Courant Institute of Mathematical Sciences

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.

A Theoretical Analysis of Feature Pooling in Visual Recognition

Abstract: Many modern visual recognition algorithms incorporate a step of spatial 'pooling', where the outputs of several nearby feature detectors are combined into a local or global 'bag of features', in a way that preserves task-related information while removing irrelevant details. Pooling is used to achieve invariance to image transformations, more compact representations, and better robustness to noise and clutter. Several papers have shown that the details of the pooling operation can greatly influence the performance, but studies have so far been purely empirical. In this paper, we show that the reasons underlying the performance of various pooling methods are obscured by several confounding factors, such as the link between the sample cardinality in a spatial pool and the resolution at which low-level features have been extracted. We provide a detailed theoretical analysis of max pooling and average pooling, and give extensive empirical comparisons for object recognition tasks.

A gene expression map of the Arabidopsis root.

Abstract: A global map of gene expression within an organ can identify genes with coordinated expression in localized domains, thereby relating gene activity to cell fate and tissue specialization. Here, we present localization of expression of more than 22,000 genes in the Arabidopsis root. Gene expression was mapped to 15 different zones of the root that correspond to cell types and tissues at progressive developmental stages. Patterns of gene expression traverse traditional anatomical boundaries and show cassettes of hormonal response. Chromosomal clustering defined some coregulated genes. This expression map correlates groups of genes to specific cell fates and should serve to guide reverse genetics.

Differentiability of Lipschitz Functions on Metric Measure Spaces

Abstract: Abstract. ((Without Abstract)).