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Understanding Sobol sequences - Mathematics Stack Exchange Sobol sequences belong to the class of Quasi Random Generators (by opposition of Pseudo Random Generators) Quasi Random Generators by construction minimize the discrepancy between the sub square (ie sub interval) Discrepancy is the (maximum) between 2 points inside sub-interval Quasi Random Generators are deterministic generators of points Sobol uses initial polynome to generate unform
algorithms - Scrambled Sobol - Mathematics Stack Exchange The method described in "On the scrambled sobol sequence" by Chi, Beerli, Evan, Mascagni (2005) seems simple enough from a coding point of view, however I don't understand how it is supposed to work
The mathematics behind Sobol sequences - Mathematics Stack Exchange I am using Sobol sequence as random number generator in a computer program Beyond just making the program work, I would like to learn the mathematics behind the Sobol sequence (and other quasi-random sequences)
How is a Halton sequence related to a Latin hypercube? I currently use a Halton sequence to choose parameter sets for a prognostic model (e g using metabolic rate and protein content parameters to predict growth rate) From my understanding, both a
Non-integer low discrepancy sequence - Mathematics Stack Exchange Summary There are many methods to calculate low discrepancy sequences and most of them generalize to higher dimensions, including Sobol, Niederreiter, Halton and Kronecker However, Sobol and Niederreiter sequences are derived by calculating a low discrepancy integer sequence and diving by fixed power
Sufficient condition for a set to be a Reduced Boundary Did you find an answer to this question? The closest thing I can find is in this paper: Ambrosio, Luigi, et al "Connected components of sets of finite perimeter and applications to image processing " JEMS In particular Theorem 7 in the planar (d=2) case
complex analysis - Mathematics Stack Exchange Recently, I read a proof of the uniformization theorem using the Ricci flow on closed Riemannian 2-manifolds It is implied by some sources that this is equivalent to the uniformization theorem for
How to effectively distribute points on plane Here are examples of 256 points distributed on the plane using each of them, with a random distribution for comparison: From left to right: Halton sequence, Sobol sequence, random sequence Images by Jheald Wikimedia Commons, licensed under the CC-By-SA 3 0 license