Topic

# Discontinuity (linguistics)

About: Discontinuity (linguistics) is a research topic. Over the lifetime, 5121 publications have been published within this topic receiving 93828 citations.

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TL;DR: By Luigi Ambrosio, Nicolo Fucso and Diego Pallara: 434 pp.

Abstract: By Luigi Ambrosio, Nicolo Fucso and Diego Pallara: 434 pp., £55.00, isbn 0-19-850254-1 (Clarendon Press, Oxford, 2000).

1,904 citations

01 Jan 2000

TL;DR: The basic issues of efficient m-term approximation, the construction of efficient adaptive representation, theConstruction of the curvelet frame, and a crude analysis of the performance of curvelet schemes are explained.

Abstract: : It is widely believed that to efficiently represent an otherwise smooth object with discontinuities along edges, one must use an adaptive representation that in some sense 'tracks' the shape of the discontinuity set. This folk-belief - some would say folk-theorem - is incorrect. At the very least, the possible quantitative advantage of such adaptation is vastly smaller than commonly believed. We have recently constructed a tight frame of curvelets which provides stable, efficient, and near-optimal representation of otherwise smooth objects having discontinuities along smooth curves. By applying naive thresholding to the curvelet transform of such an object, one can form m-term approximations with rate of L(sup 2) approximation rivaling the rate obtainable by complex adaptive schemes which attempt to track' the discontinuity set. In this article we explain the basic issues of efficient m-term approximation, the construction of efficient adaptive representation, the construction of the curvelet frame, and a crude analysis of the performance of curvelet schemes.

1,633 citations

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TL;DR: In this paper, the energy-band gap of an insulator is obtained from the eigenvalues of the one-particle density-functional equation for the ground state and a finite correction due to the discontinuity of the functional derivative of the exchange and correlation energy.

Abstract: The energy-band gap of an insulator is obtained from the eigenvalues of the one-particle density-functional equation for the ground state and a finite correction due to the discontinuity of the functional derivative of the exchange and correlation energy. This correction is expressed in terms of the improper self-energy and the density-functional exchange-correlation potential. It is evaluated for a two-plane-wave model including exchange only.

1,365 citations

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TL;DR: A new approach for modelling discrete cracks in meshfree methods is described, in which the crack can be arbitrarily oriented, but its growth is represented discretely by activation of crack surfaces at individual particles, so no representation of the crack's topology is needed.

Abstract: A new approach for modelling discrete cracks in meshfree methods is described. In this method, the crack can be arbitrarily oriented, but its growth is represented discretely by activation of crack surfaces at individual particles, so no representation of the crack's topology is needed. The crack is modelled by a local enrichment of the test and trial functions with a sign function (a variant of the Heaviside step function), so that the discontinuities are along the direction of the crack. The discontinuity consists of cylindrical planes centred at the particles in three dimensions, lines centred at the particles in two dimensions. The model is applied to several 2D problems and compared to experimental data. Copyright © 2004 John Wiley & Sons, Ltd.

1,274 citations

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TL;DR: The authors examine prior smoothness constraints of a different form, which permit the recovery of discontinuities without introducing auxiliary variables for marking the location of jumps and suspending the constraints in their vicinity.

Abstract: The linear image restoration problem is to recover an original brightness distribution X/sup 0/ given the blurred and noisy observations Y=KX/sup 0/+B, where K and B represent the point spread function and measurement error, respectively. This problem is typical of ill-conditioned inverse problems that frequently arise in low-level computer vision. A conventional method to stabilize the problem is to introduce a priori constraints on X/sup 0/ and design a cost functional H(X) over images X, which is a weighted average of the prior constraints (regularization term) and posterior constraints (data term); the reconstruction is then the image X, which minimizes H. A prominent weakness in this approach, especially with quadratic-type stabilizers, is the difficulty in recovering discontinuities. The authors therefore examine prior smoothness constraints of a different form, which permit the recovery of discontinuities without introducing auxiliary variables for marking the location of jumps and suspending the constraints in their vicinity. In this sense, discontinuities are addressed implicitly rather than explicitly. >

1,205 citations