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Discrepancy Theory and Quasi-Monte Carlo Integration
[chapter]

2014
*
Lecture notes in mathematics
*

*Discrepancy*theory was established as

*an*area

*of*research going back to

*the*seminal paper by Weyl (1916), whereas Monte Carlo (and later quasi-Monte Carlo) was invented in

*the*1940s by John von Neumann ...

*Discrepancy*theory was established as

*an*area

*of*research going back to

*the*seminal paper by Weyl (1916), whereas Monte Carlo (and later quasi-Monte Carlo) was invented in

*the*1940s by John von Neumann ...

*The*authors thank Michaela Szölgyenyi and Henryk Woźniakowski

*for*many helpful suggestions. ...

##
###
A Comparison of Popular Point Configurations on S^2
[article]

2016
*
arXiv
*
pre-print

There are many ways to generate a

arXiv:1607.04590v3
fatcat:m6pxw5f22ngmjm5qzqum5aux74
*set**of*nodes on*the*sphere*for*use in a variety*of*problems in numerical analysis. ... We analyze numerically*the*leading order asymptotics*for**the*Riesz and logarithmic potential energy*for*these configurations with total*points*N<50,000 and present some new conjectures. ... Determining*an**exact*minimal configuration*for*a fixed N and s is a highly nonlinear optimization problem. ...##
###
Information-based complexity

1989
*
Mathematics and Computers in Simulation
*

> where n = ©(e'^loge-1)^-1^2), and

doi:10.1016/0378-4754(89)90072-4
fatcat:unyblw2m7zdithdyelkwxlsoim
*the**points*x¡ are derived from*Hammersley**points*. ... Rabin [72] studied*the*class A2*for**the**exact*solution*of*linear systems, e = 0, and*for**an*arbitrary nonsingular matrix A. ...##
###
Information-based complexity

1987
*
Nature
*

> where n = ©(e'^loge-1)^-1^2), and

doi:10.1038/328029a0
fatcat:p55xu6essbgxjerpf2w37lyck4
*the**points*x¡ are derived from*Hammersley**points*. ... Rabin [72] studied*the*class A2*for**the**exact*solution*of*linear systems, e = 0, and*for**an*arbitrary nonsingular matrix A. ...##
###
Perspectives on Information-Based Complexity

1992
*
Bulletin of the American Mathematical Society
*

> where n = ©(e'^loge-1)^-1^2), and

doi:10.1090/s0273-0979-1992-00240-9
fatcat:cg6dj5jfmfadjdu4kxzguasd24
*the**points*x¡ are derived from*Hammersley**points*. ... Rabin [72] studied*the*class A2*for**the**exact*solution*of*linear systems, e = 0, and*for**an*arbitrary nonsingular matrix A. ...##
###
Information-Based Complexity

1989
*
Science
*

*the*

*points*x¡ are derived from

*Hammersley*

*points*. ... Rabin [72] studied

*the*class A2

*for*

*the*

*exact*solution

*of*linear systems, e = 0, and

*for*

*an*arbitrary nonsingular matrix A. ...

##
###
Information-Based Complexity

1986
*
Annual Review of Computer Science
*

*the*

*points*x¡ are derived from

*Hammersley*

*points*. ... Rabin [72] studied

*the*class A2

*for*

*the*

*exact*solution

*of*linear systems, e = 0, and

*for*

*an*arbitrary nonsingular matrix A. ...

##
###
DiceDesignandDiceEval: TwoRPackages for Design and Analysis of Computer Experiments

2015
*
Journal of Statistical Software
*

A two-dimensional test function will be a running example to illustrate

doi:10.18637/jss.v065.i11
fatcat:ndukgtjzh5db5c4z33f4vnbsay
*the*main functionalities*of*these packages and*an*industrial case study in five dimensions will also be detailed. ... Package DiceEval deals with*the*fit,*the*validation and*the*comparison*of*metamodels. After a brief presentation*of**the*context, we focus on*the*architecture*of*these two packages. ... We also wish to thank*the*anonymous referees*for*several helpful comments and suggestions that improved and clarified*the*presentation*of*this work. ...##
###
Recent Mathematical Tables

1953
*
Mathematics of Computation
*

*The*table can be used to find

*the*

*exact*number

*of*lattice

*points*inside or on a circle

*of*radius r by means

*of*

*the*

*formula*

*for*positive k < 100. ...

*The*author provides a table

*for*

*the*power

*of*

*the*C test to 2D against this alternative (under

*the*assumption again

*of*

*exact*normality) at

*the*95% level

*for*p = . ... But nevertheless, this restriction will make

*the*table unsuitable

*for*calculations

*of*gas flow at higher temperatures, such as

*the*flow in high pressure compressors and gas turbines. ...

##
###
Localized Bases for Kernel Spaces on the Unit Sphere

2013
*
SIAM Journal on Numerical Analysis
*

*For*a

*set*

*of*N scattered sites,

*the*standard basis

*for*such a space utilizes N globally supported kernels; computing with it is prohibitively expensive

*for*large N. ... Approximation/interpolation from spaces

*of*positive definite or conditionally positive definite kernels is

*an*increasingly popular tool

*for*

*the*analysis and synthesis

*of*scattered data, and is central ... quasi-uniform icosahadedral and

*the*low

*discrepancy*

*Hammersley*families

*of*nodes on

*the*sphere. ...

##
###
Living on the Edge: An Unified Approach to Antithetic Sampling
[article]

2021
*
arXiv
*
pre-print

This perspective enables

arXiv:2110.15124v2
fatcat:r6jhddsdx5cxxh3m22zn3z7edm
*the*derivation*of*new properties*of**the*sampling schemes: i) optimality in*the*Kullback-Leibler sense; ii) closed-form multivariate Kendall's τ and Spearman's ρ; iii)ranking in ... We introduce a new class*of*antithetic schemes that includes*the*most used antithetic proposals. ... On*the**l2*-*discrepancy**for*anchored boxes. Journal*of*Complexity, 14(4):527–556. McKay, M. D., Beckman, R. J., and Conover, W. J. (1979). ...##
###
Percolation, statistical topography, and transport in random media

1992
*
Reviews of Modern Physics
*

*For*rapidly decaying correlations

*of*g,

*the*isopotentials fall into

*the*same universality class as

*the*perimeters

*of*percolation clusters. ... A review

*of*classical percolation theory is presented, with

*an*emphasis on novel applications to statistical topography, turbulent diffusion, and heterogeneous media. ...

*For*

*the*case

*of*a

*symmetric*distribution

*of*g(x; ), they related

*the*

*exact*critical level h, = 0 to

*the*

*exact*critical probability p, (T, s)= -, ' (see Table II ). ...

##
###
Conformal invariance in two-dimensional percolation
[article]

1994
*
arXiv
*
pre-print

*The*immediate purpose

*of*

*the*paper was neither to review

*the*basic definitions

*of*percolation theory nor to rehearse

*the*general physical notions

*of*universality and renormalization (

*an*important technique ... On

*the*other hand, one ulterior purpose is to draw

*the*attention

*of*mathematicians to

*the*mathematical problems posed by

*the*physical notions. ... As we saw, both artifices have limitations (See §3.5 and §3.6.) that could cause

*the*

*discrepancy*between

*the*value

*of*π(H)

*for*S 1 and S 2 , as well as

*the*

*discrepancy*

*of*.024 betweenπ(H) andπ(0) that ...

##
###
Hyperbolic Cross Approximation
[article]

2017
*
arXiv
*
pre-print

*The*theory

*of*hyperbolic cross approximation and related theory

*of*functions with mixed smoothness are under detailed study

*for*more than 50 years. ... This and recently discovered deep connections between

*the*hyperbolic cross approximation (and related sparse grids) and other areas

*of*mathematics such as probability,

*discrepancy*, and numerical integration ...

*The*authors acknowledge

*the*fruitful discussions with D.B. Bazarkhanov, ...

##
###
Algebraic statistics

2012
*
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation - ISSAC '12
*

To test whether a given data

doi:10.1145/2442829.2442835
dblp:conf/issac/Sullivant12
fatcat:gcmhfgalwveifi2h4rug2afgga
*set*is consistent with*the*model*of*Hardy-Weinberg equilibrium, we need to perform*an**exact*test. ...*The**set**of*partially*symmetric*matrices with rank ≤ k is*an*irreducible variety, defined by*the*vanishing*of*all (k + 1) × (k + 1) subdeterminants. ...*For*instance, in*the*case*of**the*factor analysis model from Example 13.2.3 all*the*generators*of**the*ideal I G that are lists are homogeneous with respect to*the*upstream grading. ...
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