An experimental exploration of Marsaglia's xorshift generators, scrambled

Marsaglia proposed recently xorshift generators as a class of very fast, good-quality pseudorandom number generators. Subsequent analysis by Panneton and L'Ecuyer has lowered the expectations raised by Marsaglia's paper, showing several weaknesses of such generators, verified experimentally using the TestU01 suite. Nonetheless, many of the weaknesses of xorshift generators fade away if their result is scrambled by a non-linear operation (as originally suggested by Marsaglia). In this paper we explore the space of possible generators obtained by multiplying the result of a xorshift generator by a suitable constant. We sample generators at 100 equispaced points of their state space and obtain detailed statistics that lead us to choices of parameters that improve on the current ones. We then explore for the first time the space of high-dimensional xorshift generators, following another suggestion in Marsaglia's paper, finding choices of parameters providing periods of length $2^{1024} - 1$ and $2^{4096} - 1$. The resulting generators are of extremely high quality, faster than current similar alternatives, and generate long-period sequences passing strong statistical tests using only eight logical operations, one addition and one multiplication by a constant

Parallel random number generation

We present a library of 19 pseudo-random number generators, implemented for graphical processing units. The library is implemented in the OpenCL framework and empirically evaluated using the TestU01 library. Most of the presented generators pass the tests. The generators' performance is evaluated on five different devices. The Tyche-i generator is the best choice overall, while on some specific devices other generators are better

A Methodology for the Identification of Helicopter Mathematical Models From Flight Data Based on the Frequency Domain

There is considerable need for the application of system identification techniques to helicopters. These include their use in the validation and improvement of existing theoretical flight-mechanics models, and for development flight testing. In both cases, estimates of stability and control parameters are sought. Most applications of system identification techniques to helicopters have involved time-domain methods which use reduced-order mathematical models representing six-degrees-of-freedom rigid-body motion. In this document, an identification methodology which uses the frequency-domain to obtain estimates of the stability and control parameters is advocated

The Fifth Symposium on Numerical and Physical Aspects of Aerodynamic Flows

This volume contains the papers presented at the Fifth Symposium on Numerical and Physical Aspects of Aerodynamic Flows, held at the California State University, Long Beach, from 13 to 15 January 1992. The symposium, like its immediate predecessors, considers the calculation of flows of relevance to aircraft, ships, and missiles with emphasis on the solution of two-dimensional unsteady and three-dimensional equations

Notes in Pure Mathematics & Mathematical Structures in Physics

These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.Comment: Small improvements and addition