73,050 research outputs found
Some Difficult-to-pass Tests of Randomness
We describe three tests of randomness-- tests that many random number generators fail. In particular, all congruential generators-- even those based on a prime modulus-- fail at least one of the tests, as do many simple generators, such as shift register and lagged Fibonacci. On the other hand, generators that pass the three tests seem to pass all the tests in the Diehard Battery of Tests. Note that these tests concern the randomness of a generator's output as a sequence of independent, uniform 32-bit integers. For uses where the output is converted to uniform variates in [0,1), potential flaws of the output as integers will seldom cause problems after the conversion. Most generators seem to be adequate for producing a set of uniform reals in [0,1), but several important applications, notably in cryptography and number theory-- for example, establishing probable primes, complexity of factoring algorithms, random partitions of large integers-- may require satisfactory performance on the kinds of tests we describe here.
Pseudo-random number generators for Monte Carlo simulations on Graphics Processing Units
Basic uniform pseudo-random number generators are implemented on ATI Graphics
Processing Units (GPU). The performance results of the realized generators
(multiplicative linear congruential (GGL), XOR-shift (XOR128), RANECU, RANMAR,
RANLUX and Mersenne Twister (MT19937)) on CPU and GPU are discussed. The
obtained speed-up factor is hundreds of times in comparison with CPU. RANLUX
generator is found to be the most appropriate for using on GPU in Monte Carlo
simulations. The brief review of the pseudo-random number generators used in
modern software packages for Monte Carlo simulations in high-energy physics is
present.Comment: 31 pages, 9 figures, 3 table
Some comments on C. S. Wallace's random number generators
We outline some of Chris Wallace's contributions to pseudo-random number
generation. In particular, we consider his idea for generating normally
distributed variates without relying on a source of uniform random numbers, and
compare it with more conventional methods for generating normal random numbers.
Implementations of Wallace's idea can be very fast (approximately as fast as
good uniform generators). We discuss the statistical quality of the output, and
mention how certain pitfalls can be avoided.Comment: 13 pages. For further information, see
http://wwwmaths.anu.edu.au/~brent/pub/pub213.htm
A Repetition Test for Pseudo-Random Number Generators
A new statistical test for uniform pseudo-random number generators (PRNGs) is presented. The idea is that a sequence of pseudo-random numbers should have numbers reappear with a certain probability. The expectation time that a repetition occurs provides the metric for the test. For linear congruential generators (LCGs) failure can be shown theoretically. Empirical test results for a number of commonly used PRNGs are reported, showing that some PRNGs considered to have good statistical properties fail. A sample implementation of the test is provided over the Interne
JMASM1: \u3cem\u3eRANGEN\u3c/em\u3e 2.0 (\u3cem\u3eFortran\u3c/em\u3e 90/95)
Rangen 2.0 is Fortran 90 module of subroutines used to generate uniform and nonuniform pseudo-random deviates. It includes uni1, an uniform pseudo-random number generator, and non-uniform generators based on unil. The subroutines in Rangen 2.0 were written using Essential Lahey Fortran 90, a proper subset of Fortran 90. It includes both source code for the subroutines and a short description of each subroutine, its purpose, and the arguments including data type and usage
Random sampling of plane partitions
This article presents uniform random generators of plane partitions according
to the size (the number of cubes in the 3D interpretation). Combining a
bijection of Pak with the method of Boltzmann sampling, we obtain random
samplers that are slightly superlinear: the complexity is in
approximate-size sampling and in exact-size sampling
(under a real-arithmetic computation model). To our knowledge, these are the
first polynomial-time samplers for plane partitions according to the size
(there exist polynomial-time samplers of another type, which draw plane
partitions that fit inside a fixed bounding box). The same principles yield
efficient samplers for -boxed plane partitions (plane partitions
with two dimensions bounded), and for skew plane partitions. The random
samplers allow us to perform simulations and observe limit shapes and frozen
boundaries, which have been analysed recently by Cerf and Kenyon for plane
partitions, and by Okounkov and Reshetikhin for skew plane partitions.Comment: 23 page
Macroscopic noise amplification by asymmetric dyads in non-Hermitian optical systems for generative diffusion models
A new generation of sensors, hardware random number generators, and quantum
and classical signal detectors are exploiting strong responses to external
perturbations of system noise. Here, we study noise amplification by asymmetric
dyads in freely expanding non-Hermitian optical systems.
We show that modifications of the pumping strengths can counteract bias from
natural imperfections of the system's hardware, while couplings between dyads
lead to systems with non-uniform statistical distributions. Our results suggest
that asymmetric non-Hermitian dyads are promising candidates for efficient
sensors and ultra-fast random number generators. We propose that the integrated
light emission from such asymmetric dyads can be efficiently used for analog
all-optical degenerative diffusion models of machine learning to overcome the
digital limitations of such models in processing speed and energy consumption.Comment: 9 pages, 6 figure
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