Intermediate Tail Dependence: A Review and Some New Results

The concept of intermediate tail dependence is useful if one wants to quantify the degree of positive dependence in the tails when there is no strong evidence of presence of the usual tail dependence. We first review existing studies on intermediate tail dependence, and then we report new results to supplement the review. Intermediate tail dependence for elliptical, extreme value and Archimedean copulas are reviewed and further studied, respectively. For Archimedean copulas, we not only consider the frailty model but also the recently studied scale mixture model; for the latter, conditions leading to upper intermediate tail dependence are presented, and it provides a useful way to simulate copulas with desirable intermediate tail dependence structures.Comment: 25 pages, 1 figur

Deep Mid-Infrared Silicate Absorption as a Diagnostic of Obscuring Geometry Toward Galactic Nuclei

The silicate cross section peak near 10um produces emission and absorption features in the spectra of dusty galactic nuclei observed with the Spitzer Space Telescope. Especially in ultraluminous infrared galaxies, the observed absorption feature can be extremely deep, as IRAS 08572+3915 illustrates. A foreground screen of obscuration cannot reproduce this observed feature, even at large optical depth. Instead, the deep absorption requires a nuclear source to be deeply embedded in a smooth distribution of material that is both geometrically and optically thick. In contrast, a clumpy medium can produce only shallow absorption or emission, which are characteristic of optically-identified active galactic nuclei. In general, the geometry of the dusty region and the total optical depth, rather than the grain composition or heating spectrum, determine the silicate feature's observable properties. The apparent optical depth calculated from the ratio of line to continuum emission generally fails to accurately measure the true optical depth. The obscuring geometry, not the nature of the embedded source, also determines the far-IR spectral shape.Comment: To appear in ApJ

Extended matrix Gelfand-Dickey hierarchies: reduction to classical Lie algebras

The Drinfeld-Sokolov reduction method has been used to associate with $gl_n$ extensions of the matrix r-KdV system. Reductions of these systems to the fixed point sets of involutive Poisson maps, implementing reduction of $gl_n$ to classical Lie algebras of type $B, C, D$, are here presented. Modifications corresponding, in the first place to factorisation of the Lax operator, and then to Wakimoto realisations of the current algebra components of the factorisation, are also described.Comment: plain TeX, 12 page

Experimental tests of hidden variable theories from dBB to Stochastic Electrodynamics

In this paper we present some of our experimental results on testing hidden variable theories, which range from Bell inequalities measurements to a conclusive test of stochastic electrodynamics

Positive maps, majorization, entropic inequalities, and detection of entanglement

In this paper, we discuss some general connections between the notions of positive map, weak majorization and entropic inequalities in the context of detection of entanglement among bipartite quantum systems. First, basing on the fact that any positive map $\Lambda:M_{d}(\mathbb{C})\to M_{d}(\mathbb{C})$ can be written as the difference between two completely positive maps $\Lambda=\Lambda_{1}-\Lambda_{2}$, we propose a possible way to generalize the Nielsen--Kempe majorization criterion. Then we present two methods of derivation of some general classes of entropic inequalities useful for the detection of entanglement. While the first one follows from the aforementioned generalized majorization relation and the concept of the Schur--concave decreasing functions, the second is based on some functional inequalities. What is important is that, contrary to the Nielsen--Kempe majorization criterion and entropic inequalities, our criteria allow for the detection of entangled states with positive partial transposition when using indecomposable positive maps. We also point out that if a state with at least one maximally mixed subsystem is detected by some necessary criterion based on the positive map $\Lambda$, then there exist entropic inequalities derived from $\Lambda$ (by both procedures) that also detect this state. In this sense, they are equivalent to the necessary criterion [I\ot\Lambda](\varrho_{AB})\geq 0. Moreover, our inequalities provide a way of constructing multi--copy entanglement witnesses and therefore are promising from the experimental point of view. Finally, we discuss some of the derived inequalities in the context of recently introduced protocol of state merging and possibility of approximating the mean value of a linear entanglement witness.Comment: the published version, 25 pages in NJP format, 6 figure

Maximally entangled mixed states of two qubits

We consider mixed states of two qubits and show under which global unitary operations their entanglement is maximized. This leads to a class of states that is a generalization of the Bell states. Three measures of entanglement are considered: entanglement of formation, negativity and relative entropy of entanglement. Surprisingly all states that maximize one measure also maximize the others. We will give a complete characterization of these generalized Bell states and prove that these states for fixed eigenvalues are all equivalent under local unitary transformations. We will furthermore characterize all nearly entangled states closest to the maximally mixed state and derive a new lower bound on the volume of separable mixed states

The use and calibration of read-out streaks to increase the dynamic range of the Swift Ultraviolet/Optical Telescope

The dynamic range of photon counting micro-channel-plate (MCP) intensified charged-coupled device (CCD) instruments such as the Swift Ultraviolet/Optical Telescope (UVOT) and the XMM-Newton Optical Monitor (XMM-OM) is limited at the bright end by coincidence loss, the superposition of multiple photons in the individual frames recorded by the CCD. Photons which arrive during the brief period in which the image frame is transferred for read out of the CCD are displaced in the transfer direction in the recorded images. For sufficiently bright sources, these displaced counts form read-out streaks. Using UVOT observations of Tycho-2 stars, we investigate the use of these read-out streaks to obtain photometry for sources which are too bright (and hence have too much coincidence loss) for normal aperture photometry to be reliable. For read-out-streak photometry, the bright-source limiting factor is coincidence loss within the MCPs rather than the CCD. We find that photometric measurements can be obtained for stars up to 2.4 magnitudes brighter than the usual full-frame coincidence-loss limit by using the read-out streaks. The resulting bright-limit Vega magnitudes in the UVOT passbands are UVW2=8.80, UVM2=8.27, UVW1=8.86, u=9.76, b=10.53, v=9.31 and White=11.71; these limits are independent of the windowing mode of the camera. We find that a photometric precision of 0.1 mag can be achieved through read-out streak measurements. A suitable method for the measurement of read-out streaks is described and all necessary calibration factors are given.Comment: 11 pages, accepted for publication in MNRAS. Code available from the calibration link at http://www.mssl.ucl.ac.uk/www_astro/uvo

The Swift-UVOT ultraviolet and visible grism calibration

We present the calibration of the Swift UVOT grisms, of which there are two, providing low-resolution field spectroscopy in the ultraviolet and optical bands respectively. The UV grism covers the range 1700-5000 Angstrom with a spectral resolution of 75 at 2600 Angstrom for source magnitudes of u=10-16 mag, while the visible grism covers the range 2850-6600 Angstrom with a spectral resolution of 100 at 4000 Angstrom for source magnitudes of b=12-17 mag. This calibration extends over all detector positions, for all modes used during operations. The wavelength accuracy (1-sigma) is 9 Angstrom in the UV grism clocked mode, 17 Angstrom in the UV grism nominal mode and 22 Angstrom in the visible grism. The range below 2740 Angstrom in the UV grism and 5200 Angstrom in the visible grism never suffers from overlapping by higher spectral orders. The flux calibration of the grisms includes a correction we developed for coincidence loss in the detector. The error in the coincidence loss correction is less than 20%. The position of the spectrum on the detector only affects the effective area (sensitivity) by a few percent in the nominal modes, but varies substantially in the clocked modes. The error in the effective area is from 9% in the UV grism clocked mode to 15% in the visible grism clocked mode .Comment: 27 pages, 31 figures; MNRAS accepted 23 February 201

Le Chatelier principle in replicator dynamics

The Le Chatelier principle states that physical equilibria are not only stable, but they also resist external perturbations via short-time negative-feedback mechanisms: a perturbation induces processes tending to diminish its results. The principle has deep roots, e.g., in thermodynamics it is closely related to the second law and the positivity of the entropy production. Here we study the applicability of the Le Chatelier principle to evolutionary game theory, i.e., to perturbations of a Nash equilibrium within the replicator dynamics. We show that the principle can be reformulated as a majorization relation. This defines a stability notion that generalizes the concept of evolutionary stability. We determine criteria for a Nash equilibrium to satisfy the Le Chatelier principle and relate them to mutualistic interactions (game-theoretical anticoordination) showing in which sense mutualistic replicators can be more stable than (say) competing ones. There are globally stable Nash equilibria, where the Le Chatelier principle is violated even locally: in contrast to the thermodynamic equilibrium a Nash equilibrium can amplify small perturbations, though both this type of equilibria satisfy the detailed balance condition.Comment: 12 pages, 3 figure

Towards a framework for critical citizenship education

Increasingly countries around the world are promoting forms of "critical" citizenship in the planned curricula of schools. However, the intended meaning behind this term varies markedly and can range from a set of creative and technical skills under the label "critical thinking" to a desire to encourage engagement, action and political emancipation, often labelled "critical pedagogy". This paper distinguishes these manifestations of the "critical" and, based on an analysis of the prevailing models of critical pedagogy and citizenship education, develops a conceptual framework for analysing and comparing the nature of critical citizenship