A Comparative Study of Some Pseudorandom Number Generators

We present results of an extensive test program of a group of pseudorandom number generators which are commonly used in the applications of physics, in particular in Monte Carlo simulations. The generators include public domain programs, manufacturer installed routines and a random number sequence produced from physical noise. We start by traditional statistical tests, followed by detailed bit level and visual tests. The computational speed of various algorithms is also scrutinized. Our results allow direct comparisons between the properties of different generators, as well as an assessment of the efficiency of the various test methods. This information provides the best available criterion to choose the best possible generator for a given problem. However, in light of recent problems reported with some of these generators, we also discuss the importance of developing more refined physical tests to find possible correlations not revealed by the present test methods.Comment: University of Helsinki preprint HU-TFT-93-22 (minor changes in Tables 2 and 7, and in the text, correspondingly

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

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

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-

The arc arises: The links between volcanic output, arc evolution and melt composition

Subduction initiation is a key process for global plate tectonics. Individual lithologies developed during subduction initiation and arc inception have been identified in the trench wall of the Izu–Bonin–Mariana (IBM) island arc but a continuous record of this process has not previously been described. Here, we present results from International Ocean Discovery Program Expedition 351 that drilled a single site west of the Kyushu–Palau Ridge (KPR), a chain of extinct stratovolcanoes that represents the proto-IBM island arc, active for ∼25 Ma following subduction initiation. Site U1438 recovered 150 m of oceanic igneous basement and ∼1450 m of overlying sediments. The lower 1300 m of these sediments comprise volcaniclastic gravity-flow deposits shed from the evolving KPR arc front. We separated fresh magmatic minerals from Site U1438 sediments, and analyzed 304 glass (formerly melt) inclusions, hosted by clinopyroxene and plagioclase. Compositions of glass inclusions preserve a temporal magmatic record of the juvenile island arc, complementary to the predominant mid-Miocene to recent activity determined from tephra layers recovered by drilling in the IBM forearc. The glass inclusions record the progressive transition of melt compositions dominated by an early ‘calc-alkalic’, high-Mg andesitic stage to a younger tholeiitic stage over a time period of 11 Ma. High-precision trace element analytical data record a simultaneously increasing influence of a deep subduction component (e.g., increase in Th vs. Nb, light rare earth element enrichment) and a more fertile mantle source (reflected in increased high field strength element abundances). This compositional change is accompanied by increased deposition rates of volcaniclastic sediments reflecting magmatic output and maturity of the arc. We conclude the ‘calc-alkalic’ stage of arc evolution may endure as long as mantle wedge sources are not mostly advected away from the zones of arc magma generation, or the rate of wedge replenishment by corner flow does not overwhelm the rate of magma extraction

Tracing the Arguello Submarine Canyon System from Shelf Origins to an Abyssal Sink

The Arguello submarine canyon/channel system extends over 300 km from the continental shelf off Point Arguello and Point Conception in southern California westward onto the oceanic crust of the Pacific plate. In the northernmost reaches where the canyon system originates, all stages in the evolution of seafloor morphologic fluid flow features—from pockmarks to gullies to converging rills—are observed, similar to what has been described for the Ascension slope, north of Monterey Bay. These features appear to be active today and are linked to fluid leakage from the underlying hydrocarbon basin. The channel dissects a continental slope that exhibits features consistent with large-scale mass wasting. Upslope scarps may be the source of the morphological feature at the base of the slope previously referred to as the "Arguello submarine fan," with topographic expressions (e.g., large channel meanders, ridges) that are more consistent with mass transport deposits than with deep-sea fan depositional lobes. The modern canyon crosscuts these deposits and parallels an older, meandering channel/canyon to the west. Modern seismicity along the shelf and slope may have, and potentially still can, trigger landslides on the slope. Seismicity associated with seamount volcanism, past subduction, and Borderland transrotational and extensional processes most likely played a role in stimulating mass wasting. The presence of abundant nearby petroleum suggests that gas venting and hydrate dissociation cannot be ruled out as a triggering mechanism for the slope destabilization occurring today. The canyon/channel continues due south on a path possibly determined by the structural grain of north–south-aligned abyssal hills underlying oceanic basement. At latitude 33deg 18min N, the channel makes a 90deg turn (bend) to the west at the E–W-striking Arguello transform fault wall and develops into a meandering channel system that crosses over abyssal hill crustal fabric. The system ultimately straightens as it continues west before veering north, curving around a thickened crustal bulge at a corner offset in the Arguello fracture zone in complex basement structure, and then finally empties into an 800-m-deep basin depocenter

Tracing the Arguello Submarine Canyon System from Shelf Origins to an Abyssal Sink

The Arguello submarine canyon/channel system extends over 300 km from the continental shelf off Point Arguello and Point Conception in southern California westward onto the oceanic crust of the Pacific plate. In the northernmost reaches where the canyon system originates, all stages in the evolution of seafloor morphologic fluid flow features—from pockmarks to gullies to converging rills—are observed, similar to what has been described for the Ascension slope, north of Monterey Bay. These features appear to be active today and are linked to fluid leakage from the underlying hydrocarbon basin. The channel dissects a continental slope that exhibits features consistent with large-scale mass wasting. Upslope scarps may be the source of the morphological feature at the base of the slope previously referred to as the "Arguello submarine fan," with topographic expressions (e.g., large channel meanders, ridges) that are more consistent with mass transport deposits than with deep-sea fan depositional lobes. The modern canyon crosscuts these deposits and parallels an older, meandering channel/canyon to the west. Modern seismicity along the shelf and slope may have, and potentially still can, trigger landslides on the slope. Seismicity associated with seamount volcanism, past subduction, and Borderland transrotational and extensional processes most likely played a role in stimulating mass wasting. The presence of abundant nearby petroleum suggests that gas venting and hydrate dissociation cannot be ruled out as a triggering mechanism for the slope destabilization occurring today. The canyon/channel continues due south on a path possibly determined by the structural grain of north–south-aligned abyssal hills underlying oceanic basement. At latitude 33deg 18min N, the channel makes a 90deg turn (bend) to the west at the E–W-striking Arguello transform fault wall and develops into a meandering channel system that crosses over abyssal hill crustal fabric. The system ultimately straightens as it continues west before veering north, curving around a thickened crustal bulge at a corner offset in the Arguello fracture zone in complex basement structure, and then finally empties into an 800-m-deep basin depocenter

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

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

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