2,131 research outputs found
Sufficient conditions for convergence of the Sum-Product Algorithm
We derive novel conditions that guarantee convergence of the Sum-Product
algorithm (also known as Loopy Belief Propagation or simply Belief Propagation)
to a unique fixed point, irrespective of the initial messages. The
computational complexity of the conditions is polynomial in the number of
variables. In contrast with previously existing conditions, our results are
directly applicable to arbitrary factor graphs (with discrete variables) and
are shown to be valid also in the case of factors containing zeros, under some
additional conditions. We compare our bounds with existing ones, numerically
and, if possible, analytically. For binary variables with pairwise
interactions, we derive sufficient conditions that take into account local
evidence (i.e., single variable factors) and the type of pair interactions
(attractive or repulsive). It is shown empirically that this bound outperforms
existing bounds.Comment: 15 pages, 5 figures. Major changes and new results in this revised
version. Submitted to IEEE Transactions on Information Theor
Cosmic Shear Results from the Deep Lens Survey - II: Full Cosmological Parameter Constraints from Tomography
We present a tomographic cosmic shear study from the Deep Lens Survey (DLS),
which, providing a limiting magnitude r_{lim}~27 (5 sigma), is designed as a
pre-cursor Large Synoptic Survey Telescope (LSST) survey with an emphasis on
depth. Using five tomographic redshift bins, we study their auto- and
cross-correlations to constrain cosmological parameters. We use a
luminosity-dependent nonlinear model to account for the astrophysical
systematics originating from intrinsic alignments of galaxy shapes. We find
that the cosmological leverage of the DLS is among the highest among existing
>10 sq. deg cosmic shear surveys. Combining the DLS tomography with the 9-year
results of the Wilkinson Microwave Anisotropy Probe (WMAP9) gives
Omega_m=0.293_{-0.014}^{+0.012}, sigma_8=0.833_{-0.018}^{+0.011},
H_0=68.6_{-1.2}^{+1.4} km/s/Mpc, and Omega_b=0.0475+-0.0012 for LCDM, reducing
the uncertainties of the WMAP9-only constraints by ~50%. When we do not assume
flatness for LCDM, we obtain the curvature constraint
Omega_k=-0.010_{-0.015}^{+0.013} from the DLS+WMAP9 combination, which however
is not well constrained when WMAP9 is used alone. The dark energy equation of
state parameter w is tightly constrained when Baryonic Acoustic Oscillation
(BAO) data are added, yielding w=-1.02_{-0.09}^{+0.10} with the DLS+WMAP9+BAO
joint probe. The addition of supernova constraints further tightens the
parameter to w=-1.03+-0.03. Our joint constraints are fully consistent with the
final Planck results and also the predictions of a LCDM universe.Comment: Accepted for publication in Ap
Noether symmetries, energy-momentum tensors and conformal invariance in classical field theory
In the framework of classical field theory, we first review the Noether
theory of symmetries, with simple rederivations of its essential results, with
special emphasis given to the Noether identities for gauge theories. Will this
baggage on board, we next discuss in detail, for Poincar\'e invariant theories
in flat spacetime, the differences between the Belinfante energy-momentum
tensor and a family of Hilbert energy-momentum tensors. All these tensors
coincide on shell but they split their duties in the following sense:
Belinfante's tensor is the one to use in order to obtain the generators of
Poincar\'e symmetries and it is a basic ingredient of the generators of other
eventual spacetime symmetries which may happen to exist. Instead, Hilbert
tensors are the means to test whether a theory contains other spacetime
symmetries beyond Poincar\'e. We discuss at length the case of scale and
conformal symmetry, of which we give some examples. We show, for Poincar\'e
invariant Lagrangians, that the realization of scale invariance selects a
unique Hilbert tensor which allows for an easy test as to whether conformal
invariance is also realized. Finally we make some basic remarks on metric
generally covariant theories and classical field theory in a fixed curved
bakground.Comment: 31 pa
Luminosity distance in Swiss cheese cosmology with randomized voids. II. Magnification probability distributions
We study the fluctuations in luminosity distances due to gravitational
lensing by large scale (> 35 Mpc) structures, specifically voids and sheets. We
use a simplified "Swiss cheese" model consisting of a \Lambda -CDM
Friedman-Robertson-Walker background in which a number of randomly distributed
non-overlapping spherical regions are replaced by mass compensating comoving
voids, each with a uniform density interior and a thin shell of matter on the
surface. We compute the distribution of magnitude shifts using a variant of the
method of Holz & Wald (1998), which includes the effect of lensing shear. The
standard deviation of this distribution is ~ 0.027 magnitudes and the mean is ~
0.003 magnitudes for voids of radius 35 Mpc, sources at redshift z_s=1.0, with
the voids chosen so that 90% of the mass is on the shell today. The standard
deviation varies from 0.005 to 0.06 magnitudes as we vary the void size, source
redshift, and fraction of mass on the shells today. If the shell walls are
given a finite thickness of ~ 1 Mpc, the standard deviation is reduced to ~
0.013 magnitudes. This standard deviation due to voids is a factor ~ 3 smaller
than that due to galaxy scale structures. We summarize our results in terms of
a fitting formula that is accurate to ~ 20%, and also build a simplified
analytic model that reproduces our results to within ~ 30%. Our model also
allows us to explore the domain of validity of weak lensing theory for voids.
We find that for 35 Mpc voids, corrections to the dispersion due to lens-lens
coupling are of order ~ 4%, and corrections to due shear are ~ 3%. Finally, we
estimate the bias due to source-lens clustering in our model to be negligible
Inter-species variation in colour perception
Inter-species variation in colour perception poses a serious problem for the view that colours are mind-independent properties. Given that colour perception varies so drastically across species, which species perceives colours as they really are? In this paper, I argue that all do. Specifically, I argue that members of different species perceive properties that are determinates of different, mutually compatible, determinables. This is an instance of a general selectionist strategy for dealing with cases of perceptual variation. According to selectionist views, objects simultaneously instantiate a plurality of colours, all of them genuinely mind-independent, and subjects select from amongst this plurality which colours they perceive. I contrast selectionist views with relationalist views that deny the mind-independence of colour, and consider some general objections to this strategy
Structure and dynamics of topological defects in a glassy liquid on a negatively curved manifold
We study the low-temperature regime of an atomic liquid on the hyperbolic
plane by means of molecular dynamics simulation and we compare the results to a
continuum theory of defects in a negatively curved hexagonal background. In
agreement with the theory and previous results on positively curved (spherical)
surfaces, we find that the atomic configurations consist of isolated defect
structures, dubbed "grain boundary scars", that form around an irreducible
density of curvature-induced disclinations in an otherwise hexagonal
background. We investigate the structure and the dynamics of these grain
boundary scars
Persistence of a pinch in a pipe
The response of low-dimensional solid objects combines geometry and physics
in unusual ways, exemplified in structures of great utility such as a
thin-walled tube that is ubiquitous in nature and technology. Here we provide a
particularly surprising consequence of this confluence of geometry and physics
in tubular structures: the anomalously large persistence of a localized pinch
in an elastic pipe whose effect decays very slowly as an oscillatory
exponential with a persistence length that diverges as the thickness of the
tube vanishes, which we confirm experimentally. The result is more a
consequence of geometry than material properties, and is thus equally
applicable to carbon nanotubes as it is to oil pipelines.Comment: 6 pages, 3 figure
The double torus as a 2D cosmos: groups, geometry and closed geodesics
The double torus provides a relativistic model for a closed 2D cosmos with
topology of genus 2 and constant negative curvature. Its unfolding into an
octagon extends to an octagonal tessellation of its universal covering, the
hyperbolic space H^2. The tessellation is analysed with tools from hyperbolic
crystallography. Actions on H^2 of groups/subgroups are identified for SU(1,
1), for a hyperbolic Coxeter group acting also on SU(1, 1), and for the
homotopy group \Phi_2 whose extension is normal in the Coxeter group. Closed
geodesics arise from links on H^2 between octagon centres. The direction and
length of the shortest closed geodesics is computed.Comment: Latex, 27 pages, 5 figures (late submission to arxiv.org
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