Optimal Image Reconstruction in Radio Interferometry

We introduce a method for analyzing radio interferometry data which produces maps which are optimal in the Bayesian sense of maximum posterior probability density, given certain prior assumptions. It is similar to maximum entropy techniques, but with an exact accounting of the multiplicity instead of the usual approximation involving Stirling's formula. It also incorporates an Occam factor, automatically limiting the effective amount of detail in the map to that justified by the data. We use Gibbs sampling to determine, to any desired degree of accuracy, the multi-dimensional posterior density distribution. From this we can construct a mean posterior map and other measures of the posterior density, including confidence limits on any well-defined function of the posterior map.Comment: 41 pages, 11 figures. High resolution figures 8 and 9 available at http://www.astro.uiuc.edu/~bwandelt/SuttonWandelt200

Romantic Partnerships and the Dispersion of Social Ties: A Network Analysis of Relationship Status on Facebook

A crucial task in the analysis of on-line social-networking systems is to identify important people --- those linked by strong social ties --- within an individual's network neighborhood. Here we investigate this question for a particular category of strong ties, those involving spouses or romantic partners. We organize our analysis around a basic question: given all the connections among a person's friends, can you recognize his or her romantic partner from the network structure alone? Using data from a large sample of Facebook users, we find that this task can be accomplished with high accuracy, but doing so requires the development of a new measure of tie strength that we term `dispersion' --- the extent to which two people's mutual friends are not themselves well-connected. The results offer methods for identifying types of structurally significant people in on-line applications, and suggest a potential expansion of existing theories of tie strength.Comment: Proc. 17th ACM Conference on Computer Supported Cooperative Work and Social Computing (CSCW), 201

On the Enhanced Interstellar Scattering Toward B1849+005

(Abridged) This paper reports new Very Large Array (VLA) and Very Long Baseline Array (VLBA) observations of the extragalactic source B1849+005 at frequencies between 0.33 and 15 GHz and the re-analysis of archival VLA observations at 0.33, 1.5, and 4.9 GHz. The structure of this source is complex but interstellar scattering dominates the structure of the central component at least to 15 GHz. An analysis of the phase structure functions of the interferometric visibilities shows the density fluctuations along this line of sight to be anisotropic (axial ratio = 1.3) with a frequency-independent position angle, and having an inner scale of roughly a few hundred kilometers. The anisotropies occur on length scales of order 10^{15} cm (D/5 kpc), which within the context of certain magnetohydrodynamic turbulence theories indicates the length scale on which the kinetic and magnetic energy densities are comparable. A conservative upper limit on the velocity of the scattering material is 1800 km/s. In the 0.33 GHz field of view, there are a number of other sources that might also be heavily scattered. Both B1849+005 and PSR B1849+00 are highly scattered, and they are separated by only 13'. If the lines of sight are affected by the same ``clump'' of scattering material, it must be at least 2.3 kpc distant. However, a detailed attempt to account for the scattering observables toward these sources does not produce a self-consistent set of parameters for such a clump. A clump of H\alpha emission, possibly associated with the H II region G33.418-0.004, lies between these two lines of sight, but it seems unable to account for all of the required excess scattering.Comment: 23 pages, LaTeX2e AASTeX, 13 figures in 14 PostScript files, accepted for publication in Ap

Development of a unified tensor calculus for the exceptional Lie algebras

The uniformity of the decomposition law, for a family F of Lie algebras which includes the exceptional Lie algebras, of the tensor powers ad^n of their adjoint representations ad is now well-known. This paper uses it to embark on the development of a unified tensor calculus for the exceptional Lie algebras. It deals explicitly with all the tensors that arise at the n=2 stage, obtaining a large body of systematic information about their properties and identities satisfied by them. Some results at the n=3 level are obtained, including a simple derivation of the the dimension and Casimir eigenvalue data for all the constituents of ad^3. This is vital input data for treating the set of all tensors that enter the picture at the n=3 level, following a path already known to be viable for a_1. The special way in which the Lie algebra d_4 conforms to its place in the family F alongside the exceptional Lie algebras is described.Comment: 27 pages, LaTeX 2

Quantum simulations under translational symmetry

We investigate the power of quantum systems for the simulation of Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range interactions we determine time evolutions which can and those that can not be simulated. Whereas for general spin systems no finite universal set of generating interactions is shown to exist, universality turns out to be generic for quadratic bosonic and fermionic nearest-neighbor interactions when supplemented by all translationally invariant on-site Hamiltonians.Comment: 9 pages, 2 figures, references added, minor change

On the terms violating the custodial symmetry in multi-Higgs-doublet models

We prove that a generic multi-Higgs-doublet model (NHDM) generally must contain terms in the potential that violate the custodial symmetry. This is done by showing that the O(4) violating terms of the NHDM potential cannot be excluded by imposing a symmetry on the NHDM Lagrangian. Hence we expect higher-order corrections to necessarily introduce such terms. We also note, in the case of custodially symmetric Higgs-quark couplings, that vacuum alignment will lead to up-down mass degeneration; this is not true if the vacua are not aligned.Comment: 16 pages, 1 figure. Title and abstract are modified, conclusions remain the same. Section on Yukawa couplings is extended. Published versio

GSH23.0-0.7+117, a neutral hydrogen shell in the inner Galaxy

GSH23.0-0.7+117 is a well-defined neutral hydrogen shell discovered in the VLA Galactic Plane Survey (VGPS). Only the blueshifted side of the shell was detected. The expansion velocity and systemic velocity were determined through the systematic behavior of the HI emission with velocity. The center of the shell is at (l,b,v)=(23.05,-0.77,+117 km/s). The angular radius of the shell is 6.8', or 15 pc at a distance of 7.8 kpc. The HI mass divided by the volume of the half-shell implies an average density n_H = 11 +/- 4 cm^{-3} for the medium in which the shell expanded. The estimated age of GSH23.0-0.7+117 is 1 Myr, with an upper limit of 2 Myr. The modest expansion energy of 2 * 10^{48} erg can be provided by the stellar wind of a single O4 to O8 star over the age of the shell. The 3 sigma upper limit to the 1.4 GHz continuum flux density (S_{1.4} < 248 mJy) is used to derive an upper limit to the Lyman continuum luminosity generated inside the shell. This upper limit implies a maximum of one O9 star (O8 to O9.5 taking into account the error in the distance) inside the HI shell, unless most of the incident ionizing flux leaks through the HI shell. To allow this, the shell should be fragmented on scales smaller than the beam (2.3 pc). If the stellar wind bubble is not adiabatic, or the bubble has burst (as suggested by the HI channel maps), agreement between the energy and ionization requirements is even less likely. The limit set by the non-detection in the continuum provides a significant challenge for the interpretation of GSH23.0-0.7+117 as a stellar wind bubble. A similar analysis may be applicable to other Galactic HI shells that have not been detected in the continuum.Comment: 18 pages, 6 figures. Figures 1 and 4 separately in GIF format. Accepted for publication in Astrophysical Journa

Influence of symmetry and Coulomb-correlation effects on the optical properties of nitride quantum dots

The electronic and optical properties of self-assembled InN/GaN quantum dots (QDs) are investigated by means of a tight-binding model combined with configuration interaction calculations. Tight-binding single particle wave functions are used as a basis for computing Coulomb and dipole matrix elements. Within this framework, we analyze multi-exciton emission spectra for two different sizes of a lens-shaped InN/GaN QD with wurtzite crystal structure. The impact of the symmetry of the involved electron and hole one-particle states on the optical spectra is discussed in detail. Furthermore we show how the characteristic features of the spectra can be interpreted using a simplified Hamiltonian which provides analytical results for the interacting multi-exciton complexes. We predict a vanishing exciton and biexciton ground state emission for small lens-shaped InN/GaN QDs. For larger systems we report a bright ground state emission but with drastically reduced oscillator strengths caused by the quantum confined Stark effect.Comment: 15 pages, 17 figure

A note on graded Yang-Baxter solutions as braid-monoid invariants

We construct two $Osp(n|2m)$ solutions of the graded Yang-Baxter equation by using the algebraic braid-monoid approach. The factorizable S-matrix interpretation of these solutions is also discussed.Comment: 7 pages, UFSCARF-TH-94-1