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 $\lambda_1/(2\gamma)$, where $\lambda_1$ is the minimum distance of the lattice, and $\gamma \approx O(2^{n/4})$. This substantially improves the previously best known correct decoding bound $\gamma \approx {O}(2^{n})$. 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

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

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

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