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

Intervening Metal Systems in GRB and QSO sight-lines: The Mgii and Civ Question

Prochter et al. 2006 recently found that the number density of strong intervening 0.5<z<2 MgII absorbers detected in gamma-ray burst (GRB) afterglow spectra is nearly 4 times larger than in QSO spectra. We have conducted a similar study using CIV absorbers. Our CIV sample, consisting of a total of 20 systems, is drawn from 3 high resolution and high to moderate S/N VLT/UVES spectra of 3 long-duration GRB afterglows, covering the redshift interval 1.6< z<3.1. The column density distribution and number density of this sample do not show any statistical difference with the same quantities measured in QSO spectra. We discuss several possibilities for the discrepancy between CIV and MgII absorbers and conclude that a higher dust extinction in the MgII QSO samples studied up to now would give the most straightforward solution. However, this effect is only important for the strong MgII absorbers. Regardless of the reasons for this discrepancy, this result confirms once more that GRBs can be used to detect a side of the universe that was unknown before, not necessarily connected with GRBs themselves, providing an alternative and fundamental investigative tool of the cosmic evolution of the universe.Comment: 21 pages, 4 figures, ApJ accepted, Revised after Referee Repor

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

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

Dust-to-metal ratios in damped Lyman-alpha absorbers: Fresh clues to the origins of dust and optical extinction towards gamma-ray bursts

Motivated by the anomalous dust-to-metal ratios derived in the literature for gamma-ray burst (GRB) damped Lyman-alpha absorbers (DLAs), we measure these ratios using the dust-depletion pattern observed in UV/optical afterglow spectra associated with the ISM at the GRB host-galaxy redshifts. Our sample consists of 20 GRB absorbers and a comparison sample of 72 QSO-DLAs with redshift 1.2 < z < 4.0 and down to Z = 0.002 Z_Sol metallicities. The dust-to-metal ratio in QSO- and GRB-DLAs increases both with metallicity and metal column density, spanning ~10--110% of the Galactic value and pointing to a non universal dust-to-metal ratio. The low values of dust-to-metal ratio suggest that low-metallicity systems have lower dust fractions than typical spiral galaxies and perhaps that the dust in these systems is produced inefficiently, i.e. by grain growth in the low-metallicity regime with negligible contribution from supernovae (SNe) and asymptotic giant branch (AGB) stars. On the other hand, some GRB- and QSO-DLAs show high dust-to-metal ratio values out to z ~ 4, requiring rapid dust production, such as in SN ejecta, but also in AGB winds and via grain growth for the highest metallicity systems. GRB-DLAs overall follow the dust-to-metal-ratio properties of QSO-DLAs, GRBs probing up to larger column and volume densities. For comparison, the dust-to-metal ratio that we derive for the SMC and LMC are ~82--100% and ~98% of the Galactic value, respectively. The literature dust-to-metal ratio of the low-metallicity galaxy I Zw 18 (< 37%) is consistent with the distribution that we find. The dust extinction Av increases steeply with the column density of iron in dust, N(Fe)dust, calculated from relative metal abundances, confirming that dust extinction is mostly occurring in the host galaxy ISM. Most GRB-DLAs display log N(Fe)dust > 14.7, above which several QSO-DLAs reveal H2 (abridged).Comment: 14 pages, 9 figures. A&A, in pres

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

Looking for signatures of the Left-Right Twin Higgs model with the ATLAS detector at the LHC

The twin Higgs mechanism has recently been proposed to solve the little hierarchy problem. The phenomenology of this model is presented, and the possibility to observe some of the signatures predicted by this model using the ATLAS detector at the LHC is discussed

Gas and dust properties in the afterglow spectra of GRB 050730

We present early WHT ISIS optical spectroscopy of the afterglow of gamma-ray burst GRB 050730. The spectrum shows a DLA system with the highest measured hydrogen column to date: N(HI) = 22.1 +/- 0.1 at the third-highest GRB redshift z = 3.968. Our analysis of the Swift XRT X-ray observations of the early afterglow show X-ray flares accompanied by decreasing X-ray absorption. From both the optical and the X-ray spectra we constrain the dust and gas properties of the host galaxy. We find the host to be a low metallicity galaxy, with low dust content. Much of the X-ray absorbing gas is situated close to the GRB, whilst the HI absorption causing the DLA is most likely located further out.Comment: 5 pages, 2 figures. Accepted for A&A Letter