Search results for "REGULARIZATION"
showing 10 items of 189 documents
On gravitational waves in Born-Infeld inspired non-singular cosmologies
2017
We study the evolution of gravitational waves for non-singular cosmological solutions within the framework of Born-Infeld inspired gravity theories, with special emphasis on the Eddington-inspired Born-Infeld theory. We review the existence of two types of non-singular cosmologies, namely bouncing and asymptotically Minkowski solutions, from a perspective that makes their features more apparent. We study in detail the propagation of gravitational waves near these non-singular solutions and carefully discuss the origin and severity of the instabilities and strong coupling problems that appear. We also investigate the role of the adiabatic sound speed of the matter sector in the regularisatio…
Born–Infeld inspired modifications of gravity
2017
General Relativity has shown an outstanding observational success in the scales where it has been directly tested. However, modifications have been intensively explored in the regimes where it seems either incomplete or signals its own limit of validity. In particular, the breakdown of unitarity near the Planck scale strongly suggests that General Relativity needs to be modified at high energies and quantum gravity effects are expected to be important. This is related to the existence of spacetime singularities when the solutions of General Relativity are extrapolated to regimes where curvatures are large. In this sense, Born-Infeld inspired modifications of gravity have shown an extraordin…
Line Shape Measurement and Modelling for Plasma Diagnostics
2014
In this paper we discuss different methods of narrow spectral line shape measurements for a wide spectral range by means of high-resolution spectrometers such as the Fabry-Perot spectrometer, Zeeman spectrometer and Fourier transform spectrometer as well as a theoretical model for spectral line shape modelling and solving of the inverse task based on Tikhonov's regularization method. Special attention is devoted to the line shape measurements for the optically thin light sources filled with Hg, Ar, Xe, Kr for their use in high precision analysers for detection of heavy metals and benzene.
The Regularized Hadamard Expansion
2017
A local expansion is proposed for two-point distributions involving an ultraviolet regularization in a four-dimensional globally hyperbolic space-time. The regularization is described by an infinite number of functions which can be computed iteratively by solving transport equations along null geodesics. We show that the Cauchy evolution preserves the regularized Hadamard structure. The resulting regularized Hadamard expansion gives detailed and explicit information on the global dynamics of the regularization effects.
An efficient method for clustered multi-metric learning
2019
Abstract Distance metric learning, which aims at finding a distance metric that separates examples of one class from examples of the other classes, is the key to the success of many machine learning tasks. Although there has been an increasing interest in this field, learning a global distance metric is insufficient to obtain satisfactory results when dealing with heterogeneously distributed data. A simple solution to tackle this kind of data is based on kernel embedding methods. However, it quickly becomes computationally intractable as the number of examples increases. In this paper, we propose an efficient method that learns multiple local distance metrics instead of a single global one.…
Learning, regularization and ill-posed inverse problems
2005
Many works have shown that strong connections relate learning from examples to regularization techniques for ill-posed inverse problems. Nevertheless by now there was no formal evidence neither that learning from examples could be seen as an inverse problem nor that theoretical results in learning theory could be independently derived using tools from regularization theory. In this paper we provide a positive answer to both questions. Indeed, considering the square loss, we translate the learning problem in the language of regularization theory and show that consistency results and optimal regularization parameter choice can be derived by the discretization of the corresponding inverse prob…
Learning from examples as an inverse problem
2005
Many works related learning from examples to regularization techniques for inverse problems, emphasizing the strong algorithmic and conceptual analogy of certain learning algorithms with regularization algorithms. In particular it is well known that regularization schemes such as Tikhonov regularization can be effectively used in the context of learning and are closely related to algorithms such as support vector machines. Nevertheless the connection with inverse problem was considered only for the discrete (finite sample) problem and the probabilistic aspects of learning from examples were not taken into account. In this paper we provide a natural extension of such analysis to the continuo…
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
1999
We present a new method for solving total variation (TV) minimization problems in image restoration. The main idea is to remove some of the singularity caused by the nondifferentiability of the quantity $|\nabla u|$ in the definition of the TV-norm before we apply a linearization technique such as Newton's method. This is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function, which can be interpreted as the normal vector to the level sets of the image u. Our method can be viewed as a primal-dual method as proposed by Conn and Overton [ A Primal-Dual Interior Point Method for Minimizing a Sum of Euclidean Norms, preprint,…
A differential equation approach to implicit sweeping processes
2019
International audience; In this paper, we study an implicit version of the sweeping process. Based on methods of convex analysis, we prove the equivalence of the implicit sweeping process with a differential equation, which enables us to show the existence and uniqueness of the solution to the implicit sweeping process in a very general framework. Moreover, this equivalence allows us to give a characterization of nonsmooth Lyapunov pairs and invariance for implicit sweeping processes. The results of the paper are illustrated with two applications to quasistatic evolution variational inequalities and electrical circuits.
Gradient-enhanced model and its micromorphic regularization for simulation of Lüders-like bands in shape memory alloys
2018
Abstract Shape memory alloys, notably NiTi, often exhibit softening pseudoelastic response that results in formation and propagation of Luders-like bands upon loading, for instance, in uniaxial tension. A common approach to modelling softening and strain localization is to resort to gradient-enhanced formulations that are capable of restoring well-posedness of the boundary-value problem. This approach is also followed in the present paper by introducing a gradient-enhancement into a simple one-dimensional model of pseudoelasticity. In order to facilitate computational treatment, a micromorphic-type regularization of the gradient-enhanced model is subsequently performed. The formulation empl…