Renewal Approach to the Analysis of the Asynchronous State for Coupled Noisy Oscillators

We develop a framework in which the activity of nonlinear pulse-coupled oscillators is posed within the renewal theory. In this approach, the evolution of inter-event density allows for a self-consistent calculation that determines the asynchronous state and its stability. This framework, can readily be extended to the analysis of systems with more state variables. To exhibit this, we study a nonlinear pulse-coupled system, where couplings are dynamic and activity dependent. We investigate stability of this system and we show it undergoes a super-critical Hopf bifurcation to collective synchronization.Comment: 5 pages, 2 figure

How strong are correlations in strongly recurrent neuronal networks?

Cross-correlations in the activity in neural networks are commonly used to characterize their dynamical states and their anatomical and functional organizations. Yet, how these latter network features affect the spatiotemporal structure of the correlations in recurrent networks is not fully understood. Here, we develop a general theory for the emergence of correlated neuronal activity from the dynamics in strongly recurrent networks consisting of several populations of binary neurons. We apply this theory to the case in which the connectivity depends on the anatomical or functional distance between the neurons. We establish the architectural conditions under which the system settles into a dynamical state where correlations are strong, highly robust and spatially modulated. We show that such strong correlations arise if the network exhibits an effective feedforward structure. We establish how this feedforward structure determines the way correlations scale with the network size and the degree of the connectivity. In networks lacking an effective feedforward structure correlations are extremely small and only weakly depend on the number of connections per neuron. Our work shows how strong correlations can be consistent with highly irregular activity in recurrent networks, two key features of neuronal dynamics in the central nervous system

Emergent Orientation Selectivity from Random Networks in Mouse Visual Cortex

The connectivity principles underlying the emergence of orientation selectivity in primary visual cortex (V1) of mammals lacking an orientation map (such as rodents and lagomorphs) are poorly understood. We present a computational model in which random connectivity gives rise to orientation selectivity that matches experimental observations. The model predicts that mouse V1 neurons should exhibit intricate receptive fields in the two-dimensional frequency domain, causing a shift in orientation preferences with spatial frequency. We find evidence for these features in mouse V1 using calcium imaging and intracellular whole-cell recordings. Pattadkal et al. show that orientation selectivity can emerge from random connectivity, and offer a distinct perspective for how computations occur in the neocortex. They propose that a random convergence of inputs can provide signals for orientation preference in contrast with the dominant model that requires a precise arrangement.Fil: Pattadkal, Jagruti J.. University of Texas at Austin; Estados UnidosFil: Mato, German. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: van Vreeswijk, Carl. Centre National de la Recherche Scientifique; FranciaFil: Priebe, Nicholas J.. University of Texas at Austin; Estados UnidosFil: Hansel, David. Centre National de la Recherche Scientifique; Franci

Stability of Spatio-Temporal Structures in a Lattice Model of Pulse-Coupled Oscillators

We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By studying the intrinsic dynamics of each member of the population and their mutual interactions we observe the emergence of either spatio-temporal structures or synchronized regimes. We perform a linear stability analysis of these structures.Comment: 15 pages, 2 PostScript available upon request at [email protected], Accepted in Physica

Auto-structure of spike trains matters for testing on synchronous activity

Poster presentation: Coordinated neuronal activity across many neurons, i.e. synchronous or spatiotemporal pattern, had been believed to be a major component of neuronal activity. However, the discussion if coordinated activity really exists remained heated and controversial. A major uncertainty was that many analysis approaches either ignored the auto-structure of the spiking activity, assumed a very simplified model (poissonian firing), or changed the auto-structure by spike jittering. We studied whether a statistical inference that tests whether coordinated activity is occurring beyond chance can be made false if one ignores or changes the real auto-structure of recorded data. To this end, we investigated the distribution of coincident spikes in mutually independent spike-trains modeled as renewal processes. We considered Gamma processes with different shape parameters as well as renewal processes in which the ISI distribution is log-normal. For Gamma processes of integer order, we calculated the mean number of coincident spikes, as well as the Fano factor of the coincidences, analytically. We determined how these measures depend on the bin width and also investigated how they depend on the firing rate, and on rate difference between the neurons. We used Monte-Carlo simulations to estimate the whole distribution for these parameters and also for other values of gamma. Moreover, we considered the effect of dithering for both of these processes and saw that while dithering does not change the average number of coincidences, it does change the shape of the coincidence distribution. Our major findings are: 1) the width of the coincidence count distribution depends very critically and in a non-trivial way on the detailed properties of the inter-spike interval distribution, 2) the dependencies of the Fano factor on the coefficient of variation of the ISI distribution are complex and mostly non-monotonic. Moreover, the Fano factor depends on the very detailed properties of the individual point processes, and cannot be predicted by the CV alone. Hence, given a recorded data set, the estimated value of CV of the ISI distribution is not sufficient to predict the Fano factor of the coincidence count distribution, and 3) spike jittering, even if it is as small as a fraction of the expected ISI, can falsify the inference on coordinated firing. In most of the tested cases and especially for complex synchronous and spatiotemporal pattern across many neurons, spike jittering increased the likelihood of false positive finding very strongly. Last, we discuss a procedure [1] that considers the complete auto-structure of each individual spike-train for testing whether synchrony firing occurs at chance and therefore overcomes the danger of an increased level of false positives

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

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 Host Galaxy of GRB 990712

We present a comprehensive study of the z=0.43 host galaxy of GRB 990712, involving ground-based photometry, spectroscopy, and HST imaging. The broad-band UBVRIJHKs photometry is used to determine the global spectral energy distribution (SED) of the host galaxy. Comparison with that of known galaxy types shows that the host is similar to a moderately reddened starburst galaxy with a young stellar population. The estimated internal extinction in the host is Av=0.15+/-0.1 and the star-formation rate (SFR) from the UV continuum is 1.3+/-0.3 M_sun/yr, (not corrected for the effects of extinction). Other galaxy template spectra than starbursts failed to reproduce the observed SED. We also present VLT spectra leading to the detection of Halpha from the GRB host galaxy. A SFR of 2.8+/-0.7 M_sun/yr, is inferred from the Halpha line flux, and the presence of a young stellar population is supported by a large equivalent width. Images from HST/STIS show that the host has two separate knots, which could be two distinct star-forming regions.Comment: 11 pages, accepted for publication in Astronomy and Astrophysic