Political districting without geography

Geographical considerations such as contiguity and compactness are necessary elements of political districting in practice. Yet an analysis of the problem without such constraints yields mathematical insights that can inform real-world model construction. In particular, it clarifies the sharp contrast between proportionality and competitiveness and how it might be overcome in a properly formulated objective function. It also reveals serious weaknesses of the much-discussed efficiency gap as a criterion for gerrymandering.Published versio

Approximate k-state solutions to the Dirac-Yukawa problem based on the spin and pseudospin symmetry

Using an approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation with the screened Coulomb (Yukawa) potential for any arbitrary spin-orbit quantum number {\kappa}. Based on the spin and pseudospin symmetry, analytic bound state energy spectrum formulas and their corresponding upper- and lower-spinor components of two Dirac particles are obtained using a shortcut of the Nikiforov-Uvarov method. We find a wide range of permissible values for the spin symmetry constant C_{s} from the valence energy spectrum of particle and also for pseudospin symmetry constant C_{ps} from the hole energy spectrum of antiparticle. Further, we show that the present potential interaction becomes less (more) attractive for a long (short) range screening parameter {\alpha}. To remove the degeneracies in energy levels we consider the spin and pseudospin solution of Dirac equation for Yukawa potential plus a centrifugal-like term. A few special cases such as the exact spin (pseudospin) symmetry Dirac-Yukawa, the Yukawa plus centrifugal-like potentials, the limit when {\alpha} becomes zero (Coulomb potential field) and the non-relativistic limit of our solution are studied. The nonrelativistic solutions are compared with those obtained by other methods.Comment: 21 pages, 6 figure

Finding Faint Intermediate-mass Black Holes in the Radio Band

We discuss the prospects for detecting faint intermediate-mass black holes, such as those predicted to exist in the cores of globular clusters and dwarf spheroidal galaxies. We briefly summarize the difficulties of stellar dynamical searches, then show that recently discovered relations between black hole mass, X-ray luminosity and radio luminosity imply that in most cases, these black holes should be more easily detected in the radio than in the X-rays. Finally, we show upper limits from some radio observations of globular clusters, and discuss the possibility that the radio source in the core of the Ursa Minor dwarf spheroidal galaxy might be a $\sim 10,000-100,000 M_\odot$ black hole.Comment: 10 pages, no figures, to appear in From X-ray Binaries to Quasars: Black Hole Accretion on All Mass Scales, ed. T. J. Maccarone, R. P. Fender, and L. C. Ho (Dordrecht: Kluwer

A meta-analysis of genome-wide association studies of growth differentiation Factor-15 concentration in blood

Blood levels of growth differentiation factor-15 (GDF-15), also known as macrophage inhibitory cytokine-1 (MIC-1), have been associated with various pathological processes and diseases, including cardiovascular disease and cancer. Prior studies suggest genetic factors play a role in regulating blood MIC-1/GDF-15 concentration. In the current study, we conducted the largest genome-wide association study (GWAS) to date using a sample of ∼5,400 community-based Caucasian participants, to determine the genetic variants associated with MIC-1/GDF-15 blood concentration. Conditional and joint (COJO), gene-based association, and gene-set enrichment analyses were also carried out to identify novel loci, genes, and pathways. Consistent with prior results, a locus on chromosome 19, which includes nine single nucleotide polymorphisms (SNPs) (top SNP, rs888663, p = 1.690 × 10-35), was significantly associated with blood MIC-1/GDF-15 concentration, and explained 21.47% of its variance. COJO analysis showed evidence for two independent signals within this locus. Gene-based analysis confirmed the chromosome 19 locus association and in addition, a putative locus on chromosome 1. Gene-set enrichment analyses showed that the“COPI-mediated anterograde transport” gene-set was associated with MIC-1/GDF15 blood concentration with marginal significance after FDR correction (p = 0.067). In conclusion, a locus on chromosome 19 was associated with MIC-1/GDF-15 blood concentration with genome-wide significance, with evidence for a new locus (chromosome 1). Future studies using independent cohorts are needed to confirm the observed associations especially for the chromosomes 1 locus, and to further investigate and identify the causal SNPs that contribute to MIC-1/GDF-15 levels

Quasars and their host galaxies

This review attempts to describe developments in the fields of quasar and quasar host galaxies in the past five. In this time period, the Sloan and 2dF quasar surveys have added several tens of thousands of quasars, with Sloan quasars being found to z>6. Obscured, or partially obscured quasars have begun to be found in significant numbers. Black hole mass estimates for quasars, and our confidence in them, have improved significantly, allowing a start on relating quasar properties such as radio jet power to fundamental parameters of the quasar such as black hole mass and accretion rate. Quasar host galaxy studies have allowed us to find and characterize the host galaxies of quasars to z>2. Despite these developments, many questions remain unresolved, in particular the origin of the close relationship between black hole mass and galaxy bulge mass/velocity dispersion seen in local galaxies.Comment: Review article, to appear in Astrophysics Update

The Fueling and Evolution of AGN: Internal and External Triggers

In this chapter, I review the fueling and evolution of active galactic nuclei (AGN) under the influence of internal and external triggers, namely intrinsic properties of host galaxies (morphological or Hubble type, color, presence of bars and other non-axisymmetric features, etc) and external factors such as environment and interactions. The most daunting challenge in fueling AGN is arguably the angular momentum problem as even matter located at a radius of a few hundred pc must lose more than 99.99 % of its specific angular momentum before it is fit for consumption by a BH. I review mass accretion rates, angular momentum requirements, the effectiveness of different fueling mechanisms, and the growth and mass density of black BHs at different epochs. I discuss connections between the nuclear and larger-scale properties of AGN, both locally and at intermediate redshifts, outlining some recent results from the GEMS and GOODS HST surveys.Comment: Invited Review Chapter to appear in LNP Volume on "AGN Physics on All Scales", Chapter 6, in press. 40 pages, 12 figures. Typo in Eq 5 correcte

Star Formation and Dynamics in the Galactic Centre

The centre of our Galaxy is one of the most studied and yet enigmatic places in the Universe. At a distance of about 8 kpc from our Sun, the Galactic centre (GC) is the ideal environment to study the extreme processes that take place in the vicinity of a supermassive black hole (SMBH). Despite the hostile environment, several tens of early-type stars populate the central parsec of our Galaxy. A fraction of them lie in a thin ring with mild eccentricity and inner radius ~0.04 pc, while the S-stars, i.e. the ~30 stars closest to the SMBH (<0.04 pc), have randomly oriented and highly eccentric orbits. The formation of such early-type stars has been a puzzle for a long time: molecular clouds should be tidally disrupted by the SMBH before they can fragment into stars. We review the main scenarios proposed to explain the formation and the dynamical evolution of the early-type stars in the GC. In particular, we discuss the most popular in situ scenarios (accretion disc fragmentation and molecular cloud disruption) and migration scenarios (star cluster inspiral and Hills mechanism). We focus on the most pressing challenges that must be faced to shed light on the process of star formation in the vicinity of a SMBH.Comment: 68 pages, 35 figures; invited review chapter, to be published in expanded form in Haardt, F., Gorini, V., Moschella, U. and Treves, A., 'Astrophysical Black Holes'. Lecture Notes in Physics. Springer 201

Green function techniques in the treatment of quantum transport at the molecular scale

The theoretical investigation of charge (and spin) transport at nanometer length scales requires the use of advanced and powerful techniques able to deal with the dynamical properties of the relevant physical systems, to explicitly include out-of-equilibrium situations typical for electrical/heat transport as well as to take into account interaction effects in a systematic way. Equilibrium Green function techniques and their extension to non-equilibrium situations via the Keldysh formalism build one of the pillars of current state-of-the-art approaches to quantum transport which have been implemented in both model Hamiltonian formulations and first-principle methodologies. We offer a tutorial overview of the applications of Green functions to deal with some fundamental aspects of charge transport at the nanoscale, mainly focusing on applications to model Hamiltonian formulations.Comment: Tutorial review, LaTeX, 129 pages, 41 figures, 300 references, submitted to Springer series "Lecture Notes in Physics

The Unitary Gas and its Symmetry Properties

The physics of atomic quantum gases is currently taking advantage of a powerful tool, the possibility to fully adjust the interaction strength between atoms using a magnetically controlled Feshbach resonance. For fermions with two internal states, formally two opposite spin states, this allows to prepare long lived strongly interacting three-dimensional gases and to study the BEC-BCS crossover. Of particular interest along the BEC-BCS crossover is the so-called unitary gas, where the atomic interaction potential between the opposite spin states has virtually an infinite scattering length and a zero range. This unitary gas is the main subject of the present chapter: It has fascinating symmetry properties, from a simple scaling invariance, to a more subtle dynamical symmetry in an isotropic harmonic trap, which is linked to a separability of the N-body problem in hyperspherical coordinates. Other analytical results, valid over the whole BEC-BCS crossover, are presented, establishing a connection between three recently measured quantities, the tail of the momentum distribution, the short range part of the pair distribution function and the mean number of closed channel molecules.Comment: 63 pages, 8 figures. Contribution to the Springer Lecture Notes in Physics "BEC-BCS Crossover and the Unitary Fermi gas" edited by Wilhelm Zwerger. Revised version correcting a few typo