11,580 research outputs found
A Counterexample to Claimed COBE Constraints on Compact Toroidal Universe Models
It has been suggested that if the Universe satisfies a flat, multiply
connected, perturbed Friedmann-Lema^itre model, then cosmic microwave
background data from the COBE satellite implies that the minimum size of the
injectivity diameter (shortest closed spatial geodesic) must be larger than
about two fifths of the horizon diameter. To show that this claim is
misleading, a simple universe model of injectivity diameter a
quarter of this size, i.e. a tenth of the horizon diameter, is shown to be
consistent with COBE four year observational maps of the cosmic microwave
background. This is done using the identified circles principle.Comment: 11 pages, 3 figures, accepted for Classical & Quantum Gravit
New results on mixture and exponential models by Orlicz spaces
New results and improvements in the study of nonparametric exponential and
mixture models are proposed. In particular, different equivalent
characterizations of maximal exponential models, in terms of open exponential
arcs and Orlicz spaces, are given. Our theoretical results are supported by
several examples and counterexamples and provide an answer to some open
questions in the literature.Comment: Published at http://dx.doi.org/10.3150/15-BEJ698 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Screening of charged singularities of random fields
Many types of point singularity have a topological index, or 'charge',
associated with them. For example the phase of a complex field depending on two
variables can either increase or decrease on making a clockwise circuit around
a simple zero, enabling the zeros to be assigned charges of plus or minus one.
In random fields we can define a correlation function for the charge-weighted
density of singularities. In many types of random fields, this correlation
function satisfies an identity which shows that the singularities 'screen' each
other perfectly: a positive singularity is surrounded by an excess of
concentration of negatives which exactly cancel its charge, and vice-versa.
This paper gives a simple and widely applicable derivation of this result. A
counterexample where screening is incomplete is also exhibited.Comment: 12 pages, no figures. Minor revision of manuscript submitted to J.
Phys. A, August 200
Entanglement Measures under Symmetry
We show how to simplify the computation of the entanglement of formation and
the relative entropy of entanglement for states, which are invariant under a
group of local symmetries. For several examples of groups we characterize the
state spaces, which are invariant under these groups. For specific examples we
calculate the entanglement measures. In particular, we derive an explicit
formula for the entanglement of formation for UU-invariant states, and we find
a counterexample to the additivity conjecture for the relative entropy of
entanglement.Comment: RevTeX,16 pages,9 figures, reference added, proof of monotonicity
corrected, results unchange
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