Expanding the Family of Grassmannian Kernels: An Embedding Perspective

Modeling videos and image-sets as linear subspaces has proven beneficial for many visual recognition tasks. However, it also incurs challenges arising from the fact that linear subspaces do not obey Euclidean geometry, but lie on a special type of Riemannian manifolds known as Grassmannian. To leverage the techniques developed for Euclidean spaces (e.g, support vector machines) with subspaces, several recent studies have proposed to embed the Grassmannian into a Hilbert space by making use of a positive definite kernel. Unfortunately, only two Grassmannian kernels are known, none of which -as we will show- is universal, which limits their ability to approximate a target function arbitrarily well. Here, we introduce several positive definite Grassmannian kernels, including universal ones, and demonstrate their superiority over previously-known kernels in various tasks, such as classification, clustering, sparse coding and hashing

Type Ia supernovae from exploding oxygen-neon white dwarfs

The progenitor problem of Type Ia supernovae (SNe Ia) is still unsolved. Most of these events are thought to be explosions of carbon-oxygen (CO) white dwarfs (WDs), but for many of the explosion scenarios, particularly those involving the externally triggered detonation of a sub-Chandrasekhar mass WD (sub-M Ch WD), there is also a possibility of having an oxygen-neon (ONe) WD as progenitor. We simulate detonations of ONe WDs and calculate synthetic observables from these models. The results are compared with detonations in CO WDs of similar mass and observational data of SNe Ia. We perform hydrodynamic explosion simulations of detonations in initially hydrostatic ONe WDs for a range of masses below the Chandrasekhar mass (M Ch), followed by detailed nucleosynthetic postprocessing with a 384-isotope nuclear reaction network. The results are used to calculate synthetic spectra and light curves, which are then compared with observations of SNe Ia. We also perform binary evolution calculations to determine the number of SNe Ia involving ONe WDs relative to the number of other promising progenitor channels. The ejecta structures of our simulated detonations in sub-M Ch ONe WDs are similar to those from CO WDs. There are, however, small systematic deviations in the mass fractions and the ejecta velocities. These lead to spectral features that are systematically less blueshifted. Nevertheless, the synthetic observables of our ONe WD explosions are similar to those obtained from CO models. Our binary evolution calculations show that a significant fraction (3-10%) of potential progenitor systems should contain an ONe WD. The comparison of our ONe models with our CO models of comparable mass (1.2 Msun) shows that the less blueshifted spectral features fit the observations better, although they are too bright for normal SNe Ia.Comment: 6 pages, 5 figure

Deflagrations in hybrid CONe white dwarfs: a route to explain the faint Type Iax supernova 2008ha

Stellar evolution models predict the existence of hybrid white dwarfs (WDs) with a carbon-oxygen core surrounded by an oxygen-neon mantle. Being born with masses ~1.1 Msun, hybrid WDs in a binary system may easily approach the Chandrasekhar mass (MCh) by accretion and give rise to a thermonuclear explosion. Here, we investigate an off-centre deflagration in a near-MCh hybrid WD under the assumption that nuclear burning only occurs in carbon-rich material. Performing hydrodynamics simulations of the explosion and detailed nucleosynthesis post-processing calculations, we find that only 0.014 Msun of material is ejected while the remainder of the mass stays bound. The ejecta consist predominantly of iron-group elements, O, C, Si and S. We also calculate synthetic observables for our model and find reasonable agreement with the faint Type Iax SN 2008ha. This shows for the first time that deflagrations in near-MCh WDs can in principle explain the observed diversity of Type Iax supernovae. Leaving behind a near-MCh bound remnant opens the possibility for recurrent explosions or a subsequent accretion-induced collapse in faint Type Iax SNe, if further accretion episodes occur. From binary population synthesis calculations, we find the rate of hybrid WDs approaching MCh to be on the order of 1 percent of the Galactic SN Ia rate.Comment: 9 pages, 7 figures, 2 tables, accepted for publication in MNRA

Statistical analysis plan for the Stroke Oxygen Study (SO₂S): a multi-center randomized controlled trial to assess whether routine oxygen supplementation in the first 72 hours after a stroke improves long-term outcome.

BACKGROUND: The Stroke Oxygen Study (SO₂S) is a multi-center randomized controlled trial of oxygen supplementation in patients with acute stroke. The main hypothesis for the trial is that fixed-dose oxygen treatment during the first 3 days after an acute stroke improves outcome. The secondary hypothesis is that restricting oxygen supplementation to night time only is more effective than continuous supplementation. This paper describes the statistical analysis plan for the study. METHODS AND DESIGN: Patients (n = 8000) are randomized to three groups: (1) continuous oxygen supplementation for 72 hours; (2) nocturnal oxygen supplementation for three nights; and (3) no routine oxygen supplementation. Outcomes are recorded at 7 days, 90 days, 6 months, and 12 months. The primary outcome measure is the modified Rankin scale at 90 days. Data will be analyzed according to the intention-to-treat principle. Methods of statistical analysis are described, including the handling of missing data, the covariates used in adjusted analyses, planned subgroups analyses, and planned sensitivity analyses. TRIAL REGISTRATION: This trial is registered with the ISRCTN register, number ISRCTN52416964 (30 September 2005)

Three-dimensional simulations of gravitationally confined detonations compared to observations of SN 1991T

The gravitationally confined detonation (GCD) model has been proposed as a possible explosion mechanism for Type Ia supernovae in the single-degenerate evolution channel. Driven by buoyancy, a deflagration flame rises in a narrow cone towards the surface. For the most part, the flow of the expanding ashes remains radial, but upon reaching the outer, low-pressure layers of the white dwarf, an additional lateral component develops. This makes the deflagration ashes converge again at the opposite side, where the compression heats fuel and a detonation may be launched. To test the GCD explosion model, we perform a 3D simulation for a model with an ignition spot offset near the upper limit of what is still justifiable, 200 km. This simulation meets our deliberately optimistic detonation criteria and we initiate a detonation. The detonation burns through the white dwarf and leads to its complete disruption. We determine nucleosynthetic yields by post-processing 10^6 tracer particles with a 384 nuclide reaction network and we present multi-band light curves and time-dependent optical spectra. We find that our synthetic observables show a prominent viewing-angle sensitivity in UV and blue bands, which is in tension with observed SNe Ia. The strong dependence on viewing-angle is caused by the asymmetric distribution of the deflagration ashes in the outer ejecta layers. Finally, we perform a comparison of our model to SN 1991T. The overall flux-level of the model is slightly too low and the model predicts pre-maximum light spectral features due to Ca, S, and Si that are too strong. Furthermore, the model chemical abundance stratification qualitatively disagrees with recent abundance tomography results in two key areas: our model lacks low velocity stable Fe and instead has copious amounts of high-velocity 56Ni and stable Fe. We therefore do not find good agreement of the model with SN 1991T.Comment: 11 pages, accepted for publication in Astronomy & Astrophysic

Magnetic edge states in graphene in nonuniform magnetic fields

We theoretically study electronic properties of a graphene sheet on xy plane in a spatially nonuniform magnetic field, $B = B_0 \hat{z}$ in one domain and $B = B_1 \hat{z}$ in the other domain, in the quantum Hall regime and in the low-energy limit. We find that the magnetic edge states of the Dirac fermions, formed along the boundary between the two domains, have features strongly dependent on whether $B_0$ is parallel or antiparallel to $B_1$. In the parallel case, when the Zeeman spin splitting can be ignored, the magnetic edge states originating from the $n=0$ Landau levels of the two domains have dispersionless energy levels, contrary to those from the $n \ne 0$ levels. Here, $n$ is the graphene Landau-level index. They become dispersive as the Zeeman splitting becomes finite or as an electrostatic step potential is additionally applied. In the antiparallel case, the $n=0$ magnetic edge states split into electron-like and hole-like current-carrying states. The energy gap between the electron-like and hole-like states can be created by the Zeeman splitting or by the step potential. These features are attributed to the fact that the pseudo-spin of the magnetic edge states couples to the direction of the magnetic field. We propose an Aharonov-Bohm interferometry setup in a graphene ribbon for experimental study of the magnetic edge states.Comment: 8 pages, 6 figure

An equatorial wind from the massive young stellar object S140 IRS 1

The discovery of the second equatorial ionized stellar wind from a massive young stellar object is reported. High resolution radio continuum maps of S140 IRS 1 reveal a highly elongated source that is perpendicular to the larger scale bipolar molecular outflow. This picture is confirmed by location of a small scale monopolar near-IR reflection nebula at the base of the blueshifted lobe. A second epoch of observations over a five year baseline show little ordered outward proper motion of clumps as would have been expected for a jet. A third epoch, taken only 50 days after the second, did show significant changes in the radio morphology. These radio properties can all be understood in the context of an equatorial wind driven by radiation pressure from the central star and inner disc acting on the gas in the surface layers of the disc as proposed by Drew et al. (1998). This equatorial wind system is briefly compared with the one in S106IR, and contrasted with other massive young stellar objects that drive ionized jets.Comment: 19 pages, 5 figures, accepted by ApJ, minor changes in light of referees repor

Using late-time optical and near-infrared spectra to constrain Type Ia supernova explosion properties

The late-time spectra of Type Ia supernovae (SNe Ia) are powerful probes of the underlying physics of their explosions. We investigate the late-time optical and near-infrared spectra of seven SNe Ia obtained at the VLT with XShooter at $>$200 d after explosion. At these epochs, the inner Fe-rich ejecta can be studied. We use a line-fitting analysis to determine the relative line fluxes, velocity shifts, and line widths of prominent features contributing to the spectra ([Fe II], [Ni II], and [Co III]). By focussing on [Fe II] and [Ni II] emission lines in the ~7000-7500 \AA\ region of the spectrum, we find that the ratio of stable [Ni II] to mainly radioactively-produced [Fe II] for most SNe Ia in the sample is consistent with Chandrasekhar-mass delayed-detonation explosion models, as well as sub-Chandrasekhar mass explosions that have metallicity values above solar. The mean measured Ni/Fe abundance of our sample is consistent with the solar value. The more highly ionised [Co III] emission lines are found to be more centrally located in the ejecta and have broader lines than the [Fe II] and [Ni II] features. Our analysis also strengthens previous results that SNe Ia with higher Si II velocities at maximum light preferentially display blueshifted [Fe II] 7155 \AA\ lines at late times. Our combined results lead us to speculate that the majority of normal SN Ia explosions produce ejecta distributions that deviate significantly from spherical symmetry.Comment: 17 pages, 12 figure, accepted for publication in MNRA

Regional CNS responses to IFN-γ determine lesion localization patterns during EAE pathogenesis

The localization of inflammatory foci within the cerebellum is correlated to severe clinical outcomes in multiple sclerosis (MS). Previous studies of experimental autoimmune encephalomyelitis (EAE), a model of MS, revealed distinct clinical outcomes correlated with the capacity of the animal to produce IFN-γ. Outcomes were linked to localization of inflammatory cells in either the spinal cord (wild type [WT]) or the cerebellum and brain stem (IFN-γ deficient). We demonstrate, using an adoptive transfer system, that the ability of the central nervous system (CNS) to sense pathogenic T cell–produced IFN-γ during EAE initiation determines the sites of CNS pathogenesis. Transfer of WT Th1 cells into IFN-γ receptor–deficient mice results in pathogenic invasion of the brain stem and cerebellum with attendant clinical symptoms, which are identical to the disease observed after transfer of IFN-γ–deficient T cells to WT hosts. Inflammation of the spinal cord associated with classical EAE is abrogated in both IFN-γ–deficient systems. Cotransfer of CNS antigen-specific WT Th1 cells with IFN-γ–deficient T cells is sufficient to restore spinal cord invasion and block cerebellar and brain stem invasion. These data demonstrate that interaction between IFN-γ and host CNS cells during the initiation of EAE can selectively promote or suppress neuroinflammation and pathogenesis