767,021 research outputs found

    Three-dimensional alpha shapes

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    Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the ``shape'' of the set. For that purpose, this paper introduces the formal notion of the family of α\alpha-shapes of a finite point set in \Real^3. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter \alpha \in \Real controlling the desired level of detail. An algorithm is presented that constructs the entire family of shapes for a given set of size nn in time O(n2)O(n^2), worst case. A robust implementation of the algorithm is discussed and several applications in the area of scientific computing are mentioned.Comment: 32 page

    Security and Privacy Issues in Cloud Computing

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    Cloud computing transforming the way of information technology (IT) for consuming and managing, promising improving cost efficiencies, accelerate innovations, faster time-to-market and the ability to scale applications on demand (Leighton, 2009). According to Gartner, while the hype grew ex-ponentially during 2008 and continued since, it is clear that there is a major shift towards the cloud computing model and that the benefits may be substantial (Gartner Hype-Cycle, 2012). However, as the shape of the cloud computing is emerging and developing rapidly both conceptually and in reality, the legal/contractual, economic, service quality, interoperability, security and privacy issues still pose significant challenges. In this chapter, we describe various service and deployment models of cloud computing and identify major challenges. In particular, we discuss three critical challenges: regulatory, security and privacy issues in cloud computing. Some solutions to mitigate these challenges are also proposed along with a brief presentation on the future trends in cloud computing deployment

    OPE of the stress tensors and surface operators

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    We demonstrate that the divergent terms in the OPE of a stress tensor and a surface operator of general shape cannot be constructed only from local geometric data depending only on the shape of the surface. We verify this holographically at d=3 for Wilson line operators or equivalently the twist operator corresponding to computing the entanglement entropy using the Ryu-Takayanagi formula. We discuss possible implications of this result.Comment: 20 pages, no figur
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