3,730 research outputs found
Decoding by Embedding: Correct Decoding Radius and DMT Optimality
The closest vector problem (CVP) and shortest (nonzero) vector problem (SVP)
are the core algorithmic problems on Euclidean lattices. They are central to
the applications of lattices in many problems of communications and
cryptography. Kannan's \emph{embedding technique} is a powerful technique for
solving the approximate CVP, yet its remarkable practical performance is not
well understood. In this paper, the embedding technique is analyzed from a
\emph{bounded distance decoding} (BDD) viewpoint. We present two complementary
analyses of the embedding technique: We establish a reduction from BDD to
Hermite SVP (via unique SVP), which can be used along with any Hermite SVP
solver (including, among others, the Lenstra, Lenstra and Lov\'asz (LLL)
algorithm), and show that, in the special case of LLL, it performs at least as
well as Babai's nearest plane algorithm (LLL-aided SIC). The former analysis
helps to explain the folklore practical observation that unique SVP is easier
than standard approximate SVP. It is proven that when the LLL algorithm is
employed, the embedding technique can solve the CVP provided that the noise
norm is smaller than a decoding radius , where
is the minimum distance of the lattice, and . This
substantially improves the previously best known correct decoding bound . Focusing on the applications of BDD to decoding of
multiple-input multiple-output (MIMO) systems, we also prove that BDD of the
regularized lattice is optimal in terms of the diversity-multiplexing gain
tradeoff (DMT), and propose practical variants of embedding decoding which
require no knowledge of the minimum distance of the lattice and/or further
improve the error performance.Comment: To appear in IEEE Transactions on Information Theor
Evaluating VaR forecasts under stress: the German experience
We present an analysis of VaR forecasts and P&L-series of all 13 German banks that used internal models for regulatory purposes in the year 2001. To this end, we introduce the notion of well-behaved forecast systems. Furthermore, we provide a series of statistical tools to perform our analyses. The results shed light on the forecast quality of VaR models of the individual banks, the regulator's portfolio as a whole, and the main ingredients of the computation of the regulatory capital required by the Basel rules
The standstill luminosity in Z Cam systems
We consider accretion discs in close binary systems. We show that heating of
a disc at the impact point of the accretion stream contributes significantly to
the local energy budget at its outer edge. As a result the thermal balance
relation between local accretion rate and surface density (the `S-curve')
changes; the critical mass transfer rate above which no dwarf nova outbursts
occur can be up to 40% smaller than without impact heating. Standstills in ZCam
systems thus occur at smaller mass transfer rates than otherwise expected, and
are rather fainter than the peak luminosity during the dwarf nova phase as a
result.Comment: 3 pages, 3 figures. Accepted for publication in MNRA
Structure and properties of transition fronts in accretion discs
We use high-resolution time-dependent numerical simulations of accretion
discs around white dwarfs to study the structure and properties of transition
fronts in the context of the thermal-viscous disc instability model. The
thermal structure of cooling and heating fronts is dominated by radiative
cooling and viscous heating, respectively, except in a very narrow precursor
region in heating fronts where advection and radial transport of energy
dominate. Cooling fronts are much broader than heating fronts, but the widths
of both types of fronts scale with the local vertical scale height of the disc.
We confirm that during a fair fraction of the propagation time of a cooling
front, the structure of the inner disc is close to self-similar. The speed of
heating fronts is ~ a few km/s, while the speed of cooling fronts is ~ a
fraction of a km/s. We show that direct measurements of the speed of transition
fronts probably cannot discriminate between various prescriptions proposed for
the viscosity parameter alpha. A natural prediction of the disc instability
model is that fronts decelerate as they propagate in the disc, independent of
the prescription for alpha. Observation of this effect would confirm that dwarf
nova outbursts are driven by the thermal-viscous instability. Most of our
results also apply to low mass X-ray binaries in which the accreting object is
a neutron star or a black hole.Comment: LateX, 12 pages, 10 figures, uses mn.sty; Submitted to MNRA
Evaluating VaR Forecasts under Stress – The German Experience
We present an analysis of VaR forecasts and P&L-series of all 13 German banks that used internal models for regulatory purposes in the year 2001. To this end, we introduce the notion of well-behaved forecast systems. Furthermore, we provide a series of statistical tools to perform our analyses. The results shed light on the forecast quality of VaR models of the individual banks, the regulator's portfolio as a whole, and the main ingredients of the computation of the regulatory capital required by the Basel rules.banking supervision, VaR, exploratory data analysis, backtesting
Interchange instability in an accretion disc with a poloidal magnetic field
We investigate the stability to nonaxisymmetric perturbations of an accretion
disc in which a poloidal magnetic field provides part of the radial support
against gravity. Interchange instability due to radial gradients in the
magnetic field are strongly stabilized by the shear flow in the disc. For
smooth field distributions this instability is restricted to discs in which the
magnetic energy is comparable to the gravitational energy. An incompressible
model for the instability akin to the Boussinesq approximation for convection
is given which predicts the behaviour of the instability accurately. Global
axisymmetric disturbances are also considered and found to be stable for a
certain class of models. The results indicate that accretion discs may be able
to support poloidal fields which are strong enough to suppress other forms of
magnetic instability. These strong and stable field distributions are likely to
be well suited for the magnetic acceleration of jets and winds.Comment: uuencoded gzip'ed postscript, 9 page
Removal of Specular Reflections in Endoscopic Images
During an endoscopic examination, pictures from the inside of the human body are displayed on a computer monitor. Disturbing light reflections are often visible in these images. In this paper, we present an approach for removing these reflections and replacing them by an estimate obtained using a spectral deconvolution algorithm.
Modeling Infection with Multi-agent Dynamics
Developing the ability to comprehensively study infections in small
populations enables us to improve epidemic models and better advise individuals
about potential risks to their health. We currently have a limited
understanding of how infections spread within a small population because it has
been difficult to closely track an infection within a complete community. The
paper presents data closely tracking the spread of an infection centered on a
student dormitory, collected by leveraging the residents' use of cellular
phones. The data are based on daily symptom surveys taken over a period of four
months and proximity tracking through cellular phones. We demonstrate that
using a Bayesian, discrete-time multi-agent model of infection to model
real-world symptom reports and proximity tracking records gives us important
insights about infec-tions in small populations
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