41,260 research outputs found

    Fixed-Parameter Tractability of Token Jumping on Planar Graphs

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    Suppose that we are given two independent sets I0I_0 and IrI_r of a graph such that I0=Ir|I_0| = |I_r|, and imagine that a token is placed on each vertex in I0I_0. The token jumping problem is to determine whether there exists a sequence of independent sets which transforms I0I_0 into IrI_r so that each independent set in the sequence results from the previous one by moving exactly one token to another vertex. This problem is known to be PSPACE-complete even for planar graphs of maximum degree three, and W[1]-hard for general graphs when parameterized by the number of tokens. In this paper, we present a fixed-parameter algorithm for the token jumping problem on planar graphs, where the parameter is only the number of tokens. Furthermore, the algorithm can be modified so that it finds a shortest sequence for a yes-instance. The same scheme of the algorithms can be applied to a wider class of graphs, K3,tK_{3,t}-free graphs for any fixed integer t3t \ge 3, and it yields fixed-parameter algorithms

    Nutritional characteristics of moon dust for soil microorganisms

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    Approximately 46% of the lunar sample (10084,151), 125.42 mg, was solubilized in 680 ml 0.01 M salicylic acid. Atomic absorption spectroscopic analysis of the solubilized lunar sample showed the following amount of metal ions: Ca, 3.1; Mg, 4.0; K, 0.09; Na, 0.67; Fe, 7.3; Mn, 1.6; Cu, Ni, Cr, less than 0.1 each. All are in ppm. Salicylic acid used to solubilize the lunar sample was highly inhibitory to the growth of mixed soil microbes. However, the mineral part of the lunar extract stimulated the growth. For optimal growth of the soil microbes the following nutrients must be added to the moon extract; sources of carbon, nitrogen, sulfur, phosphorus, and magnesium in addition to water

    Mediation of Supersymmetry Breaking via Anti-Generation Fields

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    In the context of the weakly coupled heterotic string, we propose a new model of mediating supersymmetry breaking. The breakdown of supersymmetry in the hidden sector is transmitted to anti-generation fields via gravitational interactions. Subsequent transmission of the breaking to the MSSM sector occurs via gauge interactions. It is shown that the mass spectra of superparticles are phenomenologically viable.Comment: 8pages, LaTeX, 1 figure, final version to appear in Prog. Theor. Phys. Vol.103, No.6 (2000

    Global modeling study of potentially bioavailable iron input from shipboard aerosol sources to the ocean

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    Iron (Fe) is an essential element for phytoplankton. The majority of iron is transported from arid and semiarid regions to the open ocean, but it is mainly in an insoluble form. Since most aquatic organisms can take up iron only in the dissolved form, aerosol iron solubility is a key factor that can influence the air-sea CO2 fluxes and thus climate. Field observations have shown relatively high iron solubility in aerosols influenced by combustion sources, but specific emissions sources and their contributions to deposition fluxes largely remain uncertain. Here, a global chemical transport model is used to investigate the effect of aerosol emissions from ship plumes on iron solubility in particles from the combustion and dust sources. The model results reveal that the oil combustion from shipping mainly contributes to high iron solubility (> 10%) at low iron loading (1-110 ng m-3) observed over the high latitude North Atlantic Ocean, rather than the other combustion sources from continental industrialized regions. Due to continuing growth in global shipping and no regulations regarding particles emissions over the open ocean, the input of potentially bioavailable iron from ship plumes is likely to increase during the next century. The model results suggest that deposition of soluble iron from ships in 2100 contributes 30-60% of the soluble iron deposition over the high latitude North Atlantic and North Pacific

    Reconfiguration of Dominating Sets

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    We explore a reconfiguration version of the dominating set problem, where a dominating set in a graph GG is a set SS of vertices such that each vertex is either in SS or has a neighbour in SS. In a reconfiguration problem, the goal is to determine whether there exists a sequence of feasible solutions connecting given feasible solutions ss and tt such that each pair of consecutive solutions is adjacent according to a specified adjacency relation. Two dominating sets are adjacent if one can be formed from the other by the addition or deletion of a single vertex. For various values of kk, we consider properties of Dk(G)D_k(G), the graph consisting of a vertex for each dominating set of size at most kk and edges specified by the adjacency relation. Addressing an open question posed by Haas and Seyffarth, we demonstrate that DΓ(G)+1(G)D_{\Gamma(G)+1}(G) is not necessarily connected, for Γ(G)\Gamma(G) the maximum cardinality of a minimal dominating set in GG. The result holds even when graphs are constrained to be planar, of bounded tree-width, or bb-partite for b3b \ge 3. Moreover, we construct an infinite family of graphs such that Dγ(G)+1(G)D_{\gamma(G)+1}(G) has exponential diameter, for γ(G)\gamma(G) the minimum size of a dominating set. On the positive side, we show that Dnm(G)D_{n-m}(G) is connected and of linear diameter for any graph GG on nn vertices having at least m+1m+1 independent edges.Comment: 12 pages, 4 figure

    Reconfiguration on sparse graphs

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    A vertex-subset graph problem Q defines which subsets of the vertices of an input graph are feasible solutions. A reconfiguration variant of a vertex-subset problem asks, given two feasible solutions S and T of size k, whether it is possible to transform S into T by a sequence of vertex additions and deletions such that each intermediate set is also a feasible solution of size bounded by k. We study reconfiguration variants of two classical vertex-subset problems, namely Independent Set and Dominating Set. We denote the former by ISR and the latter by DSR. Both ISR and DSR are PSPACE-complete on graphs of bounded bandwidth and W[1]-hard parameterized by k on general graphs. We show that ISR is fixed-parameter tractable parameterized by k when the input graph is of bounded degeneracy or nowhere-dense. As a corollary, we answer positively an open question concerning the parameterized complexity of the problem on graphs of bounded treewidth. Moreover, our techniques generalize recent results showing that ISR is fixed-parameter tractable on planar graphs and graphs of bounded degree. For DSR, we show the problem fixed-parameter tractable parameterized by k when the input graph does not contain large bicliques, a class of graphs which includes graphs of bounded degeneracy and nowhere-dense graphs

    Momentum-Dependent Hybridization Gap and dispersive in-gap state of The Kondo Semiconductor SmB6

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    We report the temperature-dependent three-dimensional angle-resolved photoemission spectra of the Kondo semiconductor SmB6_6. We found a difference in the temperature dependence of the peaks at the X and Γ\Gamma points, due to hybridization between the Sm 5d conduction band and the nearly localized Sm 4f state. The peak intensity at the X point has the same temperature dependence as the valence transition below 120 K, while that at the Γ\Gamma point is consistent with the magnetic excitation at Q=(0.5,0.5,0.5) below 30 K. This suggests that the hybridization with the valence transition mainly occurs at the X point, and the initial state of the magnetic excitation is located at the Γ\Gamma point.Comment: 5 pages, 3 figure

    A numerical algorithm for optimal feedback gains in high dimensional LQR problems

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    A hybrid method for computing the feedback gains in linear quadratic regulator problems is proposed. The method, which combines the use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated so as to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantage of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed and numerical evidence of the efficacy of our ideas presented
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