9,074 research outputs found
RIPless compressed sensing from anisotropic measurements
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
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
The Bulk Dual of SYK: Cubic Couplings
The SYK model, a quantum mechanical model of Majorana fermions
, with a -body, random interaction, is a novel realization of
holography. It is known that the AdS dual contains a tower of massive
particles, yet there is at present no proposal for the bulk theory. As SYK is
solvable in the expansion, one can systematically derive the bulk. We
initiate such a program, by analyzing the fermion two, four and six-point
functions, from which we extract the tower of singlet, large dominant,
operators, their dimensions, and their three-point correlation functions. These
determine the masses of the bulk fields and their cubic couplings. We present
these couplings, analyze their structure and discuss the simplifications that
arise for large .Comment: 39 pages, v2: Evaluation of integral in Sec. 3.3.2 correcte
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