2,586 research outputs found
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
Determinantal formulae for the Casimir operators of inhomogeneous Lie algebras
Contractions of Lie algebras are combined with the classical matrix method of
Gel'fand to obtain matrix formulae for the Casimir operators of inhomogeneous
Lie algebras. The method is presented for the inhomogeneous pseudo-unitary Lie
algebras . This procedure is extended to contractions of
isomorphic to an extension by a derivation of the
inhomogeneous special pseudo-unitary Lie algebras ,
providing an additional analytical method to obtain their invariants. Further,
matrix formulae for the invariants of other inhomogeneous Lie algebras are
presented.Comment: Final ammended versio
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
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
Measuring the Generalized Friendship Paradox in Networks with Quality-dependent Connectivity
The friendship paradox is a sociological phenomenon stating that most people
have fewer friends than their friends do. The generalized friendship paradox
refers to the same observation for attributes other than degree, and it has
been observed in Twitter and scientific collaboration networks. This paper
takes an analytical approach to model this phenomenon. We consider a
preferential attachment-like network growth mechanism governed by both node
degrees and `qualities'. We introduce measures to quantify paradoxes, and
contrast the results obtained in our model to those obtained for an
uncorrelated network, where the degrees and qualities of adjacent nodes are
uncorrelated. We shed light on the effect of the distribution of node qualities
on the friendship paradox. We consider both the mean and the median to measure
paradoxes, and compare the results obtained by using these two statistics
Detection of new point-sources in WMAP Cosmic Microwave Background (CMB) maps at high Galactic latitude. A new technique to extract point sources from CMB maps
In experimental microwave maps, point-sources can strongly affect the
estimation of the power-spectrum and/or the test of Gaussianity of the Cosmic
Microwave Background (CMB) component. As a consequence, their removal from the
sky maps represents a critical step in the analysis of the CMB data. Before
removing a source, however, it is necessary to detect it and source extraction
consists of a delicate preliminary operation. In the literature, various
techniques have been presented to detect point-sources in the sky maps. The
most sophisticated ones exploit the multi-frequency nature of the observations
that is typical of the CMB experiments. These techniques have "optimal"
theoretical properties and, at least in principle, are capable of remarkable
performances. Actually, they are rather difficult to use and this deteriorates
the quality of the obtainable results. In this paper, we present a new
technique, the "weighted matched filter" (WMF), that is quite simple to use and
hence more robust in practical applications. Such technique shows particular
efficiency in the detection of sources whose spectra have a slope different
from zero. We apply this method to three Southern Hemisphere sky regions - each
with an area of 400 square degrees - of the seven years Wilkinson Microwave
Anisotropy Probe (WMAP) maps and compare the resulting sources with those of
the two seven-year WMAP point-sources catalogues. In these selected regions we
find seven additional sources not previously listed in WMAP catalogues and
discuss their most likely identification and spectral properties.Comment: Astronomy and Astrophysics, 2011, in pres
The estimation of the SZ effects with unbiased multifilters
In this work we study the performance of linear multifilters for the
estimation of the amplitudes of the thermal and kinematic Sunyaev-Zel'dovich
effects. We show that when both effects are present, estimation of these
effects with standard matched multifilters is intrinsically biased. This bias
is due to the fact that both signals have basically the same spatial profile.
We find a new family of multifilters related to the matched multifilters that
cancel this systematic bias, hence we call them Unbiased Matched Multifilters.
We test the unbiased matched multifilters and compare them with the standard
matched multifilters using simulations that reproduce the future Planck
mission's observations. We find that in the case of the standard matched
multifilters the systematic bias in the estimation of the kinematic
Sunyaev-Zel'dovich effect can be very large, even greater than the statistical
error bars. Unbiased matched multifilters cancel effectively this kind of bias.
In concordance with other works in the literature, our results indicate that
the sensitivity and resolution of Planck will not be enough to give reliable
estimations of the kinematic Sunyaev-Zel'dovich of individual clusters.
However, since the estimation with the unbiased matched multifilters is not
intrinsically biased, it can be possible to use them to statistically study
peculiar velocities in large scales using large sets of clusters.Comment: 12 pages, 6 figures, submitted to MNRA
- …