Replica theory for learning curves for Gaussian processes on random graphs

Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of training examples. We analyse a challenging problem in the area of non-parametric inference where an effectively infinite number of parameters has to be learned, specifically Gaussian process regression. When the inputs are vertices on a random graph and the outputs noisy function values, we show that replica techniques can be used to obtain exact performance predictions in the limit of large graphs. The covariance of the Gaussian process prior is defined by a random walk kernel, the discrete analogue of squared exponential kernels on continuous spaces. Conventionally this kernel is normalised only globally, so that the prior variance can differ between vertices; as a more principled alternative we consider local normalisation, where the prior variance is uniform

Radio Luminosities and Classificatory Criteria of BL Lacertae Objects

Using the sample of radio selected BL Lacertae objects (RBLs) and X-ray selected BL Lacertae objects (XBLs) presented by Sambruna et al. (1996), we calculated the luminosities of radio, optical and X-ray of each source and made the statistical analysis among the luminosities at different wave-bands, broad-band spectral indices from radio to X-ray ($\alpha_{\rm rx}$) and peak frequencies ($\nu_p$). Our results are as follows: (i) there is a positive correlation between radio luminosity $L_{\rm r}$ and $\alpha_{\rm rx}$ and a negative correlation between $L_{\rm r}$ and $\nu_p$. High-energy peak BL Lacs (HBLs) and low-energy peak BL Lacs (LBLs) can be distinguished very well, the dividing lines are probably those of $\log {L_{\rm r}}=43.25$ (erg/sec) and $\alpha_{\rm rx}>$(or $\leq$)0.75 for $L_{\rm r}$ - $\alpha_{\rm rx}$ plot and those of $\log {L_{\rm r}}\leq 43.25$ (erg/sec) and $\log {\nu_p}>14.7$ for the $L_{\rm r}$ - $\nu_p$ plot; (ii) there is a weak positive correlation between optical luminosity $L_o$ and $\alpha_{\rm rx}$ and a negatively weak correlation between $L_{\rm o}$ and $\nu_p$; (iii) there is no correlation between X-ray luminosity $L_X$ and $\alpha_{\rm rx}$ or between $L_X$ and $\nu_p$. From our analysis, we find that synchrotron radiation is the main X-ray radiation mechanism for HBLs while inverse Compton scattering for LBLs.Comment: 9 pages, 3 figures. Submitted to A&

Radio variability of 1st 3-months Fermi blazars at 5 GHz: affected by interstellar scintillation?

Blazars from the first-three-months Fermi-AGN list were observed with the Urumqi 25m radio telescope at 5GHz in IDV (Intra-Day Variability) mode and inter-month observation mode. A significant correlation between the flux density at 5GHz and the gamma-ray intensity for the Fermi-LAT detected blazars is seen. There is a higher IDV detection rate in Fermi detected blazars than those reported for other samples. Stronger variability appears at lower Galactic latitudes; IDV appears to be stronger in weaker sources, indicating that the variability is affected by interstellar scintillation.Comment: 4 pages, 4 figures, in proceedings of 'Multiwavelength Variability of Blazars' in Guangzhou Uni. of China, 22-24, Sep. 2010, to appear in JA

Physical parameters of a relativistic jet at very high redshift: the case of the blazar J1430+4204

Context. The high-redshift (z = 4.72) blazar J1430+4204 produced a major radio outburst in 2005. Such outbursts are usually associated with the emergence of a new component in the inner radio jet. Aims. We searched for possible changes in the radio structure on milli-arcsecond angular scales, to determine physical parameters that characterise the relativistic jet ejected from the centre of this source. Methods. We analysed 15-GHz radio interferometric images obtained with the Very Long Baseline Array (VLBA) before and after the peak of the outburst. Results. We did not identify any significant new jet component over a period of 569 days. We estimated the Doppler factor, the Lorentz factor, and the apparent transverse speed of a putative jet component using three different methods. The likely small jet angle to the line of sight and our values of the apparent transverse speed are consistent with not detecting a new jet feature.Comment: (6 pages, 4 figures) accepted for publication in Astronomy and Astrophysic

Into the central 10 pc of the most distant known radio quasar. VLBI imaging observations of J1429+5447 at z=6.21

Context: There are about 60 quasars known at redshifts z>5.7 to date. Only three of them are detected in the radio above 1 mJy flux density at 1.4 GHz frequency. Among them, J1429+5447 (z=6.21) is the highest-redshift radio quasar known at present. These rare, distant, and powerful objects provide important insight into the activity of the supermassive black holes in the Universe at early cosmological epochs, and on the physical conditions in their environment. Aims: We studied the compact radio structure of J1429+5447 on the milli-arcsecond (mas) angular scale, in order to compare the structural and spectral properties with those of other two z~6 radio-loud quasars, J0836+0054 (z=5.77) and J1427+3312 (z=6.12). Methods: We performed Very Long Baseline Interferometry (VLBI) imaging observations of J1429+5447 with the European VLBI Network (EVN) at 1.6 GHz on 2010 June 8, and at 5 GHz on 2010 May 27. Results: Based on its observed radio properties, the compact but somewhat resolved structure on linear scales of <100 pc, and the steep spectrum, the quasar J1429+5447 is remarkably similar to J0836+0054 and J1427+3312. To answer the question whether the compact steep-spectrum radio emission is a "universal" feature of the most distant radio quasars, it is essential to study more, yet to be discovered radio-loud active galactic nuclei at z>6.Comment: 4 pages, 2 figures, accepted for publication as a Letter to the editor in Astronomy & Astrophyic

The VLA-COSMOS Survey. II. Source Catalog of the Large Project

The VLA-COSMOS Large Project is described and its scientific objective is discussed. We present a catalog of ~3600 radio sources found in the 2 deg^2 COSMOS field at 1.4 GHz. The observations in the VLA A and C configuration resulted in a resolution of 1.5" × 1.4" and a mean rms noise of ~10.5 (15) μJy beam^(-1) in the central 1 (2) deg^2. Eighty radio sources are clearly extended consisting of multiple components, and most of them appear to be double-lobed radio galaxies. The astrometry of the catalog has been thoroughly tested, and the uncertainty in the relative and absolute astrometry are 130 and <55 mas, respectively

Radio interferometric observations of two core-dominated triple radio sources at z>3

Aims. We selected two radio quasars (J1036+1326 and J1353+5725) based on their 1.4-GHz radio structure, which is dominated by a bright central core and a pair of weaker and nearly symmetric lobes at ~10" angular separation. They are optically identified in the Sloan Digital Sky Survey (SDSS) at spectroscopic redshifts z>3. We investigate the possibility that their core-dominated triple morphology can be a sign of restarted radio activity in these quasars, involving a significant repositioning of the radio jet axis. Methods. We present the results of high-resolution radio imaging observations of J1036+1326 and J1353+5725, performed with the European Very Long Baseline Interferometry (VLBI) Network (EVN) at 1.6 GHz. These data are supplemented by archive observations from the Very Large Array (VLA).We study the large- and small-scale radio structures and the brightness temperatures, then estimate relativistic beaming parameters. Results. We show that the central emission region of these two high-redshift, core-dominated triple sources is compact but resolved at ~10 milli-arcsecond resolution. We find that it is not necessary to invoke large misalignment between the VLBI jet and the large-scale radio structure to explain the observed properties of the sources.Comment: 5 pages, 4 figures, accepted for publication in A&

Third World gap year projects: Youth transitions and the mediation of risk

This is the post-print version of the final published article. The definitive, peer-reviewed and edited version of this article is available from the link below. Copyright @ 2008 Pion.In recent years in the UK there has been a great expansion in the number of young people travelling to Third World countries between school and university in order to participate as volunteers on structured gap year projects. Travel to such places is commonly perceived as ‘risky’, and takes young people outside the protective cocoon of UK health and safety legislation. One of the functions played by the providers of gap year projects is to mediate risk. On the basis of analysis of promotional literature, interviews with organisers of gap year projects, and focus groups of returned volunteers, in this paper I argue that the various strategies of risk mediation undertaken by gap year providers serve to reconcile modernising tendencies in UK society toward risk control and structure with postmodern inclinations towards individualisation and uncertainty

High-resolution images of five radio quasars at early cosmological epochs

Context: Until now, there have only been seven quasars at z>4.5 whose the high-resolution radio structure had been studied in detail with Very Long Baseline Interferometry (VLBI) imaging. Aims: We almost double the number of VLBI-imaged quasars at these high redshifts with the aim of studying their redshift-dependent structural and physical properties in a larger sample. Methods: We observed five radio quasars (J0813+3508, J1146+4037, J1242+5422, J1611+0844, and J1659+2101) at 4.5<z<5 with the European VLBI Network (EVN) at 1.6 GHz on 29 October 2008 and at 5 GHz on 22 October 2008. The angular resolution achieved ranges from 1.5 to 25 milli-arcseconds (mas), depending on the observing frequency, the position angle in the sky, and the source's celestial position. Results: The sources are all somewhat extended on mas scales, but compact enough to be detected at both frequencies. With one exception of a flat-spectrum source (J1611+0844), their compact emission is characterised by a steep radio spectrum. We found no evidence of Doppler-boosted radio emission in the quasars in our sample. The radio structure of one of them (J0813+3508) is extended to ~7", which corresponds to 43 kpc projected linear size. Many of the highest redshift compact radio sources are likely to be young, evolving objects, far-away cousins of the powerful gigahertz peaked-spectrum (GPS) and compact steep-spectrum (CSS) sources that populate the Universe at lower redshifts.Comment: 7 pages, 2 figures, accepted for Astronomy & Astrophysic

Estimating black hole masses of blazars

Estimating black hole masses of blazars is still a big challenge. Because of the contamination of jets, using the previously suggested size -- continuum luminosity relation can overestimate the broad line region (BLR) size and black hole mass for radio-loud AGNs, including blazars. We propose a new relation between the BLR size and $H_{\beta}$ emission line luminosity and present evidences for using it to get more accurate black hole masses of radio-loud AGNs. For extremely radio-loud AGNs such as blazars with weak/absent emission lines, we suggest to use the fundamental plane relation of their elliptical host galaxies to estimate the central velocity dispersions and black hole masses, if their velocity dispersions are not known but the host galaxies can be mapped. The black hole masses of some well-known blazars, such as OJ 287, AO 0235+164 and 3C 66B, are obtained using these two methods and the M - $\sigma$ relation. The implications of their black hole masses on other related studies are also discussed.Comment: 7 pages, invited talk presented in the workshop on Multiwavelength Variability of Blazars (Guangzhou, China, Sept. 22-24, 2010). To be published in the Journal of Astrophysics and Astronom