Showing papers on "Randomness published in 1981"

Studies in astronomical time series analysis. I - Modeling random processes in the time domain

Abstract: Random process models phased in the time domain are used to analyze astrophysical time series data produced by random processes. A moving average (MA) model represents the data as a sequence of pulses occurring randomly in time, with random amplitudes. An autoregressive (AR) model represents the correlations in the process in terms of a linear function of past values. The best AR model is determined from sampled data and transformed to an MA for interpretation. The randomness of the pulse amplitudes is maximized by a FORTRAN algorithm which is relatively stable numerically. Results of test cases are given to study the effects of adding noise and of different distributions for the pulse amplitudes. A preliminary analysis of the optical light curve of the quasar 3C 273 is given.

Stochastic FEM In Settlement Predictions

Abstract: Stochastic finite element analysis is used to predict uncertainties in total and differential settlement under a large flexible footing. The results are compared with one-dimensional stochastic solutions already in the literature. Differences between the one- and two-dimensional analyses, particularly for differential settlement, are distinct. These differences seem primarily attributable to randomness in the stress field which cannot be included in one-dimensional models, and to mechanistic correlations by common dependence on the realizations of particular random variables. In principle, second-moment techniques can be extended to a broad range of analyses now performed using finite element and finite difference techniques.

On Intrinsic Randomness of Dynamical Systems

Abstract: We discuss the problem of nonunitary equivalence, via positivity-preserving similarity transformations, between the unitary groups associated with deterministic dynamical evolution and semigroups associated with stochastic processes. Dynamical systems admitting such nonunitary equivalence with stochastic Markov processes are said to be intrinsically random. In a previous work, it was found that the so-called Bernoulli systems (discrete time) are intrinsically random in this sense. This result is extended here by showing that a more general class of dynamical systems---the so-called K systems and K flows---are intrinsically random. The connection of intrinsic randomness with local instability of motion is briefly discussed. We also show that Markov processes associated through nonunitary equivalence to nonisomorphic K flows are necessarily nonisomorphic.

Compositional Applications of Stochastic Processes

Abstract: A stochastic process is a collection of random-variable quantities distributed in space or time. When a statistician makes use of a stochastic process, the object is to find basic patterns in a set of observed data that will provide more coherent information about that data. In practice, a situation of complete randomness, where there is no order, is unlikely to occur. Indeed, the concept of absolute randomness turns out to be extremely difficult to define mathematically (Chaitin 1975). Mathematicians have classified various types of stochastic structures as a basic framework for analysis of stochastic processes. When composers make use of stochastic structuring techniques in musical composition, they are usually approaching the problem from the other direction. The main interest is in a synthesis of a sequence of sound data within a structural framework. A stochastic generative scheme is a means of setting up and manipulating stochastic control structures. Although a composer has a different objective, mathematical techniques developed for analysis can be of great practical use in the formal, structured environment of computer music systems.

The Effects of Serial Order in Long Sequences of Auditory Stimuli on Event-Related Potentials

Abstract: The generalizability of the model relating P300 amplitudes to subjective probabilities, developed by Squires et al (1976) for random series of events, was examined with respect to long sequences of repetitions, which had been restricted in randomness, allowing only for sequences of between 4 and 12 frequent clicks Subjects were asked to silently count either the rarer of two clicks, presented with a probability of 10, or light stimuli occurring with the same temporal distribution Within these limits there was an increase in P300 amplitude not only to the rare clicks, but also—contrary to predictions from the model—to the frequent non-target clicks following longer series of repetitions, provided that clicks had to be counted A plausible interpretation might be that the longer the series of repetitions in long non-random sequences with low predictability, the more the subjects become involved in the “stimulus evaluation” of both kinds of events A similar increase across serial position was found for the N100 component to frequent clicks when the auditory modality was defined as task relevant, and was interpreted as progressive focusing of selective attention For the rare clicks there occurred a decrease in a slow Negative Shift with peak amplitude at 220 msec after long series of non-targets, possibly reflecting a facilitative effect of the focused attention on decision processes related to target detection There were no differences between normals and chronic alcoholics with respect to the above-mentioned effects

The Use of Random-Utility Theory in Building Location-Allocation Models

Abstract: The most important part of a location-allocation model is the allocation rule, that is, the way clients are assigned to facilities. In the well-known models of the "plant-location" family, the embedded allocation rule is the assignment of the least-travel-cost facility, This allocation rule depends on the assumption that the cost, or more generally utility, associated with each possible facility choice is deterministically known. The simplest way to generalize a plant-location model is to add a random term to travel costs, with a known probability distribution. Such randomness may be shown to arise in many real-life situations, and the resulting choice models constitute the subject of random-utility theory, This paper introduces the use of the random-utility modeling philosophy in location-allocation problems, Some relevant properties of the resulting family of models are derived, Among them, of special importance is the submodularity property, which relates the random-utility-based location models to a recent area of research in combinatorial optimization. Submodularity is exploited to develop simple heuristic algorithms, and the effectiveness of the approach is supported with some numerical results.

Random layered frustration models

Abstract: We study inhomogeneous two-dimensional Ising models with a random distribution of ferro- and antiferromagnetic couplings,Kij=±K, or equivalently a random distribution of frustrations. In particular, we considerRandom Layered Frustration models (RLF) where randomness is confined to the vertical direction. These RLF-models are solved exactly, i.e., partition function and free energy are obtained in closed form for an arbitrary random distribution of finite period. The phase transition is of Ising type. A simple formula for the transition temperature is derived which depends only on the mean coupling\(\overline {K_{ij} } \), but not on other details of the distribution. Both cases,Tc=0 andTc≠0, are possible. Groundstate energy and groundstate degeneracy, or equivalently the rest entropy, are determined. It is found that both the occurence or absence of a phase transition may be accompanied with vanishing or nonvanishing rest entropy. We also show that for the RLF-models a phase transition is excluded when all groundstates are connected with one another by local transformations which presumably holds generally. A remarkable result is that the transition of the ferromagnetic Ising model can be destroyed completely if one replaces an arbitrarily small fraction of ferromagnetic couplings by antiferromagnetic ones in a suitable way.

On correlation functions in random magnets

Abstract: In random magnets the probability distribution of the correlation function at large distance is not concentrated around its average. To illustrate this idea two examples are studied: a random Ising chain and a random cubic chain. The extension of the findings to higher dimension and the connection to Harris' criterion (1974) are discussed heuristically. It is concluded that in Monte Carlo simulations due to the combined effects of randomness and finite size effects one can only measure the most probable value of the correlation functions and not their average.

The estimation of random coefficient autogressive models. ii

Abstract: . In Nicholls and Quinn (1980) a procedure was proposed for the determination of strongly consistent estimates of random coefficient autoregressive models. These estimates are used here as starting values in a Newton-Raphson algorithm which is employed to obtain the maximum likelihood estimates of a class of random coefficient autoregressions. The maximum likelihood estimates are shown to be strongly consistent and to satisfy a central limit theorem. The problem of testing for the randomness of the coefficients is also briefly discussed. The results of a number of simulations are reported which illustrate the theoretical results obtained.

On probability distributions of single-linkage dendrograms

Abstract: There are ways to order the pairwise similarities between N objects, assuming no ties. According to single linkage (SL) clustering, each such order determines a dendrogram for the N objects. We give an algorithm for calculating the number of different SL-dendrograms on N objects. We also give an algorithm for calculating the probability distribution of the SL-dendrograms under pure randomness, i.e. assuming that all the similarity orders are equally probable. The results are used to illustrate the statistical risks for small values of N,. when SL-dendrograms are used to test cluster structure hypotheses.

Random vibration analysis for the seismic response of earth dams

Abstract: The randomness of earthquake ground motions and the sensitivity of earth dams to details of the excitation make random vibration methods of analysis attractive and economical tools with which one can directly predict statistics of the response to potential earthquakes. A new random vibration formulation is introduced in this Paper and employed to study characteristics of the dynamic behaviour of earth dams modelled as inhomogeneous shear beams and excited by strong motions consisting of vertical shear waves. Unrealistic simplifying assumptions of classical random vibration theories are avoided with this method which properly accounts for the frequency content and time evolution in intensity of the excitation. Results are presented in the form of variation with time, and distribution with depth from the crest, of statistics of displacements, accelerations, shear strains and seismic coefficients on potential sliding masses. Key factors that influence the dynamic behaviour are identified and their effect is ...

Multiple Runs Distributions: Recurrences and Critical Values

Abstract: Most traditional applications of runs tests have entailed bivariate runs distributions Extensions to more general runs tests for randomness have been hindered by the lack of exact critical values for distributions with more than two kinds of elements Combinatorial recurrences that can be used to compute exact significance levels for small sample sizes are presented for runs distributions for ν ≥ 2 kinds of elements Critical values for small sample sizes are tabled for ν = 2(1)6 More extensive tables are available from the author

Excitation Dynamics in Molecular Solids

Abstract: Excitation dynamics in molecular crystals have much in common with excitation dynamics of ionic crystals and glasses. While the optical spectroscopy of the electronic centers in solids (Chap. 1) was treated for both ionic and molecular solids in a unified way, the review of the excitation dynamics in this chapter has to be compared with somewhat parallel reviews dealing predominantly with inorganic solids (Chaps. 2-6). This is done partly for pragmatic reasons and partly in view of the unique opportunities afforded by the study of molecular crystals. In isotopic substituted molecular crystals one has essentially “perfect randomness” in the substitutional composition, as well as minimal effects due to local heterogeneities. Thus, such studies may be the best proving grounds for the testing of theoretical concepts. Also, the ease of excitation fusion in such crystals provides clear-cut criteria for the testing of long-range excitation transport in undoped crystals.

Analysis of the spatial organization of the cell: a statistical method for revealing the non-random location of an organelle.

Abstract: SUMMARY A method is proposed for testing the randomness of the location of an organelle within a given area of a cell section. The approach chosen is to analyse the distance between this organelle and a specific point considered as a point of reference. The method consists of converting this distance into the ratio of one given area to another and comparing the statistical distribution of the converted values to the uniform distribution. This method has the advantage of being valid in the absence of any restrictive assumptions concerning the heterogeneity in size and/or shape of the collection of sections sampled. Detailed examples are given to illustrate the practical use of the method, and its possible extensions are discussed.

Asymptotic efficiency of rank tests of randomness against autocorrelation

Abstract: This note is concerned with the problem of testing the hypothesisH of randomness against the alternative that the variables are auto-correlated. Two rank tests ofH are considered and their asymptotic efficiencies relative to the classical normal theory tests are obtained.

Random secants of a convex body generated by surface randomness

Abstract: Length distributions for random secants through a convex region K are derived for three types of randomness. The results are formulated in terms of geometric properties of K, e.g. the overlap surface content of K with its translated self. The distribution of distance between two random points in K, expressed in terms of the overlap volume, is shown to extend to non-convex (including disjoint) regions. GEOMETRICAL PROBABILITY; CONVEXITY; RANDOM SECANTS

On the calculation of mean first passage times for simple random walks

Abstract: The equivalence of two recently proposed methods for calculating mean first passage times in unit‐step, one‐dimensional random walks is established. An intermediate result of the demonstration is a new analytic expression for the mean accumulated residence time in any particular state. This expression is used to obtain some simple approximate results concerning (i) extreme fluctuations in unimodal systems and (ii) transitions between steady states in bimodal systems.

Polynomial local improvement algorithms in combinatorial optimization

Abstract: : The subject of this report is an analysis of the expected, or average case performance of local improvement algorithms. The first chapter presents the basic model, defines the combinatorial structures which are the basis for the analysis, and describes the randomness assumptions upon which the expectation are based. The second chapter examines these structures in more detail, including an analysis of both best and worst case performance. The third chapter discusses simulation results which predict an approximately linear average case performance, and proves an O(n2 log n) upper bound for two of the random distributions assumed. Chapter Four proves some extensions and sharper versions of this upper bound. The fifth chapter applies the model to principal pivoting algorithms for the linear complementarity problem, and to the simplex method. Although local improvement is not guaranteed to find a global optimum for all problems, most notably those that are NP-complete, it is nonetheless often used in these cases. Chapter Six discusses these appllications.

One-dimensional random walk with phase transition

Abstract: We consider a random walk on a one-dimensional lattice. The walk is asymmetric but with different asymmetry on the right and left halves of the line. As the parameter space describing the two asymmetries is covered, several qualitatively different distributions result: limiting distribution, unimodal diffusion and bimodal diffusion. The corresponding parameter space phase boundaries are obtained, as well as the precise form of the distributions.

Micrococcal nuclease cleavage of chromatin displays nonrandom properties.

Abstract: A statistical analysis of the products of digestion of chicken erythrocyte chromatin by micrococcal nuclease was used to test for randomness of the cutting process. DNA fragment size classes corresponding to mononucleosome, dinucleosome, trinucleosome, tetranucleosome, and all fragments larger than tetranucleosome were evaluated. In every case, fragments in the mononucleosome and greater-than-tetranucleosome classes were produced in excess of the level expected on the basis of random cleavage while those in the dinucleosome-tetranucleosome classes exhibited a shortage. The pattern of nonrandomness appears to depend on substrate size: the magnitude of deviations from randomness was large when substrates of genomic size are compared with polynucleosomal segments whereas the direction of deviation is identical. Nonrandomness was independent of ionic conditions known to affect the state of chromatin condensation and also appeared to be unaffected by depletion of histones H1 and H5. The possible universality of nonrandom cleavage was suggested when other data from the literature was analyzed. Some possible mechanisms to account for this property are discussed.

Random walks on finite lattices with traps. II. The case of a partially absorbing trap

Abstract: We continue our study of dissipative processes involving both chemical reaction and physical diffusion in systems for which the influence of boundaries and system size on the dynamics cannot be neglected. We present a combined numerical (Monte Carlo) and analytical study of random walks on finite and infinite (i.e., periodic) lattices with a centrally located trap, and determine the extent to which the efficiency of trapping changes when this trap is characterized by an absorbance probability other than unity. Numerical results on the average number $〈n〉$ of steps required for trapping are presented for two- and three-dimensional lattices subject to confining, reflecting, and periodic boundary conditions and for three absorption probabilities: 1.0, 0.5, and 0.1. An expression is derived for calculating the average $〈n〉$ for an arbitrary absorption probability and it is shown that the predictions of the theory are in excellent accord with the results of our Monte Carlo simulations. The use of this expression allows a characterization of the degree of reversibility per reactive encounter.

Quenched randomness in the two-dimensional ferromagnetic planar model

Abstract: A model of a disordered planar model is introduced and solved using the replica method. The model is designed to mimic the inhomogeneities known to exist in helium and granular superconducting films. The results indicate that at onset, the universal results, predicted on the basis of renormalization group analysis, hold to lowest order in the parameter measuring the disorder. The disroder has the important effect of increasing the vortex pairs couplings, resulting in an initial increase of the critical temperature. Possible consequences of the results to related experiments are also presented.

Quality evaluation of some combinations of unit uniform random number generators and unit normal transformation algorithms

Abstract: This study is concerned with evaluation of the goodness of fit and randomness of unit normal variates generated from combinations of several unit uniform generators and several normal transformation algorithms. The basic conclusion is that use of a good, theoretically exact transformation in conjunction with a theoretically good unit uniform generator does not necessarily guarantee variates with good statistical properties. In many cases generators which aren't quite so good when combined with transformation algorithms which also aren't quite so good, will yield variates with statistical properties which are superior to those of the “better” generators.