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- Ravikanth Pappu, Ben Recht, Jason Taylor, Neil Gershenfeld
- Science
- 2002

Modern cryptographic practice rests on the use of one-way functions, which are easy to evaluate but difficult to invert. Unfortunately, commonly used one-way functions are either based on unproven conjectures or have known vulnerabilities. We show that instead of relying on number theory, the mesoscopic physics of coherent transport through a disordered… (More)

- Abdolah Rahimi, Ben Recht
- 2008 46th Annual Allerton Conference on…
- 2008

Random networks of nonlinear functions have a long history of empirical success in function fitting but few theoretical guarantees. In this paper, using techniques from probability on Banach Spaces, we analyze a specific architecture of random nonlinearities, provide L<sub>infin</sub> and L<sub>2</sub> error bounds for approximating functions in Reproducing… (More)

In this paper, we focus on compressed sensing and recovery schemes for low-rank matrices, asking under what conditions a low-rank matrix can be sensed and recovered from incomplete, inaccurate, and noisy observations. We consider three schemes, one based on a certain Restricted Isometry Property and two based on directly sensing the row and column space of… (More)

- E . Candes, Ben Recht
- 2008 46th Annual Allerton Conference on…
- 2008

Suppose that one observes an incomplete subset of entries selected uniformly at random from a low-rank matrix. When is it possible to complete the matrix and recover the entries that have not been seen? We show that in very general settings, one can perfectly recover all of the missing entries from a sufficiently large random subset by solving a convex… (More)

- Ali Rahimi, Ben Recht
- 2004

We present a set of clustering algorithms that identify cluster boundaries by searching for a hyperplanar gap in unlabeled data sets. It turns out that the Normalized Cuts algorithm of Shi and Malik [1], originally presented as a graph-theoretic algorithm, can be interpreted as such an algorithm. Viewing Normalized Cuts under this light reveals that it pays… (More)

We present a methodology for robust determination of chemical reaction network interconnections. Given time series data that are collected from experiments and taking into account the measurement error, we minimize the 1-norm of the decision variables (reaction rates) keeping the data in close Euler-fit with a general model structure based on mass action… (More)

- Piotr Indyk, Andrew McGregor, +50 authors Matthias Westermann
- 2011

This document contains a list of open problems and research directions that have been suggested by participants at the Bertinoro Workshop on Sublinear Algorithms (May 2011) and IITK Workshop on Algorithms for Processing Massive Data Sets (December 2009). Many of the questions were discussed at the workshop or were posed during presentations. Further details… (More)

Pursuing a line of work begun by Whitney, Nash showed that every C manifold of dimension d can be embedded in R in such a manner that the local structure at each point is preserved isometrically. We provide an analog of this result for discrete subsets of Euclidean space. For perfect preservation of infinitesimal neighborhoods we substitute near-isometric… (More)

- Rajiv Kumar, Curt Da Silva, +5 authors Felix J. Herrmann

Despite recent developments in improved acquisition, seismic data often remains undersampled along source and receiver coordinates, resulting in incomplete data for key applications such as migration and multiple prediction. We interpret the missing-trace interpolation problem in the context of matrix completion and outline three practical principles for… (More)

- Ben Recht, Brian Whitman
- 2003

We present a method of musically expressive synthesis-by-analysis that takes advantage of recent advancements in auditory scene analysis and sound separation algorithms. Our model represents incoming audio as a sub-conceptual model using statistical decorrelation techniques that abstract away individual auditory events, leaving only the gross parameters of… (More)