22 research outputs found
Periodic orbits of the ensemble of Sinai-Arnold cat maps and pseudorandom number generation
We propose methods for constructing high-quality pseudorandom number
generators (RNGs) based on an ensemble of hyperbolic automorphisms of the unit
two-dimensional torus (Sinai-Arnold map or cat map) while keeping a part of the
information hidden. The single cat map provides the random properties expected
from a good RNG and is hence an appropriate building block for an RNG, although
unnecessary correlations are always present in practice. We show that
introducing hidden variables and introducing rotation in the RNG output,
accompanied with the proper initialization, dramatically suppress these
correlations. We analyze the mechanisms of the single-cat-map correlations
analytically and show how to diminish them. We generalize the Percival-Vivaldi
theory in the case of the ensemble of maps, find the period of the proposed RNG
analytically, and also analyze its properties. We present efficient practical
realizations for the RNGs and check our predictions numerically. We also test
our RNGs using the known stringent batteries of statistical tests and find that
the statistical properties of our best generators are not worse than those of
other best modern generators.Comment: 18 pages, 3 figures, 9 table
A generalization of short-period Tausworthe generators and its application to Markov chain quasi-Monte Carlo
A one-dimensional sequence is said to be
completely uniformly distributed (CUD) if overlapping -blocks , , are uniformly distributed
for every dimension . This concept naturally arises in Markov chain
quasi-Monte Carlo (QMC). However, the definition of CUD sequences is not
constructive, and thus there remains the problem of how to implement the Markov
chain QMC algorithm in practice. Harase (2021) focused on the -value, which
is a measure of uniformity widely used in the study of QMC, and implemented
short-period Tausworthe generators (i.e., linear feedback shift register
generators) over the two-element field that approximate CUD
sequences by running for the entire period. In this paper, we generalize a
search algorithm over to that over arbitrary finite fields
with elements and conduct a search for Tausworthe generators
over with -values zero (i.e., optimal) for dimension
and small for , especially in the case where , and . We
provide a parameter table of Tausworthe generators over , and
report a comparison between our new generators over and existing
generators over in numerical examples using Markov chain QMC
PARTICLES SIZE DISTRIBUTION EFFECT ON 3D PACKING OF NANOPARTICLES INTO A BOUNDED REGION
Abstract In this paper, the effects of two different Particle Size Distributions (PSD) on packing behavior of ideal rigid spherical nanoparticles using a novel packing model based on parallel algorithms have been reported. A mersenne twister algorithm was used to generate pseudorandom numbers for the particles initial coordinates. Also, for this purpose a nanosized tetragonal confined container with a square floor (300 * 300 nm) were used in this work. The Andreasen and the Lognormal PSDs were chosen to investigate the packing behavior in a 3D bounded region. The effects of particle numbers on packing behavior of these two PSDs have been investigated. Also the reproducibility and the distribution of packing factor of these PSDs were compared. Keyword
Spencer-Brown vs. Probability and Statistics: Entropy’s Testimony on Subjective and Objective Randomness.
This article analyzes the role of entropy in Bayesian statistics, focusing on its use as a tool for detection, recognition and validation of eigen-solutions. “Objects as eigen-solutions” is a key metaphor of the cognitive constructivism epistemological framework developed by the philosopher Heinz von Foerster. Special attention is given to some objections to the concepts of probability, statistics and randomization posed by George Spencer-Brown, a figure of great influence in the field of radical constructivism