In the last decade, there has been considerable interest in understanding when it is possible to find structured solutions to underdetermined systems of linear equations. This paper surveys some of the mathematical theories, known as compressive sensing and matrix completion, that have been developed to find sparse and low-rank solutions via convex programming techniques. Our exposition emphasi...

A few remarks on integrable dynamical systems inspired by discussions with Jürgen Moser and by his work.

Machine learning is a powerful set of techniques that has enhanced the abilities of neuroscientists to interpret information collected through EEG, fMRI, MEG, and PET data. With these new techniques come new dangers of overfitting that are not well understood by the neuroscience community. In this article, we use Support Vector Machine (SVM) classifiers, and genetic algorithms to demonstrate th...

In this paper we tried to improve upon the power consumption and quality of service by using a density based approach along with the Traffic splitting protocol. We have tried to improve things in TSP by considering the density of nodes before splitting the traffic in different paths. We have improved upon Average energy left, network load or congestion, End to end delay and number of nodes dead.

This is a quite faithful rendering of a Colloquio De Giorgi I had the honor to give at Scuola Normale Superiore on March 21, 2012. The idea was to explain some open problems in arithmetic algebraic geometry which are simple to state but which remain shrouded in mystery. 1. An interactive game: dimension zero Suppose I give you an integer N ≥ 2, and tell you that I am thinking of a monic integer...