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

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

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

Phase-locking in weakly heterogeneous neuronal networks

We examine analytically the existence and stability of phase-locked states in a weakly heterogeneous neuronal network. We consider a model of N neurons with all-to-all synaptic coupling where the heterogeneity is in the firing frequency or intrinsic drive of the neurons. We consider both inhibitory and excitatory coupling. We derive the conditions under which stable phase-locking is possible. In homogeneous networks, many different periodic phase-locked states are possible. Their stability depends on the dynamics of the neuron and the coupling. For weak heterogeneity, the phase-locked states are perturbed from the homogeneous states and can remain stable if their homogeneous conterparts are stable. For enough heterogeneity, phase-locked solutions either lose stability or are destroyed completely. We analyze the possible states the network can take when phase-locking is broken.Comment: RevTex, 27 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

Effective traffic management based on bounded rationality and indifference bands

Constrained cognitive abilities cause imperfections in drivers' choice behaviour and appear largely systematic and predictable. This study introduces the concept of 'effective control space' to build upon this knowledge as an opportunity to increase the effectiveness of Dynamic Traffic Management (DTM). Within the control space boundaries it is assumed that drivers do not act upon the effects of DTM measures, they behave as being indifferent to them. This study debates that: (i) drivers' ability to detect changes in attributes of their trip or the performance of a traffic system is limited, (ii) drivers make mistakes in estimating the value of such changes and (iii) drivers apply a great diversity of choice patterns but do not necessary adapt their choice. Hence, for some DTM measures to be effective effects should not exceed the control space boundaries, whereas other DTM measures need to give drivers an incentive that exceeds these boundaries. Knowledge on the effective control space may support road authorities to operationalise their measures most effectively. With the theories of indifference bands and decision-making as starting point a theoretical and conceptual framework are provided, supported by a numerical example to demonstrate how application can steer a system towards its optimal state

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