Results 1  10
of
544,893
On the existence of Hadamard matrices
 J. Combin. Theory Ser. A
, 1976
"... Given any natural number q> 3 we show there exists an integer t ≤ [2 log2 (q – 3)] such that an Hadamard matrix exists for every order 2 s q where s> t. The Hadamard conjecture is that s = 2. This means that for each q there is a finite number of orders 2 v q for which an Hadamard matrix is no ..."
Abstract

Cited by 22 (3 self)
 Add to MetaCart
Given any natural number q> 3 we show there exists an integer t ≤ [2 log2 (q – 3)] such that an Hadamard matrix exists for every order 2 s q where s> t. The Hadamard conjecture is that s = 2. This means that for each q there is a finite number of orders 2 v q for which an Hadamard matrix
Table of the existence of Hadamard matrices
, 1990
"... On Hadamard matrices Recent advances in the construction of Hadamard matrices have depended on the existence of BaumertHall arrays and four (1,1) matrices A, B, C, D of order m which are of Williamson type, that is pairwise satisfy (i) MNT = NMT and (ii) AAT + BBT + CCT + DDT = 4mlm. If (i) is rep ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
On Hadamard matrices Recent advances in the construction of Hadamard matrices have depended on the existence of BaumertHall arrays and four (1,1) matrices A, B, C, D of order m which are of Williamson type, that is pairwise satisfy (i) MNT = NMT and (ii) AAT + BBT + CCT + DDT = 4mlm. If (i
HADAMARD MATRICES OF ORDER 764 EXIST
, 2007
"... Two Hadamard matrices of order 764 of Goethals– Seidel type are constructed. 2000 Mathematics Subject Classification 05B20, 05B30 Recall that a Hadamard matrix of order m is a {±1}matrix A of size m ×m such that AA T = mIm, where T denotes the transpose and Im the identity matrix. We refer the re ..."
Abstract
 Add to MetaCart
= 107, was removed recently by Kharaghani and TayfehRezaie [3]. Among the remaining 14 integers n only four are less than 1000. The problem of existence of Hadamard matrices of
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 ..."
Abstract

Cited by 500 (0 self)
 Add to MetaCart
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 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 number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of realworld complex networks.
A Simple Proof of the Restricted Isometry Property for Random Matrices
 CONSTR APPROX
, 2008
"... We give a simple technique for verifying the Restricted Isometry Property (as introduced by Candès and Tao) for random matrices that underlies Compressed Sensing. Our approach has two main ingredients: (i) concentration inequalities for random inner products that have recently provided algorithmical ..."
Abstract

Cited by 636 (69 self)
 Add to MetaCart
, we obtain simple and direct proofs of Kashin’s theorems on widths of finite balls in Euclidean space (and their improvements due to Gluskin) and proofs of the existence of optimal Compressed Sensing measurement matrices. In the process, we also prove that these measurements have a certain
Good ErrorCorrecting Codes based on Very Sparse Matrices
, 1999
"... We study two families of errorcorrecting codes defined in terms of very sparse matrices. "MN" (MacKayNeal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties. The ..."
Abstract

Cited by 741 (23 self)
 Add to MetaCart
We study two families of errorcorrecting codes defined in terms of very sparse matrices. "MN" (MacKayNeal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties
Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes
 J. COMP. PHYS
, 1981
"... Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by considering a sequence of Riemann problems. It is argued that in existing schemes much of this information is degraded, and that only certain features of the exact solution ..."
Abstract

Cited by 959 (2 self)
 Add to MetaCart
Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by considering a sequence of Riemann problems. It is argued that in existing schemes much of this information is degraded, and that only certain features of the exact solution
Methodologies in spectral analysis of large dimensional random matrices, a review
 STATIST. SINICA
, 1999
"... In this paper, we give a brief review of the theory of spectral analysis of large dimensional random matrices. Most of the existing work in the literature has been stated for real matrices but the corresponding results for the complex case are also of interest, especially for researchers in Electri ..."
Abstract

Cited by 453 (37 self)
 Add to MetaCart
In this paper, we give a brief review of the theory of spectral analysis of large dimensional random matrices. Most of the existing work in the literature has been stated for real matrices but the corresponding results for the complex case are also of interest, especially for researchers
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
Abstract

Cited by 560 (10 self)
 Add to MetaCart
We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so
Results 1  10
of
544,893