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Indispensable for students, invaluable for researchers, this comprehensive treatment of contemporary quasi–Monte Carlo methods, digital nets and sequences, and discrepancy theory starts from scratch with detailed explanations of the basic concepts and then advances to current methods used in research. As deterministic versions of the Monte Carlo method,… (More)

- Josef Dick, Ian H. Sloan, Xiaoqun Wang, Henryk Wozniakowski
- Numerische Mathematik
- 2006

We study the problem of multivariate integration and the construction of good lattice rules in weighted Korobov spaces with general weights. These spaces are not necessarily tensor products of spaces of univariate functions. Sufficient conditions for tractability and strong tractability of multivariate integration in such weighted function spaces are found.… (More)

This paper is a contemporary review of QMC (" Quasi-Monte Carlo ") methods , i.e., equal-weight rules for the approximate evaluation of high dimensional integrals over the unit cube [0, 1] s , where s may be large, or even infinite. After a general introduction, the paper surveys recent developments in lattice methods, digital nets, and related themes.… (More)

- B Schwaller, J Dick, +8 authors M R Celio
- The American journal of physiology
- 1999

The calcium-binding protein parvalbumin (PV) occurs at high concentrations in fast-contracting vertebrate muscle fibers. Its putative role in facilitating the rapid relaxation of mammalian fast-twitch muscle fibers by acting as a temporary buffer for Ca2+ is still controversial. We generated knockout mice for PV (PV -/-) and compared the Ca2+ transients and… (More)

1. The functional properties of tibialis anterior muscles of normal adult (C57BL/10) and age-matched dystrophin-deficient (C57BL/10 mdx) mice have been investigated in situ. Comparisons were made between tibialis anterior muscle strength, rates of force development and relaxation, force-frequency responses and fatiguability. Subjecting mdx and C57 muscles… (More)

- Josef Dick, Ian H. Sloan, Xiaoqun Wang, Henryk Wozniakowski
- J. Complexity
- 2004

A partial answer to why quasi-Monte Carlo algorithms work well for multivariate integration was given in [15] by introducing weighted spaces. In these spaces the importance of successive coordinate directions is quantified by a sequence of weights. However, to be able to make use of weighted spaces for a particular application one has to make a choice of… (More)

- Christoph Aistleitner, Johann S. Brauchart, Josef Dick
- Discrete & Computational Geometry
- 2012

- Josef Dick
- J. Complexity
- 2004

We prove error bounds on the worst-case error for integration in certain Korobov and Sobolev spaces using rank-1 lattice rules with generating vectors constructed by the component-by-component algorithm. For a prime number of points n a rate of convergence of the worst-case error for multivariate integration in Korobov spaces of O n −α/2+δ , where α > 1 is… (More)

- G Chen, S Carroll, +7 authors B Schwaller
- American journal of physiology. Cell physiology
- 2001

The soluble Ca2+-binding protein parvalbumin (PV) is expressed at high levels in fast-twitch muscles of mice. Deficiency of PV in knockout mice (PV -/-) slows down the speed of twitch relaxation, while maximum force generated during tetanic contraction is unaltered. We observed that PV-deficient fast-twitch muscles were significantly more resistant to… (More)

- Josef Dick
- SIAM J. Numerical Analysis
- 2007

In this paper we give first explicit constructions of point sets in the s dimensional unit cube yielding quasi-Monte Carlo algorithms which achieve the optimal rate of convergence of the worst-case error for numerically integrating high dimensional periodic functions. In the classical measure P α of the worst-case error introduced by Korobov in 1959 the… (More)