Courant Institute of Mathematical Sciences

Matching pursuits with time-frequency dictionaries

The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of fun...

Singularity detection and processing with wavelets

The mathematical characterization of singularities with Lipschitz exponents is reviewed. Theorems that estimate local Lipschitz exponents of functions from the evolution across ...

Learning Hierarchical Features for Scene Labeling

Scene labeling consists of labeling each pixel in an image with the category of the object it belongs to. We propose a method that uses a multiscale convolutional network traine...

Adaptive greedy approximations

Convolutional Learning of Spatio-temporal Features

Molecular Modeling and Simulation

Ensemble Dependence of Fluctuations with Application to Machine Computations

The standard theory of fluctuations in thermodynamic variables in various ensembles is generalized to nonthermodynamic variables: e.g., the mean-square fluctuations of the kinet...

Expert-Driven Validation of Rule-Based User Models in Personalization Applications

Thermodynamic Properties of Small Systems

We investigate the dependence of the pressure of a homogeneous system, at a given density $\ensuremath{\rho}$ and temperature $T$, on the number of particles $N$. The particles ...

Multidimensional Recommender Systems: A Data Warehousing Approach