Efficient implementation of the adaptive scale pixel decomposition algorithm

Context. Most popular algorithms in use to remove the effects of a telescope's point spread function (PSF) in radio astronomy are variants of the CLEAN algorithm. Most of these algorithms model the sky brightness using the delta-function basis, which results in undesired artefacts when used on image extended emission. The adaptive scale pixel decomposition (Asp-Clean) algorithm models the sky brightness on a scale-sensitive basis and thus gives a significantly better imaging performance when imaging fields that contain both resolved and unresolved emission. Aims. However, the runtime cost of Asp-Clean is higher than that of scale-insensitive algorithms. In this paper, we identify the most expensive step in the original Asp-Clean algorithm and present an efficient implementation of it, which significantly reduces the computational cost while keeping the imaging performance comparable to the original algorithm. The PSF sidelobe levels of modern wide-band telescopes are significantly reduced, allowing us to make approximations to reduce the computing cost, which in turn allows for the deconvolution of larger images on reasonable timescales. Methods. As in the original algorithm, scales in the image are estimated through function fitting. Here we introduce an analytical method to model extended emission, and a modified method for estimating the initial values used for the fitting procedure, which ultimately leads to a lower computational cost. Results.The new implementation was tested with simulated EVLA data and the imaging performance compared well with the original Asp-Clean algorithm. Tests show that the current algorithm can recover features at different scales with lower computational cost.Comment: 6 pages; 4 figure

Algebraic characterization of X-states in quantum information

A class of two-qubit states called X-states are increasingly being used to discuss entanglement and other quantum correlations in the field of quantum information. Maximally entangled Bell states and "Werner" states are subsets of them. Apart from being so named because their density matrix looks like the letter X, there is not as yet any characterization of them. The su(2) X su(2) X u(1) subalgebra of the full su(4) algebra of two qubits is pointed out as the underlying invariance of this class of states. X-states are a seven-parameter family associated with this subalgebra of seven operators. This recognition provides a route to preparing such states and also a convenient algebraic procedure for analytically calculating their properties. At the same time, it points to other groups of seven-parameter states that, while not at first sight appearing similar, are also invariant under the same subalgebra. And it opens the way to analyzing invariant states of other subalgebras in bipartite systems.Comment: 4 pages, 1 figur

Calculation of quantum discord for qubit-qudit or N qubits

Quantum discord, a kind of quantum correlation, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. It has been discussed so far for small systems with only a few independent parameters. We extend here to a much broader class of states when the second party is of arbitrary dimension d, so long as the first, measured, party is a qubit. We present two formulae to calculate quantum discord, the first relating to the original entropic definition and the second to a recently proposed geometric distance measure which leads to an analytical formulation. The tracing over the qubit in the entropic calculation is reduced to a very simple prescription. And, when the d-dimensional system is a so-called X state, the density matrix having non-zero elements only along the diagonal and anti-diagonal so as to appear visually like the letter X, the entropic calculation can be carried out analytically. Such states of the full bipartite qubit-qudit system may be named "extended X states", whose density matrix is built of four block matrices, each visually appearing as an X. The optimization involved in the entropic calculation is generally over two parameters, reducing to one for many cases, and avoided altogether for an overwhelmingly large set of density matrices as our numerical investigations demonstrate. Our results also apply to states of a N-qubit system, where "extended X states" consist of (2^(N+2) - 1) states, larger in number than the (2^(N+1) - 1) of X states of N qubits. While these are still smaller than the total number (2^(2N) - 1) of states of N qubits, the number of parameters involved is nevertheless large. In the case of N = 2, they encompass the entire 15-dimensional parameter space, that is, the extended X states for N = 2 represent the full qubit-qubit system.Comment: 6 pages, 1 figur

The temperature dependent bandstructure of a ferromagnetic semiconductor film

The electronic quasiparticle spectrum of a ferromagnetic film is investigated within the framework of the s-f model. Starting from the exact solvable case of a single electron in an otherwise empty conduction band being exchange coupled to a ferromagnetically saturated localized spin system we extend the theory to finite temperatures. Our approach is a moment-conserving decoupling procedure for suitable defined Green functions. The theory for finite temperatures evolves continuously from the exact limiting case. The restriction to zero conduction band occupation may be regarded as a proper model description for ferromagnetic semiconductors like EuO and EuS. Evaluating the theory for a simple cubic film cut parallel to the (100) crystal plane, we find some marked correlation effects which depend on the spin of the test electron, on the exchange coupling, and on the temperature of the local-moment system.Comment: 11 pages, 9 figure

Interactive decision support in hepatic surgery

BACKGROUND: Hepatic surgery is characterized by complicated operations with a significant peri- and postoperative risk for the patient. We developed a web-based, high-granular research database for comprehensive documentation of all relevant variables to evaluate new surgical techniques. METHODS: To integrate this research system into the clinical setting, we designed an interactive decision support component. The objective is to provide relevant information for the surgeon and the patient to assess preoperatively the risk of a specific surgical procedure. Based on five established predictors of patient outcomes, the risk assessment tool searches for similar cases in the database and aggregates the information to estimate the risk for an individual patient. RESULTS: The physician can verify the analysis and exclude manually non-matching cases according to his expertise. The analysis is visualized by means of a Kaplan-Meier plot. To evaluate the decision support component we analyzed data on 165 patients diagnosed with hepatocellular carcinoma (period 1996–2000). The similarity search provides a two-peak distribution indicating there are groups of similar patients and singular cases which are quite different to the average. The results of the risk estimation are consistent with the observed survival data, but must be interpreted with caution because of the limited number of matching reference cases. CONCLUSION: Critical issues for the decision support system are clinical integration, a transparent and reliable knowledge base and user feedback

Feed-Forward Chains of Recurrent Attractor Neural Networks Near Saturation

We perform a stationary state replica analysis for a layered network of Ising spin neurons, with recurrent Hebbian interactions within each layer, in combination with strictly feed-forward Hebbian interactions between successive layers. This model interpolates between the fully recurrent and symmetric attractor network studied by Amit el al, and the strictly feed-forward attractor network studied by Domany et al. Due to the absence of detailed balance, it is as yet solvable only in the zero temperature limit. The built-in competition between two qualitatively different modes of operation, feed-forward (ergodic within layers) versus recurrent (non- ergodic within layers), is found to induce interesting phase transitions.Comment: 14 pages LaTex with 4 postscript figures submitted to J. Phys.

High-redshift blazars through nustar eyes

The most powerful sources among the blazar family are MeV blazars. Often detected at $z>2$, they usually display high X- and \gm-ray luminosities, larger-than-average jet powers and black hole masses $\gtrsim 10^9 M_{\odot}$. In the present work we perform a multiwavelength study of three high redshift blazars: 3FGL J0325.5+2223 ($z=2.06$), 3FGL J0449.0+1121 ($z= 2.15$), and 3FGL J0453.2$-$2808 ($z=2.56$), analysing quasi simultaneous data from GROND, \swift-UVOT and XRT, \nustar, and \fermi-LAT. Our main focus is on the hard X-ray band recently unveiled by \nustar~(3$-$79 keV) where these objects show a hard spectrum which enables us to constrain the inverse Compton peak and the jet power. We found that all three targets resemble the most powerful blazars, with the synchrotron peak located in the sub-millimeter range and the inverse Compton peak in the MeV range, and therefore belong to the MeV blazar class. Using a simple one zone leptonic emission model to reproduce the spectral energy distributions, we conclude that a simple combination of synchrotron and accretion disk emission reproduces the infrared-optical spectra while the X-ray to \gm-ray part is well reproduced by the inverse Compton scattering of low energy photons supplied by the broad line region. The black hole masses for each of the three sources are calculated to be $\gtrsim 4 \times 10^{8} M_{\odot}$. The three studied sources have jet power at the level of, or beyond, the accretion luminosity.Comment: 4 figures, 3 tables, accepted for publication in Ap

Are N=1 and N=2 supersymmetric quantum mechanics equivalent?

After recalling different formulations of the definition of supersymmetric quantum mechanics given in the literature, we discuss the relationships between them in order to provide an answer to the question raised in the title.Comment: 15 page

Two Qubits in the Dirac Representation

A general two qubit system expressed in terms of the complete set of unit and fifteen traceless, Hermitian Dirac matrices, is shown to exhibit novel features of this system. The well-known physical interpretations associated with the relativistic Dirac equation involving the symmetry operations of time-reversal T, charge conjugation C, parity P, and their products are reinterpreted here by examining their action on the basic Bell states. The transformation properties of the Bell basis states under these symmetry operations also reveal that C is the only operator that does not mix the Bell states whereas all others do. In a similar fashion, expressing the various logic gates introduced in the subject of quantum computers in terms of the Dirac matrices shows for example, that the NOT gate is related to the product of time-reversal and parity operators.Comment: 11 page