A study of separability criteria for mixed three-qubit states

We study the noisy GHZ-W mixture. We demonstrate some necessary but not sufficient criteria for different classes of separability of these states. It turns out that the partial transposition criterion of Peres and the criteria of G\"uhne and Seevinck dealing with matrix elements are the strongest ones for different separability classes of this 2 parameter state. As a new result we determine a set of entangled states of positive partial transpose.Comment: 18 pages, 10 figures, PRA styl

A Robust Classification of Galaxy Spectra: Dealing with Noisy and Incomplete Data

Over the next few years new spectroscopic surveys (from the optical surveys of the Sloan Digital Sky Survey and the 2 degree Field survey through to space-based ultraviolet satellites such as GALEX) will provide the opportunity and challenge of understanding how galaxies of different spectral type evolve with redshift. Techniques have been developed to classify galaxies based on their continuum and line spectra. Some of the most promising of these have used the Karhunen and Loeve transform (or Principal Component Analysis) to separate galaxies into distinct classes. Their limitation has been that they assume that the spectral coverage and quality of the spectra are constant for all galaxies within a given sample. In this paper we develop a general formalism that accounts for the missing data within the observed spectra (such as the removal of sky lines or the effect of sampling different intrinsic rest wavelength ranges due to the redshift of a galaxy). We demonstrate that by correcting for these gaps we can recover an almost redshift independent classification scheme. From this classification we can derive an optimal interpolation that reconstructs the underlying galaxy spectral energy distributions in the regions of missing data. This provides a simple and effective mechanism for building galaxy spectral energy distributions directly from data that may be noisy, incomplete or drawn from a number of different sources.Comment: 20 pages, 8 figures. Accepted for publication in A

Sensor Drift Compensation Using Fuzzy Interference System and Sparse-Grid Quadrature Filter in Blood Glucose Control

Diabetes mellitus is a serious chronic condition of the human metabolism. The development of an automated treatment has reached clinical phase in the last few years. The goal is to keep the blood glucose concentration within a certain region with minimal interaction required by the patient or medical personnel. However, there are still several prac- tical problems to solve. One of these would be that the available sensors have significant noise and drift. The latter is rather difficult to manage, because the deviating signal can cause the controller to drive the glu- cose concentration out of the safe region even in the case of frequent calibration. In this study a linear-quadratic-Gaussian (LQG) controller is employed on a widely used diabetes model and enhanced with an ad- vanced Sparse-grid quadratic filter and a fuzzy interference system-based calibration supervisor

Vortices within vortices: hierarchical nature of vortex tubes in turbulence

The JHU turbulence database [1] can be used with a state of the art visualisation tool [2] to generate high quality fluid dynamics videos. In this work we investigate the classical idea that smaller structures in turbulent flows, while engaged in their own internal dynamics, are advected by the larger structures. They are not advected undistorted, however. We see instead that the small scale structures are sheared and twisted by the larger scales. This illuminates the basic mechanisms of the turbulent cascade.Comment: 2 pages, 1 low quality video, 1 high quality vide