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136
Identity Testing, multilinearity testing, and monomials in ReadOnce/Twice Formulas and Branching Programs ⋆
"... Abstract. We study the problem of testing if the polynomial computed by an arithmetic circuit is identically zero (ACIT). We give a deterministic polynomial time algorithm for this problem when the inputs are readtwice formulas. This algorithm also computes the MLIN predicate, testing if the input ..."
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Cited by 2 (1 self)
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circuit computes a multilinear polynomial. We further study two related computational problems on arithmetic circuits. Given an arithmetic circuit C, 1) ZMC: test if a given monomial in C has zero coefficient or not, and 2) MonCount: compute the number of monomials in C. These problems were introduced
Multilinear Independent Components Analysis
 IEEE COMPUTER SOCIETY COMPUTER VISION AND PATTERN RECOGNITION (CVPR'05)
, 2005
"... Independent Components Analysis (ICA) maximizes the statistical independence of the representational components of a training image ensemble, but it cannot distinguish between the different factors, or modes, inherent to image formation, including scene structure, illumination, and imaging. We intro ..."
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Cited by 59 (1 self)
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multilinear projection algorithm which projects an unlabeled test image into the N constituent mode spaces to simultaneously infer its mode labels. In the context of facial image ensembles, where the mode labels are person, viewpoint, illumination, expression, etc., we demonstrate that the statistical
Interactive proofs and the hardness of approximating cliques
 JOURNAL OF THE ACM
, 1996
"... The contribution of this paper is twofold. First, a connection is shown between approximating the size of the largest clique in a graph and multiprover interactive proofs. Second, an efficient multiprover interactive proof for NP languages is constructed, where the verifier uses very few random b ..."
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Cited by 170 (11 self)
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bits and communication bits. Last, the connection between cliques and efficient multiprover interactive proofs, is shown to yield hardness results on the complexity of approximating the size of the largest clique in a graph. Of independent interest is our proof of correctness for the multilinearity
A multilinear Schur test and multiplier operators
 J. Func. Anal
"... Abstract. A multilinear version of Schur’s test is obtained for products of L p spaces and is used to derive boundedness for multilinear multiplier operators acting on Sobolev and Besov spaces. 1. ..."
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Cited by 8 (4 self)
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Abstract. A multilinear version of Schur’s test is obtained for products of L p spaces and is used to derive boundedness for multilinear multiplier operators acting on Sobolev and Besov spaces. 1.
Multilinearity selftesting with relative error
 In Proc. 17th STACS, LNCS 1770
, 2000
"... Abstract. We investigate selftesting programs with relative error by allowing error terms proportional to the function to be computed. Until now, in numerical computation, error terms were assumed to be either constant or proportional to the pth power of the magnitude of the input, for p ∈ [0, 1). ..."
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Cited by 3 (1 self)
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Abstract. We investigate selftesting programs with relative error by allowing error terms proportional to the function to be computed. Until now, in numerical computation, error terms were assumed to be either constant or proportional to the pth power of the magnitude of the input, for p ∈ [0, 1
Quantum Query Complexity of Multilinear Identity Testing
 in Proc. STACS 2009
"... Motivated by the quantum algorithm in [MN05] for testing commutativity of blackbox groups, we study the following problem: Given a blackbox finite ring R = 〈r1, · · · , rk 〉 where {r1, r2, · · · , rk} is an additive generating set for R and a multilinear polynomial f(x1, · · · , xm) over ..."
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Cited by 2 (0 self)
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Motivated by the quantum algorithm in [MN05] for testing commutativity of blackbox groups, we study the following problem: Given a blackbox finite ring R = 〈r1, · · · , rk 〉 where {r1, r2, · · · , rk} is an additive generating set for R and a multilinear polynomial f(x1, · · · , xm) over
HigherOrder Web Link Analysis Using Multilinear Algebra
 IEEE INTERNATIONAL CONFERENCE ON DATA MINING
, 2005
"... Linear algebra is a powerful and proven tool in web search. Techniques, such as the PageRank algorithm of Brin and Page and the HITS algorithm of Kleinberg, score web pages based on the principal eigenvector (or singular vector) of a particular nonnegative matrix that captures the hyperlink structu ..."
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Cited by 69 (18 self)
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structure of the web graph. We propose and test a new methodology that uses multilinear algebra to elicit more information from a higherorder representation of the hyperlink graph. We start by labeling the edges in our graph with the anchor text of the hyperlinks so that the associated linear algebra
New Multilinear Maps over the Integers
, 2015
"... Abstract. In the last few years, cryptographic multilinear maps have proved their tremendous potential as building blocks for new constructions, in particular the first viable approach to general program obfuscation. After the first candidate construction by Garg, Gentry and Halevi (GGH) based on id ..."
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describe a new candidate multilinear map over the integers. Our construction is based on CLT but with a new arithmetic technique that makes the zerotesting element nonlinear in the encoding, which prevents the Cheon et al. attack. Our new construction is relatively practical as its efficiency
On multilinear singular integrals of CalderónZygmund type
, 2011
"... A variety of results regarding multilinear CalderónZygmund singular integral operators is systematically presented. Several tools and techniques for the study of such operators are discussed. These include new multilinear endpoint weak type estimates, multilinear interpolation, appropriate discret ..."
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Cited by 19 (4 self)
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discrete decompositions, a multilinear version of Schur’s test, and a multilinear version of the T1 Theorem suitable for the study of multilinear pseudodifferential and translation invariant operators. A maximal operator associated with multilinear singular integrals is also introduced and employed
Results 1  10
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136