Institution
Courant Institute of Mathematical Sciences
Education•New York, New York, United States•
About: Courant Institute of Mathematical Sciences is a education organization based out in New York, New York, United States. It is known for research contribution in the topics: Nonlinear system & Boundary value problem. The organization has 2414 authors who have published 7759 publications receiving 439773 citations. The organization is also known as: CIMS & New York University Department of Mathematics.
Topics: Nonlinear system, Boundary value problem, Boundary (topology), Partial differential equation, Upper and lower bounds
Papers published on a yearly basis
Papers
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21 Aug 2011TL;DR: In this article, the authors give constructive formulas for deblurring kernels in terms of Hermite polynomials, and observe that their use yields optimal approximate deblurring solutions among the space of bounded degree functions.
Abstract: Gaussian blur, or convolution against a Gaussian kernel, is a common model for image and signal degradation. In general, the process of reversing Gaussian blur is unstable, and cannot be represented as a convolution filter in the spatial domain. If we restrict the space of allowable functions to polynomials of fixed finite degree, then a convolution inverse does exist. We give constructive formulas for the deblurring kernels in terms of Hermite polynomials, and observe that their use yields optimal approximate deblurring solutions among the space of bounded degree polynomials. The more common methods of achieving stable approximate deblurring include restrictions to band-limited functions or functions of bounded norm.
129 citations
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TL;DR: In this article, the authors proposed a new general method of boundary correction for univariate kernel density estimation, which generates a class of boundary corrected estimators, which all possess desirable properties such as local adaptivity and non-negativity.
129 citations
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TL;DR: In this article, a generalized diffusion process was proposed to describe spatio-temporal varying diffusion coefficients, advection coefficients, and dilution terms of two morphogens, and a third order activator-inhibitor mechanism for the kinetic part.
Abstract: Based on first principles, we derive a general model to describe the spatio-temporal dynamics of two morphogens. The diffusive part of the model incorporates the dynamics, growth and curvature of one- and two-dimensional domains embedded in 3. Our generalized diffusion process includes spatio-temporal varying diffusion coefficients, advection, and dilution terms. We present specific examples by analyzing a third order activator--inhibitor mechanism for the kinetic part. We carry out illustrative numerical simulations on two-dimensional growing domains having different geometries. Comparisons with former results on fixed domains show the crucial role of growth and curvature of pattern selection. Evidence is given that both effects might be biologically relevant in explaining the selection of some observed patterns and in changing or enhancing their stability.
129 citations
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TL;DR: In this paper, an algorithm to assemble large jigsaw puzzles using curve matching and combinatorial optimization techniques is presented, where pieces are photographed one by one and then the assembly algorithm, which uses only the puzzle piece shape information, is applied.
Abstract: An algorithm to assemble large jigsaw puzzles using curve matching and combinatorial optimization techniques is presented. The pieces are photographed one by one and then the assembly algorithm, which uses only the puzzle piece shape information, is applied. The algorithm was experimented successfully in the assembly of 104-piece puzzles with many almost similar pieces. It was also extended to solve an intermixed puzzle assembly problem and has successfully solved a 208-piece puzzle consisting of two intermixed 104-piece puzzles. Previous results solved puzzles with about 10 pieces, which were substantially different in shape.
129 citations
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28 Feb 2018TL;DR: This paper describes a completely general strategy that takes an arbitrary step of an ideal CRCW PRAM and automatically translates it to run efficiently and robustly on a PRAM in which processors are prone to failure.
Abstract: A parallel computing system becomes increasingly prone to failure as the number of processing elements in it increases. In this paper, we describe a completely general strategy that takes an arbitrary step of an ideal CRCW PRAM and automatically translates it to run efficiently and robustly on a PRAM in which processors are prone to failure. The strategy relies on efficient robust algorithms for solving a core problem, the Certified Write-All Problem. This problem characterizes the core of robustness, because , as we show, its complexity is equal to that of any general strategy for realizing robustness in the model. We analyze the expected parallel time and work of various algorithms for solving this problem. Our results are a non-trivial generalization of Brent's Permission to copy without fee all or part of this material is granted provided that the copies are not made or distn'buted for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. Lemma. We consider the case where the number of the available processors decreases dynamically over time, whereas Brent's Lemma is only applicable in the case where the processor availability pattern is static.
129 citations
Authors
Showing all 2441 results
Name | H-index | Papers | Citations |
---|---|---|---|
Xiang Zhang | 154 | 1733 | 117576 |
Yann LeCun | 121 | 369 | 171211 |
Benoît Roux | 120 | 493 | 62215 |
Alan S. Perelson | 118 | 632 | 66767 |
Thomas J. Spencer | 116 | 531 | 52743 |
Salvatore Torquato | 104 | 552 | 40208 |
Joel L. Lebowitz | 101 | 754 | 39713 |
Bo Huang | 97 | 728 | 40135 |
Amir Pnueli | 94 | 331 | 43351 |
Rolf D. Reitz | 93 | 611 | 36618 |
Michael Q. Zhang | 93 | 378 | 42008 |
Samuel Karlin | 89 | 396 | 41432 |
David J. Heeger | 88 | 268 | 38154 |
Luis A. Caffarelli | 87 | 353 | 32440 |
Weinan E | 84 | 323 | 22887 |