Some Systematics of Galactic Globular Clusters

The global properties of all known Galactic globular clusters are examined. The relationship between the luminosities and the metallicities of Galactic globular clusters is found to be complex. Among luminous clusters there is a correlation in the sense that the oldest clusters are slightly more metal deficient than are younger clusters. However, no such clear-cut relationship is found among the faintest globular clusters. The central concentration index C of globular clusters is seen to be independent of metallicity. The dependence of the half-light radii of globular clusters on their Galactocentric distances can be approximated by the relation $R_h \alpha R^{2/3}_{gc}$. Clusters with collapsed cores are mostly situated close to the Galactic nucleus. For $R_{gc} < 10$ kpc the luminosities and the radii of clusters appear to be uncorrelated. The Galaxy differs from the LMC and the SMC in that it appears to lack highly flattened luminous clusters. Galactic globular clusters with ages $\geq$ 13.0 Gyr are all of Oosterhoff type II, whereas almost all of those with ages $<$ 13.0 Gyr have been assigned to Oosterhoff type I. Globular clusters with ages $<$11.5 Gyr are all located in the outer Galactic halo, have below-average luminosities and above-average radii. On the other hand the very old globular cluster NGC 6522 is situated close to the Galactic nucleus.Comment: PASP, in pres

First Report of Transmission of Soybean Mosaic Virus and Alfalfa Mosaic Virus by Aphis glycines in the New World

Originating text in English.Citation: Hill, J. H., Alleman, R., Hogg, D. B., Grau, C. R. (2001). First Report of Transmission of Soybean Mosaic Virus and Alfalfa Mosaic Virus by Aphis glycines in the New World. Plant Disease, 85(5), 561-561

Imaging of Ultraluminous Infrared Galaxies in the Near-UV

We present the first ground-based U' (3410 angstroms) images of Ultraluminous Infrared Galaxies (ULIGs). Strong U' emission (median total M_U' = -20.8) is seen in all systems and in some cases the extended tidal features (both the smooth stellar distribution and compact star-forming features) contribute up to 60-80% of the total flux. The star-forming regions in both samples are found to have ages based on spectral synthesis models in the range 10-100 Myrs, and most differences in color between them can be attributed to the effects of dust reddening. Additionally, it is found that star-formation in compact knots in the tidal tails is most prominent in those ULIGs which have double nuclei, suggesting that the star-formation rate in the tails peaks prior to the actual coalescence of the galaxy nuclei and diminishes quickly thereafter. Similar to results at other wavelengths, the observed star formation at U' can only account for a small fraction of the known bolometric luminosity of the ULIGs. Azimuthally averaged radial light profiles at U' are characterized by a sersic law with index n=2, which is intermediate between an exponential disk and an r^(-1/4) law and closely resembles the latter at large radii. The implications of this near-ultraviolet imaging for optical/near-infrared observations of high redshift counterparts of ULIGs are discussed.Comment: 30 pages, 4 tables, and 9 figures, 2 of which are JPEGs. To appear in the August, 2000 edition of the Astronomical Journa

Quantum Portfolios

Quantum computation holds promise for the solution of many intractable problems. However, since many quantum algorithms are stochastic in nature they can only find the solution of hard problems probabilistically. Thus the efficiency of the algorithms has to be characterized both by the expected time to completion {\it and} the associated variance. In order to minimize both the running time and its uncertainty, we show that portfolios of quantum algorithms analogous to those of finance can outperform single algorithms when applied to the NP-complete problems such as 3-SAT.Comment: revision includes additional data and corrects minor typo

Fast computation by block permanents of cumulative distribution functions of order statistics from several populations

The joint cumulative distribution function for order statistics arising from several different populations is given in terms of the distribution function of the populations. The computational cost of the formula in the case of two populations is still exponential in the worst case, but it is a dramatic improvement compared to the general formula by Bapat and Beg. In the case when only the joint distribution function of a subset of the order statistics of fixed size is needed, the complexity is polynomial, for the case of two populations.Comment: 21 pages, 3 figure

Extremal Optimization at the Phase Transition of the 3-Coloring Problem

We investigate the phase transition of the 3-coloring problem on random graphs, using the extremal optimization heuristic. 3-coloring is among the hardest combinatorial optimization problems and is closely related to a 3-state anti-ferromagnetic Potts model. Like many other such optimization problems, it has been shown to exhibit a phase transition in its ground state behavior under variation of a system parameter: the graph's mean vertex degree. This phase transition is often associated with the instances of highest complexity. We use extremal optimization to measure the ground state cost and the ``backbone'', an order parameter related to ground state overlap, averaged over a large number of instances near the transition for random graphs of size $n$ up to 512. For graphs up to this size, benchmarks show that extremal optimization reaches ground states and explores a sufficient number of them to give the correct backbone value after about $O(n^{3.5})$ update steps. Finite size scaling gives a critical mean degree value $\alpha_{\rm c}=4.703(28)$. Furthermore, the exploration of the degenerate ground states indicates that the backbone order parameter, measuring the constrainedness of the problem, exhibits a first-order phase transition.Comment: RevTex4, 8 pages, 4 postscript figures, related information available at http://www.physics.emory.edu/faculty/boettcher

Can the Copernican principle be tested by cosmic neutrino background?

The Copernican principle, stating that we do not occupy any special place in our universe, is usually taken for granted in modern cosmology. However recent observational data of supernova indicate that we may live in the under-dense center of our universe, which makes the Copernican principle challenged. It thus becomes urgent and important to test the Copernican principle via cosmological observations. Taking into account that unlike the cosmic photons, the cosmic neutrinos of different energies come from the different places to us along the different worldlines, we here propose cosmic neutrino background as a test of the Copernican principle. It is shown that from the theoretical perspective cosmic neutrino background can allow one to determine whether the Copernican principle is valid or not, but to implement such an observation the larger neutrino detectors are called for.Comment: JHEP style, 10 pages, 4 figures, version to appear in JCA

Nested quantum search and NP-complete problems

A quantum algorithm is known that solves an unstructured search problem in a number of iterations of order $\sqrt{d}$, where $d$ is the dimension of the search space, whereas any classical algorithm necessarily scales as $O(d)$. It is shown here that an improved quantum search algorithm can be devised that exploits the structure of a tree search problem by nesting this standard search algorithm. The number of iterations required to find the solution of an average instance of a constraint satisfaction problem scales as $\sqrt{d^\alpha}$, with a constant $\alpha<1$ depending on the nesting depth and the problem considered. When applying a single nesting level to a problem with constraints of size 2 such as the graph coloring problem, this constant $\alpha$ is estimated to be around 0.62 for average instances of maximum difficulty. This corresponds to a square-root speedup over a classical nested search algorithm, of which our presented algorithm is the quantum counterpart.Comment: 18 pages RevTeX, 3 Postscript figure

The overdensities of galaxy environments as a function of luminosity and color

We study the mean environments of galaxies in the Sloan Digital Sky Survey as a function of rest-frame luminosity and color. Overdensities in galaxy number are estimated in $8 h^{-1} \mathrm{Mpc}$ and $1 h^{-1} \mathrm{Mpc}$ spheres centered on $125,000$ galaxies taken from the SDSS spectroscopic sample. We find that, at constant color, overdensity is independent of luminosity for galaxies with the blue colors of spirals. This suggests that, at fixed star-formation history, spiral-galaxy mass is a very weak function of environment. Overdensity does depend on luminosity for galaxies with the red colors of early types; both low-luminosity and high-luminosity red galaxies are found to be in highly overdense regions.Comment: submitted to ApJ