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Discrete LowDiscrepancy Sequences
, 2009
"... Holroyd and Propp used Hall’s marriage theorem to show that, given a probability distribution π on a finite set S, there exists an infinite sequence s1, s2,... in S such that for all integers k ≥ 1 and all s in S, the number of i in [1, k] with si = s differs from k π(s) by at most 1. We prove a gen ..."
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Cited by 2 (1 self)
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, and the work of Holroyd and Propp [8] on derandomized Markov chains. Here we focus on derandomizing something even more fundamental to probability theory: the notion of an independent sequence of discrete random variables. Key words: rotor router; discrepancy; quasirandom sequence; lowdiscrepancy sequence
LowDiscrepancy Simulation
"... Summary. This article presents a survey of lowdiscrepancy sequences and their applications to quasiMonte Carlo methods for multidimensional numerical integration. QuasiMonte Carlo methods are deterministic versions of Monte Carlo methods which outperform Monte Carlo methods for many types of int ..."
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of integrals and have thus been found enormously useful in computational finance. First a general background on quasiMonte Carlo methods is given. Then we describe principles for the construction of lowdiscrepancy sequences, with a special emphasis on the currently most powerful constructions based
EVOLUTIONARY OPTIMIZATION OF LOWDISCREPANCY SEQUENCES
, 2012
"... Abstract. Lowdiscrepancy sequences provide a way to generate quasirandom numbers of high dimensionality with a very high level of uniformity. The nearly orthogonal Latin hypercube and the generalized Halton sequence are two popular methods when it comes to generate lowdiscrepancy sequences. In th ..."
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Cited by 2 (0 self)
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Abstract. Lowdiscrepancy sequences provide a way to generate quasirandom numbers of high dimensionality with a very high level of uniformity. The nearly orthogonal Latin hypercube and the generalized Halton sequence are two popular methods when it comes to generate lowdiscrepancy sequences
The Skill Content of Recent Technological Change: An Empirical Exploration
, 2000
"... Recent empirical and case study evidence documents a strong association between the adoption of computers and increased use of college educated or nonproduction workers. With few exceptions, the conceptual link explaining how computer technology complements skilled labor or substitutes for unskille ..."
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Cited by 607 (29 self)
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Recent empirical and case study evidence documents a strong association between the adoption of computers and increased use of college educated or nonproduction workers. With few exceptions, the conceptual link explaining how computer technology complements skilled labor or substitutes
On the corner avoidance properties of various lowdiscrepancy sequences
, 2004
"... The minimum distance of QMC sample points to the boundary of the unit cube is an important quantity in the error analysis of QMC integration for functions with singularities. Sobol ’ and recently Owen show that the Sobol ’ and Halton sequences avoid a hyperbolically shaped region around the corners ..."
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Cited by 5 (3 self)
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The minimum distance of QMC sample points to the boundary of the unit cube is an important quantity in the error analysis of QMC integration for functions with singularities. Sobol ’ and recently Owen show that the Sobol ’ and Halton sequences avoid a hyperbolically shaped region around
Efficient similarity search in sequence databases
, 1994
"... We propose an indexing method for time sequences for processing similarity queries. We use the Discrete Fourier Transform (DFT) to map time sequences to the frequency domain, the crucial observation being that, for most sequences of practical interest, only the first few frequencies are strong. Anot ..."
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Cited by 505 (21 self)
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We propose an indexing method for time sequences for processing similarity queries. We use the Discrete Fourier Transform (DFT) to map time sequences to the frequency domain, the crucial observation being that, for most sequences of practical interest, only the first few frequencies are strong
THE DYNAMICAL POINT OF VIEW OF LOWDISCREPANCY SEQUENCES
, 2013
"... uniform distribution theory ..."
Incremental lowdiscrepancy lattice methods for motion planning
 In Proc. IEEE International Conference on Robotics and Automation
, 2003
"... We present deterministic sequences for use in samplingbased approaches to motion planning. They simultaneously combine the qualities found in many other sequences: i) the incremental and selfavoiding tendencies of pseudorandom sequences, ii) the lattice structure provided by multiresolution grids ..."
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Cited by 31 (7 self)
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grids, and iii) lowdiscrepancy and lowdispersion measures of uniformity provided by quasirandom sequences. The resulting sequences can be considered as multiresolution grids in which points may be added one at a time, while satisfying the sampling qualities at each iteration. An efficient, recursive
Basecalling of automated sequencer traces using phred. I. Accuracy Assessment
 GENOME RES
, 1998
"... The availability of massive amounts of DNA sequence information has begun to revolutionize the practice of biology. As a result, current largescale sequencing output, while impressive, is not adequate to keep pace with growing demand and, in particular, is far short of what will be required to obta ..."
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Cited by 1602 (4 self)
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The availability of massive amounts of DNA sequence information has begun to revolutionize the practice of biology. As a result, current largescale sequencing output, while impressive, is not adequate to keep pace with growing demand and, in particular, is far short of what will be required
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