3,347 research outputs found
The role of weight normalization in competitive learning
The effect of different kinds of weight normalization on the outcome of a simple competitive learning rule is analyzed. It is shown that there are important differences in the representation formed depending on whether the constraint is enforced by dividing each weight by the same amount (''divisive enforcement'') or subtracting a fixed amount from each weight (''subtractive enforcement''). For the divisive cases weight vectors spread out over the space so as to evenly represent ''typical'' inputs, whereas for the subtractive cases the weight vectors tend to the axes of the space, so as to represent ''extreme'' inputs. The consequences of these differences are examined
A catalog of radio observations of Jupiter 1961-1964
Catalog of radio observations of Jupiter 1961 to 196
Observable Effects of Scalar Fields and Varying Constants
We show by using the method of matched asymptotic expansions that a
sufficient condition can be derived which determines when a local experiment
will detect the cosmological variation of a scalar field which is driving the
spacetime variation of a supposed constant of Nature. We extend our earlier
analyses of this problem by including the possibility that the local region is
undergoing collapse inside a virialised structure, like a galaxy or galaxy
cluster. We show by direct calculation that the sufficient condition is met to
high precision in our own local region and we can therefore legitimately use
local observations to place constraints upon the variation of "constants" of
Nature on cosmological scales.Comment: Invited Festscrift Articl
On the Possibility of Anisotropic Curvature in Cosmology
In addition to shear and vorticity a homogeneous background may also exhibit
anisotropic curvature. Here a class of spacetimes is shown to exist where the
anisotropy is solely of the latter type, and the shear-free condition is
supported by a canonical, massless 2-form field. Such spacetimes possess a
preferred direction in the sky and at the same time a CMB which is isotropic at
the background level. A distortion of the luminosity distances is derived and
used to test the model against the CMB and supernovae (using the Union
catalog), and it is concluded that the latter exhibit a higher-than-expected
dependence on angular position. It is shown that future surveys could detect a
possible preferred direction by observing ~ 20 / (\Omega_{k0}^2) supernovae
over the whole sky.Comment: Extended SNe analysis and corrected some CMB results. Text also
extended and references added. 8 pages, 5 figure
The future asymptotics of Bianchi VIII vacuum solutions
Bianchi VIII vacuum solutions to Einstein's equations are causally
geodesically complete to the future, given an appropriate time orientation, and
the objective of this article is to analyze the asymptotic behaviour of
solutions in this time direction. For the Bianchi class A spacetimes, there is
a formulation of the field equations that was presented in an article by
Wainwright and Hsu, and we analyze the asymptotic behaviour of solutions in
these variables. We also try to give the analytic results a geometric
interpretation by analyzing how a normalized version of the Riemannian metric
on the spatial hypersurfaces of homogeneity evolves.Comment: 34 pages, no figure
New Isotropic and Anisotropic Sudden Singularities
We show the existence of an infinite family of finite-time singularities in
isotropically expanding universes which obey the weak, strong, and dominant
energy conditions. We show what new type of energy condition is needed to
exclude them ab initio. We also determine the conditions under which
finite-time future singularities can arise in a wide class of anisotropic
cosmological models. New types of finite-time singularity are possible which
are characterised by divergences in the time-rate of change of the
anisotropic-pressure tensor. We investigate the conditions for the formation of
finite-time singularities in a Bianchi type universe with anisotropic
pressures and construct specific examples of anisotropic sudden singularities
in these universes.Comment: Typos corrected. Published versio
Research in interactive scene analysis
Cooperative (man-machine) scene analysis techniques were developed whereby humans can provide a computer with guidance when completely automated processing is infeasible. An interactive approach promises significant near-term payoffs in analyzing various types of high volume satellite imagery, as well as vehicle-based imagery used in robot planetary exploration. This report summarizes the work accomplished over the duration of the project and describes in detail three major accomplishments: (1) the interactive design of texture classifiers; (2) a new approach for integrating the segmentation and interpretation phases of scene analysis; and (3) the application of interactive scene analysis techniques to cartography
Impossible shadows and lightness constancy
The intersection between an illumination and a reflectance edge is characterised by the
`ratio-invariant' property, that is the luminance ratio of the regions under different illumination
remains the same.
In a CRT experiment, we shaped two areas, one surrounding the other, and simulated
an illumination edge dividing them in two frames of illumination. The portion of the illumina-
tion edge standing on the surrounding area (labelled contextual background) was the contextual
edge, while the portion standing on the enclosed area (labelled mediating background) was the
mediating edge. On the mediating background, there were two patches, one per illumination
frame. Observers were asked to adjust the luminance of the patch in bright illumination to
equate the lightness of the other. We compared conditions in which the luminance ratio at the
contextual edge could be (i) equal (possible shadow), or (ii) larger (impossible shadow) than
that at the mediating edge. In addition, we manipulated the reflectance of the backgrounds.
It could be higher for the contextual than for the mediating background; or, vice versa, lower
for the contextual than for the mediating background. Results reveal that lightness constancy
significantly increases when: (i) the luminance ratio at the contextual edge is larger than that at
the mediating edge creating an impossible shadow, and (ii) the reflectance of the contextual
background is lower than that of the mediating one. We interpret our results according to the
albedo hypothesis, and suggest that the scission process is facilitated when the luminance ratio
at the contextual edge is larger than that at the mediating edge and/or the reflectance of the
including area is lower than that of the included one. This occurs even if the ratio-invariant
property is violated
Structure and stability of the Lukash plane-wave spacetime
We study the vacuum, plane-wave Bianchi spacetimes described by
the Lukash metric. Combining covariant with orthonormal frame techniques, we
describe these models in terms of their irreducible kinematical and geometrical
quantities. This covariant description is used to study analytically the
response of the Lukash spacetime to linear perturbations. We find that the
stability of the vacuum solution depends crucially on the background shear
anisotropy. The stronger the deviation from the Hubble expansion, the more
likely the overall linear instability of the model. Our analysis addresses
rotational, shear and Weyl curvature perturbations and identifies conditions
sufficient for the linear growth of these distortions.Comment: Revised version, references added. To appear in Class. Quantum Gra
Cosmology in three dimensions: steps towards the general solution
We use covariant and first-order formalism techniques to study the properties
of general relativistic cosmology in three dimensions. The covariant approach
provides an irreducible decomposition of the relativistic equations, which
allows for a mathematically compact and physically transparent description of
the 3-dimensional spacetimes. Using this information we review the features of
homogeneous and isotropic 3-d cosmologies, provide a number of new solutions
and study gauge invariant perturbations around them. The first-order formalism
is then used to provide a detailed study of the most general 3-d spacetimes
containing perfect-fluid matter. Assuming the material content to be dust with
comoving spatial 2-velocities, we find the general solution of the Einstein
equations with non-zero (and zero) cosmological constant and generalise known
solutions of Kriele and the 3-d counterparts of the Szekeres solutions. In the
case of a non-comoving dust fluid we find the general solution in the case of
one non-zero fluid velocity component. We consider the asymptotic behaviour of
the families of 3-d cosmologies with rotation and shear and analyse their
singular structure. We also provide the general solution for cosmologies with
one spacelike Killing vector, find solutions for cosmologies containing scalar
fields and identify all the PP-wave 2+1 spacetimes.Comment: 35 pages, 2 figure
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