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

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

Near-infrared Spectroscopy of GRB Host Galaxies at z >~ 1.5: Insights into Host Galaxy Dynamics and Interpretations of Afterglow Absorption Spectra

This paper presents near-infrared echellette spectra of faint galaxies in the fields around GRB 050820A at redshift z=2.613 and GRB 060418 at z=1.490. The spectroscopic data show that both GRBs originate in a dynamic environment of interacting galaxies separated by < 15 h^{-1} kpc in projected distance and |dv| <~ 60 km/s in line-of-sight velocity. The optical afterglows revealed in early-epoch Hubble Space Telescope images are at least 2.5 h^{-1} kpc (or 0.4") away from the high surface brightness regions of the interacting members, indicating that the GRB events occurred either in the outskirts of a compact star-forming galaxy or in a low surface brightness satellite. Comparisons of the systemic redshifts of the host galaxies and the velocity distribution of absorbing clouds revealed in early-time afterglow spectra further show that the majority of the absorbing clouds are redshifted from these compact star-forming galaxies. These include the gas producing fine-structure absorption lines at physical distances d ~ a few x 100 pc from the GRB afterglow. The lack of blueshifted absorbing clouds and the spatial offset of the GRB event from the star-forming regions make it difficult to attribute the observed large velocity spread (~ 200-400 km/s) of absorbing gas in the GRB host to galactic-scale outflows. We consider a scenario in which the GRB event occurred in a dwarf satellite of the interacting group and interpret the broad absorption signatures in the afterglow spectra as a collective effect of the turbulent halo gas and the host star-forming ISM. We briefly discuss the implications for the absorption properties observed in the afterglow spectra.Comment: 10 pages, 6 figures, accepted for publication in MNRA

The Star Formation History of the GRB 050730 Host Galaxy

The long GRB 050730 observed at redshift z ~ 4 allowed the determination of the elemental abundances for a set of different chemical elements. We use detailed chemical evolution models taking into account also dust production to constrain the star formation history of the host galaxy of this long GRB. For the host galaxy of GRB 050730, we derive also some dust-related quantities and the the specific star formation rate, namely the star formation rate per unit stellar mass. We copare the properties of the GRB host galaxy with the ones of Quasar Damped Lyman Alpha absorbers.Comment: 7 pages, talk presented at the conference "Low-Metallicity Star Formation: From the First Stars to Dwarf Galaxies" held in Rapallo, Italy, June 200

A spectroscopic search for White Dwarf companions to 101 nearby M dwarfs

Recent studies of the stellar population in the solar neighborhood (<20 pc) suggest that there are undetected white dwarfs (WDs) in multiple systems with main sequence companions. Detecting these hidden stars and obtaining a more complete census of nearby WDs is important for our understanding of binary and galactic evolution, as well as the study of explosive phenomena. In an attempt to uncover these hidden WDs, we present intermediate resolution spectroscopy over the wavelength range 3000-25000 \AA\ of 101 nearby M dwarfs (dMs), observed with the Very Large Telescope X-Shooter spectrograph. For each star we search for a hot component superimposed on the dM spectrum. X-Shooter has excellent blue sensitivity and thus can reveal a faint hot WD despite the brightness of its red companion. Visual examination shows no clear evidence of a WD in any of the spectra. We place upper limits on the effective temperatures of WDs that may still be hiding by fitting dM templates to the spectra, and modeling WD spectra. On average our survey is sensitive to WDs hotter than about 5300 K. This suggests that the frequency of WD companions of T<5300 K with separation of order <50 AU among the local dM population is <3% at the 95% confidence level. The reduced spectra are made available on via WISeREP repository.Comment: 41 pages, 105 figures, 2 tables. Submitted to AAS journal

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

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