9,229 research outputs found

    RIPless compressed sensing from anisotropic measurements

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    Compressed sensing is the art of reconstructing a sparse vector from its inner products with respect to a small set of randomly chosen measurement vectors. It is usually assumed that the ensemble of measurement vectors is in isotropic position in the sense that the associated covariance matrix is proportional to the identity matrix. In this paper, we establish bounds on the number of required measurements in the anisotropic case, where the ensemble of measurement vectors possesses a non-trivial covariance matrix. Essentially, we find that the required sampling rate grows proportionally to the condition number of the covariance matrix. In contrast to other recent contributions to this problem, our arguments do not rely on any restricted isometry properties (RIP's), but rather on ideas from convex geometry which have been systematically studied in the theory of low-rank matrix recovery. This allows for a simple argument and slightly improved bounds, but may lead to a worse dependency on noise (which we do not consider in the present paper).Comment: 19 pages. To appear in Linear Algebra and its Applications, Special Issue on Sparse Approximate Solution of Linear System

    Methods and means used in programming intelligent searches of technical documents

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    In order to meet the data research requirements of the Safety, Reliability & Quality Assurance activities at Kennedy Space Center (KSC), a new computer search method for technical data documents was developed. By their very nature, technical documents are partially encrypted because of the author's use of acronyms, abbreviations, and shortcut notations. This problem of computerized searching is compounded at KSC by the volume of documentation that is produced during normal Space Shuttle operations. The Centralized Document Database (CDD) is designed to solve this problem. It provides a common interface to an unlimited number of files of various sizes, with the capability to perform any diversified types and levels of data searches. The heart of the CDD is the nature and capability of its search algorithms. The most complex form of search that the program uses is with the use of a domain-specific database of acronyms, abbreviations, synonyms, and word frequency tables. This database, along with basic sentence parsing, is used to convert a request for information into a relational network. This network is used as a filter on the original document file to determine the most likely locations for the data requested. This type of search will locate information that traditional techniques, (i.e., Boolean structured key-word searching), would not find

    String field theory, non-commutative Chern-Simons theory and Lie algebra cohomology

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    Motivated by noncommutative Chern-Simons theory, we construct an infinite class of field theories that satisfy the axioms of Witten's string field theory. These constructions have no propagating open string degrees of freedom. We demonstrate the existence of non-trivial classical solutions. We find Wilson loop-like observables in these examples.Comment: 10 pages, RevTe
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