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Journal ArticleDOI

FUNCTIONS OF BOUNDED VARIATION AND FREE DISCONTINUITY PROBLEMS (Oxford Mathematical Monographs)

TLDR
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).

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Gradient Flows: In Metric Spaces and in the Space of Probability Measures

TL;DR: In this article, Gradient flows and curves of Maximal slopes of the Wasserstein distance along geodesics are used to measure the optimal transportation problem in the space of probability measures.
Journal ArticleDOI

Filling-in by joint interpolation of vector fields and gray levels

TL;DR: A variational approach for filling-in regions ofMissing data in digital images is introduced, based on joint interpolation of the image gray levels and gradient/isophotes directions, smoothly extending in an automatic fashion the isophote lines into the holes of missing data.
Journal ArticleDOI

Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments

TL;DR: In this paper, a modified regularized formulation of the Ambrosio-Tortorelli type was proposed to avoid crack interpenetration and predicts asymmetric results in traction and in compression.
Book

Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control

TL;DR: In this paper, a model problem is formulated for optimal control of semiconcave functions with exit time with the objective of minimizing the cost of the control problem with respect to the exit time.
Book ChapterDOI

Safety Verification of Deep Neural Networks

TL;DR: A novel automated verification framework for feed-forward multi-layer neural networks based on Satisfiability Modulo Theory (SMT) is developed, which defines safety for an individual decision in terms of invariance of the classification within a small neighbourhood of the original image.