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10,681
Approximation of Measures on S n by discrete Measures
, 2006
"... We study the asymptotic behavior, as ρ → ∞, of discrete measures on S n−1 that are induced by radially projecting point masses concentrated on the integral latticepoints within dilates ρD of a compact body D, for various classes of D. The results depend sensitively on the differential geometric pro ..."
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We study the asymptotic behavior, as ρ → ∞, of discrete measures on S n−1 that are induced by radially projecting point masses concentrated on the integral latticepoints within dilates ρD of a compact body D, for various classes of D. The results depend sensitively on the differential geometric
Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
, 2004
"... Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear m ..."
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Cited by 1513 (20 self)
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Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear
Hierarchical Dirichlet processes.
 Journal of the American Statistical Association,
, 2006
"... We consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups. We assume that the number of mixture components is unknown a priori and is to be inferred from the data. In this s ..."
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Cited by 942 (78 self)
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consider a hierarchical model, specifically one in which the base measure for the child Dirichlet processes is itself distributed according to a Dirichlet process. Such a base measure being discrete, the child Dirichlet processes necessarily share atoms. Thus, as desired, the mixture models
FFTW: An Adaptive Software Architecture For The FFT
, 1998
"... FFT literature has been mostly concerned with minimizing the number of floatingpoint operations performed by an algorithm. Unfortunately, on presentday microprocessors this measure is far less important than it used to be, and interactions with the processor pipeline and the memory hierarchy have ..."
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Cited by 602 (4 self)
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FFT literature has been mostly concerned with minimizing the number of floatingpoint operations performed by an algorithm. Unfortunately, on presentday microprocessors this measure is far less important than it used to be, and interactions with the processor pipeline and the memory hierarchy have
Compression of multivariate discrete measures and applications ∗
, 2014
"... We discuss two methods for the compression of multivariate discrete measures, with applications to node reduction in numerical cubature and leastsquares approximation. The methods are implemented in the Matlab computing environment, in dimension two. ..."
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Cited by 2 (1 self)
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We discuss two methods for the compression of multivariate discrete measures, with applications to node reduction in numerical cubature and leastsquares approximation. The methods are implemented in the Matlab computing environment, in dimension two.
Optimal Quantum Trajectories for Discrete Measurements
"... Using the method of quantum trajectories we show that a known pure state can be optimally monitored through time when subject to a sequence of discrete measurements. By modifying the way we extract information from the measurement apparatus we can minimise the average algorithmic information of the ..."
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Using the method of quantum trajectories we show that a known pure state can be optimally monitored through time when subject to a sequence of discrete measurements. By modifying the way we extract information from the measurement apparatus we can minimise the average algorithmic information
On Generating Orthogonal Polynomials for Discrete Measures
, 1997
"... Introduction Let oe be a given positive measure with infinite support S(oe) and finite moments of all orders. Then there exists a unique family of monic polynomials ~ ß j with Z ~ ß l (x)~ß j (x) doe(x) = 0 for l ! j and Z ~ ß 2 j (x) doe(x) = fl \Gamma2 j ? 0; j = 0; 1; : : : (1) (fl j is ..."
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Cited by 5 (1 self)
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Introduction Let oe be a given positive measure with infinite support S(oe) and finite moments of all orders. Then there exists a unique family of monic polynomials ~ ß j with Z ~ ß l (x)~ß j (x) doe(x) = 0 for l ! j and Z ~ ß 2 j (x) doe(x) = fl \Gamma2 j ? 0; j = 0; 1; : : : (1) (fl j
Gaussian quadratures with respect to discrete measures
, 2006
"... In analogy to the subject of Gaussian integration formulas we present an overview of some Gaussian summation formulas. The derivation involve polynomials that are orthogonal under discrete inner products and the resulting formulas are useful as a numerical device for summing fairly general series. S ..."
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Cited by 2 (1 self)
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In analogy to the subject of Gaussian integration formulas we present an overview of some Gaussian summation formulas. The derivation involve polynomials that are orthogonal under discrete inner products and the resulting formulas are useful as a numerical device for summing fairly general series
INVARIANCE METHODS IN DISCRETE MEASURE THEORY
"... Abstract. Let Ω be a multiply Leibniz isometry equipped with a solvable, analytically natural graph. Recent developments in commutative analysis [5, 16] have raised the question of whether every hyperpartial graph is Noetherian and smoothly Poncelet. We show that ..."
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Abstract. Let Ω be a multiply Leibniz isometry equipped with a solvable, analytically natural graph. Recent developments in commutative analysis [5, 16] have raised the question of whether every hyperpartial graph is Noetherian and smoothly Poncelet. We show that
Results 1  10
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10,681