The clustering and bias of radio-selected AGN and star-forming galaxies in the COSMOS field

Dark matter haloes in which galaxies reside are likely to have a significant impact on their evolution. We investigate the link between dark matter haloes and their constituent galaxies by measuring the angular two-point correlation function of radio sources, using recently released 3 GHz imaging over $\sim 2 \ \mathrm{deg}^2$of the COSMOS field. We split the radio source population into Star Forming Galaxies (SFGs) and Active Galactic Nuclei (AGN), and further separate the AGN into radiatively efficient and inefficient accreters. Restricting our analysis to$z<1$, we find SFGs have a bias,$b = 1.5 ^{+0.1}_{-0.2}$, at a median redshift of$z=0.62$. On the other hand, AGN are significantly more strongly clustered with$b = 2.1\pm 0.2$at a median redshift of 0.7. This supports the idea that AGN are hosted by more massive haloes than SFGs. We also find low-accretion rate AGN are more clustered ($b = 2.9 \pm 0.3$) than high-accretion rate AGN ($b = 1.8^{+0.4}_{-0.5}$) at the same redshift ($z \sim 0.7$), suggesting that low-accretion rate AGN reside in higher mass haloes. This supports previous evidence that the relatively hot gas that inhabits the most massive haloes is unable to be easily accreted by the central AGN, causing them to be inefficient. We also find evidence that low-accretion rate AGN appear to reside in halo masses of$M_{h} \sim 3-4 \times 10^{13}h^{-1}$M$_{\odot}$at all redshifts. On the other hand, the efficient accreters reside in haloes of$M_{h} \sim 1-2 \times 10^{13}h^{-1}$M$_{\odot}$at low redshift but can reside in relatively lower mass haloes at higher redshifts. This could be due to the increased prevalence of cold gas in lower mass haloes at$z \ge 1$compared to$z<1$.Comment: 20 pages, 10 figures, 1 table, accepted by MNRA

A note on monopole moduli spaces

We discuss the structure of the framed moduli space of Bogomolny monopoles for arbitrary symmetry breaking and extend the definition of its stratification to the case of arbitrary compact Lie groups. We show that each stratum is a union of submanifolds for which we conjecture that the natural $L^2$ metric is hyperKahler. The dimensions of the strata and of these submanifolds are calculated, and it is found that for the latter, the dimension is always a multiple of four.Comment: 17 pages, LaTe

A close-pair binary in a distant triple supermassive black-hole system

Galaxies are believed to evolve through merging, which should lead to multiple supermassive black holes in some. There are four known triple black hole systems, with the closest pair being 2.4 kiloparsecs apart (the third component is more distant at 3 kiloparsecs), which is far from the gravitational sphere of influence of a black hole with mass $\sim$10$^9$ M$_\odot$ (about 100 parsecs). Previous searches for compact black hole systems concluded that they were rare, with the tightest binary system having a separation of 7 parsecs. Here we report observations of a triple black hole system at redshift z=0.39, with the closest pair separated by $\sim$140 parsecs. The presence of the tight pair is imprinted onto the properties of the large-scale radio jets, as a rotationally-symmetric helical modulation, which provides a useful way to search for other tight pairs without needing extremely high resolution observations. As we found this tight pair after searching only six galaxies, we conclude that tight pairs are more common than hitherto believed, which is an important observational constraint for low-frequency gravitational wave experiments.Comment: 21 pages, 6 figures. Published online by Nature on 25 June 2014. Extremely minor differences with published version exis

Hopf algebras and characters of classical groups

Schur functions provide an integral basis of the ring of symmetric functions. It is shown that this ring has a natural Hopf algebra structure by identifying the appropriate product, coproduct, unit, counit and antipode, and their properties. Characters of covariant tensor irreducible representations of the classical groups GL(n), O(n) and Sp(n) are then expressed in terms of Schur functions, and the Hopf algebra is exploited in the determination of group-subgroup branching rules and the decomposition of tensor products. The analysis is carried out in terms of n-independent universal characters. The corresponding rings, CharGL, CharO and CharSp, of universal characters each have their own natural Hopf algebra structure. The appropriate product, coproduct, unit, counit and antipode are identified in each case.Comment: 9 pages. Uses jpconf.cls and jpconf11.clo. Presented by RCK at SSPCM'07, Myczkowce, Poland, Sept 200

Syzygies of torsion bundles and the geometry of the level l modular variety over M_g

We formulate, and in some cases prove, three statements concerning the purity or, more generally the naturality of the resolution of various rings one can attach to a generic curve of genus g and a torsion point of order l in its Jacobian. These statements can be viewed an analogues of Green's Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space R_{g,l} of twisted level l curves of genus g and use this to derive results about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3} is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is greater than or equal to 19. In the last section we explain probabilistically the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the statement of Prop 2.

Covariance, correlation and entanglement

Some new identities for quantum variance and covariance involving commutators are presented, in which the density matrix and the operators are treated symmetrically. A measure of entanglement is proposed for bipartite systems, based on covariance. This works for two- and three-component systems but produces ambiguities for multicomponent systems of composite dimension. Its relationship to angular momentum dispersion for symmetric symmetric spin states is described.Comment: 30 pages, Latex, to appear in J Phys

Lyapunov exponent and natural invariant density determination of chaotic maps: An iterative maximum entropy ansatz

We apply the maximum entropy principle to construct the natural invariant density and Lyapunov exponent of one-dimensional chaotic maps. Using a novel function reconstruction technique that is based on the solution of Hausdorff moment problem via maximizing Shannon entropy, we estimate the invariant density and the Lyapunov exponent of nonlinear maps in one-dimension from a knowledge of finite number of moments. The accuracy and the stability of the algorithm are illustrated by comparing our results to a number of nonlinear maps for which the exact analytical results are available. Furthermore, we also consider a very complex example for which no exact analytical result for invariant density is available. A comparison of our results to those available in the literature is also discussed.Comment: 16 pages including 6 figure

Estrogens promote misfolded proinsulin degradation to protect insulin production and delay diabetes

Summary: Conjugated estrogens (CE) delay the onset of type 2 diabetes (T2D) in postmenopausal women, but the mechanism is unclear. In T2D, the endoplasmic reticulum (ER) fails to promote proinsulin folding and, in failing to do so, promotes ER stress and β cell dysfunction. We show that CE prevent insulin-deficient diabetes in male and in female Akita mice using a model of misfolded proinsulin. CE stabilize the ER-associated protein degradation (ERAD) system and promote misfolded proinsulin proteasomal degradation. This involves activation of nuclear and membrane estrogen receptor-α (ERα), promoting transcriptional repression and proteasomal degradation of the ubiquitin-conjugating enzyme and ERAD degrader, UBC6e. The selective ERα modulator bazedoxifene mimics CE protection of β cells in females but not in males. : Estrogens prevent diabetes in women, but the mechanism is poorly understood. Xu et al. report that estrogens activate the endoplasmic-reticulum-associated protein degradation pathway, which promotes misfolded proinsulin degradation, suppresses endoplasmic reticulum stress, and protects insulin secretion in mice and in human pancreatic β cells. Keywords: estrogens, beta cell, islet, endoplasmic reticulum stress, proinsulin misfolding, diabetes, bazedoxifene, sex dimorphism, ERAD, SER

Sharks of the order Carcharhiniformes from the British Coniacian, Santonian and Campanian (Upper Cretaceous).

Bulk sampling of phosphate-rich horizons within the British Coniacian to Campanian (Upper Cretaceous) yielded very large samples of shark and ray teeth. All of these samples yielded teeth of diverse members of the Carcharhiniformes, which commonly dominate the fauna. The following species are recorded and described: Pseudoscyliorhinus reussi (Herman, 1977) comb. nov., Crassescyliorhinus germanicus (Herman, 1982) gen. nov., Scyliorhinus elongatus (Davis, 1887), Scyliorhinus brumarivulensis sp. nov., ? Palaeoscyllium sp., Prohaploblepharus riegrafi (Müller, 1989) gen. nov., ? Cretascyliorhinus sp., Scyliorhinidae inc. sedis 1, Scyliorhinidae inc. sedis 2, Pteroscyllium hermani sp. nov., Protoscyliorhinus sp., Leptocharias cretaceus sp. nov., Palaeogaleus havreensis Herman, 1977, Paratriakis subserratus sp. nov., Paratriakis tenuis sp. nov., Paratriakis sp. indet. and ? Loxodon sp. Taxa belonging to the families ?Proscylliidae, Leptochariidae, and Carcharhinidae are described from the Cretaceous for the first time. The evolutionary and palaeoecological implications of these newly recognised faunas are discussed