Institution
Paris Dauphine University
Education•Paris, France•
About: Paris Dauphine University is a education organization based out in Paris, France. It is known for research contribution in the topics: Context (language use) & Population. The organization has 1766 authors who have published 6909 publications receiving 162747 citations. The organization is also known as: Paris Dauphine & Dauphine.
Topics: Context (language use), Population, Approximation algorithm, Bounded function, Nonlinear system
Papers published on a yearly basis
Papers
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TL;DR: This work proposes a method that “propagates” improvement of the worst-case complexity for “sparse” instances to “denser” ones and shows an easy though non-trivial application of it to the min set cover problem.
Abstract: We first propose a method, called “bottom-up method” that, informally, “propagates” improvement of the worst-case complexity for “sparse” instances to “denser” ones and we show an easy though non-trivial application of it to the min set cover problem. We then tackle max independent set. Here, we propagate improvements of worst-case complexity from graphs of average degree d to graphs of average degree greater than d. Indeed, using algorithms for max independent set in graphs of average degree 3, we successively solve max independent set in graphs of average degree 4, 5 and 6. Then, we combine the bottom-up technique with measure and conquer techniques to get improved running times for graphs of maximum degree 5 and 6 but also for general graphs. The computation bounds obtained for max independent set are O ∗(1.1571 n ), O ∗(1.1895 n ) and O ∗(1.2050 n ), for graphs of maximum (or more generally average) degree 4, 5 and 6 respectively, and O ∗(1.2114 n ) for general graphs. These results improve upon the best known results for these cases for polynomial space algorithms.
74 citations
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12 Dec 2000TL;DR: In this paper, the value function for an optimal control problem with endpoint and state constraints is characterized as the unique lower semi-continuous generalized solution of the Hamilton-Jacobi equation under a constraint qualification (CQ) concerning the interaction of the state and dynamic constraints.
Abstract: In this paper, the value function for an optimal control problem with endpoint and state constraints is characterized as the unique lower semi-continuous generalized solution of the Hamilton-Jacobi equation. This is achieved under a constraint qualification (CQ) concerning the interaction of the state and dynamic constraints. The novelty of the results reported here is partly the nature of (CQ) and partly the proof techniques employed, which are based on new estimates of the distance of the set of state trajectories satisfying a state constraint from a given trajectory which violates the constraint.
74 citations
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74 citations
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TL;DR: In this article, the existence, multiplicity and bifurcation of solutions of a model nonlinear degenerate elliptic differential equation were investigated, and it was shown that there exists an infinite number of connected branches of solutions which bifurocate from the bottom of the essential spectrum of the corresponding linear operator.
73 citations
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30 May 2007TL;DR: A best basis extension of compressed sensing recovery is proposed that makes use of sparsity in a tree-structured dictionary of orthogonal bases and improves the recovery with respect to fixed sparsity priors.
Abstract: This paper proposes an extension of compressed sensing that allows to express the sparsity prior in a dictionary of bases. This enables the use of the random sampling strategy of compressed sensing together with an adaptive recovery process that adapts the basis to the structure of the sensed signal. A fast greedy scheme is used during reconstruction to estimate the best basis using an iterative refinement. Numerical experiments on sounds and geometrical images show that adaptivity is indeed crucial to capture the structures of complex natural signals.
73 citations
Authors
Showing all 1819 results
Name | H-index | Papers | Citations |
---|---|---|---|
Pierre-Louis Lions | 98 | 283 | 57043 |
Laurent D. Cohen | 94 | 417 | 42709 |
Chris Bowler | 87 | 288 | 35399 |
Christian P. Robert | 75 | 535 | 36864 |
Albert Cohen | 71 | 368 | 19874 |
Gabriel Peyré | 65 | 303 | 16403 |
Kerrie Mengersen | 65 | 737 | 20058 |
Nader Masmoudi | 62 | 245 | 10507 |
Roland Glowinski | 61 | 393 | 20599 |
Jean-Michel Morel | 59 | 302 | 29134 |
Nizar Touzi | 57 | 224 | 11018 |
Jérôme Lang | 57 | 277 | 11332 |
William L. Megginson | 55 | 169 | 18087 |
Alain Bensoussan | 55 | 417 | 22704 |
Yves Meyer | 53 | 128 | 14604 |