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LOCAL ANTITHETIC SAMPLING WITH SCRAMBLED NETS
, 811
"... We consider the problem of computing an approximation to the integral I = ∫ [0,1] d f(x)dx. Monte Carlo (MC) sampling typically attains a root mean squared error (RMSE) of O(n −1/2) from n independent random function evaluations. By contrast, quasiMonte Carlo (QMC) sampling using carefully equispac ..."
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Cited by 4 (1 self)
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variates have found worthwhile improvements, but no change in the error rate. This paper extends the classical variance reduction method of antithetic sampling and combines it with RQMC. One such method is shown to bring a modest improvement in the RMSE rate, attaining O(n −3/2−1/d+ε) for any ε> 0
The Laplacian Pyramid as a Compact Image Code
, 1983
"... We describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions. The representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space. Pixeltopixel correlations a ..."
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Cited by 1387 (12 self)
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are first removed by subtracting a lowpass filtered copy of the image from the image itself. The result is a net data compression since the difference, or error, image has low variance and entropy, and the lowpass filtered image may represented at reduced sample density. Further data compression
Variance and Discrepancy with Alternative Scramblings
, 2002
"... This paper analyzes some schemes for reducing the computational burden of digital scrambling. Some such schemes have been shown not to affect the mean squared L² discrepancy. This paper shows that some discrepancypreserving alternative scrambles can change the variance in scrambled net quadrature. ..."
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Cited by 5 (1 self)
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This paper analyzes some schemes for reducing the computational burden of digital scrambling. Some such schemes have been shown not to affect the mean squared L² discrepancy. This paper shows that some discrepancypreserving alternative scrambles can change the variance in scrambled net quadrature
Combination of General Antithetic Transformations and Control Variables
, 2003
"... Several methods for reducing the variance in the context of Monte Carlo simulation are based on correlation induction. This includes antithetic variates, Latin hypercube sampling, and randomized version of quasiMonte Carlo methods such as lattice rules and digital nets, where the resulting estimato ..."
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Cited by 5 (1 self)
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Several methods for reducing the variance in the context of Monte Carlo simulation are based on correlation induction. This includes antithetic variates, Latin hypercube sampling, and randomized version of quasiMonte Carlo methods such as lattice rules and digital nets, where the resulting
Antithetic variates in higher dimensions
, 902
"... We introduce the concept of multidimensional antithetic as the absolute minimum of the covariance function O(N) → R defined by A ↦ → Cov (f(ξ), f(Aξ)) where ξ is a standard Ndimensional normal random variable and f: R N → R is an almost everywhere differentiable function. The antithetic matrix is ..."
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We introduce the concept of multidimensional antithetic as the absolute minimum of the covariance function O(N) → R defined by A ↦ → Cov (f(ξ), f(Aξ)) where ξ is a standard Ndimensional normal random variable and f: R N → R is an almost everywhere differentiable function. The antithetic matrix
Higher order scrambled digital nets achieve the optimal rate of the root mean square error for smooth integrands∗ Josef Dick
, 2010
"... We study numerical approximations of integrals [0,1]s f(x) dx by averaging the function at some sampling points. Monte Carlo (MC) sampling yields a convergence of the root mean square error (RMSE) of order N−1/2 (where N is the number of samples). QuasiMonte Carlo (QMC) sampling on the other hand ..."
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achieves a convergence of order N−1+ε, for any ε> 0. Randomized QMC (RQMC), a combination of MC and QMC, achieves a RMSE of order N−3/2+ε. A combination of RQMC with local antithetic sampling achieves a convergence of the RMSE of order N−3/2−1/s+ε (where s ≥ 1 is the dimension). QMC, RQMC and RQMC
KANTITHETIC VARIATES IN MONTE CARLO
"... Abstract. Standard Monte Carlo simulation needs prohibitive time to achieve reasonable estimations. for untractable integrals (i.e. multidimensional integrals and/or intergals with complex integrand forms). Several statistical technique, called variance reduction methods, are used to reduce the sim ..."
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the simulation time. In this note, we propose a generalization of the well known antithetic variate method. Principally we propose a K−antithetic variate estimator (KAVE) based on the generation of K correlated uniform variates. Some numerical examples are presented to show the improvenment of our proposition. 1.
Coil sensitivity encoding for fast MRI. In:
 Proceedings of the ISMRM 6th Annual Meeting,
, 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
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Cited by 192 (3 self)
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denotes the factor by which the number of samples is reduced with respect to full Fourier encoding: The rightmost squareroot expression in Eq. [21] strongly depends on coil geometry and is thus called the local geometry factor g, which is always at least equal to one: Note that by virtue of condition [15
Scrambling with Matrix Black Holes
"... If black holes are not to be dreaded syncs of information but be fully described by unitary evolution, they must scramble infalling data and eventually leak it through Hawking radiation. Sekino and Susskind have conjectured that black holes are fast scramblers: they generate entanglement at a remar ..."
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If black holes are not to be dreaded syncs of information but be fully described by unitary evolution, they must scramble infalling data and eventually leak it through Hawking radiation. Sekino and Susskind have conjectured that black holes are fast scramblers: they generate entanglement at a
Results 1  10
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558,084