Stephen's Research Interests

Current interests

• Largescale first-order algorithms for convex optimization (e.g. for linear inverse problems)
• Applying compressed sensing techniques to reconstruct low-rank matrices

Papers published on these topics:
• NESTA: a fast and accurate first-order method for sparse recovery by S. Becker, J. Bobin and E.J. Candès is submitted for publication, April 21 2009. For code, please visit the NESTA website.
• I have helped with the software release for Singular Value Thresholding (SVT): software available at svt.caltech.edu.

Relevant links:

• My files on the ACM server (requires a password).
• Emmanuel Candès' list of publications
• Rice University maintains the de facto standard of compressed sensing and compressive sampling resources.
• Terence Tao's blog posts about CS
• Other misc. links: Optimization Online is a repository of e-prints; the UCLA applied math reports and RICE applied math reports repositories.
• Handbook of Semidefinite Programming, with typos and the online bibliography.

For an general overview of compressed sensing, the March 2008 issue of IEEE Signal Processing magazine is devoted to compressed sensing and provides an excellent introduction.

Concurrent interests

• Quantum state tomography

Papers published on this topic:
• Quantum state tomography via compressed sensing by Gross, Liu, Flammia, Becker and Eisert, is on the Arxiv, Sept 20 2009
• Analog-to-information

The well-known Shannon-Nyquist sampling theorem states that in order to preserve the amount of information in an arbitrary signal of bandwidth B, one must sample at rate 1/(2*B) (for an infinite length of time, unless the signal is periodic). However, if there is a prior on the signal (in addition to the fact that it is bandlimited), then the worst-case estimate of the Shannon-Nyquist sampling rate need not apply; indeed, there are practical cases where signals can be sampled at much less than the Shannon-Nyquist rate and still be stably recovered. The DARPA has put out a call for so-called "Analog-to-information" converters, intended to replace convention analog-to-digital converters by exploiting these signal priors.

We are interested in such "analog-to-information" systems. For more information, see the Rice/Michigan A-to-I website (note: I am not involved with the Rice/Michigan effort).

Summer 2007 with abInventio

• A founding researcher in the Taste Predictor group, developing algorithms similar to those involved in the netflix prize.
• Relevant files (requires password)

Previous topics of interest

• Supercooled water
  
  Liquid water can be supercooled to below the equilibrium freezing temperature. In this regime, many of water's unusual properties are amplified, and it also has some features, such as a liquid-liquid phase transition, that do not appear at higher temperatures. My undergraduate work on this was supervised by my thesis advisor Francis Starr of the Department of Physics at Wesleyan University. My thesis was focused on the interplay of translational and rotational dynamics in supercooled water. Research was conducted by Molecular Dynamics simulation of ST2 water on computer clusters at both Wesleyan University in Connecticut and St. Francis Xavier University in Nova Scotia. Collaboration was also done with Peter Poole of St. Francis Xavier University.
  
  Papers published on this topic:
  • May 2007: "Relation between the Widom line and the breakdown of the Stokes-Einstein relation in supercooled water", Kumar, Buldyrev, Becker, Poole, Starr and Stanley; in Proceedings of the National Academy of Sciences, vol. 104
  • August 2006: "Fractional Stokes-Einstein and Debye-Stokes-Einstein Relations in a Network-Forming Liquid", Becker, Poole, Starr; in Physical Review Letters, vol. 97
  
  
  
• Falling Dominos
  Papers published on this topic:
  • "The Dynamics of Falling Dominoes", Wagon, Pontarelli, Becker, Briggs; in UMAP, vol. 26, 2005. PDF available here

Content last updated April 2, 2008

Page last modified Nov 23, 2009