256 points from the first 256 points for the 2,3 Sobol’ sequence (top) compared with a pseudorandom number source (bottom). The Sobol’ sequence covers the space more evenly. (red=1,..,10, blue=11,..,100, green=101,..,256)
Sobol’ sequences (also called LPτ sequences or (t, s) sequences in base 2) are an example of quasi-random low-discrepancy sequences. They were first introduced by the Russian mathematician Ilya M. Sobol’ (Илья Меерович Соболь) in 1967.[1]
These sequences use a base of two to form successively finer uniform partitions of the unit interval and then reorder the coordinates in each dimension.
^Sobol’, I.M.
(1967), "Distribution of points in a cube and approximate evaluation of integrals". Zh. Vych. Mat. Mat. Fiz.7: 784–802 (in Russian); U.S.S.R Comput. Maths. Math. Phys.7: 86–112 (in English).
Sobol’ sequences (also called LPτ sequences or (t, s) sequences in base 2) are an example of quasi-random low-discrepancy sequences. They were first introduced...
Sobol, Oklahoma, United States Sobolsequence, a kind of quasi-random sequence All pages with titles containing Sobol Sobel (disambiguation) Sobole (disambiguation)...
on the use of so-called "quasi-random" methods such as the use of Sobolsequences. The Monte Carlo method encompasses any technique of statistical sampling...
can often be done with low-discrepancy sequences, such as the Sobolsequence – due to mathematician Ilya M. Sobol or Latin hypercube sampling, although...
In mathematics, he has made important contributions to the field of Sobolsequences; while in Mathematical Finance, he has been influential in the development...
Anargyros; Traub, J. F. (1996). "Beating Monte Carlo". Risk. 9 (6): 63–65. Sobol, Ilya M (1998). "On quasi-monte carlo integrations". Mathematics and Computers...
doi:10.1016/S1471-4914(02)02434-6. PMID 12470990. Gonçalves A, Viens P, Sobol H, Maraninchi D, Bertucci F (2005). "[Molecular alterations in breast cancer:...
1 1-17. Toshimitsu HOMMA and Andrea SALTELLI, 2005, Use of Sobol's Quasirandom Sequence Generator for Integration of Modified Uncertainty Importance...
Tolokonnikova and Lucy Shtein, as well as opposition politician Lyubov Sobol and former Russian state media journalist Marina Ovsyannikova, was prevented...
1371/journal.pone.0006126. PMC 2699479. PMID 19568438. Cohen S, Agmon N, Sobol O, Segal D (March 2010). "Extrachromosomal circles of satellite repeats...
(4): 500–9. doi:10.1002/ana.23831. PMID 23401021. S2CID 13908127. Klar J, Sobol M, Melberg A, Mäbert K, Ameur A, Johansson AC, et al. (April 2013). "Welander...
aired in 1973 on Canada's CTV television network. He filmed a few FMV sequences for a re-released copy of the game Star Trek Starfleet Academy for PCs...
auditorium as cats in order to be able to comply with the distance rules. The sequence as well as the choreography had to be adapted and changed – these changes...
PMID 23222681. Chiosea S, Jelezcova E, Chandran U, Acquafondata M, McHale T, Sobol RW, Dhir R (Nov 2006). "Up-regulation of dicer, a component of the MicroRNA...
preparing an exposé shortly before he became violently ill, Navalny ally Lyubov Sobol stated "I can't reveal all the details, but Navalny was on a work trip....
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