Showing papers on "Randomness published in 1973"

An Asymptotically Random Tausworthe Sequence

Abstract: The theoretical limitations on the orders of equidistribution attainable by Tausworthe sequences are derived from first principles and are stated in the form of a criterion to be achieved. A second criterion, extending these limitations to multidimensional uniformity, is also defined. A sequence possessing both properties is said to be asymptotically random as no other sequence of the same period could be more random in these respects.An algorithm is presented which, for any Tausworthe sequence based on a primitive trinomial over GF(2), establishes how closely or otherwise the conditions necessary for the criteria are achieved. Given that the necessary conditions are achieved, the conditions sufficient for the first criterion are derived from Galois theory and always apply. For the second criterion, however, the period must be prime.An asymptotically random 23-bit number sequence of astronomic period, 2607 - 1, is presented. An initialization program is required to provide 607 starting values, after which the sequence can be generated with a three-term recurrence of the Fibonacci type. In addition to possessing the theoretically demonstrable randomness properties associated with Tausworthe sequences, the sequence possesses equidistribution and multidimensional uniformity properties vastly in excess of anything that has yet been shown for conventional congruentially generated sequences. It is shown that, for samples of a size it is practicable to generate, there can exist no purely empirical test of the sequence as it stands capable of distinguishing between it and an ∞-distributed sequence. Bounds for local nonrandomness in respect of runs above (below) the mean and runs of equal numbers are established theoretically.The claimed randomness properties do not necessarily extend to subsequences, though it is not yet known which particular subsequences are at fault.Accordingly, the sequence is at present suggested only for simulations with no fixed dimensionality requirements.

An Objective Theory of Probability

Abstract: Part One: The Special Sciences in General 1. Von Mises' Philosophy of Science: Its Machian Origins 2. Force and Mass 3. Conceptual Innovation in the Exact Sciences Part Two: The Axiomatic Superstructure 4. Probability and Frequency 5. Repeatability and Independence 6. Deduction of the Law of Excluded Gambling Systems: The Role of Randomness in Probability Theory 7. Probabilities of Single Events: Popper's Propensity Theory Part Three: A Falsifying Rule for Probability Statements 8. The Falsification Problem for Probability Statements 9. Formulation of a Falsifying Rule 10. Evaluation of the Falsifying Rule 11. The Neyman-Pearson Theory

Statistical Tests of Some Widely Used and Recently Proposed Uniform Random Number Generators

Abstract: : Several widely used uniform random number generators have been extensively subjected to three commonly used statistical tests of uniformity and randomness. The object was (1) to examine the power of these statistical tests to discriminate between good and bad random number generators, (2) to correlate these results with recently proposed mathematical characterizations of random number generators which might also be useful in such a discrimination, and (3) to examine the effect of shuffling on the random number generators. Briefly the results show that the commonly used runs test has virtually no power to discriminate between good and bad generators, while serial tests perform better. Also shuffling does help, although much more needs to be done in this area. And finally, there is some utility to the mathematical characterizations, but many unanswered questions.

Wave propagation in random anisotropic media

Abstract: Publisher Summary This chapter discusses wave propagation in random anisotropic media. It describes some important properties of the electromagnetic field excited by a current element embedded in a random anisotropic medium. The permittivity tensor for the medium consists of two parts, one deterministic and the other random. Both the deterministic and random permittivity tensors are considered to be uniaxial, that is diagonal where two of the three elements are equal. The chapter presents the calculation of an effective permittivity tensor which provides a deterministic description of the medium. Using this medium description, the mean dyadic Green's function can be determined. Mathematical techniques are used to examine the influence of random fluctuations. Two important properties of the mean ordinary and mean extraordinary waves are: (1) the introduction of an effective conductive term which differs from that because of absorption and is caused by the scattering of the wave as it propagates, and (2) the increase in the real part of the dielectric constant, again caused by the random inhomogeneities, which causes the waves to travel at speeds slower than when the randomness was zero.

Random pulse generator

Abstract: An exemplary embodiment of the present invention provides a source of random width and random spaced rectangular voltage pulses whose mean or average frequency of operation is controllable within prescribed limits of about 10 hertz to 1 megahertz. A pair of thin-film metal resistors are used to provide a differential white noise voltage pulse source. Pulse shaping and amplification circuitry provide relatively short duration pulses of constant amplitude which are applied to anti-bounce logic circuitry to prevent ringing effects. The pulse outputs from the anti-bounce circuits are then used to control two one-shot multivibrators whose output comprises the random length and random spaced rectangular pulses. Means are provided for monitoring, calibrating and evaluating the relative randomness of the generator.

On off-diagonal randomness in the theory of binary alloys

Abstract: Various theories are now available for treating binary alloys of different constituent bandwidths within a single site approximation. A comparison of three approaches is given, together with a discussion of the form of the Hamiltonian required to describe the effective medium.

Random transfer integrals in disordered alloys

Abstract: The Koster-Slater formula expressing the change in the density of states introduced by the presence of localized impurities in metals is generalized to the case of random transfer integrals. It is then shown that the single site approximation first introduced by Shiba (1971) to deal with off diagonal randomness in binary alloys is consistent with this generalization and gives correctly the density of states in the dilute limit. The theory is discussed in the locator formulation and possible extensions to the calculation of transport properties are suggested. Numerical examples are presented to discuss the nature of impurity states when both diagonal and nondiagonal disorder are present.

Numerical studies of the one-dimensional random Anderson model

Abstract: Results are reported of exact numerical calculations of the eigenvalues and eigenstates of a one-dimensional random Anderson model. The complete set of eigenstates is obtained for lattices containing up to 500 sites, and the degree of localization of the states is examined as a function of the eigenvalue of the state, the degree of randomness, and the number of lattice sites. Curves of degree of localization versus eigenvalue appear to show a central 'band' of extended states separated by a 'critical energy' from a 'tail' of localized states. However it is shown that the separation is only apparent, in that it is caused by the spatial extent of the eigenstates becoming comparable with the size of the finite lattice.

Improvements of the Coherent Potential Approximation for the Random Lattice Problems

Abstract: The perturbation term of the one-particle Green's function of an electron in a random lattice is expressed as a sum of terms related with one site, two sites, three sites, and so on. The coherent potential approximation is rederived under the assumption that the sum of the terms related with two or more sites can be ignored if the unperturbed Hamiltonian is chosen in such a way that the sum of the one-site terms is put equal to zero. The next approximation is obtained by assuming that the sum of the terms related with the clusters of sites other than the one sites and the nearest neighbor pairs of sites can be ignored, when the unperturbed Hamiltonian is so chosen that the sum of the terms related with a one site or a nearest nighbor pair of sites is put equal to zero. This approximation is applicable to the random alloy problems where the diagonal as well as off-diagonal randomness exist. If the randomness is restricted only to the diagonal one, the approximation is equivalent to the one proposed by Cyro...

Boltzmann equation with fluctuations

Abstract: From the Liouville equation, by the method of multiple-time-scales, a generalized Boltzmann-equation with fluctuations is obtained on the statistical considerations of the randomness of the many-particle correlations in the macroscopic picture. These fluctuations lead to anH theorem in which theH function decreases, with fluctuations with time toward equilibrium. These fluctuations furnish a source for a random force term introduced by Fox and Uhlenbeck in the Boltzmann equation.

Serial statistics. Is radioactive decay random

Abstract: Based on more than 10/sup 8/ counts obtained from gamma emissions arising from /sup 60/Co and /sup 137/Cs nuclei, serial statistical tests--the sum of squares of 0,l standardized slopes of linear regressions and the sum of squares of the closely related 0,1 standardized correlation coefficients-- exhibit significant deviations from the theoretic (random) expectation as a function of differences in the source environment. On the other hand, more conventioral, nonserial statistical tests---the X-square goodness-of-fit and index of dispersion tests-- derived from the same data are indistinguishable from those expected for random events. These serial discrepancies raise a substantial question as to the randomness of the detected emissions and, insofar as emissions and decay events are appropriately interrelated, the independence of the events themselves. (auth)

Stochastic Programs with Recourse: Random Recourse Costs Only

Abstract: In this paper we discuss the class of stochastic programs with recourse in which the only randomness present is in the recourse costs. Two economic interpretations are given. We present results which enable one to check if the convex deterministic equivalent program possesses all the “nice” properties of convex programs---feasibility, boundedness, solvability and dualizability. The simple recourse problem is then discussed. The specific form of the convex deterministic equivalent for the case of simple recourse is exhibited.

It’s a Random world

Abstract: Random semiconductors, alloys, and magnetic materials have recently received considerable attention by solid state physicists, and a variety of theoretical approaches have been developed However, these developments are only part of an extensive history of randomness in physical situations This paper is a report on some of the related history in other fields where randomness has been an ingredient; a basic bibliography is provided

Populations and Habitats

Abstract: Bacteria are open systems and they selectively take in substances in solution (osmotrophically), ‘‘process” these in various ways, and then return all or part of them to the environment. When the rates of such activities are constant, the system is said to be in a steady state It should be stressed that this is a dynamic condition and not one of stasis. As an organism increases the complexity of its own organization, it reduces that of its environment. In other words, a living bacterium accumulates negentropy by producing and maintaining a less probable state of matter in itself. When bacteria are in an isolated system the total energy content remains constant, hence they obey the First Law of Thermodynamics. What about the Second Law? This states that a system in isolation tends toward greater randomness. Entropy is a measure of randomness in a closed system, and it increases as the system tends toward greater randomness. Reactions in closed systems proceed as long as reactants differ in free energy content, but eventually there is no free energy difference and a condition of equilibrium is reached, and a state of maximum entropy or randomness is achieved. Bacteria growing in a closed system appear to decrease their entropy and achieve an increasing degree of nonrandomness; do they, then, not obey the Second Law of thermodynamics? In fact they do, for the following reasons: The highly improbable state of matter in bacteria and other living beings is maintained because of the free energy taken from the environment, and the randomness of the latter is therefore continually increasing during bacterial multiplication and growth. Bacteria are nonequilibrium systems and their environments do not reach the randomness of a closed system as long as a constant supply of energy is available to maintain a steady state. With these points in mind we will turn to some characteristics of bacterial multiplication and growth.

Tests for Uniform Clustering and Randomness

Abstract: In statistical problems associated with particulate matter,geographic areas and stersology one is often interested in clustering patterns of certain phasesParticularly, one may be interested in whether or not the cluster sizes are relatively unifrom throughout the mediam and whether or not particules and to occur in random arrangementThis paper presents tests for uniform clustering and randomness based on runs observed in lines or core samples The results are presented for a dichotomous classification of particles,but extensions can be made

Gravitational-Wave Antenna Design to Detect Random Gravitational Waves

Abstract: A design is proposed for an antenna system capable of detecting random gravitational waves and separating their effects from random fluctuations in the antenna. The strongest known signal should be the random signal from all of the binary stars in the galaxy. This design may allow one to penetrate the background noise of the Earth itself and recover this signal.

Moment approach to random systems including off-diagonal randomness and short-range order

Abstract: The function of this work is twofold One is to present exact values for the first ten moments of the density of states for various disordered alloy models (including off-diagonal randomness and short-range order) These may serve as a standard for the comparison of various approximate theories In particular, it is shown that the truncation in the range of the T matrix or the mass operator often assumed in multiple scattering formalisms can introduce serious errors when there is off-diagonal randomness Second, the moments are used to generate approximate expressions for the density of states In particular it is shown how the technique yields a sensitive test for the effective band edges This is a new use of a rather old technique The strengths and weaknesses of the approach are discussed

Tests de générateurs pseudo-aléatoires

Abstract: In computers, pseudo-random numbers are usually generated through a linear congruential sequence. Coveyou and MacPherson [1] propose a test of the randomness of n-uples, Dieter [2] proposes another test for the pairs ; both are theoretical tests. These are described and applied to some generators. Arithmetic routines handling integer numbers without limitation of size have been developped to implement the first test, they are outlined in the paper.

Sporadic E layer as a random process in time

Abstract: ABS>Translated from Geomagn. Aeron.; 13: No. 2, 267-271(1973). It is shown that the temporal variation of sporadic formations is a random process. Empirical autocorrelation functions of the frequency parameters of the layer are determined. A complex spectral composition of the wind shift is the chief cause of random variation of the electron concentration of the E/sub s/ layer. (auth)

Relative-Frequency and Probability

Abstract: This chapter discusses the rationale behind some of the formal structure of the concepts of random events, independence, and probability. The view of probability is that it is a physical characteristic or description of the occurrence of events in the performance of an experiment. As a physical or empirical property of random events, probability should be objectively measurable from data and should be interpretable in terms of predictions about random events. It describes the pattern of occurrence of outcomes of what seem to be nondeterministically predictable experiments. The chapter presents the range of a physical interpretation of probability to the frequency of outcomes in an indefinitely repeated sequence of experiments. It also explores the possibility of a less ambitious undertaking—the measurement of comparative rather than quantitative probability.

Self consistent random static field approximations in the electron correlation problem

Abstract: A random static self-consistent approximation to the Hubbard Hamiltonian is presented. The electronic and magnetic properties of the system as predicted by the present approximation are discussed first qualitatively. Some preliminary quantitative results at H = 0, T = 0 are presented. Extensions of the formalism to incorporate the possibility of magnetic ordering and the inclusion of an external magnetic field at finite temperatures are outlined. The formalism can be generalized to the case where randomness is present, e.g., in impurity bands in crystalline semiconductors.