14,668 research outputs found

    Cubical Cohomology Ring of 3D Photographs

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    Cohomology and cohomology ring of three-dimensional (3D) objects are topological invariants that characterize holes and their relations. Cohomology ring has been traditionally computed on simplicial complexes. Nevertheless, cubical complexes deal directly with the voxels in 3D images, no additional triangulation is necessary, facilitating efficient algorithms for the computation of topological invariants in the image context. In this paper, we present formulas to directly compute the cohomology ring of 3D cubical complexes without making use of any additional triangulation. Starting from a cubical complex QQ that represents a 3D binary-valued digital picture whose foreground has one connected component, we compute first the cohomological information on the boundary of the object, Q\partial Q by an incremental technique; then, using a face reduction algorithm, we compute it on the whole object; finally, applying the mentioned formulas, the cohomology ring is computed from such information

    A Tool for Integer Homology Computation: Lambda-At Model

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    In this paper, we formalize the notion of lambda-AT-model (where λ\lambda is a non-null integer) for a given chain complex, which allows the computation of homological information in the integer domain avoiding using the Smith Normal Form of the boundary matrices. We present an algorithm for computing such a model, obtaining Betti numbers, the prime numbers p involved in the invariant factors of the torsion subgroup of homology, the amount of invariant factors that are a power of p and a set of representative cycles of generators of homology mod p, for each p. Moreover, we establish the minimum valid lambda for such a construction, what cuts down the computational costs related to the torsion subgroup. The tools described here are useful to determine topological information of nD structured objects such as simplicial, cubical or simploidal complexes and are applicable to extract such an information from digital pictures.Comment: Journal Image and Vision Computing, Volume 27 Issue 7, June, 200

    Some notes on the Big Trip

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    The big trip is a cosmological process thought to occur in the future by which the entire universe would be engulfed inside a gigantic wormhole and might travel through it along space and time. In this paper we discuss different arguments that have been raised against the viability of that process, reaching the conclusions that the process can actually occur by accretion of phantom energy onto the wormholes and that it is stable and might occur in the global context of a multiverse model. We finally argue that the big trip does not contradict any holographic bounds on entropy and information.Comment: 8 pages, no figures, LaTe

    Dark energy without dark energy

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    It is proposed that the current acceleration of the universe is not originated by the existence of a mysterious dark energy fluid nor by the action of extra terms in the gravity Lagrangian, but just from the sub-quantum potential associated with the CMB particles. The resulting cosmic scenario corresponds to a benigner phantom model which is free from the main problems of the current phantom approaches.Comment: 4 pages, 1 figure, to appear in AIP proceedings of "Dark side of the Universe
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