Pseudorandom Number Generators and the Square Site Percolation Threshold

A select collection of pseudorandom number generators is applied to a Monte Carlo study of the two dimensional square site percolation model. A generator suitable for high precision calculations is identified from an application specific test of randomness. After extended computation and analysis, an ostensibly reliable value of pc = 0.59274598(4) is obtained for the percolation threshold.Comment: 11 pages, 6 figure

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

Optimal Unambiguous State Discrimination of two density matrices and its link with the Fidelity

Recently the problem of Unambiguous State Discrimination (USD) of mixed quantum states has attracted much attention. So far, bounds on the optimum success probability have been derived [1]. For two mixed states they are given in terms of the fidelity. Here we give tighter bounds as well as necessary and sufficient conditions for two mixed states to reach these bounds. Moreover we construct the corresponding optimal measurement strategies. With this result, we provide analytical solutions for unambiguous discrimination of a class of generic mixed states. This goes beyond known results which are all reducible to some pure state case. Additionally, we show that examples exist where the bounds cannot be reached.Comment: 10 page

The Early Paleozoic history of the Cuyania (greater Precordillera) terrane of western Argentina : evidence from geochronology of detrital zircons from Middle Cambrian sandstones

U-Pb geochronology of large detrital zircons populations is a powerful tool for interpreting sandstone provenance. Here, it is applied to three Middle Cambrian sandstones from the Precordillera of Argentina with the purpose of using the provenance interpretations to test paleogeographic and paleotectonic models proposed for the Cuyania or Precordillera terrane. Two samples from the La Laja Formation have distinctive detrital zircon age distributions. All zircon grains fall within unimodal populations of 1688-1200 Ma in one sample and 1559- 1316 Ma in the other. Of these grains, 23% and 65%, respectively, are within the age range of the North American magmatic gap (1610-1490 Ma), indicating a non-Laurentian provenance. A very different sample was taken from a sandstone interval in a large olistolith within the Estancia San Isidro Formation. Its zircon population is dominated by a single, prominent 615-511 Ma age cluster, which is indicative of a provenance in a Brasiliano orogenic belt. The absence of zircons with Grenvillian ages (1200 to 950 Ma) is difficult to reconcile with paleogeographic and geotectonic models in which Cuyania rifted from Laurentia in Cambrian or Ordovician time. The data are most consistent with models in which Cuyania rifted from the southern margin of West Gondwana. Given a Cambrian association with Gondwana and a post-Ordovician arrival at its present position in Gondwana, the Cuyania terrane must have migrated along the southern and western margins of Gondwana during the Ordovician Period

A diffusion equation for the density of the ratio of two jointly distributed Gaussian variables and the numerical inversion of Laplace transform

It is shown that the density of the ratio of two random variables with the same variance and joint Gaussian density satisfies a non stationary diffusion equation. Implications of this result for kernel density estimation of the condensed density of the generalized eigenvalues of a random matrix pencil useful for the numerical inversion of the Laplace transform is discussed.Comment: 25 pages, 2 figures, Theorem 3.3 has been adde

A Pseudo Random Numbers Generator Based on Chaotic Iterations. Application to Watermarking

In this paper, a new chaotic pseudo-random number generator (PRNG) is proposed. It combines the well-known ISAAC and XORshift generators with chaotic iterations. This PRNG possesses important properties of topological chaos and can successfully pass NIST and TestU01 batteries of tests. This makes our generator suitable for information security applications like cryptography. As an illustrative example, an application in the field of watermarking is presented.Comment: 11 pages, 7 figures, In WISM 2010, Int. Conf. on Web Information Systems and Mining, volume 6318 of LNCS, Sanya, China, pages 202--211, October 201

Mean-field critical behaviour and ergodicity break in a nonequilibrium one-dimensional RSOS growth model

We investigate the nonequilibrium roughening transition of a one-dimensional restricted solid-on-solid model by directly sampling the stationary probability density of a suitable order parameter as the surface adsorption rate varies. The shapes of the probability density histograms suggest a typical Ginzburg-Landau scenario for the phase transition of the model, and estimates of the "magnetic" exponent seem to confirm its mean-field critical behaviour. We also found that the flipping times between the metastable phases of the model scale exponentially with the system size, signaling the breaking of ergodicity in the thermodynamic limit. Incidentally, we discovered that a closely related model not considered before also displays a phase transition with the same critical behaviour as the original model. Our results support the usefulness of off-critical histogram techniques in the investigation of nonequilibrium phase transitions. We also briefly discuss in an appendix a good and simple pseudo-random number generator used in our simulations.Comment: LaTeX2e, 15 pages (large fonts and spacings), 5 figures. Accepted for publication in the Int. J. Mod. Phys.

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

Numerical study of a non-equilibrium interface model

We have carried out extensive computer simulations of one-dimensional models related to the low noise (solid-on-solid) non-equilibrium interface of a two dimensional anchored Toom model with unbiased and biased noise. For the unbiased case the computed fluctuations of the interface in this limit provide new numerical evidence for the logarithmic correction to the subnormal L^(1/2) variance which was predicted by the dynamic renormalization group calculations on the modified Edwards-Wilkinson equation. In the biased case the simulations are in close quantitative agreement with the predictions of the Collective Variable Approximation (CVA), which gives the same L^(2/3) behavior of the variance as the KPZ equation.Comment: 15 pages revtex, 4 Postscript 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