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Compressed modular matrix multiplication
 IN: MILESTONES IN COMPUTER ALGEBRA
, 2008
"... We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo. Modular Multiplication is not directly accessible but modular dot product can be performed by an int ..."
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Cited by 5 (2 self)
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by an integer multiplication by the reverse integer. Modular multiplication by a word containing a single residue is a also possible. Therefore matrix multiplication can be performed on such a compressed storage. We here give bounds on the sizes of primes and matrices for which such a compression is possible
Finding community structure in networks using the eigenvectors of matrices
, 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
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Cited by 502 (0 self)
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divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a
Control and Implementation of a New Modular Matrix Converter
"... Abstract — Implementation of a new modular ACAC matrix converter and its control system are described. The converter consists of a matrix connection of capacitorclamped Hbridge switch cells. The AC output of each switch cell can assume three voltage levels during conduction. Input and output thre ..."
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Abstract — Implementation of a new modular ACAC matrix converter and its control system are described. The converter consists of a matrix connection of capacitorclamped Hbridge switch cells. The AC output of each switch cell can assume three voltage levels during conduction. Input and output
Capacitor Voltage Balancing Control for a Modular Matrix Converter
"... Abstract — This paper describes a simplified capacitor voltage balancing scheme for a modular matrix converter operating in twolevel switching mode. The proposed scheme is based on the conventional space vector modulation technique. By using two additional space vectors having opposite direction, t ..."
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Abstract — This paper describes a simplified capacitor voltage balancing scheme for a modular matrix converter operating in twolevel switching mode. The proposed scheme is based on the conventional space vector modulation technique. By using two additional space vectors having opposite direction
SelfTesting/Correcting with Applications to Numerical Problems
, 1990
"... Suppose someone gives us an extremely fast program P that we can call as a black box to compute a function f . Should we trust that P works correctly? A selftesting/correcting pair allows us to: (1) estimate the probability that P (x) 6= f(x) when x is randomly chosen; (2) on any input x, compute ..."
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Cited by 361 (27 self)
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of numerical problems, including integer multiplication, modular multiplication, matrix multiplicatio...
FINDING STRUCTURE WITH RANDOMNESS: PROBABILISTIC ALGORITHMS FOR CONSTRUCTING APPROXIMATE MATRIX DECOMPOSITIONS
"... Lowrank matrix approximations, such as the truncated singular value decomposition and the rankrevealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which demonstrates that randomization offers a powerful tool for ..."
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Cited by 253 (6 self)
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for performing lowrank matrix approximation. These techniques exploit modern computational architectures more fully than classical methods and open the possibility of dealing with truly massive data sets. This paper presents a modular framework for constructing randomized algorithms that compute partial matrix
Applying the Design Structure Matrix to system decomposition and integration problems: a review and new directions
 IEEE Transactions on Engineering Management
"... organizations requires tools and techniques for system decomposition and integration. A design structure matrix (DSM) provides a simple, compact, and visual representation of a complex system that supports innovative solutions to decomposition and integration problems. The advantages of DSMs visà ..."
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Cited by 199 (8 self)
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and their relationships. Index Terms—Design structure matrix, information flow, integration analysis, modularity, organization design, product architecture, product development, project management, project planning, scheduling, systems engineering. I.
On fusion algebras and modular matrices
 Commun. Math. Phys
, 1999
"... Abstract: We consider the fusion algebras arising in e.g. WessZuminoWitten conformal field theories, affine KacMoody algebras at positive integer level, and quantum groups at roots of unity. Using properties of the modular matrix S, we find small sets of primary fields (equivalently, sets of high ..."
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Cited by 8 (3 self)
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Abstract: We consider the fusion algebras arising in e.g. WessZuminoWitten conformal field theories, affine KacMoody algebras at positive integer level, and quantum groups at roots of unity. Using properties of the modular matrix S, we find small sets of primary fields (equivalently, sets
Modular Sequences and Modular
"... For every n divisible by 4, we construct a square matrix H of size n, with coefficients \Sigma1, such that H \Delta H j nI mod 32. This solves the 32modular version of the classical Hadamard conjecture. We also determine the set of lengths of 16modular Golay sequences. ..."
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For every n divisible by 4, we construct a square matrix H of size n, with coefficients \Sigma1, such that H \Delta H j nI mod 32. This solves the 32modular version of the classical Hadamard conjecture. We also determine the set of lengths of 16modular Golay sequences.
Results 1  10
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654