criteria for the assessment of random number generators abstract for any finite sequence of pseudo random numbers special simulation problems can be constructed such that this sequence yields useless results in order to study the quality of the result of a simulation the assessment of a pseudorandom number generator based on theoretical considerations is a great advantage several criteria for the assessment of random number generators are known the most important criteria are discussed

distribution of bipartite entanglement for random pure states we calculate analytic expressions for the distribution of bipartite entanglement for pure random quantum states all moments of the purity distribution are derived and an asymptotic expansion for the distribution itself is deduced an approximate expression for moments and distribution of meyer wallach entanglement for random pure states is then obtained

computation of critical distances within multiplicative congruential pseudorandom number sequences abstract multiplicative congruential pseudorandom number generators with prime moduli are considered recently it has been shown by two of the authors eichenauer herrmann and grothe 1989 that terms located far apart in the generated sequences are strongly correlated however the critical distances between the terms were not obtained explicitly since a straight approach for computing them through tabulations cannot be used for large values of the modulus an efficient method has been developed and is described in the present note the resulting algorithm has been applied to several generators and tables of the most critical distances for two generators with large moduli are included

hecke algebras of classical groups over p adic fields and supercuspidal representations let k be a p adic field with involution 0 and let k 0 be its fixed subfield of k let v be a finite dimensional vector space defined over k equipped with e hermitian form v k 0 is large

statistical properties of random density matrices statistical properties of ensembles of random density matrices are investigated we compute traces and von neumann entropies averaged over ensembles of random density matrices distributed according to the bures measure the eigenvalues of the random density matrices are analysed we derive the eigenvalue distribution for the bures ensemble which is shown to be broader then the quarter circle distribution characteristic of the hilbert schmidt ensemble for measures induced by partial tracing over the environment we compute exactly the two point eigenvalue correlation function

hecke algebras and harmonic analysis on p adic groups we compute plancherel measures and formal degrees for unipotent representations of p adic groups using hecke algebra isomorphisms the results verify special cases of the conjectural uniformity of formal degrees in an l packet

a statistical evaluation of multiplicative congruential random number generators with modulus 231 1 abstract this article presents the results of empirically testing 16 alternative multipliers for a multiplicative congruential random number generator with modulus 231 1 two of the multipliers are in common use six are the best of 50 candidate multipliers according to the theoretical spectral and lattice tests and eight are the worst with regard to 2 tuples among the 50 the test results raise serious doubts about several of the multipliers including one in common use the tests were also applied to a well known theoretically poor generator randu and gave strong empirical evidence of its inadequacy since comparison of the results of the first eight multipliers with those for the eight worst multipliers failed to show any apparent gross differences one may want to relax the currently employed stringent criteria for acceptable performance on the lattice and spectral tests

slope estimation in the presence of informative right censoring modeling the number of observations as a geometric random variable summary a method is proposed for the estimation of rate of change from incomplete longitudinal data where the number of observations made for each subject is assumed to vary depending on the level of the response variable the proposed method involves a random slope model in which the number of observations is modeled as a geometric distribution with its mean dependent on the individual subject s rate of change the method adjusts for informative right censoring and provides estimates of the slopes of individual subjects as well as of the population under noninformative right censoring these estimators of the slopes are equivalent to bayes estimators fearn 1975 biometrika 62 89 100 the simulation study demonstrates that in cases where the censoring process is informative the proposed estimator is more efficient than either the unweighted or weighted estimator of slope the method is illustrated by the analysis of renal transplant data

a parallel poisson generator using parallel prefix in this paper we use the renewal theory to develop a poisson random number algorithm without restart a parallel poisson random number generator is designed based on this algorithm and prefix computation this generator iteratively produces m poisson random numbers with mean in average time complexity o m n f n p on erew pram where f n p is the time for computing an n element parallel prefix on p processors in each iteration assuming that parallel uniform random numbers can be generated at the rate of one number per unit time per processor if n is selected near m it achieves linear speedup when p is small and the average time complexity is o log m when p is o m

multiplicative congruential random number generators with modulus 2 an exhaustive analysis for 32 and a partial analysis for 48 this paper presents the results of a search to find optimal maximal period multipliers for multiplicative congruential random number generators with moduli 2 32 and 2 48 here a multiplier is said to be optimal if the distance between adjacent parallel hyperplanes on which k tuples lie does not exceed the minimal achievable distance by more than 25 percent for k 2 6

buehler confidence bounds for a reliability maintainability measure this article presents an upper confidence bound for a measure of reliability maintainability of a series system in which component repair is assumed to restore the system to its original status under exponentiality of component repair time and survival time distributions the measure m is the ratio of expected system repair time to expected system survival time moreover under this exponentiality assumption the bound is uniformly minimum among all bounds of specified level that are nondecreasing functions of the maximum likelihood estimator of m as a matter of practical interest the measure m has been incorporated into military standard mil std 470b and is an official statistic of the air force reliability maintainability information system

the student s t approximation in a stationary first order autoregressive model the basic model is a gaussian ar 1 model with an intercept but no additional exogenous variables the paper studies the distribution of the t statistic for testing the value of the autoregressive parameter when the model is estimated by least squares the monte carlo estimates of the quantiles of the t statistic show that student s t is not a satisfactory approximation for sample sizes typical in economic applications the main problem is not the shape of the distribution of the t statistic but its location adjusting the t statistic so that it has the same mean and standard deviation as student s t the distribution of this adjusted t statistic is accurately approximated by student s t techniques are presented for accurately approximating the mean and standard deviation of the t statistic such that the adjusted t statistic can be readily calculated in practice the analysis is extended in two directions the first is to examine the effect of introducing an exogenous variable into the basic model in the expanded model student s t also accurately approximates the distribution of the t statistic for testing the autoregressive parameter and for testing the coefficient of the exogenous variable after these t statistics are adjusted for mean and standard deviation the problem of obtaining a feasible adjustment procedure is that the moments of these t statistics now depend on nuisance parameters the second is to examine the robustness of the results in the basic model to several nonnormal error distributions for each nonnormal distribution the t statistic is adjusted using the mean and standard deviation appropriate for the case of normal errors and then the distribution of the modified t statistic is compared with that of student s t

a revised forward and backward heuristic for two term multiple recursive random number generators abstract this paper is concerned with designing a full period two term k th order multiple recursive generator mrg with the objective of maximizing the spectral value a new heuristic that combines a forward and backward method with random and best improving is presented we adopt a statistical analysis to compare the performance of the new heuristic to the random search method for the full period two term mrgs of orders three and four we also perform a single longer experiment with maximum allowed cpu 604 800 s to compare the spectral value found using the new heuristic with the best of the previously published one the results presented in this paper show that our method is indeed very effective with respect to the spectral value therefore the new heuristic is a good way of obtaining an ideal two term mrg of higher orders

new features of quantum discord uncovered by q entropies the notion of quantum discord introduced by ollivier and zurek phys rev lett 88 2001 017901 see also henderson and vedral j phys a 34 2001 6899 has attracted increasing attention in recent years as an entropic quantifier of non classical features pertaining to the correlations exhibited by bipartite quantum systems here we generalize the notion so as to encompass power law q entropies that reduce to the standard shannon entropy in the limit q 1 and study the concomitant consequences the ensuing new discord like measures we advance describe aspects of non classicality that are different from those associated with the standard quantum discord a particular manifestation of this difference concerns a feature related to order let d1 stand for the standard shannon based discord measure and dq for the q 1 one if two quantum states a b are such that d1 a d1 b this order relation does not remain invariant under a change from d1 to dq

compound random number generators abstract recently marsaglia 1984 proceedings of the sixteenth symposium on the interface noted a trend toward increasingly more demanding use of random number generators after observing that for current uses generators must pass increasingly more sophisticated tests for randomness in order to provide acceptable results marsaglia described a class of combination generators and recommended two specific combination generators that passed an extensive battery of stringent tests for randomness the present article describes an alternative class of generators which produce random values by compounding or intermixing several different sequences of random values these compound generators are easier to implement especially on smaller computers than are marsaglia s recommended generators five specific compound generators two standard generators and marsaglia s two combination generators were subjected to several tests for randomness including marsaglia s stringent tests the standard generator

parallelization of random number generators and long range correlations partitions of pseudo random sequences generated by congruential schemes are investigated for use on computer systems where multiple processing units run in parallel for the solution of a monte carlo problem a special partition is suggested which ensures independence between the units working simultaneously and yields reproducible sequences the analysis performed has brought out the existence of strong autocorrelations between terms located far apart in the sequences dependent only on the congruential nature of the generators the study of these correlations carried out in a number theoretic framework points out that only small fractions of the sequences can be safely used

the serial test for pseudo random numbers generated by the linear congruential method we consider the linear congruential method for pseudo random number generation and establish effective criteria for the choice of parameters in this method which guarantee statistical almost independence of successive pseudo random numbers applications to numerical integration are also discussed

statistical independence of a new class of inversive congruential pseudorandom numbers linear congruential pseudorandom numbers show several undesirable regularities which can render them useless for certain stochastic simulations this was the motiviation for important recent developments in nonlinear congruential methods for generating uniform pseudorandom numbers it is particularly promising to achieve nonlinearity by employing the operation of multiplicative inversion with respect to a prime modulus in the present paper a new class of such inversive congruential generators is introduced and analyzed it is shown that they have excellent statistical independence properties and model true random numbers very closely the methods of proof rely heavily on weil stepanov bounds for rational exponential sums 39 refs

computer simulation results for the two point probability function of composite media computer simulation results are reported for the two point matrix probability function s sub 2 of two phase random media composed of disks distributed with an arbitrary degree of impenetrability lambda the novel technique employed to sample s sub 2 r which gives the probability of finding the endpoints of a line segment of length r in the matrix is very accurate and has a fast execution time results for the limiting cases lambda 0 fully penetrable disks and lambda 1 hard disks respectively compare very favorably with theoretical predictions made by torquato and beasley and by torquato and lado results are also reported for several values of lambda that lie between these two extremes cases which heretofore have not been examined copyright 1988 academic press inc

upper bounds in spectral test for multiple recursive random number generators with missing terms abstract one method for generating random numbers rns of long period recommended by many scholars is the multiple recursive generator mrg in that the current rn is essentially a linear combination of the k preceding ones in this paper the upper bounds for a figure of merit adopted in the spectral test are derived for the k th order mrg with p k terms as p gets smaller the bounds become smaller as well the simplest form of the k th order mrg with two terms frequently discussed in literature is found to have the worst bound

fieller s confidence intervals for the ratio of two means in the assessment of average bioequivalence from crossover data the two period crossover design is the most commonly used study design for bioequivalence of one test formulation to be assessed in comparison to one reference formulation consequently in this paper all derivation is based on this particular design it is assumed that for the underlying statistical model the usual assumptions of normality and additivity are satisfied on the original scale of measurement and that it is wanted to base the assessment of average bioavailability on the ratio of the unknown population means for the test and reference formulation the purpose of this paper is to illustrate that it is reasonable to assume a uniform covariance structure for the two period crossover design because the demand of equal variability in bioavailabilities in addition to equal average bioavailabilities for the reference and test formulation makes the assumption of uniform covariance structure very realistic and also because the properties of a decision rule based upon a fieller s confidence interval under a uniform covariance structure are competitive with those of the corresponding rule based on a general covariance structure

construction of tame supercuspidal representations the notion of depth is defined by moy prasad mp2 the notion of a generic character will be defined in 9 when g gln or g is the multiplicative group of a central division algebra of dimension n with n p 1 our generic characters are just the generic characters in my where the definition is due to kutzko moreover in these cases our construction literally specializes to howe s construction as formulated in my and it is known that the construction yields all supercuspidal representations my hm notice that the initial datum in our construction consists of very simple objects linear characters and supercuspidal representations of depth zero the latter are well understood by the work of moy prasad and morris see 3 by the work of howe irreducible supercuspidal representations of gln f with n p 1 are parametrized by certain characters of e as e varies through

character expansions and unrefined minimal k types let k be a p adic field let g be the group of k rational points of a connected reductive group g defined over k and let inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i be its lie algebra under certain hypotheses on g and k we get a new character expansion called a asymptotic expansion for representations of positive depth inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i this character expansion is valid on the g domain inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i which is bigger than that where the harish chandra howe character expansion is known to be valid

an analysis of linear congruential random number generators when multiplier restrictions exist abstract this research conducts an exhaustive search for the best spectral test performance in a full period linear congruential generator lcg with the largest prime modulus smaller than 2b for bit sizes b 8 9 31 three types of restrictions on multipliers are presented and some full period lcgs are presented for use in three different spectral test dimensions according to the exhaustive searches we perform the results indicate differences exist among the numbers of possible multipliers for the three types of multiplier restrictions we demonstrate that these differences can affect the performance of spectral tests for different dimensions

numerical simulation of randomly forced turbulent flows several authors have proposed studying randomly forced turbulent flows e g e a novikov soviet physics jetp 20 5 1290 1965 more recently theoretical investigations e g renormalization group have focused on white noise forced navier stokes equations v yakhot and s a orszag j sci comput 1 1 3 1986 the present article aims to provide an appropriate numerical method for the simulation of randomly forced turbulent systems the spatial discretization is based on the classical fourier spectral method the time integration is performed by a second order runge kutta scheme the consistency of an extension of this scheme to treat additive noise stochastic differential equations is proved the random number generator is based on lagged fibonacci series results are presented for two randomly forced problems the burgers and the incompressible navier stokes equations with a white noise in time forcing term characterized by a power law correlation function in spectral space a variety of statistics are computed for both problems including the structure functions the third order structure functions are compared with their exact expressions in the inertial subrange the influence of the dissipation mechanism viscous or hyperviscous on the inertial subrange is discussed in particular probability density functions of velocity increments are computed for the navier stokes simulation finally for both burgers and navier stokes problems our results support the view that random sweeping is the dominant effect of the large scale motion on the small scales

pseudorandom vector generation by the multiple recursive matrix method pseudorandom vectors are of importance for parallelized simulation methods in this paper we carry out an in depth analysis of the multiple recursive matrix method for the generation of uniform pseudorandom vectors which was introduced in an earlier paper of the author we study in particular the periodicity properties the lattice structure and the behavior under the serial test for sequences of pseudorandom vectors generated by this method

decoding spherical codes for the gaussian channel a decoding algorithm for permutation codes that is equivalent to maximum likelihood decoding but less complex than the correlation decoder is presented a general construction for iteratively maximum likelihood decodable imld codes is proved and used to construct imld codes for every dimension n d slepian 1965 defined permutation modulation codes and presented an efficient algorithm for their decoding slepian s decoding scheme is one of the principal components of the permutation code decoding algorithm presented

existence of maximum likelihood estimates for interval censored data from some three parameter models with a shifted origin summary given data in the form of interval censored observations from a three parameter distribution practical criteria are established for the existence of maximum likelihood estimates for three kinds of parameter space these criteria can be derived by analysing the behaviour of the log likelihood near a type of boundary of the parameter space called the probability contents inner boundary the effectiveness of the criteria is discussed in the case where the underlying distribution is a three parameter log normal distribution the efficiency of the criteria is evaluated by simulation

asymptotic expected performance of some tsp heuristics an empirical evaluation abstract this paper presents an empirical study on the performance of some heuristics for the travelling salesman problem our study indicates that the expected tour lengths through n points in a unit square produced by these heuristics are all proportional to sqrt n asymptotically in this study the average tour lengths generated by each heuristic are approximated by a linear function of sqrt n the model parameters are estimated by the linear regression method the possible effect of different random number generators which are used to perform the statistical analysis is also investigated

supercuspidal representations an exhaustion theorem let be a reductive adic group we prove that all supercuspidal representations of arise through yu s construction subject to certain hypotheses on depending on as a corollary under the same hypotheses we see that any supercuspidal representation is compactly induced from a representation of an open subgroup which is compact modulo the center

average entropy of a subsystem from its average tsallis entropy in the nonextensive tsallis scenario page s conjecture for the average entropy of a subsystem phys rev lett 71 1291 1993 as well as its demonstration are generalized i e when a pure quantum system whose hilbert space dimension is mn is considered the average tsallis entropy of an m dimensional subsystem is obtained this demonstration is expected to be useful to study systems where the usual entropy does not give satisfactory results

a remark on long range correlations in multiplicative congruential pseudo random number generators in dematteis and pagnutti 1 multiplicative congruential pseudo random number generators with composite moduli are analysed and it is proved that there are strong correlations between terms located far apart in the generated sequences in this note the same result is obtained for multiplicative congruential generators with prime moduli

occupancy numbers in testing random number generators the classical occupancy problem where n balls are placed in n cells is used for testing of random number generators we show that the statistics of appropriately chosen occupancy numbers are incompatible with the statistics of many pseudorandom number generators prngs evenif they are trun cated more thanthat the in compatibility shows up onrelatively small samples long before the period of the prng is reached we introduce generalized fermi dirac models as idealized models for prngs these models are used to make educated guesses of how large the sample sizes should be to detect the deficiencies of the prngs under study we use the developed occupancy tests together with some other ones to examine the performance of several widely used random number generators including random of the unix c library we found that random failed two of the conducted tests rather badly we also tested a true random number generator based on decay which passed all our relevant tests successfully

matrices and the structure of random number sequences abstract this note provides a short self contained treatment using linear algebra and matrix theory for establishing maximal periods underlying structure and choice of starting values for shift register and lagged fibonacci random number generators

quasi stationary states of the nrt nonlinear schrodinger equation abstract with regards to the nonlinear schrodinger equation recently advanced by nobre rego monteiro and tsallis nrt based on tsallis q thermo statistical formalism we investigate the existence and properties of its quasi stationary solutions which have the time and space dependences separated in a q deformed fashion one recovers the normal factorization into purely spatial and purely temporal factors corresponding to the standard linear schrodinger equation when the deformation vanishes q 1 we discuss various specific examples of exact quasi stationary solutions of the nrt equation in particular we obtain a quasi stationary solution for the moshinsky model providing the first example of an exact solution of the nrt equation for a system of interacting particles

superconsistent estimation and inference in structural econometric models using extreme order statistics abstract data generating processes whose distributions supports depend on unknown parameters arise naturally in empirical applications in such situations the maximum likelihood estimator is often difficult to calculate and usually has a nonstandard limiting distribution that depends on nuisance parameters we propose an alternative estimation strategy that is typically simpler to implement than the likelihood approach and allows one to conduct inference using simulation methods our proposed estimators are based on the analog estimation principle and bear a striking resemblance to generalized method of moments estimators although here the estimators are generally parameter consistent at rate t rather than the usual rate t

random number generation with the recursion x t x t 3p x t 3q abstract a generalized feedback shift register gfsr algorithm proposed by lewis and payne 1973 uses a primitive trinomial to generate a sequence of pseudorandom numbers we propose a similar algorithm which uses a primitive polynomial with many nonzero terms but generates a number as fast as the original gfsr algorithm our sequence is guaranteed to be equidistributed in higher dimensions and to have a good autocorrelation property extensive statistical tests have been performed on the sequences generated by our algorithm and the results were quite satisfactory

random number generations generators on vector supercomputers and other advanced architectures this paper is divided into three parts the first part surveys the more common techniques for generating and testing uniformly distributed random numbers the second part considers the efficient ge

on the periods of generalized fibonacci recurrences we give a simple condition for a linear recurrence mod 2w of degree r to have the maximal possible period 2m 1 2 1 it follows that the period is maximal in the cases of interest for pseudorandom number gen eration i e for three term linear recurrences defined by trinomials which are primitive mod 2 and of degree r 2 we consider the enumeration of cer tain exceptional polynomials which do not give maximal period and list all such polynomials of degree less than 15