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

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

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

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

Pattern selection in a lattice of pulse-coupled oscillators

We study spatio-temporal pattern formation in a ring of N oscillators with inhibitory unidirectional pulselike interactions. The attractors of the dynamics are limit cycles where each oscillator fires once and only once. Since some of these limit cycles lead to the same pattern, we introduce the concept of pattern degeneracy to take it into account. Moreover, we give a qualitative estimation of the volume of the basin of attraction of each pattern by means of some probabilistic arguments and pattern degeneracy, and show how are they modified as we change the value of the coupling strength. In the limit of small coupling, our estimative formula gives a perfect agreement with numerical simulations.Comment: 7 pages, 8 figures. To be published in Physical Review

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

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

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.

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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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