Monkey tests for random number generators

AbstractThis article describes some very simple, as well as some quite sophisticated, tests that shed light on the suitability of certain random number generators

A Fast and Compact Quantum Random Number Generator

We present the realization of a physical quantum random number generator based on the process of splitting a beam of photons on a beam splitter, a quantum mechanical source of true randomness. By utilizing either a beam splitter or a polarizing beam splitter, single photon detectors and high speed electronics the presented devices are capable of generating a binary random signal with an autocorrelation time of 11.8 ns and a continuous stream of random numbers at a rate of 1 Mbit/s. The randomness of the generated signals and numbers is shown by running a series of tests upon data samples. The devices described in this paper are built into compact housings and are simple to operate.Comment: 23 pages, 6 Figs. To appear in Rev. Sci. Inst

A new test for random number generators: Schwinger-Dyson equations for the Ising model

We use a set of Schwinger-Dyson equations for the Ising Model to check several random number generators. For the model in two and three dimensions, it is shown that the equations are sensitive tests of bias originated by the random numbers. The method is almost costless in computer time when added to any simulation.Comment: 6 pages, 3 figure

Hurst's Rescaled Range Statistical Analysis for Pseudorandom Number Generators used in Physical Simulations

The rescaled range statistical analysis (R/S) is proposed as a new method to detect correlations in pseudorandom number generators used in Monte Carlo simulations. In an extensive test it is demonstrated that the RS analysis provides a very sensitive method to reveal hidden long run and short run correlations. Several widely used and also some recently proposed pseudorandom number generators are subjected to this test. In many generators correlations are detected and quantified.Comment: 12 pages, 12 figures, 6 tables. Replaces previous version to correct citation [19

Numerical Study of a Mixed Ising Ferrimagnetic System

We present a study of a classical ferrimagnetic model on a square lattice in which the two interpenetrating square sublattices have spins one-half and one. This model is relevant for understanding bimetallic molecular ferrimagnets that are currently being synthesized by several experimental groups. We perform exact ground-state calculations for the model and employ Monte Carlo and numerical transfer-matrix techniques to obtain the finite-temperature phase diagram for both the transition and compensation temperatures. When only nearest-neighbor interactions are included, our nonperturbative results indicate no compensation point or tricritical point at finite temperature, which contradicts earlier results obtained with mean-field analysis.Comment: Figures can be obtained by request to [email protected] or [email protected]

To what extent is Gluon Confinement an empirical fact?

Experimental verifications of Confinement in hadron physics have established the absence of charges with a fraction of the electron's charge by studying the energy deposited in ionization tracks at high energies, and performing Millikan experiments with charged droplets at rest. These experiments test only the absence of particles with fractional charge in the asymptotic spectrum, and thus "Quark" Confinement. However what theory suggests is that Color is confined, that is, all asymptotic particles are color singlets. Since QCD is a non-Abelian theory, the gluon force carriers (indirectly revealed in hadron jets) are colored. We empirically examine what can be said about Gluon Confinement based on the lack of detection of appropriate events, aiming at an upper bound for high-energy free-gluon production.Comment: 14 pages, 12 figures, version accepted at Few Body Physic

Physical tests for Random Numbers in Simulations

We propose three physical tests to measure correlations in random numbers used in Monte Carlo simulations. The first test uses autocorrelation times of certain physical quantities when the Ising model is simulated with the Wolff algorithm. The second test is based on random walks, and the third on blocks of n successive numbers. We apply the tests to show that recent errors in high precision simulations using generalized feedback shift register algorithms are due to short range correlations in random number sequences. We also determine the length of these correlations.Comment: 16 pages, Post Script file, HU-TFT-94-

Simulation of truncated normal variables

We provide in this paper simulation algorithms for one-sided and two-sided truncated normal distributions. These algorithms are then used to simulate multivariate normal variables with restricted parameter space for any covariance structure.Comment: This 1992 paper appeared in 1995 in Statistics and Computing and the gist of it is contained in Monte Carlo Statistical Methods (2004), but I receive weekly requests for reprints so here it is

Fast Differentially Private Matrix Factorization

Differentially private collaborative filtering is a challenging task, both in terms of accuracy and speed. We present a simple algorithm that is provably differentially private, while offering good performance, using a novel connection of differential privacy to Bayesian posterior sampling via Stochastic Gradient Langevin Dynamics. Due to its simplicity the algorithm lends itself to efficient implementation. By careful systems design and by exploiting the power law behavior of the data to maximize CPU cache bandwidth we are able to generate 1024 dimensional models at a rate of 8.5 million recommendations per second on a single PC

Searching a bitstream in linear time for the longest substring of any given density

Given an arbitrary bitstream, we consider the problem of finding the longest substring whose ratio of ones to zeroes equals a given value. The central result of this paper is an algorithm that solves this problem in linear time. The method involves (i) reformulating the problem as a constrained walk through a sparse matrix, and then (ii) developing a data structure for this sparse matrix that allows us to perform each step of the walk in amortised constant time. We also give a linear time algorithm to find the longest substring whose ratio of ones to zeroes is bounded below by a given value. Both problems have practical relevance to cryptography and bioinformatics.Comment: 22 pages, 19 figures; v2: minor edits and enhancement