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791
ON THE LPCONVERGENCE FOR MULTIDIMENSIONAL ARRAYS OF RANDOM VARIABLES
, 2005
"... For a ddimensional array of random variables {Xn, n ∈ Zd+} such that {Xnp, n ∈ Zd+} is uniformly integrable for some 0 < p < 2, the Lpconvergence is established for the sums (1/n1/p)( ∑ j≺n(Xj − aj)), where aj = 0 if 0 < p < 1, and aj = EXj if 1 ≤ p < 2. 1. ..."
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For a ddimensional array of random variables {Xn, n ∈ Zd+} such that {Xnp, n ∈ Zd+} is uniformly integrable for some 0 < p < 2, the Lpconvergence is established for the sums (1/n1/p)( ∑ j≺n(Xj − aj)), where aj = 0 if 0 < p < 1, and aj = EXj if 1 ≤ p < 2. 1.
ON THE L PCONVERGENCE FOR MULTIDIMENSIONAL ARRAYS OF RANDOM VARIABLES
, 2005
"... For a ddimensional array of random variables {Xn, n ∈ Zd +} such that {Xn  p, n ∈ Zd +} is uniformly integrable for some 0 <p<2, the Lpconvergence is established for the sums (1/n  1/p) ( ∑ j≺n(Xj − aj)), where aj = 0if0<p<1, and aj = EXj if 1 ≤ p<2. 1. ..."
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For a ddimensional array of random variables {Xn, n ∈ Zd +} such that {Xn  p, n ∈ Zd +} is uniformly integrable for some 0 <p<2, the Lpconvergence is established for the sums (1/n  1/p) ( ∑ j≺n(Xj − aj)), where aj = 0if0<p<1, and aj = EXj if 1 ≤ p<2. 1.
Approximate Computation of Multidimensional Aggregates of Sparse Data Using Wavelets
"... Computing multidimensional aggregates in high dimensions is a performance bottleneck for many OLAP applications. Obtaining the exact answer to an aggregation query can be prohibitively expensive in terms of time and/or storage space in a data warehouse environment. It is advantageous to have fast, a ..."
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Cited by 198 (3 self)
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and spaceefficient representation of the underlying multidimensional array, based upon a multiresolution wavelet decomposition. In the online phase, each aggregation query can generally be answered using the compact data cube in one I/O or a small number of I/Os, depending upon the desired accuracy. We
ON THE L P CONVERGENCE FOR MULTIDIMENSIONAL ARRAYS OF RANDOM VARIABLES
"... is uniformly integrable for some 0 < p < 2, the L p convergence is established for the sums (1/n 1/p )( j≺n (X j − a j )), where a j = 0 if 0 < p < 1, and a j = EX j if 1 ≤ p < 2. ..."
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is uniformly integrable for some 0 < p < 2, the L p convergence is established for the sums (1/n 1/p )( j≺n (X j − a j )), where a j = 0 if 0 < p < 1, and a j = EX j if 1 ≤ p < 2.
Fast manipulation of multidimensional arrays in Matlab
, 2002
"... Probabilistic inference in graphical models with discrete random variables requires performing various operations ..."
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Cited by 1 (1 self)
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Probabilistic inference in graphical models with discrete random variables requires performing various operations
Shao’s theorem on the maximum of standardized random walk increments for multidimensional arrays
, 1999
"... We generalize a theorem of Shao (1995, Proc. Am. Math. Soc. 123, 575582) on the almostsure limiting behavior of the maximum of standardized random walk increments to multidimensional arrays of i.i.d. random variables. The main difficulty is the absence of an appropriate strong approximation resu ..."
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Cited by 7 (5 self)
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We generalize a theorem of Shao (1995, Proc. Am. Math. Soc. 123, 575582) on the almostsure limiting behavior of the maximum of standardized random walk increments to multidimensional arrays of i.i.d. random variables. The main difficulty is the absence of an appropriate strong approximation
Rectangular Tiling in MultiDimensional Arrays
 In Proceedings of the 10th Annual ACMSIAM Symposium on Discrete Algorithms, 786–794
, 1999
"... We study the following tiling problem in d dimensions: given a ddimensional rectangular array of nonnegative numbers and an integer p, partition the array into at most p rectangular subarrays so that the maximum weight of any subarray is minimized; the weight of a subarray is the sum of its ele ..."
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Cited by 10 (0 self)
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algorithm for the dual tiling problem, where the goal is to compute a tiling of weight at most W using as few tiles as possible. Our algorithm yields an approximation factor (2d + 1). We implemented our algorithm and ran simulation tests on multidimensional arrays with random data. In our limited
Scanning and prediction in multidimensional data arrays
, 2001
"... Abstract—The problem of sequentially scanning and predicting data arranged in a multidimensional array is considered. We introduce the notion of a scandictor, which is any scheme for the sequential scanning and prediction of such multidimensional data. The scandictability of any finite (probabilis ..."
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Cited by 3 (3 self)
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Abstract—The problem of sequentially scanning and predicting data arranged in a multidimensional array is considered. We introduce the notion of a scandictor, which is any scheme for the sequential scanning and prediction of such multidimensional data. The scandictability of any finite
POSITIVE DEFINITE FUNCTIONS AND MULTIDIMENSIONAL VERSIONS OF RANDOM VARIABLES
, 903
"... Abstract. We say that a random vector X = (X1,..., Xn) in R n is an ndimensional version of a random variable Y if for any a ∈ R n the random variables ∑ aiXi and γ(a)Y are identically distributed, where γ: R n → [0, ∞) is called the standard of X. An old problem is to characterize those functions ..."
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Abstract. We say that a random vector X = (X1,..., Xn) in R n is an ndimensional version of a random variable Y if for any a ∈ R n the random variables ∑ aiXi and γ(a)Y are identically distributed, where γ: R n → [0, ∞) is called the standard of X. An old problem is to characterize those functions
Lyapounov Exponents and Quenched Large Deviations for Multidimensional Random Walk in Random Environment
, 1997
"... this paper that the vectors (!(z; z + e)) jej=1 ; z 2 Z d ; are independent and identically distributed random vectors on some probability space with sample space and probability measure P. For the sake of simplicity we denote the elements of by !, too. Each such ! serves as environment for a Ma ..."
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Cited by 39 (0 self)
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2 M. P. W. Zerner 300 0 300 300 0 300 Fig. 1. Density plot of the distribution of the displacement vector Xn after n = 15000 steps in two dimensions. The environment ! is a realization of !(x; x+e) = (x; x+e)= P e 0 (x; x+e 0 ), where the random variables (x; x + e) (x 2 Z d ; jej = 1
Results 1  10
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791