An augmented moment method for stochastic ensembles with delayed couplings: II. FitzHugh-Nagumo model

Dynamics of FitzHugh-Nagumo (FN) neuron ensembles with time-delayed couplings subject to white noises, has been studied by using both direct simulations and a semi-analytical augmented moment method (AMM) which has been proposed in a recent paper [H. Hasegawa, E-print: cond-mat/0311021]. For $N$-unit FN neuron ensembles, AMM transforms original $2N$-dimensional {\it stochastic} delay differential equations (SDDEs) to infinite-dimensional {\it deterministic} DEs for means and correlation functions of local and global variables. Infinite-order recursive DEs are terminated at the finite level $m$ in the level-$m$ AMM (AMM$m$), yielding $8(m+1)$-dimensional deterministic DEs. When a single spike is applied, the oscillation may be induced if parameters of coupling strength, delay, noise intensity and/or ensemble size are appropriate. Effects of these parameters on the emergence of the oscillation and on the synchronization in FN neuron ensembles have been studied. The synchronization shows the {\it fluctuation-induced} enhancement at the transition between non-oscillating and oscillating states. Results calculated by AMM5 are in fairly good agreement with those obtained by direct simulations.Comment: 15 pages, 3 figures; changed the title with correcting typos, accepted in Phys. Rev. E with some change

On inferring extinction laws in z~6 quasars as signatures of supernova dust

Unusual extinction curves of high-redshift QSOs have been taken as evidence that dust is primarily produced by supernovae at high redshift. In particular, the 3000 A Todini-Ferrara-Maiolino kink in the extinction curve of the z = 6.20 SDSS J1048+4637 has been attributed to supernova dust. Here we discuss the challenges in inferring robust extinction curves of high-redshift QSOs and critically assess previous claims of detection of supernova dust. In particular, we address the sensitivity to the choice of intrinsic QSO spectrum, the need for a long wavelength baseline, and the drawbacks in fitting theoretical extinction curves. In a sample of 21 QSOs at z ~ 6 we detect significant ultraviolet extinction using existing broad-band optical, near-infrared, and Spitzer photometry. The median extinction curve is consistent with a Small Magellanic Cloud curve with A_1450 ~ 0.7 mag and does not exhibit any conspicuous (restframe) 2175 A or 3000 A features. For two QSOs, SDSS J1044-0125 at z = 5.78 and SDSS J1030+0524 at z = 6.31, we further present X-shooter spectra covering the wavelength range 0.9-2.5 um. The resulting non-parametric extinction curves do not exhibit the 3000 A kink. Finally, in a re-analysis of literature spectra of SDSS J1048+4637, we do not find evidence for a conspicuous kink. We conclude that the existing evidence for a 3000 A feature is weak and that the overall dust properties at high and low redshift show no significant differences. This, however, does not preclude supernovae from dominating the dust budget at high redshift.Comment: 13 pages, 13 figures, ApJ, in pres

The host galaxy of GRB010222: The strongest damped Lyman-alpha system known

Analysis of the absorption lines in the afterglow spectrum of the gamma-ray burst GRB010222 indicates that its host galaxy (at a redshift of z=1.476) is the strongest damped Lyman-alpha (DLA) system known, having a very low metallicity and modest dust content. This conclusion is based on the detection of the red wing of Lyman-alpha plus a comparison of the equivalent widths of ultraviolet Mg I, Mg II, and Fe II lines with those in other DLAs. The column density of H I, deduced from a fit to the wing of Lyman-alpha, is (5 +/- 2) 10^22 cm^-2. The ratio of the column densities of Zn and Cr lines suggests that the dust content in our line of sight through the galaxy is low. This could be due to either dust destruction by the ultraviolet emission of the afterglow or to an initial dust composition different to that of the diffuse interstellar material, or a combination of both.Comment: Submitted to MNRAS 12 page

Dynamically-Coupled Oscillators -- Cooperative Behavior via Dynamical Interaction --

We propose a theoretical framework to study the cooperative behavior of dynamically coupled oscillators (DCOs) that possess dynamical interactions. Then, to understand synchronization phenomena in networks of interneurons which possess inhibitory interactions, we propose a DCO model with dynamics of interactions that tend to cause 180-degree phase lags. Employing an approach developed here, we demonstrate that although our model displays synchronization at high frequencies, it does not exhibit synchronization at low frequencies because this dynamical interaction does not cause a phase lag sufficiently large to cancel the effect of the inhibition. We interpret the disappearance of synchronization in our model with decreasing frequency as describing the breakdown of synchronization in the interneuron network of the CA1 area below the critical frequency of 20 Hz.Comment: 10 pages, 3 figure

Photometric Variability in the Faint Sky Variability Survey

The Faint Sky Variability Survey (FSVS) is aimed at finding photometric and/or astrometric variable objects between 16th and 24th mag on time-scales between tens of minutes and years with photometric precisions ranging from 3 millimag to 0.2 mag. An area of 23 deg$^2$, located at mid and high Galactic latitudes, was covered using the Wide Field Camera (WFC) on the 2.5-m Isaac Newton Telescope (INT) on La Palma. Here we present some preliminary results on the variability of sources in the FSVS.Comment: 4 pages, 3 figures, to appear in 14th European Workshop on White Dwarfs, ASP Conference Series, eds. D. Koester, S. Moehle

The discovery of polarization in the afterglow of GRB 990510 with the ESO Very Large Telescope

Following a BeppoSAX alert (Piro 1999a) and the discovery of the OT at SAAO (Vreeswijk et al. 1999a), we observed GRB 990510 with the FORS instrument on ESO's VLT Unit 1 (`Antu'). The burst is unremarkable in gamma rays, but in optical is the first one to show good evidence for jet-like outflow (Stanek et al. 1999, Harrison et al. 1999). We report the detection of significant linear polarization in the afterglow: it is (1.6 +/- 0.2)% 0.86 days after trigger, and after 1.81 days is consistent with that same value, but much more uncertain. The polarization angle is constant on a time scale of hours, and may be constant over one day. We conclude that the polarization is intrinsic to the source and due to the synchrotron nature of the emission, and discuss the random and ordered field geometries that may be responsible for it.Comment: submitted to ApJ Lett., 5 pages including 2 figures, uses emulateapj.st

SCUBA observations of the host galaxies of four dark gamma-ray bursts

We present the results of a search for submillimetre-luminous host galaxies of optically dark gamma-ray bursts (GRBs) using the Submillimetre Common-User Bolometer Array (SCUBA) on the James Clerk Maxwell Telescope (JCMT). We made photometry measurements of the 850-micron flux at the location of four `dark bursts', which are those with no detected optical afterglow despite rapid deep searches, and which may therefore be within galaxies containing substantial amounts of dust. We were unable to detect any individual source significantly. Our results are consistent with predictions for the host galaxy population as a whole, rather than for a subset of dusty hosts. This indicates that optically dark GRBs are not especially associated with very submillimetre-luminous galaxies and so cannot be used as reliable indicators of dust-enshrouded massive star-formation activity. Further observations are required to establish the relationship between the wider GRB host galaxy population and SCUBA galaxies.Comment: 6 pages. Accepted for publication in MNRA

Adaptation Reduces Variability of the Neuronal Population Code

Sequences of events in noise-driven excitable systems with slow variables often show serial correlations among their intervals of events. Here, we employ a master equation for general non-renewal processes to calculate the interval and count statistics of superimposed processes governed by a slow adaptation variable. For an ensemble of spike-frequency adapting neurons this results in the regularization of the population activity and an enhanced post-synaptic signal decoding. We confirm our theoretical results in a population of cortical neurons.Comment: 4 pages, 2 figure

GRB990712: First Indication of Polarization Variability in a Gamma-ray Burst Afterglow

We report the detection of significant polarization in the optical afterglow of GRB990712 on three instances 0.44, 0.70 and 1.45 days after the gamma-ray burst, with (P, theta) being (2.9% +- 0.4%, 121.1 degr +- 3.5 degr), (1.2% +- 0.4%, 116.2 degr +- 10.1 degr) and (2.2% +- 0.7%, 139.2 degr +- 10.4 degr) respectively. The polarization is intrinsic to the afterglow. The degree of polarization is not constant, and smallest at the second measurement. The polarization angle does not vary significantly during these observations. We find that none of the existing models predict such polarization variations at constant polarization angle, and suggest ways in which these models might be modified to accommodate the observed behavior of this afterglow.Comment: 10 pages including 6 figures, accepted by ApJ. Uses aastex 5.

iPTF13beo: The Double-Peaked Light Curve of a Type Ibn Supernova Discovered Shortly after Explosion

We present optical photometric and spectroscopic observations of the Type Ibn (SN 2006jc-like) supernova iPTF13beo. Detected by the intermediate Palomar Transient Factory ~3 hours after the estimated first light, iPTF13beo is the youngest and the most distant (~430 Mpc) Type Ibn event ever observed. The iPTF13beo light curve is consistent with light curves of other Type Ibn SNe and with light curves of fast Type Ic events, but with a slightly faster rise-time of two days. In addition, the iPTF13beo R-band light curve exhibits a double-peak structure separated by ~9 days, not observed before in any Type Ibn SN. A low-resolution spectrum taken during the iPTF13beo rising stage is featureless, while a late-time spectrum obtained during the declining stage exhibits narrow and intermediate-width He I and Si II features with FWHM ~ 2000-5000 km/s and is remarkably similar to the prototypical SN Ibn 2006jc spectrum. We suggest that our observations support a model of a massive star exploding in a dense He-rich circumstellar medium (CSM). A shock breakout in a CSM model requires an eruption releasing a total mass of ~0.1 Msun over a time scale of couple of weeks prior to the SN explosion.Comment: 8 pages, 5 figures, submitted to MNRA