Reduction criterion for separability

We introduce a separability criterion based on the positive map Γ:ρ→(Tr ρ)-ρ, where ρ is a trace-class Hermitian operator. Any separable state is mapped by the tensor product of Γ and the identity into a non-negative operator, which provides a simple necessary condition for separability. This condition is generally not sufficient because it is vulnerable to the dilution of entanglement. In the special case where one subsystem is a quantum bit, Γ reduces to time reversal, so that this separability condition is equivalent to partial transposition. It is therefore also sufficient for 2×2 and 2×3 systems. Finally, a simple connection between this map for two qubits and complex conjugation in the “magic” basis [Phys. Rev. Lett. 78, 5022 (1997)] is displayed

Photometric redshifts as a tool to study the Coma cluster galaxy populations

We investigate the Coma cluster galaxy luminosity function (GLF) at faint magnitudes, in particular in the u* band by applying photometric redshift techniques applied to deep u*, B, V, R, I images covering a region of ~1deg2 (R 24). Global and local GLFs in the B, V, R and I bands obtained with photometric redshift selection are consistent with our previous results based on a statistical background subtraction. In the area covered only by the u* image, the GLF was also derived after applying a statistical background subtraction. The GLF in the u* band shows an increase of the faint end slope towards the outer regions of the cluster (from alpha~1 in the cluster center to alpha~2 in the cluster periphery). This could be explained assuming a short burst of star formation in these galaxies when entering the cluster. The analysis of the multicolor type spatial distribution reveals that late type galaxies are distributed in clumps in the cluster outskirts, where X-ray substructures are also detected and where the GLF in the u* band is steeper.Comment: 14 pages, 2 figures in jpeg format, accepted in A&

On the nature of faint Low Surface Brightness galaxies in the Coma cluster

This project is the continuation of our study of faint Low Surface Brightness Galaxies (fLSBs) in one of the densest nearby galaxy regions known, the Coma cluster. Our goal is to improve our understanding of the nature of these objects by comparing the broad band spectral energy distribution with population synthesis models. The data were obtained with the MEGACAM and CFH12K cameras at the CFHT. We used the resulting photometry in 5 broad band filters (u*, B, V, R, and I), that included new u*-band data, to fit spectral models. With these spectral fits we inferred a cluster membership criterium, as well as the ages, dust extinctions, and photometric types of these fLSBs. We show that about half of the Coma cluster fLSBs have a spectral energy distribution well represented in our template library while the other half present a flux deficit at ultraviolet wavelengths. Among the well represented, ~80% are probably part of the Coma cluster based on their spectral energy distribution. They are relatively young (younger than 2.3 Gyrs for 90% of the sample) non-starburst objects. The later their type, the younger fLSBs are. A significant part of the fLSBs are quite dusty objects. fLSBs are low stellar mass objects (the later their type the less massive they are), with stellar masses comparable to globular clusters for the faintest ones. Their characteristics are correlated with infall directions, confirming the disruptive origin for part of them.Comment: Accepted for publication in A&A, 10 pages, 10 figure

A Possible Case of Neurogenic Pulmonary Edema in a Sheep following Intracranial Surgery

A 3-year-old female crossbred sheep weighing 64 kg was anaesthetized for intracranial surgery as a part of a research project. Premedication and induction of anesthesia were uneventful as well as tracheal intubation. Anesthesia was maintained with isoflurane in a 50% mixture of oxygen and air, fentanyl (5-15 µg kg-1h-1) and lidocaine (1.8 mg kg-1h-1). During anesthesia, an increased alveolar-arterial oxygen gradient was calculated on the basis of arterial blood gas analysis: inspiratory fraction of oxygen was increased and a recruitment manoeuvre was performed. After 210 minutes of anesthesia, the sheep was let recover with oxygen supplementation under monitoring of pulse-oxymetry, capnography, inspired and expired oxygen, temperature and invasive blood pressure. At tracheal extubation no signs of regurgitation or aspiration were noticed. Twenty-five minutes later, the sheep showed deterioration of neurological status and clonic seizure responsive to diazepam. After transient tachycardia, blood pressure rose acutely and sinus bradycardia followed. Severe tachypnea started in few minutes accompanied by loud respiratory noises and harsh diffuse crackles on both sides of the thorax. Foamy blood nasal exudates discharged from the nostrils. Neurogenic pulmonary edema as a sequel of increased intracranial pressure was suspected and treated with intravenous mannitol (0.5 gkg-1) and furosemide (4 mgKg-1). Hypoxemia was successfully managed with oxygen supplementation. Motor and cognitive functions improved progressively and were deemed normal within 12 hours from the episode, when arterial partial pressure of oxygen was 11.7 kPa (88 mmHg) at room air

Coma cluster object populations down to M_R~-9.5

This study follows a recent analysis of the galaxy luminosity functions and colour-magnitude red sequences in the Coma cluster (Adami et al. 2007). We analyze here the distribution of very faint galaxies and globular clusters in an east-west strip of $\sim 42 \times 7$ arcmin$^2$ crossing the Coma cluster center (hereafter the CS strip) down to the unprecedented faint absolute magnitude of M$_R \sim -9.5$. This work is based on deep images obtained at the CFHT with the CFH12K camera in the B, R, and I bands. The analysis shows that the observed properties strongly depend on the environment, and thus on the cluster history. When the CS is divided into four regions, the westernmost region appears poorly populated, while the regions around the brightest galaxies NGC 4874 and NGC 4889 (NGC 4874 and NGC 4889 being masked) are dominated by faint blue galaxies. They show a faint luminosity function slope of -2, very significantly different from the field estimates. Results are discussed in the framework of galaxy destruction (which can explain part of the very faint galaxy population) and of structures infalling on to Coma.Comment: To be published in A&

Stability and symmetry-breaking bifurcation for the ground states of a NLS with a δ′\delta^\prime interaction

We determine and study the ground states of a focusing Schr\"odinger equation in dimension one with a power nonlinearity $|\psi|^{2\mu} \psi$ and a strong inhomogeneity represented by a singular point perturbation, the so-called (attractive) $\delta^\prime$ interaction, located at the origin. The time-dependent problem turns out to be globally well posed in the subcritical regime, and locally well posed in the supercritical and critical regime in the appropriate energy space. The set of the (nonlinear) ground states is completely determined. For any value of the nonlinearity power, it exhibits a symmetry breaking bifurcation structure as a function of the frequency (i.e., the nonlinear eigenvalue) $\omega$. More precisely, there exists a critical value \om^* of the nonlinear eigenvalue \om, such that: if \om_0 < \om < \om^*, then there is a single ground state and it is an odd function; if \om > \om^* then there exist two non-symmetric ground states. We prove that before bifurcation (i.e., for \om < \om^*) and for any subcritical power, every ground state is orbitally stable. After bifurcation (\om =\om^*+0), ground states are stable if $\mu$ does not exceed a value $\mu^\star$ that lies between 2 and 2.5, and become unstable for $\mu > \mu^*$. Finally, for $\mu > 2$ and \om \gg \om^*, all ground states are unstable. The branch of odd ground states for \om \om^*, obtaining a family of orbitally unstable stationary states. Existence of ground states is proved by variational techniques, and the stability properties of stationary states are investigated by means of the Grillakis-Shatah-Strauss framework, where some non standard techniques have to be used to establish the needed properties of linearization operators.Comment: 46 pages, 5 figure

Critical and Near-Critical Branching Processes

Scale-free dynamics in physical and biological systems can arise from a variety of causes. Here, we explore a branching process which leads to such dynamics. We find conditions for the appearance of power laws and study quantitatively what happens to these power laws when such conditions are violated. From a branching process model, we predict the behavior of two systems which seem to exhibit near scale-free behavior--rank-frequency distributions of number of subtaxa in biology, and abundance distributions of genotypes in an artificial life system. In the light of these, we discuss distributions of avalanche sizes in the Bak-Tang-Wiesenfeld sandpile model.Comment: 9 pages LaTex with 10 PS figures. v.1 of this paper contains results from non-critical sandpile simulations that were excised from the published versio

The CFH Optical PDCS survey (COP) I: The Data

This paper presents and gives the COP (COP: CFHT Optical PDCS; CFHT: Canada-France-Hawaii Telescope; PDCS: Palomar Distant Cluster Survey) survey data. We describe our photometric and spectroscopic observations with the MOS multi-slit spectrograph at the CFH telescope. A comparison of the photometry from the PDCS (Postman et al. 1996) catalogs and from the new images we have obtained at the CFH telescope shows that the different magnitude systems can be cross-calibrated. After identification between the PDCS catalogues and our new images, we built catalogues with redshift, coordinates and V, I and Rmagnitudes. We have classified the galaxies along the lines of sight into field and structure galaxies using a gap technique (Katgert et al. 1996). In total we have observed 18 significant structures along the 10 lines of sight.Comment: 40 pages, 13 figures, accepted in A