network feature is known to improve
overall connectivity in 2D random networks operating at low channel path loss.
To this end, we advance recently established results to obtain analytic
expressions for the mean degree of 3D networks for simple but practical
anisotropic gain profiles, including those of patch, dipole and end-fire array
antennas. Our analysis reveals that for homogeneous systems (i.e. neglecting
boundary effects) directional radiation patterns are superior to the isotropic
case only when the path loss exponent is less than the spatial dimension.
Moreover, we establish that ad hoc networks utilizing directional transmit and
isotropic receive antennas (or vice versa) are always sub-optimally connected
regardless of the environment path loss. We extend our analysis to investigate
boundary effects in inhomogeneous systems, and study the geometrical reasons
why directional radiating nodes are at a disadvantage to isotropic ones.
Finally, we discuss multi-directional gain patterns consisting of many equally
spaced lobes which could be used to mitigate boundary effects and improve
overall network connectivity.Comment: 12 pages, 10 figure
Connectivity in Dense Networks Confined within Right Prisms
We consider the probability that a dense wireless network confined within a
given convex geometry is fully connected. We exploit a recently reported theory
to develop a systematic methodology for analytically characterizing the
connectivity probability when the network resides within a convex right prism,
a polyhedron that accurately models many geometries that can be found in
practice. To maximize practicality and applicability, we adopt a general
point-to-point link model based on outage probability, and present example
analytical and numerical results for a network employing
multiple-input multiple-output (MIMO) maximum ratio combining (MRC) link level
transmission confined within particular bounding geometries. Furthermore, we
provide suggestions for extending the approach detailed herein to more general
convex geometries.Comment: 8 pages, 6 figures. arXiv admin note: text overlap with
arXiv:1201.401
Optimal Non-uniform Deployments in Ultra-Dense Finite-Area Cellular Networks
Network densification and heterogenisation through the deployment of small
cellular access points (picocells and femtocells) are seen as key mechanisms in
handling the exponential increase in cellular data traffic. Modelling such
networks by leveraging tools from Stochastic Geometry has proven particularly
useful in understanding the fundamental limits imposed on network coverage and
capacity by co-channel interference. Most of these works however assume
infinite sized and uniformly distributed networks on the Euclidean plane. In
contrast, we study finite sized non-uniformly distributed networks, and find
the optimal non-uniform distribution of access points which maximises network
coverage for a given non-uniform distribution of mobile users, and vice versa.Comment: 4 Pages, 6 Figures, Letter for IEEE Wireless Communication
Convex Clustering via Optimal Mass Transport
We consider approximating distributions within the framework of optimal mass
transport and specialize to the problem of clustering data sets. Distances
between distributions are measured in the Wasserstein metric. The main problem
we consider is that of approximating sample distributions by ones with sparse
support. This provides a new viewpoint to clustering. We propose different
relaxations of a cardinality function which penalizes the size of the support
set. We establish that a certain relaxation provides the tightest convex lower
approximation to the cardinality penalty. We compare the performance of
alternative relaxations on a numerical study on clustering.Comment: 12 pages, 12 figure
Escape through a time-dependent hole in the doubling map
We investigate the escape dynamics of the doubling map with a time-periodic
hole. We use Ulam's method to calculate the escape rate as a function of the
control parameters. We consider two cases, oscillating or breathing holes,
where the sides of the hole are moving in or out of phase respectively. We find
out that the escape rate is well described by the overlap of the hole with its
images, for holes centred at periodic orbits.Comment: 9 pages, 7 figures. To appear in Physical Review E in 201
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