The Complexity of Computing Minimal Unidirectional Covering Sets

Given a binary dominance relation on a set of alternatives, a common thread in the social sciences is to identify subsets of alternatives that satisfy certain notions of stability. Examples can be found in areas as diverse as voting theory, game theory, and argumentation theory. Brandt and Fischer [BF08] proved that it is NP-hard to decide whether an alternative is contained in some inclusion-minimal upward or downward covering set. For both problems, we raise this lower bound to the Theta_{2}^{p} level of the polynomial hierarchy and provide a Sigma_{2}^{p} upper bound. Relatedly, we show that a variety of other natural problems regarding minimal or minimum-size covering sets are hard or complete for either of NP, coNP, and Theta_{2}^{p}. An important consequence of our results is that neither minimal upward nor minimal downward covering sets (even when guaranteed to exist) can be computed in polynomial time unless P=NP. This sharply contrasts with Brandt and Fischer's result that minimal bidirectional covering sets (i.e., sets that are both minimal upward and minimal downward covering sets) are polynomial-time computable.Comment: 27 pages, 7 figure

INTEGRAL upper limits on gamma-ray emission associated with the gravitational wave event GW150914

Using observations of the INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL), we put upper limits on the gamma-ray and hard X-ray prompt emission associated with the gravitational wave event GW150914, discovered by the LIGO/Virgo collaboration. The omni-directional view of the INTEGRAL/SPI-ACS has allowed us to constrain the fraction of energy emitted in the hard X-ray electromagnetic component for the full high-probability sky region of LIGO trigger. Our upper limits on the hard X-ray fluence at the time of the event range from $F_{\gamma}=2 \times 10^{-8}$ erg cm$^{-2}$ to $F_{\gamma}=10^{-6}$ erg cm$^{-2}$ in the 75 keV - 2 MeV energy range for typical spectral models. Our results constrain the ratio of the energy promptly released in gamma-rays in the direction of the observer to the gravitational wave energy E$_\gamma/$E$_\mathrm{GW}<10^{-6}$. We discuss the implication of gamma-ray limits on the characteristics of the gravitational wave source, based on the available predictions for prompt electromagnetic emission.Comment: accepted for publication in ApJ

Low Energy Analyzing Powers in Pion-Proton Elastic Scattering

Analyzing powers of pion-proton elastic scattering have been measured at PSI with the Low Energy Pion Spectrometer LEPS as well as a novel polarized scintillator target. Angular distributions between 40 and 120 deg (c.m.) were taken at 45.2, 51.2, 57.2, 68.5, 77.2, and 87.2 MeV incoming pion kinetic energy for pi+ p scattering, and at 67.3 and 87.2 MeV for pi- p scattering. These new measurements constitute a substantial extension of the polarization data base at low energies. Predictions from phase shift analyses are compared with the experimental results, and deviations are observed at low energies.Comment: 15 pages, 4 figure

Genetic-Algorithm-based Light Curve Optimization Applied to Observations of the W UMa star BH Cas

I have developed a procedure utilizing a Genetic-Algorithm-based optimization scheme to fit the observed light curves of an eclipsing binary star with a model produced by the Wilson-Devinney code. The principal advantages of this approach are the global search capability and the objectivity of the final result. Although this method can be more efficient than some other comparably global search techniques, the computational requirements of the code are still considerable. I have applied this fitting procedure to my observations of the W UMa type eclipsing binary BH Cassiopeiae. An analysis of V-band CCD data obtained in 1994/95 from Steward Observatory and U- and B-band photoelectric data obtained in 1996 from McDonald Observatory provided three complete light curves to constrain the fit. In addition, radial velocity curves obtained in 1997 from McDonald Observatory provided a direct measurement of the system mass ratio to restrict the search. The results of the GA-based fit are in excellent agreement with the final orbital solution obtained with the standard differential corrections procedure in the Wilson-Devinney code.Comment: 9 pages, 2 figures, 2 tables, uses emulateapj.st

A Real-Space Full Multigrid study of the fragmentation of Li11+ clusters

We have studied the fragmentation of Li11+ clusters into the two experimentally observed products (Li9+,Li2) and (Li10+,Li) The ground state structures for the two fragmentation channels are found by Molecular Dynamics Simulated Annealing in the framework of Local Density Functional theory. Energetics considerations suggest that the fragmentation process is dominated by non-equilibrium processes. We use a real-space approach to solve the Kohn-Sham problem, where the Laplacian operator is discretized according to the Mehrstellen scheme, and take advantage of a Full MultiGrid (FMG) strategy to accelerate convergence. When applied to isolated clusters we find our FMG method to be more efficient than state-of-the-art plane wave calculations.Comment: 9 pages + 6 Figures (in gzipped tar file

Ultra-heavy cosmic-ray science--Are r-process nuclei in the cosmic rays produced in supernovae or binary neutron star mergers?

The recent detection of 60Fe in the cosmic rays provides conclusive evidence that there is a recently synthesized component (few MY) in the GCRs (Binns et al. 2016). In addition, these nuclei must have been synthesized and accelerated in supernovae near the solar system, probably in the Sco-Cen OB association subgroups, which are about 100 pc distant from the Sun. Recent theoretical work on the production of r-process nuclei appears to indicate that it is difficult for SNe to produce the solar system abundances relative to iron of r-process elements with high atomic number (Z), including the actinides (Th, U, Np, Pu, and Cm). Instead, it is believed by many that the heaviest r-process nuclei, or perhaps even all r-process nuclei, are produced in binary neutron star mergers. Since we now know that there is at least a component of the GCRs that has been recently synthesized and accelerated, models of r-process production by SNe and BNSM can be tested by measuring the relative abundances of these ultra-heavy r-process nuclei, and especially the actinides, since they are radioactive and provide clocks that give the time interval from nucleosynthesis to detection at Earth. Since BNSM are believed to be much less frequent in our galaxy than SNe (roughly 1000 times less frequent, the ratios of the actinides, each with their own half-life, will enable a clear determination of whether the heaviest r-process nuclei are synthesized in SNe or in BNSM. In addition, the r-process nuclei for the charge range from 34 to 82 can be used to constrain models of r-process production in BNSM and SNe. Thus, GCRs become a multi-messenger component in the study of BNSM and SNe.Comment: Astro2020 Science White Pape

The INTEGRAL view of the Soft Gamma-ray Repeater SGR 1806-20

We present the results obtained by INTEGRAL on the Soft-Gamma Ray Repeater SGR 1806-20. In particular we report on the temporal and spectral properties of the bursts detected during a moderately active period of the source in September and October 2003 and on the search for quiescent emission.Comment: To appear in the proceedings (ESA-SP) of the 5th INTEGRAL Workshop, "The INTEGRAL UNIVERSE", Munich, 16-20 February 200

The nature of localization in graphene under quantum Hall conditions

Particle localization is an essential ingredient in quantum Hall physics [1,2]. In conventional high mobility two-dimensional electron systems Coulomb interactions were shown to compete with disorder and to play a central role in particle localization [3]. Here we address the nature of localization in graphene where the carrier mobility, quantifying the disorder, is two to four orders of magnitude smaller [4,5,6,7,8,9,10]. We image the electronic density of states and the localized state spectrum of a graphene flake in the quantum Hall regime with a scanning single electron transistor [11]. Our microscopic approach provides direct insight into the nature of localization. Surprisingly, despite strong disorder, our findings indicate that localization in graphene is not dominated by single particle physics, but rather by a competition between the underlying disorder potential and the repulsive Coulomb interaction responsible for screening.Comment: 18 pages, including 5 figure

Elemental Abundances of Ultra-Heavy GCRs measured by SuperTIGER and ACE-CRIS and the Origin of Galactic Cosmic Rays

The Super Trans-Iron Galactic Element Recorder (SuperTIGER) long-duration balloon instrument and the Cosmic Ray Isotope Spectrometer (CRIS) on the NASA Advanced Composition Explorer (ACE) satellite have measured the abundances of galactic cosmic-ray elements from _(10)Ne to _(40)Zr with high statistics and single-element resolution. SuperTIGER launched from Williams Field, McMurdo Station, Antarctica, on December 8, 2012, flying for a record 55 days. During that flight we detected ∼1,300 nuclei with atomic number Z ≥ 30. The resolution in charge (Z) of SuperTIGER is excellent, with σ_Z ≈ 0.16 c.u. at _(26)Fe. SuperTIGER is sensitive to nuclei with energy at the top of the atmosphere of E > 0.8 GeV/nucleon. The instrument has now been recovered and preparations are underway for its next flight. ACE/CRIS has been taking data in space for more than 17 years since launch in 1997, has collected ∼625 nuclei with atomic number Z ≥ 30, and shows excellent resolution with clear separation between the charges for 30 ≤ Z ≤ 40. ACE/CRIS is sensitive to nuclei in the energy range 150 ≤ E ≤ 600 MeV/nucleon. Preliminary results from the balloon-borne SuperTIGER show good agreement with ACE measurements in space, validating our corrections to SuperTIGER abundances for nuclear interactions in the atmosphere. The results from these experiments will be discussed in the context of the OB association model for the origin of galactic cosmic rays. Future missions to measure elemental abundances to higher Z, the SuperTIGER-II LDB instrument and the orbiting Heavy Nuclei eXplorer (HNX) mission, will also be discussed