14,115 research outputs found
Network Information Flow with Correlated Sources
In this paper, we consider a network communications problem in which multiple
correlated sources must be delivered to a single data collector node, over a
network of noisy independent point-to-point channels. We prove that perfect
reconstruction of all the sources at the sink is possible if and only if, for
all partitions of the network nodes into two subsets S and S^c such that the
sink is always in S^c, we have that H(U_S|U_{S^c}) < \sum_{i\in S,j\in S^c}
C_{ij}. Our main finding is that in this setup a general source/channel
separation theorem holds, and that Shannon information behaves as a classical
network flow, identical in nature to the flow of water in pipes. At first
glance, it might seem surprising that separation holds in a fairly general
network situation like the one we study. A closer look, however, reveals that
the reason for this is that our model allows only for independent
point-to-point channels between pairs of nodes, and not multiple-access and/or
broadcast channels, for which separation is well known not to hold. This
``information as flow'' view provides an algorithmic interpretation for our
results, among which perhaps the most important one is the optimality of
implementing codes using a layered protocol stack.Comment: Final version, to appear in the IEEE Transactions on Information
Theory -- contains (very) minor changes based on the last round of review
Models for the 3-D axisymmetric gravitational potential of the Milky Way Galaxy - A detailed modelling of the Galactic disk
Aims. Galaxy mass models based on simple and analytical functions for the
density and potential pairs have been widely proposed in the literature. Disk
models constrained by kinematic data alone give information on the global disk
structure only very near the Galactic plane. We attempt to circumvent this
issue by constructing disk mass models whose three-dimensional structures are
constrained by a recent Galactic star counts model in the near-infrared and
also by observations of the hydrogen distribution in the disk. Our main aim is
to provide models for the gravitational potential of the Galaxy that are fully
analytical but also with a more realistic description of the density
distribution in the disk component. Methods. From the disk model directly based
on the observations (here divided into the thin and thick stellar disks and the
HI and H disks subcomponents), we produce fitted mass models by combining
three Miyamoto-Nagai disk profiles of any "model order" (1, 2, or 3) for each
disk subcomponent. The Miyamoto-Nagai disks are combined with models for the
bulge and "dark halo" components and the total set of parameters is adjusted by
observational kinematic constraints. A model which includes a ring density
structure in the disk, beyond the solar Galactic radius, is also investigated.
Results. The Galactic mass models return very good matches to the imposed
observational constraints. In particular, the model with the ring density
structure provides a greater contribution of the disk to the rotational support
inside the solar circle. The gravitational potential models and their
associated force-fields are described in analytically closed forms, and in
addition, they are also compatible with our best knowledge of the stellar and
gas distributions in the disk component. The gravitational potential models are
suited for investigations of orbits in the Galactic disk.Comment: 22 pages, 13 figures, 11 tables, accepted for publication in A&
A new model for gravitational potential perturbations in disks of spiral galaxies. An application to our Galaxy
We propose a new, more realistic, description of the perturbed gravitational
potential of spiral galaxies, with spiral arms having Gaussian-shaped groove
profiles. We investigate the stable stellar orbits in galactic disks, using the
new perturbed potential. The influence of the bulge mass on the stellar orbits
in the inner regions of a disk is also investigated. The new description offers
the advantage of easy control of the parameters of the Gaussian profile of its
potential. We find a range of values for the perturbation amplitude from 400 to
800 km^2 s^{-2} kpc^{-1} which implies a maximum ratio of the tangential force
to the axisymmetric force between 3% and 6%, approximately. Good
self-consistency of arm shapes is obtained between the Inner Lindblad resonance
(ILR) and the 4:1 resonance. Near the 4:1 resonance the response density starts
to deviate from the imposed logarithmic spiral form. This creates bifurcations
that appear as short arms. Therefore the deviation from a perfect logarithmic
spiral in galaxies can be understood as a natural effect of the 4:1 resonance.
Beyond the 4:1 resonance we find closed orbits which have similarities with the
arms observed in our Galaxy. In regions near the center, in the presence of a
massive bulge, elongated stellar orbits appear naturally, without imposing any
bar-shaped potential, but only extending the spiral perturbation a little
inward of the ILR. This suggests that a bar is formed with a half-size around 3
kpc by a mechanism similar to that of the spiral arms. The potential energy
perturbation that we adopted represents an important step in the direction of
self-consistency, compared to previous sine function descriptions of the
potential. Our model produces a realistic description of the spiral structure,
able to explain several details that were not yet understood.Comment: 12 pag., 11 fig. Accepted for publication in A&A, 2012 December 1
Novel magnetic orderings in the kagome Kondo-lattice model
We consider the Kondo-lattice model on the kagome lattice and study its
weak-coupling instabilities at band filling fractions for which the Fermi
surface has singularities. These singularites include Dirac points, quadratic
Fermi points in contact with a flat band, and Van Hove saddle points. By
combining a controlled analytical approach with large-scale numerical
simulations, we demonstrate that the weak-coupling instabilities of the
Kondo-lattice model lead to exotic magnetic orderings. In particular, some of
these magnetic orderings produce a spontaneous quantum anomalous Hall state.Comment: 15 pages, 11 figure
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