Realising formal groups

We show that a large class of formal groups can be realised functorially by even periodic ring spectra. The main advance is in the construction of morphisms, not of objects.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-8.abs.htm

Common subbundles and intersections of divisors

Let V_0 and V_1 be complex vector bundles over a space X. We use the theory of divisors on formal groups to give obstructions in generalised cohomology that vanish when V_0 and V_1 can be embedded in a bundle U in such a way that V_0\cap V_1 has dimension at least k everywhere. We study various algebraic universal examples related to this question, and show that they arise from the generalised cohomology of corresponding topological universal examples. This extends and reinterprets earlier work on degeneracy classes in ordinary cohomology or intersection theory.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-42.abs.htm

Complex cobordism of involutions

We give a simple and explicit presentation of the Z/2-equivariant complex cobordism ring.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper11.abs.htm

Scalable iterative methods for sampling from massive Gaussian random vectors

Sampling from Gaussian Markov random fields (GMRFs), that is multivariate Gaussian ran- dom vectors that are parameterised by the inverse of their covariance matrix, is a fundamental problem in computational statistics. In this paper, we show how we can exploit arbitrarily accu- rate approximations to a GMRF to speed up Krylov subspace sampling methods. We also show that these methods can be used when computing the normalising constant of a large multivariate Gaussian distribution, which is needed for both any likelihood-based inference method. The method we derive is also applicable to other structured Gaussian random vectors and, in particu- lar, we show that when the precision matrix is a perturbation of a (block) circulant matrix, it is still possible to derive O(n log n) sampling schemes.Comment: 17 Pages, 4 Figure

An approach to the synthesis of biological tissue

Mathematical phantoms developed to synthesize realistic complex backgrounds such as those obtained when imaging biological tissue, play a key role in the quantitative assessment of image quality for medical and biomedical imaging. We present a modeling framework for the synthesis of realistic tissue samples. The technique is demonstrated using radiological breast tissue. The model employs a two-component image decomposition consisting of a slowly, spatially varying mean-background and a residual texture image. Each component is synthesized independently. The approach and results presented here constitute an important step towards developing methods for the quantitative assessment of image quality in medical and biomedical imaging, and more generally image science

Feedback in the local LBG Analog Haro 11 as probed by far-UV and X-ray observations

We have re-analyzed FUSE data and obtained new Chandra observations of Haro 11, a local (D_L=88 Mpc) UV luminous galaxy. Haro 11 has a similar far-UV luminosity (10^10.3 L_\odot), UV surface brightness (10^9.4 L_\odot kpc^-2), SFR, and metallicity to that observed in Lyman Break Galaxies (LBGs). We show that Haro 11 has extended, soft thermal (kT~0.68 keV) X-ray emission with a luminosity and size which scales with the physical properties (e.g. SFR, stellar mass) of the host galaxy. An enhanced alpha/Fe, ratio of ~4 relative to solar abundance suggests significant supernovae enrichment. These results are consistent with the X-ray emission being produced in a shock between a supernovae driven outflow and the ambient material. The FUV spectra show strong absorption lines similar to those observed in LBG spectra. A blueshifted absorption component is identified as a wind outflowing at ~200-280 km/s. OVI\lambda\lambda1032,1038 emission, the dominant cooling mechanism for coronal gas at T~10^5.5 K is also observed. If associated with the outflow, the luminosity of the OVI emission suggests that <20% of the total mechanical energy from the supernovae and solar winds is being radiated away. This implies that radiative cooling through OVI is not significantly inhibiting the growth of the outflowing gas. In contradiction to the findings of Bergvall et al 2006, we find no convincing evidence of Lyman continuum leakage in Haro 11. We conclude that the wind has not created a `tunnel' allowing the escape of a significant fraction of Lyman continuum photons and place a limit on the escape fraction of f_{esc}<2%. Overall, both Haro 11 and a previously observed LBG analogue VV 114, provide an invaluable insight into the X-ray and FUV properties of high redshift LBGs.Comment: Accepted for publication in ApJ, 40 pages, 17 figure

Spatially Resolved Spitzer-IRS Spectroscopy of the Central Region of M82

We present high spatial resolution (~ 35 parsec) 5-38 um spectra of the central region of M82, taken with the Spitzer Infrared Spectrograph. From these spectra we determined the fluxes and equivalent widths of key diagnostic features, such as the [NeII]12.8um, [NeIII]15.5um, and H_2 S(1)17.03um lines, and the broad mid-IR polycyclic aromatic hydrocarbon (PAH) emission features in six representative regions and analysed the spatial distribution of these lines and their ratios across the central region. We find a good correlation of the dust extinction with the CO 1-0 emission. The PAH emission follows closely the ionization structure along the galactic disk. The observed variations of the diagnostic PAH ratios across M82 can be explained by extinction effects, within systematic uncertainties. The 16-18um PAH complex is very prominent, and its equivalent width is enhanced outwards from the galactic plane. We interpret this as a consequence of the variation of the UV radiation field. The EWs of the 11.3um PAH feature and the H_2 S(1) line correlate closely, and we conclude that shocks in the outflow regions have no measurable influence on the H_2 emission. The [NeIII]/[NeII] ratio is on average low at ~0.18, and shows little variations across the plane, indicating that the dominant stellar population is evolved (5 - 6 Myr) and well distributed. There is a slight increase of the ratio with distance from the galactic plane of M82 which we attribute to a decrease in gas density. Our observations indicate that the star formation rate has decreased significantly in the last 5 Myr. The quantities of dust and molecular gas in the central area of the galaxy argue against starvation and for negative feedback processes, observable through the strong extra-planar outflows.Comment: 15 pages, 12 figures, 3 tables, ApJ, emulateap

Laser Stabilization at 1536 nm Using Regenerative Spectral Hole Burning

Laser frequency stabilization giving a 500-Hz Allan deviation for a 2-ms integration time with drift reduced to 7 kHz/min over several minutes was achieved at 1536 nm in the optical communication band. A continuously regenerated spectral hole in the inhomogeneously broadened 4I15/2(1)!4I13/2(1) optical absorption of an Er31:Y2SiO5 crystal was used as the short-term frequency reference, while a variation on the locking technique allowed simultaneous use of the inhomogeneously broadened absorption line as a long-term reference. The reported frequency stability was achieved without vibration isolation. Spectral hole burning frequency stabilization provides ideal laser sources for high-resolution spectroscopy, real-time optical signal processing, and a range of applications requiring ultra-narrow-band light sources or coherent detection; the time scale for stability and the compatibility with spectral hole burning devices make this technique complementary to other frequency references for laser stabilization