Showing papers on "Parametric statistics published in 1977"

Efficient numerical treatment of periodic systems with application to stability problems

Abstract: Two efficient numerical methods for dealing with the stability of linear periodic systems are presented. Both methods combine the use of multivariable Floquet-Liapunov theory with an efficient numerical scheme for computing the transition matrix at the end of one period. The numerical properties of these methods are illustrated by applying them to the simple parametric excitation problem of a fixed end column. The practical value of these methods is shown by applying them to some helicopter rotor blade aeroelastic and structural dynamics problems. It is concluded that these methods are numerically efficient, general and practical for dealing with the stability of large periodic systems.

Observation of parametric instabilities in lower hybrid radio frequency heating of tokamaks

Abstract: Experimental data are presented which shows that during lower hybrid radio frequency heating of the Princeton ATC Tokamak, parametric instabilities are excited, and the ion heating correlates with the presence of the parametric spectra. A theoretical interpretation of the parametric instabilities is presented.

Exceptional Paper—Parametric and Postoptimality Analysis in Integer Linear Programming

Abstract: The purpose of this paper is to take stock of what is known and to suggest some conceptual foundations for future progress in the areas of postoptimality analysis and parametric optimization techniques for integer programming.

Effects of parametric uncertainty and technological change on input--output models

Abstract: A method for restructuring input-output (I-O) models is demonstrated so that real technological options are more accurately reflected. Parameters are reordered to provide information on (1) how to set priorities for acquiring updated data; (2) how to construct more accurate I-O tables for a given cost; and (3) how to identify technologies where a small change will have a large impact on a policy goal. Selective updating of a model's parameters allows uncertainties to be reduced. Only two percent of the parameters were updated in the demonstration for each of four classes of functions (scalar, vector, submatrix, and Leontif inverse), which was sufficient for the scalar and vector importance functions. A reduction in tolerance occurs as the range space increases and wider classes of potential problems are introduced. 23 references. (DCK)

Improved non-parametric statistical methods for the estimation of Michaelis-Menten kinetic parameters by the direct linear plot

Abstract: The theoretical basis for the direct linear plot [Eisenthal & Cornish-Bowden (1974) Biochem. J. 139, 715-720], a non-parametric statistical method for the analysis of data-fitting the Michaelis-Menten equation, was reinvestigated in order to accommodate additional experimental designs and to provide estimates of precision more directly comparable with those obtained by parametric statistical methods. Methods are given for calculating upper and lower confidence limits for the estimated parameters, for accommodating replicate measurements and for comparing the results of two separate experiments. Factors that influence the proper design of experiments are discussed.

Model for parametric acoustic sources

Abstract: A theoretical model for the difference‐frequency radiation from a parametric acoustic array is developed. The (two‐frequency) primary wave is assumed to be radiated by a piston source and may be effectively limited in either the nearfield or the farfield of the piston. Either small‐signal absorption or saturation of the primary beam may serve as the limiting mechanism. The parametric gain is defined as a complex number whose (i) magnitude is the ratio of secondary and primary source pressures and (ii) phase is an indication of how much generation occurs within the nearfield and how much within the farfield of the primary beam. The parametric gain is evaluated as a function of the primary‐to‐secondary frequency (downshift) ratio, the amount of small‐signal primary absorption within the nearfield, and a ’’scaled’’ primary source level. Then, the parametric gain may be used to determine the beam pattern characteristics via a simple closed‐form expression. The theoretical results are found to be in good agreement with other theoretical treatments (within their realms of applicability) and in fair agreement with experimental results from various types of parametric sources. The discrepancies that do exist appear to stem from the approximation that the primary nearfield can be treated as a plane wave.

Regularity and singularity estimates on hypersurfaces minimizing parametric elliptic variational integrals

Abstract: Introduction In this paper we study the structure of n dimensional rectifiable currents in R n+l which minimize the integrals of parametric elliptic integrands. The existence of such minimizing surfaces is well known [7, 5.1.6] as is their regularity almost everywhere [7, 5.3.19]. In Par t I of the present paper we give a new geometric construction from which regularity estimates can be obtained for minimizing hypersurfaces. In this construction we replace the parametric problem for n dimensional surfaces in R ~§ by a nonparametric problem for which the minimizing hypersurfaee is a graph in R n§ with horizontal slices closely approximating in a certain sense the hypersuffaee(s) minimizing the original problem. Analysis of the associated Euler-Lagrange partial differential equation carried out in w 2 of Part I yields an upper bound for the integral of the square of the second fundamental form over the approximating graphs, hence over the regular parts of the original surface. Since a neighbourhood of a singular point must contribute substantially to this integral (see Theorem 1.3 and the remark following it), we can thus conclude by an argument similar to that given by Miranda [13] tha t the Hausdorff ( n 2)-dimensional measure of the interior singular set is locally finite (Theorem 3.1). In Par t I I of this work we show that the singular sets in question must have Hausdorff

Toward a statistical theory of reasoning

Abstract: It is argued that the observed variability of responding in reasoning tasks might usefully be described by mathematical models based on stochastic processes. The data of a number of experiments employing Wason's selection task are reanalysed and it is shown that selection probabilities of individual cards are statistically independent. This is consistent with a class of simple stochastic models and renders conventional “insight” explanations of the data unparsi-monious. A provisional stochastic model is formulated and subjected to a limited parametric test with reasonably satisfactory results. Some general directions for future research along these lines are suggested.

Tests of equality of dependent correlation coefficients

Abstract: SUMMARY A parametric test given known variance ratios, and a nonparametric test, both for the equality of correlation coefficients of one variable with a set of other variables, are proposed and their power functions are compared

Visual interaction with overhauser curves and surfaces

Abstract: The method of parabolic blending for curve and surface interpolation originally conceived by A. W. Overhauser is applied to the interactive free-form design of three dimensional objects. A significant advantage of the algorithm is the user-oriented control of surface shape that is achieved because one interactively manipulates only coordinates on the design surface, as opposed to parametric slopes or design points.The algorithm is demonstrated using an interactive 3D design system that executes in a dual-minicomputer refresh graphics environment without special 3D hardware. The system provides high level data generation commands and direct visual interaction with structured 3D data using a multi-purpose 3D cursor and shaping tool. Objects composed of points, lines, curves and surfaces of different forms may be interactively created and manipulated.

Parametric instabilities in the presence of space‐time random fluctuations

Abstract: The effect of a finite bandwidth driver or of turbulence on the parametric instability is considered. First, exact equations are obtained for special values of the group velocity of the fluctuations V0, with bandwidth modeled by a Kubo–Anderson process. Next, a method which enables one to deal with the space‐time problem for arbitrary V0 is given. For the averaged amplitudes it reduces to the Bourret approximation and for the correlation function it gives the kinetic equation for random phase waves. Convective and absolute instability thresholds are given. It is found that for absolute instabilities the threshold obtained from the averaged intensities is lower than the one obtained from the averaged amplitudes.

On the theory of the evaluation of joint orientation measurements

Abstract: On the Theory of the Evaluation of Joint Orientation Measurements The current procedure for the evaluation of sets of joint-orientation measurements in terms of regional stresses is critically reviewed. It is shown that the counting circles on a sphere for constructing density diagrams are not circles on an equal-area (Lambert) projection of such a sphere; the correct curves are presented. It is shown that the search for modal maxima in the density diagrams corresponds to a nonparametric statistic for which it is difficult to give confidence limits. General considerations about the statistics of experiments yield the result that 12–15 joint measurements in an outcrop are sufficient to define 3 maxima, if such maxima exist at all. In order to give confidence limits, it is best to introduce a parametric model for the distribution of joint orientations. For a single cluster of orientations the probability density function is chosen as proportional to exp (k2 cos2θ) whereθ is the polar deviation angle from the “mean” direction; since the basic joint-orientations havethree fundamental directions, three probability density functions of the above type have to be superposed. These are determined by giving 11 parameters which can be determined by a function-minimization procedure from a given set of measurements. This procedure is best carried out on a computer. In this fashion, confidence limits for the preferred joint directions can be obtained. For the determination of the stresses, only two preferred sets of joints are required reducing the necessary number of parameters to 7. According to the usual theory of the statistics of trials, it is seen that 21 measurements are required to determine them. Thus, using a parametric statistic, it is seen that 21 measurements of joint orientations in an outcrop should suffice to determine the stress field that produced them. If the sharpness of the distributions is assumed as a priori known, this reduces again to the 15 or 20 measurements required for a non-parametric evaluation.

Statistical inference on stationary random fields

Abstract: Statistical methods are developed to model random processes on multidimensional Euclidean space from observed data. Statistical inference techniques are used to estimate model parameters and test hypotheses concerning stationarity, isotropy, and number of parameters. Algorithms are described for fitting parametric models and testing between alternative model structures. Stochastic partial difference equation models of multidimensional processes are discussed in detail. Computer generated data from a known model are used to directly demonstrate the statistical procedures.

A parametric cubic modelling system for general solids of composite material

Abstract: A new approach to modelling solids that are anisotropic and heterogeneous is presented with applications to structures of composite material. A parametric cubic modelling system is presented for lines, surfaces, volumes, and physical data that uses construction-in-context to generate numerical data. This system automates the construction of discrete element models and can reduce input data requirements by more than an order of magnitude. A tricubic isoparametric discrete element is presented that does not require displacement derivatives to define connectivity. This element is capable of exact displacement and strain continuity over a surface while permitting strain discontinuities at heterogeneous material interfaces. The shape of an element can be any hexahedron, pentahedron, or tetrahedron and the material properties are allowed to vary over the volume. Evaluation of modelling error with respect to closed-form solutions for curved geometries indicate a single element can model up to 90-degree segments with stresses accurate to 1 per cent. Applications of the system to composite structures are presented for interlaminar edge effects and attachment stresses in a sandwich panel.

On Nonlinear Parametric Excitation Problems

Abstract: Publisher Summary This chapter highlights that one of the most interesting areas in the theory of vibrations is parametric excitation problems Systems under parametric excitation can exhibit extremely complex behavior patterns and stability character The unraveling of this complexity is not only a mathematically challenging problem, but also has great practical significance It is, therefore, not surprising that a great deal of work has been devoted to this class of problems Being essentially based upon the theory of differential equations with variable coefficients, the theory of parametric excitation has applications in many fields of science and engineering The chapter explores that in mechanics, besides the classical problems of strings, columns, and plates under axial or in-plane oscillatory loads, the parametric excitation problems of shells have attracted increasing attention in recent years Some of the interest is connected with the dynamic snap-through instability phenomenon Most of the studies on parametric excitation deal with linear systems While a linear analysis provides us with important information, it by itself is inadequate in many instances

Parametric excitation of light in the picosecond rang

Abstract: An experimental and theoretical investigation is made of energy conversion in the three-photon parametric interaction of ultrashort light packets Calculations are made both in the constant pump field approximation and for strong energy exchange between packets A parametric two-stage oscillator generating ultrashort light pulses is described: it has an energy conversion efficiency of 12%, a line width of the output radiation of 4–5 cm–1, and a high pulse repetition frequency (up to 25 Hz) A parametric small-signal gain of 109–1010 can be achieved The competition between stimulated Raman scattering (STRS) and stimulated parametric scattering, observed in a number of nonlinear crystals (α-HIO3, KDP, LiIO3), is discussed The characteristics of picosecond optical parametric oscillators (OPO's) using α-HIO3, KDP, LiIO3, and LiNbO3 crystals are given An automatic measuring system incorporating amplitude analyzers, a data terminal, and a computer has been developed to investigate the energy and temporal characteristics

Optical parametric oscillators (review)

Abstract: Fundamentals of the theory of the optical parametric oscillators (OPO's) are reviewed and formulas are presented for the calculation of the main OPO parameters (Secs. 1–6). Experimental results obtained in the development and investigation of various types of OPO and their applications are discussed (Sec. 7). Methods for extending the tuning ranges of OPO's (Sec. 8) and the possibility of realization of four-photon oscillators (Sec. 9) are considered. The review concludes with a comparison of various types of tunable laser (Sec. 10).

Reference signals for closed-loop identification

Abstract: The peculiar identification problems which arise in the study of feedback systems often require the use of an external reference signal. This paper discusses the properties of non-parametric and parametric closed-loop identification schemes which rely upon such a signal. For the non-parametric case the statistical properties of an unbiased frequency-response estimator are developed and compared with the conventional estimator. The use of reference signals in parametric estimation is discussed in a way which enables the correct structure of a feedback system to be unambiguously determined.

An empirical study of scanner system parameters

Abstract: The selection of the correct combination of parametric values (instantaneous field of view, number and location of spectral bands, signal-to-noise ratio, etc.) of a multispectral scanner is a complex problem due to the strong interrelationship these parameters have with one another. In this paper the results of an empirical study of this problem are presented. The study was done with the proposed scanner, known as the thematic mapper, in mind. Since an adequate theoretical procedure for this problem has apparently not yet been devised, an empirical simulation approach was used with candidate parameter values selected by heuristic means. The results obtained using a conventional maximum likelihood pixel classifier suggest that although the classification accuracy declines slightly as the instantaneous field of view (IFOV) is decreased this is more than made up by an improved mensuration accuracy. Further, the use of a classifier involving both spatial and spectral features shows a very substantial tendency to resist degradation as the signal-to-noise ratio is decreased. Finally, further evidence is provided of the importance of having at least one spectral band in each of the major available portions of the optical spectrum.

An evaluation of some non-parametric and parametric tests for location equality

Abstract: The Kruskal-Wallis and normal scores non-parametric tests of location equality are compared to the parametric analysis of variance F test. In addition to quantifying and manipulating degrees of variance heterogeneity due to combining heterogeneous variances with unequal sample sizes, the tests are compared for their sensitivity, as well as rates of Type I error, under varying conditions of mean variability when sampling from Gaussian and exponential distributions. Even though the asymptotic literature (Pratt, 1964; Puri, 1964) favours the normal scores test, it is found that the Kruskal-Wallis test is preferable to the normal scores test while the choice between the Kruskal-Wallis and analysis of variance tests depends upon population shape.

Parametric solution of the stable exact model matching problem

Abstract: The set of all stable solutions to the exact model matching problem is presented in parametric form. The result is obtained simply by means of a Smith-McMillan form constructed over the principal ideal domain of stable, proper, rational transfer functions.

Estimability and Linear Hypotheses

Abstract: A proposition is given which provides an easily justified reason as to why attention should be confined to estimable parametric vectors when formulating linear hypotheses. The possibility of justifying one's linear estimation effort on the estimable parametric functions via an identifiability condition is also mentioned.