262,716 research outputs found

    The group of causal automorphisms

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    The group of causal automorphisms on Minkowski space-time is given and its structure is analyzed

    The q-component static model : modeling social networks

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    We generalize the static model by assigning a q-component weight on each vertex. We first choose a component (μ)(\mu) among the q components at random and a pair of vertices is linked with a color μ\mu according to their weights of the component (μ)(\mu) as in the static model. A (1-f) fraction of the entire edges is connected following this way. The remaining fraction f is added with (q+1)-th color as in the static model but using the maximum weights among the q components each individual has. This model is motivated by social networks. It exhibits similar topological features to real social networks in that: (i) the degree distribution has a highly skewed form, (ii) the diameter is as small as and (iii) the assortativity coefficient r is as positive and large as those in real social networks with r reaching a maximum around f0.2f \approx 0.2.Comment: 5 pages, 6 figure

    Polyhedral graph abstractions and an approach to the Linear Hirsch Conjecture

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    We introduce a new combinatorial abstraction for the graphs of polyhedra. The new abstraction is a flexible framework defined by combinatorial properties, with each collection of properties taken providing a variant for studying the diameters of polyhedral graphs. One particular variant has a diameter which satisfies the best known upper bound on the diameters of polyhedra. Another variant has superlinear asymptotic diameter, and together with some combinatorial operations, gives a concrete approach for disproving the Linear Hirsch Conjecture.Comment: 16 pages, 4 figure