Replica symmetric evaluation of the information transfer in a two-layer network in presence of continuous+discrete stimuli

In a previous report we have evaluated analytically the mutual information between the firing rates of N independent units and a set of multi-dimensional continuous+discrete stimuli, for a finite population size and in the limit of large noise. Here, we extend the analysis to the case of two interconnected populations, where input units activate output ones via gaussian weights and a threshold linear transfer function. We evaluate the information carried by a population of M output units, again about continuous+discrete correlates. The mutual information is evaluated solving saddle point equations under the assumption of replica symmetry, a method which, by taking into account only the term linear in N of the input information, is equivalent to assuming the noise to be large. Within this limitation, we analyze the dependence of the information on the ratio M/N, on the selectivity of the input units and on the level of the output noise. We show analytically, and confirm numerically, that in the limit of a linear transfer function and of a small ratio between output and input noise, the output information approaches asymptotically the information carried in input. Finally, we show that the information loss in output does not depend much on the structure of the stimulus, whether purely continuous, purely discrete or mixed, but only on the position of the threshold nonlinearity, and on the ratio between input and output noise.Comment: 19 pages, 4 figure

On the cool gaseous haloes of quasars

We present optical spectroscopy of projected QSO pairs to investigate the MgII and the CIV absorption features imprinted on the spectrum of the background object by the gaseous halo surrounding the foreground QSO. We observed 13 projected pairs in the redshift range 0.7<z<2.2 spanning projected separations between 60 kpc and 120 kpc. In the spectra of the background QSOs, we identify MgII intervening absorption systems associated to the foreground QSOs in 7 out of 10 pairs, and 1 absorption system out of 3 is found for CIV. The distribution of the equivalent width as a function of the impact parameter shows that, unlike the case of normal galaxies, some strong absorption systems (EWr > 1 Ang) are present also beyond a projected radius of ~70 kpc. If we take into account the mass of the galaxies as an additional parameter that influence the extent of the gaseous haloes, the distribution of the absorptions connected to the QSOs is consistent to that of galaxies. In the spectra of the foreground QSOs we do not detect any MgII absorption lines originated by the gas surrounding the QSO itself, but in 2 cases these features are present for CIV. The comparison between the absorption features observed in the transverse direction and those along the line of sight allows us to comment on the distribution of the absorbing gas and on the emission properties of the QSOs. Based on observations undertaken at the European Southern Observatory (ESO) Very Large Telescope (VLT) under Programmes 085.B-0210(A) and 086.B-0028(A).Comment: 15 pages, 3 tables, 9 figures. Accepted to be published on MNRA

A replica free evaluation of the neuronal population information with mixed continuous and discrete stimuli: from the linear to the asymptotic regime

Recent studies have explored theoretically the ability of populations of neurons to carry information about a set of stimuli, both in the case of purely discrete or purely continuous stimuli, and in the case of multidimensional continuous angular and discrete correlates, in presence of additional quenched disorder in the distribution. An analytical expression for the mutual information has been obtained in the limit of large noise by means of the replica trick. Here we show that the same results can actually be obtained in most cases without the use of replicas, by means of a much simpler expansion of the logarithm. Fitting the theoretical model to real neuronal data, we show that the introduction of correlations in the quenched disorder improves the fit, suggesting a possible role of signal correlations-actually detected in real data- in a redundant code. We show that even in the more difficult analysis of the asymptotic regime, an explicit expression for the mutual information can be obtained without resorting to the replica trick despite the presence of quenched disorder, both with a gaussian and with a more realistic thresholded-gaussian model. When the stimuli are mixed continuous and discrete, we find that with both models the information seem to grow logarithmically to infinity with the number of neurons and with the inverse of the noise, even though the exact general dependence cannot be derived explicitly for the thresholded gaussian model. In the large noise limit lower values of information were obtained with the thresholded-gaussian model, for a fixed value of the noise and of the population size. On the contrary, in the asymptotic regime, with very low values of the noise, a lower information value is obtained with the gaussian model.Comment: 34 pages, 5 figure

Circum-galactic medium in the halo of quasars

The properties of circum-galactic gas in the halo of quasar host galaxies are investigated analyzing Mg II 2800 and C IV 1540 absorption-line systems along the line of sight close to quasars. We used optical spectroscopy of closely aligned pairs of quasars (projected distance $\leq$ 200 kpc, but at very different redshift) obtained at the VLT and Gran Telescopio Canarias to investigate the distribution of the absorbing gas for a sample of quasars at z$\sim$1. Absorption systems of EW $\geq$ 0.3 $\rm{\AA}$ associated with the foreground quasars are revealed up to 200 kpc from the centre of the host galaxy, showing that the structure of the absorbing gas is patchy with a covering fraction quickly decreasing beyond 100 kpc. In this contribution we use optical and near-IR images obtained at VLT to investigate the relations between the properties of the circum-galactic medium of the host galaxies and of the large scale galaxy environments of the foreground quasars.Comment: 6 pages, 3 figures, proceedings of the conference "QUASARS at all cosmic epochs", accepted for publication on Frontiers in Astronomy and Space Scienc

The black hole mass of BL Lac objects from the stellar velocity dispersion of the host galaxy

The correlation between black hole mass M(BH) and stellar velocity dispersion sigma in nearby elliptical galaxies affords a novel way to determine M(BH) in active galaxies. We report on measurements of sigma from optical spectra of 7 BL Lac host galaxies. The derived values of sigma are in the range of 160 - 290 km/s corresponding to M(BH) of 5 x 10^7 to 1 x 10^9 Msun. The average ratio of M(BH) to the host galaxy mass is 1.4 x 10^-3, consistent with that estimated in other active and inactive galaxies. The velocity dispersions and the derived values of M(BH) of the BL Lacs are similar to those obtained for low redshift radio galaxies, in good agreement with the predictions of the unified models for radio-loud active galaxies.Comment: 11 pages, Astrophysical Journal (Letters), accepte

Host Galaxies of low z Radio-loud Quasars: A search of HST archives

We searched the HST archives for unpublished WFPC2 images of low redshift (z<0.5) radio loud quasars (RLQ). This led to the identification of 11 objects. We present here the results of the analysis of these images from which we derive the properties of their host galaxies. All objects are clearly resolved and their surrounding nebulosity is consistent with an elliptical galaxy model. These new data, together with previous published HST observations, form a sample of 34 sources which significantly expands all previous studies of low redshift RLQ based on HST data. For this full sample we derive the average absolute magnitude of the host galaxies =-24.01+/-0.48, and the effective radius =10.5+/-3.7kpc. No significant correlation is found between the nucleus and the host galaxy luminosity. Using the relationship between black hole mass (M_BH) and bulge luminosity we investigate the relation between M_BH and total radio power for RLQ and compare with other classes of radio sources. The overall distribution of AGN in the plane M_BH-P(radio) exhibits a trend for increasing M_BH with increasing P(radio) but with a substantial spread. RLQ occupy the region of most powerful sources and most massive BH. The quasars appear to emit over a wide range of power with respect to their Eddington luminosity as deduced by the estimated M_BH.Comment: 23 pages, 8 figures, ApJ in pres

Near-infrared adaptive optics imaging of high redshift quasars

The properties of high redshift quasar host galaxies are studied, in order to investigate the connection between galaxy evolution, nuclear activity, and the formation of supermassive black holes. We combine new near-infrared observations of three high redshift quasars (2 < z < 3), obtained at the ESO Very Large Telescope equipped with adaptive optics, with selected data from the literature. For the three new objects we were able to detect and characterize the properties of the host galaxy, found to be consistent with those of massive elliptical galaxies of M(R) ~ -24.7 for the one radio loud quasar, and M(R) ~ -23.8 for the two radio quiet quasars. When combined with existing data at lower redshift, these new observations depict a scenario where the host galaxies of radio loud quasars are seen to follow the expected trend of luminous (~5L*) elliptical galaxies undergoing passive evolution. This trend is remarkably similar to that followed by radio galaxies at z > 1.5. Radio quiet quasars hosts also follow a similar trend but at a lower average luminosity (~0.5 mag dimmer). The data indicate that quasar host galaxies are already fully formed at epochs as early as ~2 Gyr after the Big Bang and then passively fade in luminosity to the present epoch.Comment: Accepted for publication in ApJ, 24 pages, 10 figure

The Neutron Stars Census

The paucity of old isolated accreting neutron stars in ROSAT observations is used to derive a lower limit on the mean velocity of neutron stars at birth. The secular evolution of the population is simulated following the paths of a statistical sample of stars for different values of the initial kick velocity, drawn from an isotropic Gaussian distribution with mean velocity $0\leq < V>\leq 550$ ${\rm km s^{-1}}$. The spin--down, induced by dipole losses and the interaction with the ambient medium, is tracked together with the dynamical evolution in the Galactic potential, allowing for the determination of the fraction of stars which are, at present, in each of the four possible stages: Ejector, Propeller, Accretor, and Georotator. Taking from the ROSAT All Sky Survey an upper limit of $\sim 10$ accreting neutron stars within $\sim 140$ pc from the Sun, we infer a lower bound for the mean kick velocity, $\gtrsim 200-300$ ${\rm km s^{-1}},$ corresponding to a velocity dispersion $\sigma_V\gtrsim 125-190$ km s$^{-1}$. The same conclusion is reached for both a constant magnetic field ($B\sim 10^{12}$ G) and a magnetic field decaying exponentially with a timescale $\sim 10^9$ yr. Such high velocities are consistent with those derived from radio pulsar observations. Present results, moreover, constrain the fraction of low velocity stars, which could have escaped pulsar statistics, to less than 1%.Comment: 13 pages, 6 PostScript figures, accepted to Ap

XMM-Newton View of PKS 2155-304: Characterizing the X-ray Variability Properties with EPIC-PN

Starting from XMM-Newton EPIC-PN data, we present the X-ray variability characteristics of PKS 2155-304 using a simple analysis of the excess variance, \xs, and of the fractional rms variability amplitude, fvar. The scatter in \xs\ and \fvar, calculated using 500 s long segments of the light curves, is smaller than the scatter expected for red noise variability. This alone does not imply that the underlying process responsible for the variability of the source is stationary, since the real changes of the individual variance estimates are possibly smaller than the large scatters expected for a red noise process. In fact the averaged \xs and \fvar, reducing the fluctuations of the individual variances, chang e with time, indicating non-stationary variability. Moreover, both the averaged \sqxs (absolute rms variability amplitude) and \fvar show linear correlation with source flux but in an opposite sense: \sqxs correlates with flux, but \fvar anti-correlates with flux. These correlations suggest that the variability process of the source is strongly non-stationary as random scatters of variances should not yield any correlation. \fvar spectra were constructed to compare variability amplitudes in different energy bands. We found that the fractional rms variability amplitude of the source, when significant variability is observed, increases logarithmically with the photon energy, indicating significant spectral variability. The point-to-point variability amplitude may also track this trend, suggesting that the slopes of the power spectral density of the source are energy-independent. Using the normalized excess variance the black hole mass of \pks was estimated to be about $1.45 \times 10^8 M_{\bigodot}$. This is compared and contrasted with the estimates derived from measurements of the host galaxies.Comment: Accepted for publication in The Astrophysical Journa