The structure of graphs with a vital linkage of order 2

A linkage of order k of a graph G is a subgraph with k components, each of which is a path. A linkage is vital if it spans all vertices, and no other linkage connects the same pairs of end vertices. We give a characterization of the graphs with a vital linkage of order 2: they are certain minors of a family of highly structured graphs

Thin Animals

Lattice animals provide a discretized model for the theta transition displayed by branched polymers in solvent. Exact graph enumeration studies have given some indications that the phase diagram of such lattice animals may contain two collapsed phases as well as an extended phase. This has not been confirmed by studies using other means. We use the exact correspondence between the q --> 1 limit of an extended Potts model and lattice animals to investigate the phase diagram of lattice animals on phi-cubed random graphs of arbitrary topology (``thin'' random graphs). We find that only a two phase structure exists -- there is no sign of a second collapsed phase. The random graph model is solved in the thermodynamic limit by saddle point methods. We observe that the ratio of these saddle point equations give precisely the fixed points of the recursion relations that appear in the solution of the model on the Bethe lattice by Henkel and Seno. This explains the equality of non-universal quantities such as the critical lines for the Bethe lattice and random graph ensembles.Comment: Latex, 10 pages plus 6 ps/eps figure

The Yang Lee Edge Singularity on Feynman Diagrams

We investigate the Yang-Lee edge singularity on non-planar random graphs, which we consider as the Feynman Diagrams of various d=0 field theories, in order to determine the value of the edge exponent. We consider the hard dimer model on phi3 and phi4 random graphs to test the universality of the exponent with respect to coordination number, and the Ising model in an external field to test its temperature independence. The results here for generic (``thin'') random graphs provide an interesting counterpoint to the discussion by Staudacher of these models on planar random graphs.Comment: LaTeX, 6 pages + 3 figure

A Potts/Ising Correspondence on Thin Graphs

We note that it is possible to construct a bond vertex model that displays q-state Potts criticality on an ensemble of phi3 random graphs of arbitrary topology, which we denote as ``thin'' random graphs in contrast to the fat graphs of the planar diagram expansion. Since the four vertex model in question also serves to describe the critical behaviour of the Ising model in field, the formulation reveals an isomorphism between the Potts and Ising models on thin random graphs. On planar graphs a similar correspondence is present only for q=1, the value associated with percolation.Comment: 6 pages, 5 figure

Active Galactic Nuclei with Candidate Intermediate-Mass Black Holes

We present an initial sample of 19 intermediate-mass black hole candidates in active galactic nuclei culled from the First Data Release of the Sloan Digital Sky Survey. Using the linewidth-luminosity-mass scaling relation established for broad-line active nuclei, we estimate black hole masses in the range of 8 x 10^4 - 10^6 solar masses, a regime in which only two objects are currently known. The absolute magnitudes are faint for active galactic nuclei, ranging from M_g of -15 to -18 mag, while the bolometric luminosities are all close to the Eddington limit. The entire sample formally satisfies the linewidth criterion for so-called narrow-line Seyfert 1 galaxies; however, they display a wider range of FeII and [OIII] (5007) line strengths than is typically observed in this class of objects. Although the available imaging data are of insufficient quality to ascertain the detailed morphologies of the host galaxies, it is likely that the majority of the hosts are relatively late-type systems. The host galaxies have estimated g-band luminosities ~ 1 mag fainter than M* for the general galaxy population at z of 0.1. Beyond simply extending the known mass range of central black holes in galactic nuclei, these objects provide unique observational constraints on the progenitors of supermassive black holes. They are also expected to contribute significantly to the integrated signal for future gravitational wave experiments.Comment: ApJ Accepted, 13 pages, 9 figures, uses emulateapj.cl

A Search for Binary Active Galactic Nuclei: Double-Peaked [OIII] AGN in the Sloan Digital Sky Survey

We present AGN from the Sloan Digital Sky Survey (SDSS) having double-peaked profiles of [OIII] 5007,4959 and other narrow emission-lines, motivated by the prospect of finding candidate binary AGN. These objects were identified by means of a visual examination of 21,592 quasars at z < 0.7 in SDSS Data Release 7 (DR7). Of the spectra with adequate signal-to-noise, 148 spectra exhibit a double-peaked [OIII] profile. Of these, 86 are Type 1 AGN and 62 are Type 2 AGN. Only two give the appearance of possibly being optically resolved double AGN in the SDSS images, but many show close companions or signs of recent interaction. Radio-detected quasars are three times more likely to exhibit a double-peaked [OIII] profile than quasars with no detected radio flux, suggesting a role for jet interactions in producing the double-peaked profiles. Of the 66 broad line (Type 1) AGN that are undetected in the FIRST survey, 0.9% show double peaked [OIII] profiles. We discuss statistical tests of the nature of the double-peaked objects. Further study is needed to determine which of them are binary AGN rather than disturbed narrow line regions, and how many additional binaries may remain undetected because of insufficient line-of-sight velocity splitting. Previous studies indicate that 0.1% of SDSS quasars are spatially resolved binaries, with typical spacings of ~10 to 100 kpc. If a substantial fraction of the double-peaked objects are indeed binaries, then our results imply that binaries occur more frequently at smaller separations (< 10 kpc). This suggests that simultaneous fueling of both black holes is more common as the binary orbit decays through these spacings.Comment: 33 pages, 5 figures, LaTeX. Major revisions. Accepted for publication in ApJ

ISO-SWS spectroscopy of NGC 1068

We present ISO-SWS spectroscopy of NGC 1068 for the wavelength range 2.4 to 45um, detecting a total of 36 emission lines. Most of the observed transitions are fine structure and recombination lines originating in the narrow line region. We compare the line profiles of optical lines and reddening-insensitive infrared lines to constrain the dynamical structure and extinction properties of the NLR. The considerable differences found are most likely explained by two effects. (1) The spatial structure of the NLR is a combination of a highly ionized outflow cone and lower excitation extended emission. (2) Parts of the NLR, mainly in the receding part at velocities above systemic, are subject to extinction that is significantly suppressing optical emission. Line asymmetries and net blueshifts remain, however, even for infrared fine structure lines suffering very little obscuration. This may be either due to an intrinsic asymmetry of the NLR, or due to a very high column density obscuring component which is hiding part of the NLR even from infrared view. Mid-infrared emission of molecular hydrogen in NGC 1068 arises in a dense molecular medium at temperatures of a few hundred Kelvin that is most likely closely related to the warm and dense components seen in the near-infrared H2 transitions, and in millimeter wave tracers of molecular gas. Any emission of the putative pc-scale molecular torus is likely overwhelmed by this larger scale emission.Comment: aastex (V4), 9 eps figures. Accepted by Ap

Statistical Properties of Radio Emission from the Palomar Seyfert Galaxies

We have carried out an analysis of the radio and optical properties of a statistical sample of 45 Seyfert galaxies from the Palomar spectroscopic survey of nearby galaxies. We find that the space density of bright galaxies (-22 mag <= M_{B_T} <= -18 mag) showing Seyfert activity is (1.25 +/- 0.38) X 10^{-3} Mpc^{-3}, considerably higher than found in other Seyfert samples. Host galaxy types, radio spectra, and radio source sizes are uncorrelated with Seyfert type, as predicted by the unified schemes for active galaxies. Approximately half of the detected galaxies have flat or inverted radio spectra, more than expected based on previous samples. Surprisingly, Seyfert 1 galaxies are found to have somewhat stronger radio sources than Seyfert 2 galaxies at 6 and 20 cm, particularly among the galaxies with the weakest nuclear activity. We suggest that this difference can be accommodated in the unified schemes if a minimum level of Seyfert activity is required for a radio source to emerge from the vicinity of the active nucleus. Below this level, Seyfert radio sources might be suppressed by free-free absorption associated with the nuclear torus or a compact narrow-line region, thus accounting for both the weakness of the radio emission and the preponderance of flat spectra. Alternatively, the flat spectra and weak radio sources might indicate that the weak active nuclei are fed by advection-dominated accretion disks.Comment: 18 pages using emulateapj5, 13 embedded figures, accepted by Ap

Multivariate Granger Causality and Generalized Variance

Granger causality analysis is a popular method for inference on directed interactions in complex systems of many variables. A shortcoming of the standard framework for Granger causality is that it only allows for examination of interactions between single (univariate) variables within a system, perhaps conditioned on other variables. However, interactions do not necessarily take place between single variables, but may occur among groups, or "ensembles", of variables. In this study we establish a principled framework for Granger causality in the context of causal interactions among two or more multivariate sets of variables. Building on Geweke's seminal 1982 work, we offer new justifications for one particular form of multivariate Granger causality based on the generalized variances of residual errors. Taken together, our results support a comprehensive and theoretically consistent extension of Granger causality to the multivariate case. Treated individually, they highlight several specific advantages of the generalized variance measure, which we illustrate using applications in neuroscience as an example. We further show how the measure can be used to define "partial" Granger causality in the multivariate context and we also motivate reformulations of "causal density" and "Granger autonomy". Our results are directly applicable to experimental data and promise to reveal new types of functional relations in complex systems, neural and otherwise.Comment: added 1 reference, minor change to discussion, typos corrected; 28 pages, 3 figures, 1 table, LaTe

Epidemiological patterns of hepatitis B virus (HBV) in highly endemic areas

This paper uses meta-analysis of published data and a deterministic mathematical model of hepatitis B virus (HBV) transmission to describe the patterns of HBV infection in high endemicity areas. We describe the association between the prevalence of carriers and a simple measure of the rate of infection, the age at which half the population have been infected (A50), and assess the contribution of horizontal and perinatal transmission to this association. We found that the two main hyper-endemic areas of sub-Saharan Africa and east Asia have similar prevalences of carriers and values of A50, and that there is a negative nonlinear relationship between A50 and the prevalence of carriers in high endemicity areas (Spearman's Rank, P = 0·0086). We quantified the risk of perinatal transmission and the age-dependent rate of infection to allow a comparison between the main hyper-endemic areas. East Asia was found to have higher prevalences of HBeAg positive mothers and a greater risk of perinatal transmission from HBeAg positive mothers than sub-Saharan Africa, though the differences were not statistically significant. However, the two areas have similar magnitudes and age-dependent rates of horizontal transmission. Results of a simple compartmental model suggest that similar rates of horizontal transmission are sufficient to generate the similar patterns between A50 and the prevalences of carriers. Interrupting horizontal transmission by mass immunization is expected to have a significant, nonlinear impact on the rate of acquisition of new carriers