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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446 citations
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TL;DR: In this article, the authors consider a class of zero-sum two-player stochastic games called tug-of-war and use them to prove that every bounded real-valued Lipschitz function F on a subset Y of a length space X admits a unique AM extension to X.
Abstract: We consider a class of zero-sum two-player stochastic games called tug-of-war and use them to prove that every bounded real-valued Lipschitz function F on a subset Y of a length space X admits a unique absolutely minimal (AM) extension to X, i.e., a unique Lipschitz extension u : X → ℝ for which Lip U u = Lip ∂u u for all open U ⊂ X \ Y.
438 citations
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University of Cambridge1, Mansfield University of Pennsylvania2, Imperial College London3, Fritz Haber Institute of the Max Planck Society4, University of Graz5, University of Bonn6, University of Southampton7, Radboud University Nijmegen8, Princeton University9, Panjab University, Chandigarh10, University of Toronto11, Tulane University12, Carnegie Mellon University13, Cornell University14, Utrecht University15, OpenEye Scientific Software16, University of Utah17, Facultad de Ciencias Exactas y Naturales18, Toyohashi University of Technology19, University College London20, Polaris Industries21, University of Silesia in Katowice22, Argonne National Laboratory23, Rutgers University24, University of Luxembourg25, Max Planck Society26, New York University27, Courant Institute of Mathematical Sciences28, New York University Shanghai29, Loyola University Chicago30
TL;DR: The results of the sixth blind test of organic crystal structure prediction methods are presented and discussed, highlighting progress for salts, hydrates and bulky flexible molecules, as well as on-going challenges.
Abstract: The sixth blind test of organic crystal structure prediction (CSP) methods has been held, with five target systems: a small nearly rigid molecule, a polymorphic former drug candidate, a chloride salt hydrate, a co-crystal and a bulky flexible molecule. This blind test has seen substantial growth in the number of participants, with the broad range of prediction methods giving a unique insight into the state of the art in the field. Significant progress has been seen in treating flexible molecules, usage of hierarchical approaches to ranking structures, the application of density-functional approximations, and the establishment of new workflows and `best practices' for performing CSP calculations. All of the targets, apart from a single potentially disordered Z' = 2 polymorph of the drug candidate, were predicted by at least one submission. Despite many remaining challenges, it is clear that CSP methods are becoming more applicable to a wider range of real systems, including salts, hydrates and larger flexible molecules. The results also highlight the potential for CSP calculations to complement and augment experimental studies of organic solid forms.
435 citations
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TL;DR: In this article, the authors investigated the time scales associated with the shedding of the trailing and leading edge vortices, as well as the corresponding time-dependent forces, and presented a generic mechanism of the frequency selection as a result of unsteady aerodynamics.
Abstract: Motivated by our interest in unsteady aerodynamics of insect flight, we devise a computational tool to solve the Navier–Stokes equation around a two-dimensional moving wing, which mimics biological locomotion. The focus of the present work is frequency selection in forward flapping flight. We investigate the time scales associated with the shedding of the trailing- and leading-edge vortices, as well as the corresponding time-dependent forces. We present a generic mechanism of the frequency selection as a result of unsteady aerodynamics.
435 citations
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TL;DR: The notion of centered alignment has been used as a similarity measure between kernels or kernel matrices as mentioned in this paper, which has been shown to consistently outperform the so-called uniform combination solution that has proven to be difficult to improve upon in the past.
Abstract: This paper presents new and effective algorithms for learning kernels. In particular, as shown by our empirical results, these algorithms consistently outperform the so-called uniform combination solution that has proven to be difficult to improve upon in the past, as well as other algorithms for learning kernels based on convex combinations of base kernels in both classification and regression. Our algorithms are based on the notion of centered alignment which is used as a similarity measure between kernels or kernel matrices. We present a number of novel algorithmic, theoretical, and empirical results for learning kernels based on our notion of centered alignment. In particular, we describe efficient algorithms for learning a maximum alignment kernel by showing that the problem can be reduced to a simple QP and discuss a one-stage algorithm for learning both a kernel and a hypothesis based on that kernel using an alignment-based regularization. Our theoretical results include a novel concentration bound for centered alignment between kernel matrices, the proof of the existence of effective predictors for kernels with high alignment, both for classification and for regression, and the proof of stability-based generalization bounds for a broad family of algorithms for learning kernels based on centered alignment. We also report the results of experiments with our centered alignment-based algorithms in both classification and regression.
432 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 |