Large Deviations for Nonlocal Stochastic Neural Fields

We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a $Q$-Wiener process and focus on noise-induced transitions and escape. We argue that proving a sharp Kramers' law for neural fields poses substanial difficulties but that one may transfer techniques from stochastic partial differential equations to establish a large deviation principle (LDP). Then we demonstrate that an efficient finite-dimensional approximation of the stochastic neural field equation can be achieved using a Galerkin method and that the resulting finite-dimensional rate function for the LDP can have a multi-scale structure in certain cases. These results form the starting point for an efficient practical computation of the LDP. Our approach also provides the technical basis for further rigorous study of noise-induced transitions in neural fields based on Galerkin approximations.Comment: 29 page

Dependence of Galaxy Shape on Environment in the Sloan Digital Sky Survey

Using a sample of galaxies from the Sloan Digital Sky Survey (SDSS) Data Release 4, we study the trends relating surface brightness profile type and apparent axis ratio to the local galaxy environment. We use the SDSS parameter `fracDeV' to quantify the profile type. We find that galaxies with M_r > -18 are mostly described by exponential profiles in all environments. Galaxies with -21 < M_r < -18 mainly have exponential profiles in low density environments and de Vaucouleurs profiles in high density environments. The most luminous galaxies, with M_r < -21, are mostly described by de Vaucouleurs profiles in all environments. For galaxies with M_r < -19, the fraction of de Vaucouleurs galaxies is a monotonically increasing function of local density, while the fraction of exponential galaxies is monotonically decreasing. For a fixed surface brightness profile type, apparent axis ratio is frequently correlated with environment. As the local density of galaxies increases, we find that for -20 < M_r < -18, galaxies of all profile types become slightly rounder, on average; for -22 < M_r < -20, galaxies with exponential profiles tend to become flatter, while galaxies with de Vaucouleurs profiles become rounder; for M_r < -22, galaxies with exponential profiles become flatter, while the de Vaucouleurs galaxies become rounder in their inner regions, yet exhibit no change in their outer regions. We comment on how the observed trends relate to the merger history of galaxies.Comment: 23 pages, 7 figures, accepted by Ap

QCD Corrections to Hadronic Z and tau Decays

We present a brief (mainly bibliographical) report on recently performed calculations of terms of order O(\alpha_s^4 n_f^2) and O(\alpha_s^4 n_f^2 m_q^2) for hadronic Z and \tau decay rates. A few details about the analytical evaluation of the masters integrals appearing in the course of calculations are presented.Comment: revised version (some references corrected); 3 pages, talk given at International Europhysics Conference on High Energy Physics, Aachen, Germany, 17-23 July 200

Automated image analysis to improve bead ingestion toxicity test counts in the protozoan Tetrahymena pyriformis

Prova de tipográfica (In Press).Aims: To improve bead ingestion counts in Tetrahymena pyriformis by automated image analysis as an alternative to direct-counts. Methods and Results: Fluorescent latex beads were added to T. pyriformis cultures for ingestion tests. The number of beads ingested by 25 cells was counted directly by epifluorescence microscopy and compared with similar data from image analysis. ANOVA indicated that counts were not significantly different (P < 0.05). The image analysis particularly provided advantages in terms of speed. Conclusions: The image analysis is superior to direct beads counting in T. pyriformis particularly in terms of speed of analysis. Significance and Impact of the Study: The image analysis method is very rapid and will allow many more toxicological analyses to be undertaken with less operator error

The Nature of the H2-Emitting Gas in the Crab Nebula

Understanding how molecules and dust might have formed within a rapidly expanding young supernova remnant is important because of the obvious application to vigorous supernova activity at very high redshift. In previous papers, we found that the H2 emission is often quite strong, correlates with optical low-ionization emission lines, and has a surprisingly high excitation temperature. Here we study Knot 51, a representative, bright example, for which we have available long slit optical and NIR spectra covering emission lines from ionized, neutral, and molecular gas, as well as HST visible and SOAR Telescope NIR narrow-band images. We present a series of CLOUDY simulations to probe the excitation mechanisms, formation processes and dust content in environments that can produce the observed H2 emission. We do not try for an exact match between model and observations given Knot 51's ambiguous geometry. Rather, we aim to explain how the bright H2 emission lines can be formed from within the volume of Knot 51 that also produces the observed optical emission from ionized and neutral gas. Our models that are powered only by the Crab's synchrotron radiation are ruled out because they cannot reproduce the strong, thermal H2 emission. The simulations that come closest to fitting the observations have the core of Knot 51 almost entirely atomic with the H2 emission coming from just a trace molecular component, and in which there is extra heating. In this unusual environment, H2 forms primarily by associative detachment rather than grain catalysis. In this picture, the 55 H2-emitting cores that we have previously catalogued in the Crab have a total mass of about 0.1 M_sun, which is about 5% of the total mass of the system of filaments. We also explore the effect of varying the dust abundance. We discuss possible future observations that could further elucidate the nature of these H2 knots.Comment: 51 pages, 15 figures, accepted for publication in MNRAS, revised Figure 12 results unchange

Photonic ring resonator filters for astronomical OH suppression

Ring resonators provide a means of filtering specific wavelengths from a waveguide, and optionally dropping the filtered wavelengths into a second waveguide. Both of these features are potentially useful for astronomical instruments. In this paper we focus on their use as notch filters to remove the signal from atmospheric OH emission lines from astronomical spectra, however we also briefly discuss their use as frequency combs for wavelength calibration and as drop filters for Doppler planet searches. We derive the design requirements for ring resonators for OH suppression from theory and finite difference time domain simulations. We find that rings with small radii (<10 microns) are required to provide an adequate free spectral range, leading to high index contrast materials such as Si and Si$_{3}$N$_{4}$. Critically coupled rings with high self-coupling coefficients should provide the necessary Q factors, suppression depth, and throughput for efficient OH suppression. We report on our progress in fabricating both Si and Si$_{3}$N$_{4}$ rings for OH suppression, and give results from preliminary laboratory tests. Our early devices show good control over the free spectral range and wavelength separation of multi-ring devices. The self-coupling coefficients are high (>0.9), but further optimisation is required to achieve higher Q and deeper notches, with current devices having $Q \approx 4000$ and $\approx 10$ dB suppression. The overall prospects for the use of ring resonators in astronomical instruments is promising, provided efficient fibre-chip coupling can be achieved.Comment: Submitted to Optics Express feature issue on Recent Advances in Astrophotonics (27 pages, 20 figs

The relation between SAR and the electromagnetic field distribution for heterogeneous exposure conditions

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