A Dichotomy Theorem for the Approximate Counting of Complex-Weighted Bounded-Degree Boolean CSPs

We determine the computational complexity of approximately counting the total weight of variable assignments for every complex-weighted Boolean constraint satisfaction problem (or CSP) with any number of additional unary (i.e., arity 1) constraints, particularly, when degrees of input instances are bounded from above by a fixed constant. All degree-1 counting CSPs are obviously solvable in polynomial time. When the instance's degree is more than two, we present a dichotomy theorem that classifies all counting CSPs admitting free unary constraints into exactly two categories. This classification theorem extends, to complex-weighted problems, an earlier result on the approximation complexity of unweighted counting Boolean CSPs of bounded degree. The framework of the proof of our theorem is based on a theory of signature developed from Valiant's holographic algorithms that can efficiently solve seemingly intractable counting CSPs. Despite the use of arbitrary complex weight, our proof of the classification theorem is rather elementary and intuitive due to an extensive use of a novel notion of limited T-constructibility. For the remaining degree-2 problems, in contrast, they are as hard to approximate as Holant problems, which are a generalization of counting CSPs.Comment: A4, 10pt, 20 pages. This revised version improves its preliminary version published under a slightly different title in the Proceedings of the 4th International Conference on Combinatorial Optimization and Applications (COCOA 2010), Lecture Notes in Computer Science, Springer, Vol.6508 (Part I), pp.285--299, Kailua-Kona, Hawaii, USA, December 18--20, 201

A Laboratory Evaluation of Leachate from the Jim Bridger Power Plant Scrubber Wastes

Introduction: Scrubber wastes obtained in an affort to limit air pollution generated by coal-fired pwoer plants may contribute to another possible sources of pollution. To date, scrubber wastse have been in a liquid phase which causes disposal problems partially due to the liquid characteristics. The use of solid scrubber wastes and the land deposition of such wastes is proposed. The feasibility of solid scrubber wastes disposal in landfills is under question. The primary area of concern is the effect that water percolation through such wastes would have on groundwater quality parameters. Contamination could result either as precipitation travels downward through the wastes and into the water table or as the water table rises into the scrubber wastes and then retreats. Groundwater contamination is a key concern because it is largely irreversible and has long term consequences. Objective: Disposal methods for coal-fired power plant fly ask and scrubber wastes present a potential for the contamination of groundwater aquifers. In this study the general objective was to evaluate the physical and chemical characteristics of the leachates of scrubber weastes and associated disposal materials separately and in appropriate combinations using laboratory bench scale techniques. Two appraoches, namely column leaching and batch elutriation, were developed and used to provide indicators characterisitic of the materials tested

Trophic diversity in two grassland ecosystems

The roles of consumers (top-down forces) versus resources (bottom-up forces) as determinants of alpha diversity in a community are not well studied. Numerous community ecology models and empirical studies have provided a framework for understanding how density at various trophic levels responds to variation in the relative strength of top-down and bottom-up forces. The resulting trophic theory can be applied to understanding variation in insect diversity at different trophic levels. The objective of this research was to elucidate the strengths of direct and indirect interactions between plants and entire arthropod communities to determine the effects of trophic interactions on arthropod diversity. Grassland plant and insect diversity was measured in July 2001 to document patterns of diversity at multiple trophic levels. The study site includes riparian grasslands in North-Central Colorado on the Carpenter Ranch, owned and managed by The Nature Conservancy. This pastureland consists of sites with different management regimes: unmanaged pasture intermixed along riparian forest, and cattle grazed pasture with flood irrigation. Plant abundance and richness were higher on the grazed-irrigated pasture versus the unmanaged field. Path analysis revealed strong effects of herbivore diversity on diversity of other trophic levels. For the managed fields, top-down forces were important, with increases in enemy diversity depressing herbivore diversity, which in turn depressed plant abundance. For the unmanaged fields, bottom-up forces dominated, with increases in plant diversity causing increased herbivore diversity, which in turn increased enemy diversity. These results support hypotheses from other empirical studies, demonstrating that changes in diversity of a single trophic level can cascade to effect diversity at other, nonadjacent trophic levels

The statistical mechanics of combinatorial optimization problems with site disorder

We study the statistical mechanics of a class of problems whose phase space is the set of permutations of an ensemble of quenched random positions. Specific examples analyzed are the finite temperature traveling salesman problem on several different domains and various problems in one dimension such as the so called descent problem. We first motivate our method by analyzing these problems using the annealed approximation, then the limit of a large number of points we develop a formalism to carry out the quenched calculation. This formalism does not require the replica method and its predictions are found to agree with Monte Carlo simulations. In addition our method reproduces an exact mathematical result for the Maximum traveling salesman problem in two dimensions and suggests its generalization to higher dimensions. The general approach may provide an alternative method to study certain systems with quenched disorder.Comment: 21 pages RevTex, 8 figure

Rations for wintering ewes

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Fine Structures of Shock of SN 1006 with the Chandra Observation

The north east shell of SN 1006 is the most probable acceleration site of high energy electrons (up to ~ 100 TeV) with the Fermi acceleration mechanism at the shock front. We resolved non-thermal filaments from thermal emission in the shell with the excellent spatial resolution of Chandra. The thermal component is extended widely over about ~ 100 arcsec (about 1 pc at 1.8 kpc distance) in width, consistent with the shock width derived from the Sedov solution. The spectrum is fitted with a thin thermal plasma of kT = 0.24 keV in non-equilibrium ionization (NEI), typical for a young SNR. The non-thermal filaments are likely thin sheets with the scale widths of ~ 4 arcsec (0.04 pc) and ~ 20 arcsec (0.2 pc) at upstream and downstream, respectively. The spectra of the filaments are fitted with a power-law function of index 2.1--2.3, with no significant variation from position to position. In a standard diffusive shock acceleration (DSA) model, the extremely small scale length in upstream requires the magnetic field nearly perpendicular to the shock normal. The injection efficiency (eta) from thermal to non-thermal electrons around the shock front is estimated to be ~ 1e-3 under the assumption that the magnetic field in upstream is 10 micro G. In the filaments, the energy densities of the magnetic field and non-thermal electrons are similar to each other, and both are slightly smaller than that of thermal electrons. in the same order for each other. These results suggest that the acceleration occur in more compact region with larger efficiency than previous studies.Comment: 24 pages, 11 figures, Accepted for publication in ApJ, the paper with full resolution images in http://www-cr.scphys.kyoto-u.ac.jp/member/bamba/Paper/SN1006.pd

Spatially-resolved Thermal Continuum Absorption against the Supernova Remnant W49B

We present sub-arcminute resolution imaging of the Galactic supernova remnant W49B at 74 MHz (25") and 327 MHz (6"), the former being the lowest frequency at which the source has been resolved. While the 327 MHz image shows a shell-like morphology similar to that seen at higher frequencies, the 74 MHz image is considerably different, with the southwest region of the remnant almost completely attenuated. The implied 74 MHz optical depth (~ 1.6) is much higher than the intrinsic absorption levels seen inside two other relatively young remnants, Cas A and the Crab Nebula, nor are natural variations in the relativistic electron energy spectra expected at such levels. The geometry of the absorption is also inconsistent with intrinsic absorption. We attribute the absorption to extrinsic free-free absorption by a intervening cloud of thermal electrons. Its presence has already been inferred from the low-frequency turnover in the integrated continuum spectrum and from the detection of radio recombination lines toward the remnant. Our observations confirm the basic conclusions of those measurements, and our observations have resolved the absorber into a complex of classical HII regions surrounded either partially or fully by low-density HII gas. We identify this low-density gas as an extended HII region envelope (EHE), whose statistical properties were inferred from low resolution meter- and centimeter-wavelength recombination line observations. Comparison of our radio images with HI and H_2CO observations show that the intervening thermal gas is likely associated with neutral and molecular material as well.Comment: 18 pages, LaTeX with AASTeX-5, 5 figures in 7 PostScript files; accepted for publication in the Ap