2,920 research outputs found
Finite Projective Spaces, Geometric Spreads of Lines and Multi-Qubits
Given a (2N - 1)-dimensional projective space over GF(2), PG(2N - 1, 2), and
its geometric spread of lines, there exists a remarkable mapping of this space
onto PG(N - 1, 4) where the lines of the spread correspond to the points and
subspaces spanned by pairs of lines to the lines of PG(N - 1, 4). Under such
mapping, a non-degenerate quadric surface of the former space has for its image
a non-singular Hermitian variety in the latter space, this quadric being {\it
hyperbolic} or {\it elliptic} in dependence on N being {\it even} or {\it odd},
respectively. We employ this property to show that generalized Pauli groups of
N-qubits also form two distinct families according to the parity of N and to
put the role of symmetric operators into a new perspective. The N=4 case is
taken to illustrate the issue.Comment: 3 pages, no figures/tables; V2 - short introductory paragraph added;
V3 - to appear in Int. J. Mod. Phys.
The Optimal Gravitational Lens Telescope
Given an observed gravitational lens mirage produced by a foreground
deflector (cf. galaxy, quasar, cluster,...), it is possible via numerical lens
inversion to retrieve the real source image, taking full advantage of the
magnifying power of the cosmic lens. This has been achieved in the past for
several remarkable gravitational lens systems. Instead, we propose here to
invert an observed multiply imaged source directly at the telescope using an
ad-hoc optical instrument which is described in the present paper. Compared to
the previous method, this should allow one to detect fainter source features as
well as to use such an optimal gravitational lens telescope to explore even
fainter objects located behind and near the lens. Laboratory and numerical
experiments illustrate this new approach
Probing the distribution of dark matter in the Abell 901/902 supercluster with weak lensing
We present a weak shear analysis of the Abell 901/902 supercluster, composed
of three rich clusters at z=0.16. Using a deep R-band image from the 0.5 x 0.5
degree MPG/ESO Wide Field Imager together with supplementary B-band
observations, we build up a comprehensive picture of the light and mass
distributions in this region. We find that, on average, the light from the
early-type galaxies traces the dark matter fairly well, although one cluster is
a notable exception to this rule. The clusters themselves exhibit a range of
mass-to-light (M/L) ratios, X-ray properties, and galaxy populations. We
attempt to model the relation between the total mass and the light from the
early-type galaxies with a simple scale-independent linear biasing model. We
find M/L_B=130h for the early type galaxies with zero stochasticity, which, if
taken at face value, would imply Omega_m < 0.1. However, this linear relation
breaks down on small scales and on scales equivalent to the average cluster
separation (approximately 1 Mpc), demonstrating that a single M/L ratio is not
adequate to fully describe the mass-light relation in the supercluster. Rather,
the scatter in M/L ratios observed for the clusters supports a model
incorporating non-linear biasing or stochastic processes. Finally, there is a
clear detection of filamentary structure connecting two of the clusters, seen
in both the galaxy and dark matter distributions, and we discuss the effects of
cluster-cluster and cluster-filament interactions as a means to reconcile the
disparate descriptions of the supercluster.Comment: 23 pages, 19 figures. ApJ, accepte
Cassiopeia A: dust factory revealed via submillimetre polarimetry
If Type-II supernovae - the evolutionary end points of short-lived, massive
stars - produce a significant quantity of dust (>0.1 M_sun) then they can
explain the rest-frame far-infrared emission seen in galaxies and quasars in
the first Gyr of the Universe. Submillimetre observations of the Galactic
supernova remnant, Cas A, provided the first observational evidence for the
formation of significant quantities of dust in Type-II supernovae. In this
paper we present new data which show that the submm emission from Cas A is
polarised at a level significantly higher than that of its synchrotron
emission. The orientation is consistent with that of the magnetic field in Cas
A, implying that the polarised submm emission is associated with the remnant.
No known mechanism would vary the synchrotron polarisation in this way and so
we attribute the excess polarised submm flux to cold dust within the remnant,
providing fresh evidence that cosmic dust can form rapidly. This is supported
by the presence of both polarised and unpolarised dust emission in the north of
the remnant, where there is no contamination from foreground molecular clouds.
The inferred dust polarisation fraction is unprecedented (f_pol ~ 30%) which,
coupled with the brief timescale available for grain alignment (<300 yr),
suggests that supernova dust differs from that seen in other Galactic sources
(where f_pol=2-7%), or that a highly efficient grain alignment process must
operate in the environment of a supernova remnant.Comment: In press at MNRAS, 10 pages, print in colou
Optimal control strategies for tuberculosis treatment: a case study in Angola
We apply optimal control theory to a tuberculosis model given by a system of
ordinary differential equations. Optimal control strategies are proposed to
minimize the cost of interventions. Numerical simulations are given using data
from Angola.Comment: This is a preprint of a paper whose final and definite form will
appear in the international journal Numerical Algebra, Control and
Optimization (NACO). Paper accepted for publication 15-March-201
Modelling high resolution ALMA observations of strongly lensed highly star forming galaxies detected by <i>Herschel</i>
We have modelled ∼ 0.1 arcsec resolution ALMA imaging of six strong gravitationally lensed galaxies detected by the Herschel Space Observatory. Our modelling recovers mass properties of the lensing galaxies and, by determining magnification factors, intrinsic properties of the lensed sub-millimetre sources. We find that the lensed galaxies all have high ratios of star formation rate to dust mass, consistent with or higher than the mean ratio for high redshift sub-millimetre galaxies and low redshift ultra-luminous infra-red galaxies. Source reconstruction reveals that most galaxies exhibit disturbed morphologies. Both the cleaned image plane data and the directly observed interferometric visibilities have been modelled, enabling comparison of both approaches. In the majority of cases, the recovered lens models are consistent between methods, all six having mass density profiles that are close to isothermal. However, one system with poor signal to noise shows mildly significant differences
Elementary processes governing the evolution of road networks
Urbanisation is a fundamental phenomenon whose quantitative characterisation
is still inadequate. We report here the empirical analysis of a unique data set
regarding almost 200 years of evolution of the road network in a large area
located north of Milan (Italy). We find that urbanisation is characterised by
the homogenisation of cell shapes, and by the stability throughout time of
high-centrality roads which constitute the backbone of the urban structure,
confirming the importance of historical paths. We show quantitatively that the
growth of the network is governed by two elementary processes: (i)
`densification', corresponding to an increase in the local density of roads
around existing urban centres and (ii) `exploration', whereby new roads trigger
the spatial evolution of the urbanisation front. The empirical identification
of such simple elementary mechanisms suggests the existence of general, simple
properties of urbanisation and opens new directions for its modelling and
quantitative description.Comment: 10 pages, 6 figure
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