14,668 research outputs found
Cubical Cohomology Ring of 3D Photographs
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 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, 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
In this paper, we formalize the notion of lambda-AT-model (where 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
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
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
- …