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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TL;DR: In this article, the authors search for locally optimal solutions of a nonsmooth optimization problem that is built to incorporate minimization objectives and constraints for multiple plants, and report on the success of this approach using our public-domain matlab toolbox hifoo 2.0.
187 citations
TL;DR: In this paper, a transform operator that maps the system of large number of ordinary differential equations of motion of the particles into a partial differential equation with the Riesz fractional derivative of order α was constructed.
187 citations
TL;DR: An idea of Szekely is applied to prove a general upper bound on the number of incidences between a set of m points and a sets of n ‘well-behaved’ curves in the plane.
Abstract: We apply an idea of Szekely to prove a general upper bound on the number of incidences between a set of m points and a set of n ‘well-behaved’ curves in the plane.
187 citations
16 May 2000
TL;DR: This work presents the AJAX system applied to two real world problems: the consolidation of a telecommunication database, and the conversion of a dirty database of bibliographic references into a set of clean, normalized, and redundancy free relational tables maintaining the same data.
Abstract: @ that permits users to determine the source and processing of data for debugging purposes.We will present the AJAX system applied to two real world problems: the consolidation of a telecommunication database, and the conversion of a dirty database of bibliographic references into a set of clean, normalized, and redundancy free relational tables maintaining the same data.
186 citations
Proceedings Article•
01 Dec 2004TL;DR: This paper provides confidence intervals for the AUC based on a statistical and combinatorial analysis using only simple parameters such as the error rate and the number of positive and negative examples, which can be viewed as the equivalent for AUC of the standard confidence intervals given in the case of the errors.
Abstract: In many applications, good ranking is a highly desirable performance for a classifier. The criterion commonly used to measure the ranking quality of a classification algorithm is the area under the ROC curve (AUC). To report it properly, it is crucial to determine an interval of confidence for its value. This paper provides confidence intervals for the AUC based on a statistical and combinatorial analysis using only simple parameters such as the error rate and the number of positive and negative examples. The analysis is distribution-independent, it makes no assumption about the distribution of the scores of negative or positive examples. The results are of practical use and can be viewed as the equivalent for AUC of the standard confidence intervals given in the case of the error rate. They are compared with previous approaches in several standard classification tasks demonstrating the benefits of our analysis.
186 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 |