Set Of Random Numbers Research Articles

Trichuris suis therapy for active ulcerative colitis: A randomized controlled trial

Ulcerative colitis is most common in Western industrialized countries. Inflammatory bowel disease is uncommon in developing countries where helminths are frequent. People with helminths have an altered immunological response to antigens. In animal models, helminths prevent or improve colitis by the induction of regulatory T cells and modulatory cytokines. This study determined the efficacy and safety of the helminth Trichuris suis in therapy of ulcerative colitis. This was a randomized, double blind, placebo-controlled trial conducted at the University of Iowa and select private practices. Trichuris suis ova were obtained from the US Department of Agriculture. The trial included 54 patients with active colitis, defined by an Ulcerative Colitis Disease Activity Index of > or =4. Patients were recruited from physician participants and were randomly assigned to receive placebo or ova treatment. Patients received 2500 Trichuris suis ova or placebo orally at 2-week intervals for 12 weeks. The primary efficacy variable was improvement of the Disease Activity Index to > or =4. After 12 weeks of therapy, improvement according to the intent-to-treat principle occurred in 13 of 30 patients (43.3%) with ova treatment compared with 4 of 24 patients (16.7%) given placebo (P = .04). Improvement was also found with the Simple Index that was significant by week 6. The difference in the proportion of patients who achieved an Ulcerative Colitis Disease Activity Index of 0-1 was not significant. Treatment induced no side effects. Ova therapy seems safe and effective in patients with active colitis.

A spatial rainfall simulator for crop production modeling in Southern Africa

This paper describes a methodology for simulating rainfall in dekads across a set of spatial units in areas where long-term meteorological records are available for a small number of sites only. The work forms part of a larger simulation model of the food system in a district of Zimbabwe, which includes a crop production component for yields of maize, small grains and groundnuts. Only a limited number of meteorological stations are available within or surrounding the district that have long time series of rainfall records. Preliminary analysis of rainfall data for these stations suggested that intra-seasonal temporal correlation was negligible, but that rainfall at any given station was correlated with rainfall at neighbouring stations. This spatial correlation structure can be modeled using a multivariate normal distribution consisting of 30 related variables, representing dekadly rainfall in each of the 30 wards. For each ward, log-transformed rainfall for each of the 36 dekads in the year was characterized by a mean and standard deviation, which were interpolated from surrounding meteorological stations. A covariance matrix derived from a distance measure was then used to represent the spatial correlation between wards. Sets of random numbers were then drawn from this distribution to simulate rainfall across the wards in any given dekad. Cross-validation of estimated rainfall parameters against observed parameters for the one meteorological station within the district suggests that the interpolation process works well. The methodology developed is useful in situations where long-term climatic records are scarce and where rainfall shows pronounced spatial correlation, but negligible temporal correlation.

Analyses of imaging performance degradation caused by birefringence residual in lens materials

Influences of stress birefringence residual in lens elements of high-resolution projection optics are investigated based on a partially coherent imaging formula that has been modified to incorporate the change of the polarization state by birefringence. Birefringent properties are represented by two-dimensional distribution functions with respect to magnitude and fast-axis direction, and they are determined using random numbers to reproduce actual distributions observed in such materials as calcium fluoride. By repeating calculations using lens data created with different sets of random numbers, the degree of imaging performance degradation is analyzed statistically in terms of the magnitude of birefringence in each lens element, the number of lens element composing a projection lens, and the randomness of fast-axis distributions. It is found that the image contrast for a five-bar line/space pattern decreases squarely proportional to the magnitude, whereas the value decreases linearly proportional to the element number. The influence of randomness is understood in relation to image formations through random phase media.

Physiological time-series analysis using approximate entropy and sample entropy

Entropy, as it relates to dynamical systems, is the rate of information production. Methods for estimation of the entropy of a system represented by a time series are not, however, well suited to analysis of the short and noisy data sets encountered in cardiovascular and other biological studies. Pincus introduced approximate entropy (ApEn), a set of measures of system complexity closely related to entropy, which is easily applied to clinical cardiovascular and other time series. ApEn statistics, however, lead to inconsistent results. We have developed a new and related complexity measure, sample entropy (SampEn), and have compared ApEn and SampEn by using them to analyze sets of random numbers with known probabilistic character. We have also evaluated cross-ApEn and cross-SampEn, which use cardiovascular data sets to measure the similarity of two distinct time series. SampEn agreed with theory much more closely than ApEn over a broad range of conditions. The improved accuracy of SampEn statistics should make them useful in the study of experimental clinical cardiovascular and other biological time series.

An Extension of Alias Sampling Method for Parametrized Probability Distributions

An extension of the alias sampling technique for distribution functions depending on a number of parameters was developed. It takes advantage of modern computer architectures with large amounts of cheap memory, by using discrete representations of probability distribution functions. The sampling is done by fast interpolation techniques involving only elementary logical and arithmetical operations, allowing one to keep a higher degree of accuracy as the grids spacing is controlled by the user. By this method it is possible to obtain the value of interest by direct interpolation between the sampled values obtained with the same set of random numbers for the grid values of the parameters adjacent to the values of interest. Sampling tests carried for the case of Molière electron multi-scatter angle distribution show that this method can be successfully used in Monte Carlo codes for sampling complex probability distributions.

ROBUSTNESS OF OPTIMAL DESIGN SOLUTIONS TO REDUCE VIBRATION TRANSMISSION IN A LIGHTWEIGHT 2-D STRUCTURE, PART I: GEOMETRIC DESIGN

A two-dimensional lightweight cantilever structure is studied, comprising 40 rigidly joined beams, of which the geometry is optimized to reduce vibration transmission over a given bandwidth. In this paper, the optimization is achieved by using genetic algorithms. Ten optimized design candidates were achieved for each of three cases resulting from minimizing an objective function (the vibration transmission between two points on the structure) which is calculated (i) using a single frequency, (ii) the frequency average over a narrow bandwidth, and (iii) the frequency average over a broad frequency range. All the candidates show performance improvements and normally the best performance is taken to be the best candidate. This paper then considers the sensitivity of each optimal candidate to small changes in the geometry of the structure. If the performance of a structure is too sensitive to perturbations its practical application is limited or may not be realizable in practice. Therobustness of the optimized candidates is studied in order to find those candidates which are least sensitive to changing design parameters. This is achieved by perturbing the positions of the joints by an ensemble of sets of random numbers. The statistical effect on the objective function is investigated, and some candidates are seen to be more robust to such perturbations than others and generally the greater the bandwidth over which the structure is optimized the more robust the design. A selection criterion is then applied which enables the best candidates to be identified on grounds of both nominal optimized performance and robustness. Finally, the advantage of using genetic algorithms over traditional “hill-climbing” optimization methods is shown, on the grounds of both nominal performance and robustness.

A FORTRAN program for fitting Weibull distribution and generating samples

A computer program has been developed to estimate the parameters of the two-parameter Weibull distribution describing a given data set and to generate random numbers following a given Weibull distribution. The Weibull distribution parameters, namely Weibull modulus and scale parameter, are estimated using two methods: (i) linear regression after logarithmic transformation of the data and (ii) maximum-likelihood estimator. The cumulative distribution function (i.e. probability of failure of a specimen if the data set characterize strength of a component or probability of drought if the data represent water level, etc.) has been estimated using the order statistics. Both the Weibull modulus and scale parameter are necessary to generate random numbers with a specified Weibull distribution. Two example problems using published data sets are used to verify the code. Values of Weibull distribution parameters, estimated using this code, match published solutions obtained graphically. Parameters estimated from one of the example problems are used to generate a set of random numbers. Descriptive statistics and Weibull parameters estimated from the generated data match well with those obtained from the original data.

萌芽的研究発表論文 磁気コセラ連続体理論と磁性粒子の磁場中成形時の配向挙動解析

Numerical method based on the Cosserat continuum theory is proposed for simulation of a magnetic powder in an applied magnetic field. The Maxwell stress is induced in the magnetic powder. During powder forming process in the magnetic field, the magnetic particles are thus rotated and transferred by both mechanical and magnetic interaction. To simulate this powder behavior, new finite element method considering Maxwell is formulated on the basis of the Cosserat continuum theory of compressible plasticity. The powder behavior with magnetic alignment during compaction in magnetic field is simulated by the proposed method to discus the effect of couple-stress on the powder behaviour. The relationship between the direction of magnetic field and the compaction process can be also analyzed: difference of magnetization in cross compaction, transverse compaction and isostatic compaction. In the calculation, the directions of the easy axes are given by a set of random numbers. The rotation of the axes is thus calculated at various conditions of applied magnetic field. The results are discussed comparing with those by particle dynamics simulation.

粉末プロセスの制御と製品評価 磁気コセラ連続体理論による磁性粉体の磁場中成形時の粒子配向と圧粉方法に関する研究

In the Cosserat continuum theory, couple stress and micro rotation of the material are taken into account. To simulate the behaviour of magnetic powder during compaction in magnetic field, we have developed the magneto-Cosserat continuum theory. In this theory, the Maxwell stress that is related to the distribution of magnetic flux density in the powder and particles' easy axes for magnetization are taken into account. By implementing the magneto-Cosserat continuum theory in FEM scheme, it is possible to simulate magnetic alignment in powders with magnetic anisotropy during compaction in an applied magnetic field. In the present paper, we analyze the relationship between the direction of magnetic field and compaction process, such as cross compaction, transverse compaction and isostatic compaction. In the calculation, the directions of the easy axes are given by a set of random numbers. The rotation of the axes is thus calculated at various conditions of applied magnetic field. The results are discussed comparing with those by particle dynamics simulation.

The influence of small solute clearance on dietary protein intake in continuous ambulatory peritoneal dialysis patients: A methodologic analysis based on cross-sectional and prospective studies

The statistical relationship between solute clearance (expressed as Kt/V) and dietary protein intake (DPI; estimated from the normalized protein catabolic rate [NPCR] has led to the assumption that dialysis dose is one of the most important determinants of DPI in continuous ambulatory peritoneal dialysis patients. However, there is increasing concern about the clinical value of such a correlation between variables that contain common components. We have investigated the statistical nature of the cross-sectional correlation between Kt/V and NPCR using mathematical modelling. In addition, in a prospective study, the impact of increasing Kt/V on protein intake estimated from the NPCR and from 3-day food diaries (DPI) was evaluated in 59 patients over a 1-year period. Two thousand sets of random numbers were generated for the components, from which Kt/V and NPCR were calculated. The subsequent cross-sectional correlation between the randomly generated Kt/V and NPCR was highly significant ( r = 0.64 to 0.74). In contrast, there was a much weaker cross-sectional correlation between relatively independent measures of dialysis dose (urea clearance) and protein intake measured from food diaries ( r = 0.36). Analysis of the prospective relationship revealed a significant correlation with a decrease in urea clearance (due to loss of renal function) accompanied by a decrease in both PCR ( r = −0.80) and DPI ( r = −0.51). In contrast, when Kt/V was increased (by larger volume exchanges) there was no significant increase in protein intake. This study has demonstrated that the strength of the cross-sectional relationship between Kt/V and NPCR is due to mathematical coupling of “like with like,” and this correlation cannot be used to substantiate a link between dialysis dose and nutrition. Prospective analysis does show a dependence of protein intake on urea clearance. However, this dependence is only seen in those patients undergoing a reduction in clearance due to loss of renal function. Increasing exchange volume to offset such losses was not accompanied by improvements in protein intake.

Analytical and computational models for a laser radiation field scattered by rough surfaces

A 2-D spectral formalism using a superposition in plane waves for scattered and transmitted laser fields, to find solutions for Helmholtz equations, is described. The formalism is used to obtain the angular spectral amplitudes (ASA) of the laser radiation field scattered by rough surfaces. The equations are solved by numerical computation. To simulate the scattering from a real rough surface, various determin- istic profiles, combinations of them, and a random rough surface with Gaussian statistics are used. The latter is generated in an original man- ner, by using a filter function to transform the uniformly distributed ran- dom numbers, generated by computer, into a set of random numbers with Gaussian statistics. The formalism is tested by applying it to laser radiation scattered by a flat surface and the results are as expected. Eight different surfaces with the same average height and the same root mean square (rms) roughness are considered and they are supposed to be illuminated at various incidence angles by laser radiation with a known wavelength. For each surface, the ASA versus scattering angle dependence, corresponding to five angles of incidence, is represented. © 1996 Society of Photo-Optical Instrumentation Engineers. Subject terms: surface roughness; laser scattering; angular spectral amplitude; deterministic surface profile; random rough surface profile.

Constructions of particular random processes

This paper reviews how to construct sets of random numbers with particular amplitude distributions and correlations among values. These constructions support both high-fidelity Monte Carlo simulation and analytic design studies. A variety of constructions is presented to free engineering models from "white or normal" limitations embodied in many current simulations. The methods support constructions of conventional stationary and normally distributed processes, nonstationary, nonnormal signal and interference waveforms, nonhomogeneous random scenes, nonhomogeneous volumetric clutter realizations, and snapshots of randomly evolving, nonhomogeneous scenes. Each case will have specified amplitude statistics, e.g., normal, log-normal, uniform, Weibull, or discrete amplitude statistics; and selected correlation, e.g., white, pink, or patchy statistics, clouds. or speckles. Sets of random numbers with correlation, nonstationarities, various tails for the amplitude distributions, and multimodal distributions can be constructed. The paper emphasizes aspects of probability theory necessary to engineering modeling.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On Efficiency of Methods of Simulated Moments and Maximum Simulated Likelihood Estimation of Discrete Response Models

This article considers methods of simulated moments for estimation of discrete response models. It is possible to use the same set of random numbers to simulate the choice probabilities for each individual in the sample. In addition to the method of simulated moments of McFadden, we have considered also maximum simulated likelihood estimation methods. An asymptotic theory for such procedures is provided. The estimators are shown to be consistent and asymptotically normal by the theory of generalizedU-statistics. Asymptotic efficiency is discussed. Monte Carlo experiments on the finite sample performance of the estimators are reported.

A model to simulate the behaviour of rectangular block heaps-I

The behaviour of heaps is a major research project in a number of areas of science and engineering, especially powder technology and chemical engineering. A computer model was developed to build rectangular block heaps and calculate the force distribution at the base of the heap of blocks, in which the blocks were of arbitrary but equal height and length and every top block was at the centre of the space between its two supports. A set of random numbers from Brownlee were used to generate the block widths and the space between two adjacent blocks. In 230 heaps analysed, the results from about 33% show good agreement with both the experimental results of Smid and Novosad and the theoretical results of Bagster et al. in cylindrical rod heaps. For relatively small-and large-sized heaps the vertical forces show a peaked distribution. Which is similar to that obtained by Clough and Woodward using finite element analysis within earth dams. In the case of large-scale heaps, the forces vary about their average distribution. Any further study should consider more complex and random heaps in order to make certain the force distribution in rectangular block heaps.

A Test of the Equivalence of Four Random Number Generators – A Simulation Study

Four pseudo random number generators were tested for equivalence. Using two different seed values for each generator, the robustness of a one-sample t-statistic was assessed under a stationary auto-regressive process. The degree of autocorrelation, sample size and significance level were varied for the eight sets of random numbers generated. Results showed an interaction effect between random number generator and alpha level of the t-distribution, suggesting that simulation results could depend on the random number generator selected.

On the Lower Bound of Confidence Coefficients for a Confidence Interval on Variance Components

Consider the one-factor nested components-of-variance model Yij = A + ai + eij, where a2 and eij are jointly independent normal random variables with zero means and variances 2 and a2, respectively, for i = 1, 2, . .. , I; and j = 1, 2, . . ., J. The confidence interval on the among variance component a2 is of interest to the investigators. Except for an artificial method (see Healy, 1961) that uses a set of random numbers which is of no use in practical situations, an exact-size confidence interval on a 2 has not yet been derived. Several approximate procedures are available for obtaining a confidence interval on 2. Satterthwaite (1946) approximates the distribution of the estimate of a linear combination of variances by a chi-squared distribution times a constant. Satterthwaite urges caution in using the method when any of the coefficients of the linear combination are negative, as is the case when estimating a2. Gaylor and Hopper (1969) provide a criterion based on the F-statistics from the ANOVA table for determining when Satterthwaite's procedure may be safely used for setting confidence limits on the among variance components. Welch (1956) offers a series approximation, using the Cornish-Fisher (1937) expansion, for setting approximate confidence intervals on the linear combinations of several variances. Another approximation is given by Moriguti (1954) and repeated by Bulmer (1957). They derive a confidence interval on a2 by assuming the confidence limit is of certain form and solving for it by forcing the confidence coefficient to be exact under certain limiting conditions. Williams (1962) constructed an approximate confidence interval with a guaranteed lower confidence coefficient of 1 2a by a geometrical projection. This confidence interval is identical to the one proposed by Tukey (1951). Howe (1974) also derives confidence limits on a2 through a modified Cornish-Fisher expansion. Boardman (1974) presents a simulation study that investigates the actual probability coverage of the Satterthwaite, Welch, Moriguti-Bulmer, and Tukey-Williams intervals. The results of the study show that the Moriguti-Bulmer and Tukey-Williams procedures give adequate coverage at the nominal 95% confidence coefficient. Both Satterthwaite and Welch procedures behaved poorly in the simulation, giving inadequate coverage at the nominal 95% level. Although Howe's interval was not included in the study, the method

On Ranges of Confidence Coefficients for Confidence Intervals on Variance Components

The among variance component in the balanced one-factor nested components-of-variance model is of interest in many fields of application. Except for an artificial method that uses a set of random numbers which is of no use in practical situations, an exact-size confidence interval on the among variance has not yet been derived. This paper provides a detailed comparison of three approximate confidence intervals which possess certain desired properties and have been shown to be the better methods among many available approximate procedures. Specifically, the minimum and the maximum of the confidence coefficients for the one- and two-sided intervals of each method are obtained. The expected lengths of the intervals are also compared.

On Ranges of Confidence Coefficients for Confidence Intervals on Variance Components

The among variance component in the balanced one-factor nested components-of-variance model is of interest in many fields of application. Except for an artificial method that uses a set of random numbers which is of no use in practical situations, an exact-size confidence interval on the among variance has not yet been derived. This paper provides a detailed comparison of three approximate confidence intervals which possess certain desired properties and have been shown to be the better methods among many available approximate procedures. Specifically, the minimum and the maximum of the confidence coefficients for the one- and two-sided intervals of each method are obtained. The expected lengths of the intervals are also compared.

A BASIC Program for Generating Integer Means and Variances

This article describes a BASIC computer program for generating different sets of random numbers that have integer means and variances. The user can select either the biased or unbiased formula for the standard deviation. Suggestions for use and limitations of the program are noted.

PARTICLE DISPERSION IN ANISOTROPIC HOMOGENEOUS TURBULENCE

ABSTRACT A numerical study of particle dispersion in anisotropic homogeneous turbulent flows is reported. The stochastic turbulent field is represented by a set of random numbers with a pre-set covariance simulating the Reynolds stress in a turbulent flow. The effects of turbulence intensity, aerodynamic response time and Reynolds stress on the particle dispersion are presented.