85 research outputs found

    The Gravitational Universe

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    The last century has seen enormous progress in our understanding of the Universe. We know the life cycles of stars, the structure of galaxies, the remnants of the big bang, and have a general understanding of how the Universe evolved. We have come remarkably far using electromagnetic radiation as our tool for observing the Universe. However, gravity is the engine behind many of the processes in the Universe, and much of its action is dark. Opening a gravitational window on the Universe will let us go further than any alternative. Gravity has its own messenger: Gravitational waves, ripples in the fabric of spacetime. They travel essentially undisturbed and let us peer deep into the formation of the first seed black holes, exploring redshifts as large as z ~ 20, prior to the epoch of cosmic re-ionisation. Exquisite and unprecedented measurements of black hole masses and spins will make it possible to trace the history of black holes across all stages of galaxy evolution, and at the same time constrain any deviation from the Kerr metric of General Relativity. eLISA will be the first ever mission to study the entire Universe with gravitational waves. eLISA is an all-sky monitor and will offer a wide view of a dynamic cosmos using gravitational waves as new and unique messengers to unveil The Gravitational Universe. It provides the closest ever view of the early processes at TeV energies, has guaranteed sources in the form of verification binaries in the Milky Way, and can probe the entire Universe, from its smallest scales around singularities and black holes, all the way to cosmological dimensions

    Acyclic, Star, and Injective Colouring: Bounding the diameter

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    We examine the effect of bounding the diameter for a number of natural and well-studied variants of the COLOURING problem. A colouring is acyclic, star, or injective if any two colour classes induce a forest, star forest or disjoint union of vertices and edges, respectively. The corresponding decision problems are ACYCLIC COLOURING, STAR COLOURING and INJECTIVE COLOURING. The last problem is also known as L ( 1 , 1 ) -LABELLING and we also consider the framework of L ( a , b ) -LABELLING. We prove a number of (almost-)complete complexity classifications. In particular, we show that for graphs of diameter at most~ d , ACYCLIC 3 -COLOURING is polynomial-time solvable if d ≤ 2 but NP-complete if d ≥ 4 , and STAR 3 -COLOURING is polynomial-time solvable if d ≤ 3 but NP-complete for d ≥ 8. As far as we are aware, STAR 3 -COLOURING is the first problem that exhibits a complexity jump for some d ≥ 3. Our third main result is that L ( 1 , 2 ) -LABELLING is NP-complete for graphs of diameter~ 2 ; we relate the latter problem to a special case of HAMILTONIAN PATH

    Infection rates after 3175 total hip and total knee replacements performed with and without a horizontal unidirectional filtered air-flow system

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    To determine the effect of the ventilation system on infection rates after total hip and total knee arthroplasties performed in operating rooms with and without a horizontal unidirectional filtered air-flow system, using modern antiseptic conditions and antibiotic prophylaxis, all of the single-stage procedures (3175 of a total of 4769) were subjected to statistical analysis and fifty-seven matched pairs for controls were established. A reduced infection rate after total hip replacement (from 1.4 to 0.9 per cent) and an increased infection rate after total knee replacement (from 1.4 to 3.9 per cent) were found when patients operated on in the filtered laminar air-flow operating room were compared with those whose operations were done in two conventional rooms. This pattern was statistically significant and was believed to be due to the positions of the operating team and of the wound with respect to the air flow. Prospectively accumulated factors (such as the experience of the surgeon, the duration of surgery, the diagnosis, and the patient's age) as well as retrospectively accumulated factors (such as predisposing conditions of the patient) did not explain the observed patterns of infection

    Partitioning H-free graphs of bounded diameter

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    A natural way of increasing our understanding of NP-complete graph problems is to restrict the input to a special graph class. Classes of H-free graphs, that is, graphs that do not contain some graph H as an induced subgraph, have proven to be an ideal testbed for such a complexity study. However, if the forbidden graph H contains a cycle or claw, then these problems often stay NP-complete. A recent complexity study (MFCS 2019) on the k-Colouring problem shows that we may still obtain tractable results if we also bound the diameter of the H-free input graph. We continue this line of research by initiating a complexity study on the impact of bounding the diameter for a variety of classical vertex partitioning problems restricted to H-free graphs. We prove that bounding the diameter does not help for Independent Set, but leads to new tractable cases for problems closely related to 3-Colouring. That is, we show that Near-Bipartiteness, Independent Feedback Vertex Set, Independent Odd Cycle Transversal, Acyclic 3-Colouring and Star 3-Colouring are all polynomial-time solvable for chair-free graphs of bounded diameter. To obtain these results we exploit a new structural property of 3-colourable chair-free graphs

    Partitioning H-free graphs of bounded diameter

    Get PDF
    A natural way of increasing our understanding of NP-complete graph problems is to restrict the input to a special graph class. Classes of H-free graphs, that is, graphs that do not contain some graph H as an induced subgraph, have proven to be an ideal testbed for such a complexity study. However, if the forbidden graph H contains a cycle or claw, then these problems often stay NP-complete. A recent complexity study (MFCS 2019) on the k-Colouring problem shows that we may still obtain tractable results if we also bound the diameter of the H-free input graph. We continue this line of research by initiating a complexity study on the impact of bounding the diameter for a variety of classical vertex partitioning problems restricted to H-free graphs. We prove that bounding the diameter does not help for Independent Set, but leads to new tractable cases for problems closely related to 3-Colouring. That is, we show that Near-Bipartiteness, Independent Feedback Vertex Set, Independent Odd Cycle Transversal, Acyclic 3-Colouring and Star 3- Colouring are all polynomial-time solvable for chair-free graphs of bounded diameter. To obtain these results we exploit a new structural property of 3-colourable chair-free graphs
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