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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(More)
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)
— 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)
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 1 manifold of dimension d can be embedded in R 2d+2 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(More)
This thesis proposes a model of creative activity on the computer incorporating the elements of programming, graphics, sound generation, and physical interaction. An interface for manipulating these elements is suggested, based on the concept of a disk-jockey turntable as a performance instrument. A system is developed around this idea, enabling optical(More)