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

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 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

Integrate and Fire Neural Networks, Piecewise Contractive Maps and Limit Cycles

We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the stable asymptotic dynamics consists of limit cycles. We also find sufficient conditions for the synchronization of networks containing excitatory neurons. The proofs are based on the analysis of the equivalent dynamics of a piecewise continuous Poincar\'e map associated to the system. We show that for strong interactions the Poincar\'e map is piecewise contractive. Using this contraction property, we prove that there exist a countable number of limit cycles attracting all the orbits dropping into the stable subset of the phase space. This result applies not only to the Poincar\'e map under study, but also to a wide class of general n-dimensional piecewise contractive maps.Comment: 46 pages. In this version we added many comments suggested by the referees all along the paper, we changed the introduction and the section containing the conclusions. The final version will appear in Journal of Mathematical Biology of SPRINGER and will be available at http://www.springerlink.com/content/0303-681

SCUBA sub-millimeter observations of gamma-ray bursters. I. GRB 970508, 971214, 980326, 980329, 980519, 980703

We discuss the first results of our ongoing program of Target of Opportunity observations of gamma-ray bursts (GRBs) using the SCUBA instrument on the James Clerk Maxwell Telescope. We present the results for GRB 970508, 971214, 980326, 980329, 980519, and 980703. Our most important result to date is the detection of a fading counterpart to GRB 980329 at 850 microns. Although it proved to be difficult to find the infrared counterpart to this burst, the sub-millimeter flux was relatively bright. This indicates that intrinsically the brightness of this counterpart was very similar to GRB 970508. The radio through sub-millimeter spectrum of GRB 980329 is well fit by a power law with index alpha = +0.9. However, we cannot exclude a nu^(1/3) power law attenuated by synchrotron self-absorption. An alpha = +1 VLA-SCUBA power law spectrum is definitely ruled out for GRB 980703, and possibly also for GRB 980519. We cannot rule out that part of the sub-millimeter flux from GRB 980329 comes from a dusty star-forming galaxy at high redshift, such as the ones recently discovered by SCUBA. Any quiescent dust contribution will be much larger at sub-millimeter than at radio wavelengths. Both a high redshift and large dust extinction would help explain the reddening of the counterpart to GRB 980329, and a redshift of z = 5 has been suggested. The large intensity of this burst might then indicate that beaming is important.Comment: 6 pages, 3 figures, submitted to Astronomy and Astrophysic

The Supreme Court and the American Civil Liberties Union\u27s Colorblind Protection of Cross Burning in First Amendment Jurisprudence Legitimates White Supremacy

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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.

VLT observations of GRB 990510 and its environment

We present BVRI photometry and spectrophotometry of GRB990510 obtained with the ESO VLT/Antu telescope during the late decline phase. Between days 8 and 29 after the burst, the afterglow faded from R=24.2 to ~26.4. The spectral flux distribution and the light curve support the interpretation of the afterglow as synchrotron emission from a jet. The light curve is consistent with the optical transient alone but an underlying SN with maximum brightness R>27.4 or a galaxy with R>27.6 (3-sigma upper limits) cannot be ruled out. To a 5-sigma detection threshold of R=26.1, no galaxy is found within 6'' of the transient. A very blue V~24.5 extended object which may qualify as a starburst galaxy is located 12'' SE, but at unknown redshift.Comment: 5 pages A&A Latex, accepted for publication in A&A Letter

The star-formation rate in the host of GRB 990712

We have observed the host galaxy of GRB 990712 at 1.4 GHz with the Australia Telescope Compact Array, to obtain an estimate of its total star-formation rate. We do not detect a source at the position of the host. The 2 sigma upper limit of 70 microJy implies that the total star-formation rate is lower than 100 Msun/yr, using conservative values for the spectral index and cosmological parameters. This upper limit is in stark contrast with recent reports of radio/submillimeter-determined star-formation rates of roughly 500 Msun/yr for two other GRB host galaxies. Our observations present the deepest radio-determined star-formation rate limit on a GRB host galaxy yet, and show that also from the unobscured radio point-of-view, not every GRB host galaxy is a vigorous starburst.Comment: A&A Letters, in press, 5 pages; a high-resolution color gif version of the paper figure is also supplie