3,900 research outputs found
Central extensions of the families of quasi-unitary Lie algebras
The most general possible central extensions of two whole families of Lie
algebras, which can be obtained by contracting the special pseudo-unitary
algebras su(p,q) of the Cartan series A_l and the pseudo-unitary algebras
u(p,q), are completely determined and classified for arbitrary p,q. In addition
to the su(p,q) and u({p,q}) algebras, whose second cohomology group is well
known to be trivial, each family includes many non-semisimple algebras; their
central extensions, which are explicitly given, can be classified into three
types as far as their properties under contraction are involved. A closed
expression for the dimension of the second cohomology group of any member of
these families of algebras is given.Comment: 23 pages. Latex2e fil
The family of quaternionic quasi-unitary Lie algebras and their central extensions
The family of quaternionic quasi-unitary (or quaternionic unitary
Cayley--Klein algebras) is described in a unified setting. This family includes
the simple algebras sp(N+1) and sp(p,q) in the Cartan series C_{N+1}, as well
as many non-semisimple real Lie algebras which can be obtained from these
simple algebras by particular contractions. The algebras in this family are
realized here in relation with the groups of isometries of quaternionic
hermitian spaces of constant holomorphic curvature. This common framework
allows to perform the study of many properties for all these Lie algebras
simultaneously. In this paper the central extensions for all quasi-simple Lie
algebras of the quaternionic unitary Cayley--Klein family are completely
determined in arbitrary dimension. It is shown that the second cohomology group
is trivial for any Lie algebra of this family no matter of its dimension.Comment: 17 pages, LaTe
A fast Bayesian approach to discrete object detection in astronomical datasets - PowellSnakes I
A new fast Bayesian approach is introduced for the detection of discrete
objects immersed in a diffuse background. This new method, called PowellSnakes,
speeds up traditional Bayesian techniques by: i) replacing the standard form of
the likelihood for the parameters characterizing the discrete objects by an
alternative exact form that is much quicker to evaluate; ii) using a
simultaneous multiple minimization code based on Powell's direction set
algorithm to locate rapidly the local maxima in the posterior; and iii)
deciding whether each located posterior peak corresponds to a real object by
performing a Bayesian model selection using an approximate evidence value based
on a local Gaussian approximation to the peak. The construction of this
Gaussian approximation also provides the covariance matrix of the uncertainties
in the derived parameter values for the object in question. This new approach
provides a speed up in performance by a factor of `hundreds' as compared to
existing Bayesian source extraction methods that use MCMC to explore the
parameter space, such as that presented by Hobson & McLachlan. We illustrate
the capabilities of the method by applying to some simplified toy models.
Furthermore PowellSnakes has the advantage of consistently defining the
threshold for acceptance/rejection based on priors which cannot be said of the
frequentist methods. We present here the first implementation of this technique
(Version-I). Further improvements to this implementation are currently under
investigation and will be published shortly. The application of the method to
realistic simulated Planck observations will be presented in a forthcoming
publication.Comment: 30 pages, 15 figures, revised version with minor changes, accepted
for publication in MNRA
Detection/estimation of the modulus of a vector. Application to point source detection in polarization data
Given a set of images, whose pixel values can be considered as the components
of a vector, it is interesting to estimate the modulus of such a vector in some
localised areas corresponding to a compact signal. For instance, the
detection/estimation of a polarized signal in compact sources immersed in a
background is relevant in some fields like astrophysics. We develop two
different techniques, one based on the Neyman-Pearson lemma, the Neyman-Pearson
filter (NPF), and another based on prefiltering-before-fusion, the filtered
fusion (FF), to deal with the problem of detection of the source and estimation
of the polarization given two or three images corresponding to the different
components of polarization (two for linear polarization, three including
circular polarization). For the case of linear polarization, we have performed
numerical simulations on two-dimensional patches to test these filters
following two different approaches (a blind and a non-blind detection),
considering extragalactic point sources immersed in cosmic microwave background
(CMB) and non-stationary noise with the conditions of the 70 GHz \emph{Planck}
channel. The FF outperforms the NPF, especially for low fluxes. We can detect
with the FF extragalactic sources in a high noise zone with fluxes >=
(0.42,0.36) Jy for (blind/non-blind) detection and in a low noise zone with
fluxes >= (0.22,0.18) Jy for (blind/non-blind) detection with low errors in the
estimated flux and position.Comment: 11 pages, 5 figure
SAT based Enforcement of Domotic Effects in Smart Environments
The emergence of economically viable and efficient sensor technology provided impetus to the development of smart devices (or appliances). Modern smart environments are equipped with a multitude of smart devices and sensors, aimed at delivering intelligent services to the users of smart environments. The presence of these diverse smart devices has raised a major problem of managing environments. A rising solution to the problem is the modeling of user goals and intentions, and then interacting with the environments using user defined goals. `Domotic Effects' is a user goal modeling framework, which provides Ambient Intelligence (AmI) designers and integrators with an abstract layer that enables the definition of generic goals in a smart environment, in a declarative way, which can be used to design and develop intelligent applications. The high-level nature of domotic effects also allows the residents to program their personal space as they see fit: they can define different achievement criteria for a particular generic goal, e.g., by defining a combination of devices having some particular states, by using domain-specific custom operators. This paper describes an approach for the automatic enforcement of domotic effects in case of the Boolean application domain, suitable for intelligent monitoring and control in domotic environments. Effect enforcement is the ability to determine device configurations that can achieve a set of generic goals (domotic effects). The paper also presents an architecture to implement the enforcement of Boolean domotic effects, and results obtained from carried out experiments prove the feasibility of the proposed approach and highlight the responsiveness of the implemented effect enforcement architectur
A Bayesian approach to filter design: detection of compact sources
We consider filters for the detection and extraction of compact sources on a
background. We make a one-dimensional treatment (though a generalization to two
or more dimensions is possible) assuming that the sources have a Gaussian
profile whereas the background is modeled by an homogeneous and isotropic
Gaussian random field, characterized by a scale-free power spectrum. Local peak
detection is used after filtering. Then, a Bayesian Generalized Neyman-Pearson
test is used to define the region of acceptance that includes not only the
amplification but also the curvature of the sources and the a priori
probability distribution function of the sources. We search for an optimal
filter between a family of Matched-type filters (MTF) modifying the filtering
scale such that it gives the maximum number of real detections once fixed the
number density of spurious sources. We have performed numerical simulations to
test theoretical ideas.Comment: 10 pages, 2 figures. SPIE Proceedings "Electronic Imaging II", San
Jose, CA. January 200
Casimir invariants for the complete family of quasi-simple orthogonal algebras
A complete choice of generators of the center of the enveloping algebras of
real quasi-simple Lie algebras of orthogonal type, for arbitrary dimension, is
obtained in a unified setting. The results simultaneously include the well
known polynomial invariants of the pseudo-orthogonal algebras , as
well as the Casimirs for many non-simple algebras such as the inhomogeneous
, the Newton-Hooke and Galilei type, etc., which are obtained by
contraction(s) starting from the simple algebras . The dimension of
the center of the enveloping algebra of a quasi-simple orthogonal algebra turns
out to be the same as for the simple algebras from which they come by
contraction. The structure of the higher order invariants is given in a
convenient "pyramidal" manner, in terms of certain sets of "Pauli-Lubanski"
elements in the enveloping algebras. As an example showing this approach at
work, the scheme is applied to recovering the Casimirs for the (3+1)
kinematical algebras. Some prospects on the relevance of these results for the
study of expansions are also given.Comment: 19 pages, LaTe
A multifrequency method based on the Matched Multifilter for the detection of point sources in CMB maps
In this work we deal with the problem of simultaneous multifrequency
detection of extragalactic point sources in maps of the Cosmic Microwave
Background. We apply a linear filtering technique that uses spatial information
and the cross-power spectrum. To make this, we simulate realistic and
non-realistic flat patches of the sky at two frequencies of Planck: 44 and 100
GHz. We filter to detect and estimate the point sources and compare this
technique with the monofrequency matched filter in terms of completeness,
reliability, flux and spectral index accuracy. The multifrequency method
outperforms the matched filter at the two frequencies and in all the studied
cases in the work.Comment: 14 pages, 6 figures, 1 tabl
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