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:
Relevant links:
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:
- 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).
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