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Locally Testable Codes and Cayley Graphs
, 2013
"... We give two new characterizations of (F2linear) locally testable errorcorrecting codes in terms of Cayley graphs over Fh2: 1. A locally testable code is equivalent to a Cayley graph over Fh2 whose set of generators is significantly larger than h and has no short linear dependencies, but yields a ..."
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Cited by 1 (0 self)
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We give two new characterizations of (F2linear) locally testable errorcorrecting codes in terms of Cayley graphs over Fh2: 1. A locally testable code is equivalent to a Cayley graph over Fh2 whose set of generators is significantly larger than h and has no short linear dependencies, but yields a
Using Linear Algebra for Intelligent Information Retrieval
 SIAM REVIEW
, 1995
"... Currently, most approaches to retrieving textual materials from scientific databases depend on a lexical match between words in users' requests and those in or assigned to documents in a database. Because of the tremendous diversity in the words people use to describe the same document, lexical ..."
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Cited by 672 (18 self)
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Currently, most approaches to retrieving textual materials from scientific databases depend on a lexical match between words in users' requests and those in or assigned to documents in a database. Because of the tremendous diversity in the words people use to describe the same document, lexical methods are necessarily incomplete and imprecise. Using the singular value decomposition (SVD), one can take advantage of the implicit higherorder structure in the association of terms with documents by determining the SVD of large sparse term by document matrices. Terms and documents represented by 200300 of the largest singular vectors are then matched against user queries. We call this retrieval method Latent Semantic Indexing (LSI) because the subspace represents important associative relationships between terms and documents that are not evident in individual documents. LSI is a completely automatic yet intelligent indexing method, widely applicable, and a promising way to improve users...
Locally Testable Codes and Expanders
, 2012
"... A locally testable code is a code defined by a robust set of local constraints. Namely, the distance of a vector from the code is well approximated by the fraction of local constraints that it violates. A constraint graph of an LTC is a graph whose vertices are labeled by the coordinates of the code ..."
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A locally testable code is a code defined by a robust set of local constraints. Namely, the distance of a vector from the code is well approximated by the fraction of local constraints that it violates. A constraint graph of an LTC is a graph whose vertices are labeled by the coordinates
Synchronization and linearity: an algebra for discrete event systems
, 2001
"... The first edition of this book was published in 1992 by Wiley (ISBN 0 471 93609 X). Since this book is now out of print, and to answer the request of several colleagues, the authors have decided to make it available freely on the Web, while retaining the copyright, for the benefit of the scientific ..."
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Cited by 369 (11 self)
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The first edition of this book was published in 1992 by Wiley (ISBN 0 471 93609 X). Since this book is now out of print, and to answer the request of several colleagues, the authors have decided to make it available freely on the Web, while retaining the copyright, for the benefit of the scientific community. Copyright Statement This electronic document is in PDF format. One needs Acrobat Reader (available freely for most platforms from the Adobe web site) to benefit from the full interactive machinery: using the package hyperref by Sebastian Rahtz, the table of contents and all LATEX crossreferences are automatically converted into clickable hyperlinks, bookmarks are generated automatically, etc.. So, do not hesitate to click on references to equation or section numbers, on items of thetableofcontents and of the index, etc.. One may freely use and print this document for one’s own purpose or even distribute it freely, but not commercially, provided it is distributed in its entirety and without modifications, including this preface and copyright statement. Any use of thecontents should be acknowledged according to the standard scientific practice. The
Iterative construction of cayley expander graphs
 Theory of Computing
"... Abstract We construct a sequence of groups Gn, and explicit sets of generators Yn ae Gn, such that allgenerating sets have bounded size, and the associated Cayley graphs are all expanders. The group G1 isthe alternating group Ad, the set of even permutations on the elements {1, 2,..., d}. The group ..."
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Cited by 6 (0 self)
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Abstract We construct a sequence of groups Gn, and explicit sets of generators Yn ae Gn, such that allgenerating sets have bounded size, and the associated Cayley graphs are all expanders. The group G1 isthe alternating group Ad, the set of even permutations on the elements {1, 2,..., d}. The group
Twosided Cayley graphs
"... We introduce a family of graphs that generalises the class of Cayley graphs. For nonempty subsets L,R of a group G, the twosided Cayley graph 2SCay(G;L,R) is the directed graph with vertex set G and an arc from x to y if and only if y = `−1xr for some ` ∈ L and r ∈ R. Thus, in common with Cayley ..."
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We introduce a family of graphs that generalises the class of Cayley graphs. For nonempty subsets L,R of a group G, the twosided Cayley graph 2SCay(G;L,R) is the directed graph with vertex set G and an arc from x to y if and only if y = `−1xr for some ` ∈ L and r ∈ R. Thus, in common with Cayley
Discrete mechanics and variational integrators
 Acta Numer
, 2001
"... This paper gives a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles. The variational technique gives a unified treatment of many symplectic schemes, including those of higher order, as well as a natural treatment of the disc ..."
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Cited by 284 (34 self)
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This paper gives a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles. The variational technique gives a unified treatment of many symplectic schemes, including those of higher order, as well as a natural treatment of the discrete Noether theorem. The approach also allows us to include forces, dissipation and constraints in a natural way. Amongst the many specific schemes treated as examples, the Verlet, SHAKE, RATTLE, Newmark, and the symplectic
Fault Localization with Nearest Neighbor Queries
, 2003
"... We present a method for performing fault localization using similar program spectra. Our method assumes the existence of a faulty run and a larger number of correct runs. It then selects according to a distance criterion the correct run that most resembles the faulty run, compares the spectra corres ..."
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Cited by 227 (2 self)
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We present a method for performing fault localization using similar program spectra. Our method assumes the existence of a faulty run and a larger number of correct runs. It then selects according to a distance criterion the correct run that most resembles the faulty run, compares the spectra
Results 1  10
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