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Spectral Norm of Symmetric Functions

by Anil Ada, Omar Fawzi, Hamed Hatami , 2012
"... The spectral norm of a Boolean function f: {0, 1} n → {−1, 1} is the sum of the absolute values of its Fourier coefficients. This quantity provides useful upper and lower bounds on the complexity of a function in areas such as learning theory, circuit complexity, and communication complexity. In thi ..."
Abstract - Cited by 3 (0 self) - Add to MetaCart
. In this paper, we give a combinatorial characterization for the spectral norm of symmetric functions. We show that the logarithm of the spectral norm is of the same order of magnitude as r(f) log(n/r(f)) where r(f) = max{r0, r1}, and r0 and r1 are the smallest integers less than n/2 such that f(x) or f

Chebyshev and Fourier Spectral Methods

by John P. Boyd , 1999
"... ..."
Abstract - Cited by 778 (12 self) - Add to MetaCart
Abstract not found

Spectral asymmetry and Riemannian geometry

by M. F. Atiyah, V. K. Patodi, I. M. Singer - , 1973
"... ..."
Abstract - Cited by 623 (4 self) - Add to MetaCart
Abstract not found

Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones

by Jos F. Sturm , 1998
"... SeDuMi is an add-on for MATLAB, that lets you solve optimization problems with linear, quadratic and semidefiniteness constraints. It is possible to have complex valued data and variables in SeDuMi. Moreover, large scale optimization problems are solved efficiently, by exploiting sparsity. This pape ..."
Abstract - Cited by 1334 (4 self) - Add to MetaCart
SeDuMi is an add-on for MATLAB, that lets you solve optimization problems with linear, quadratic and semidefiniteness constraints. It is possible to have complex valued data and variables in SeDuMi. Moreover, large scale optimization problems are solved efficiently, by exploiting sparsity. This paper describes how to work with this toolbox.

Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering

by Mikhail Belkin, Partha Niyogi - Advances in Neural Information Processing Systems 14 , 2001
"... Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in a higher ..."
Abstract - Cited by 664 (8 self) - Add to MetaCart
Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in a higher dimensional space. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering. Several applications are considered.

A standardized set of 260 pictures: Norms for name agreement, image agreement, familiarity, and visual complexity

by Joan Gay Snodgrass, Mary Vanderwart - JOURNAL OF EXPERIMENTAL PSYCHOLOGY: HUMAN LEARNING AND MEMORY , 1980
"... In this article we present a standardized set of 260 pictures for use in experiments investigating differences and similarities in the processing of pictures and words. The pictures are black-and-white line drawings executed according to a set of rules that provide consistency of pictorial represent ..."
Abstract - Cited by 615 (1 self) - Add to MetaCart
In this article we present a standardized set of 260 pictures for use in experiments investigating differences and similarities in the processing of pictures and words. The pictures are black-and-white line drawings executed according to a set of rules that provide consistency of pictorial representation. The pictures have been standardized on four variables of central relevance to memory and cognitive processing: name agreement, image agreement, familiarity, and visual complexity. The intercorrelations among the four measures were low, suggesting that the) ' are indices of different attributes of the pictures. The concepts were selected to provide exemplars from several widely studied semantic categories. Sources of naming variance, and mean familiarity and complexity of the exemplars, differed significantly across the set of categories investigated. The potential significance of each of the normative variables to a number of semantic and episodic memory tasks is discussed.

Evaluating the Accuracy of Sampling-Based Approaches to the Calculation of Posterior Moments

by John Geweke - IN BAYESIAN STATISTICS , 1992
"... Data augmentation and Gibbs sampling are two closely related, sampling-based approaches to the calculation of posterior moments. The fact that each produces a sample whose constituents are neither independent nor identically distributed complicates the assessment of convergence and numerical accurac ..."
Abstract - Cited by 583 (14 self) - Add to MetaCart
accuracy of the approximations to the expected value of functions of interest under the posterior. In this paper methods from spectral analysis are used to evaluate numerical accuracy formally and construct diagnostics for convergence. These methods are illustrated in the normal linear model

Stochastic Perturbation Theory

by G. W. Stewart , 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a first-order perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
Abstract - Cited by 886 (35 self) - Add to MetaCart
the variation in the perturbed quantity. Up to the higher-order terms that are ignored in the expansion, these statistics tend to be more realistic than perturbation bounds obtained in terms of norms. The technique is applied to a number of problems in matrix perturbation theory, including least squares

Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization

by Farid Alizadeh - SIAM Journal on Optimization , 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
Abstract - Cited by 557 (12 self) - Add to MetaCart
We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized

GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems

by Youcef Saad, Martin H. Schultz - SIAM J. SCI. STAT. COMPUT , 1986
"... We present an iterative method for solving linear systems, which has the property ofminimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from the Arnoldi process for constructing an l2-orthogonal basis of Krylov subspaces. It can be considered a ..."
Abstract - Cited by 2046 (40 self) - Add to MetaCart
We present an iterative method for solving linear systems, which has the property ofminimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from the Arnoldi process for constructing an l2-orthogonal basis of Krylov subspaces. It can be considered
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