Showing papers on "Parametric statistics published in 1968"
TL;DR: In this article, a theoretical study on the optimization of second harmonic generation (SHG) and parametric generation (PG) by a laser beam in a uniaxial nonlinear crystal is presented.
Abstract: A theoretical study is presented on the optimization of second harmonic generation (SHG) and parametric generation (PG) by a laser beam in a uniaxial nonlinear crystal. Numerically computed curves show the dependence of the SHG power, and the reciprocal of the PG threshold power, on the parameter l/b, where l is the optical path length in the crystal and b is the confocal parameter (determined by the focal length of the focusing lens and the minimum radius of the laser beam, assumed to be in the TEM00 mode of an optical resonator). The calculations take full account of diffraction and double refraction. In the absence of double refraction, the optimum focusing condition is found to be l/b=2.84. For PG the optimization of the crystal length l is also discussed, and curves are given showing the dependence of the threshold on l for the case in which signal and idler have the same losses. It is shown that the computed functions are also relevant to the mixing of two Gaussian beams and to parametric amplificat...
1,700 citations
TL;DR: This paper presents a theoretical analysis of the performance of an orthogonal multiplexing data transmission scheme (parallel transmission scheme) subject to a number of degrading factors normally encountered by a practical operating system.
Abstract: This paper presents a theoretical analysis of the performance of an orthogonal multiplexing data transmission scheme (parallel transmission scheme) subject to a number of degrading factors normally encountered by a practical operating system. The factors considered jointly are sampling time error, carrier phase offset, and nonideal phase characteristics of transmitting and receiving filters. Performance is measured by the familiar criterion of eye opening of the received data signal. A closed-form expression for the eye opening is obtained. It is shown that the lengthy nonlinear functions in the solution can be closely approximated by simple piecewise linear functions for parameter values of interest. The optimum settings of the sampling time and the carrier phase are determined for given filter phase distortion. Also, considering all factors, simple formulas are developed for computing interchannel interferences, intersymbol interference, and the resulting eye opening. Simple relationships between the eye opening and filter phase distortion are explored, and a concept of parametric eye is introduced to aid in filter design. An illustrative example is considered which shows that the impairment of the system performance is not excessive for a reasonable range of system design parameters.
384 citations
TL;DR: In this article, it was shown that there are no countably additive exchangeable distributions on the space of observations which give ties probability 0 and for which a next observation is conditionally equally likely to fall in any of the open intervals between successive order statistics of a given sample.
Abstract: A Bayesian approach to inference about the percentiles and other characteristics of a finite population is proposed. The approach does not depend upon, though it need not exclude, the use of parametric models.Some related questions concerning the existence of exchangeable distributions are considered. It is shown that there are no countably additive exchangeable distributions on the space of observations which give ties probability 0 and for which a next observation is conditionally equally likely to fall in any of the open intervals between successive order statistics of a given sample.
248 citations
TL;DR: It has been shown that deficiencies in starting designs or initial network geometries may be corrected automatically by the computerized procedure, and that the effects of changes in network mode of operation or boundary conditions, or both, can easily be studied.
Abstract: The design of optimal hydraulic networks is formulated as a mathematical optimization problem. This formulation is of interest as a possible substitute for the current practice of parametric studies, as such studies are lengthy and not guaranteed to yield an optimum solution. The applicability of optimization techniques and the economical feasibility of the whole process have been investigated, and are illustrated with a sample problem. It is also shown that deficiencies in starting designs or initial network geometries may be corrected automatically by the computerized procedure, and that the effects of changes in network mode of operation or boundary conditions, or both, can easily be studied. Results may be applicable to larger hydraulic-network design problems, because the form of the mathematical expressions remains the same.
65 citations
TL;DR: In this article, the authors used Hsu and Bolotin's method to construct stability boundaries for two cases of parametric excitation: the first problem considers periodic, axial, tension variation of axially moving materials such as band saws, belts, tapes, strings and chains; the second case investigates instability caused by periodic, in-plane, edge loading in axial moving materials.
Abstract: This paper determines approximate stability-instability region boundaries for two cases of parametric excitation. The first problem considers periodic, axial, tension variation of slender, axially moving materials such as band saws, belts, tapes, strings and chains; the second case investigates instability caused by periodic, in-plane, edge loading in axially moving materials. The governing equation of motion is reduced by means of a coordinate function expansion and Galerkin's method to a set of coupled Mathieu equations. The methods of Hsu and Bolotin are used to construct stability boundaries for the two cases. Results are compared with analog computer stability boundaries for a moving string; the string was spatially discretized by replacing spatial derivatives by equivalent difference expressions. Boundaries predicted by the two methods are close for moderate material axial velocities but separate as the axial velocity increases.
60 citations
TL;DR: This paper deals with the statistical analysis (both parametric and non-parametric) of 'mixed model' experiments and illustrated in detail in two numerical examples the relative performances of the different test criteria for a situation in which the null hypothesis is essentially true.
Abstract: This paper deals with the statistical analysis (both parametric and non-parametric) of 'mixed model' experiments. The general structure of such experiments involves n randomly chosen subjects who respond once to each of p distinct treatments. Thus the subject or block effects are random and treatment effects are fixed. The hypothesis of no treatment effects is considered under several different combinations of assumptions concerning the joint distribution of the observations corresponding to each of the particular subjects. For each situation, an appropriate test procedure is discussed and its properties studied. The different methods considered in the paper are illustrated in detail in two numerical examples. These examples have been chosen to illustrate the relative performances of the different test criteria for a situation in which the null hypothesis is essentially true (Example 1) and for a situation in which the null hypothesis is essentially false (Example 2). The reader may wish to begin by studying these examples for a better understanding of the theory. Finally, the section on examples contains algorithms for the efficient computation of the various test criteria. A computer program based on these algorithms has been written and can be made available to any interested persons.
47 citations
46 citations
TL;DR: The problem of finding shortest distances (and paths) is a component part of many network problems, though it is also of independent interest as discussed by the authors, and the computational process includes as a very essential element the discovery of all the shortest distances for the new values of the parameters.
Abstract: THE problem of finding shortest distances (and paths) is a component part of many network problems, though it is also of independent interest Solving such problems, for example, by the method of successive calculations [21, involves the repeated calculation of the extreme value of a target function by the variation of one or several parameters (for example, the length of arc). Therefore, the computational process includes as a very essential element the discovery of all the shortest distances for the new values of the parameters.
39 citations
TL;DR: In this paper, a review of the latest works at the University of Moscow in the field of pulsed parametric oscillators and the new application of parametric light interaction-nonlinear spectrograph is presented.
Abstract: The paper presents the review of the latest works at the University of Moscow in the field of pulsed parametric oscillators and the new application of parametric light interaction-nonlinear spectrograph. This spectrograph is based on the steep frequency dependence of phase-matched angles for nonlinear mixing processes. Two new types of oscillators are considered: one having a cavity without dielectric coatings, the other a travelling-wave oscillator that is really an amplifier of parametric superluminescence. The latter has a narrow spectrum of radiation (1-2 A). The most possible applications of oscillators and their necessary characteristics are given.
28 citations
TL;DR: In this paper, a theoretical study on the optimization of second harmonic generation (SHG) and parametric generation (PG) by a laser beam in a uniaxial nonlinear crystal is presented.
Abstract: A theoretical study is presented on the optimization of second harmonic generation (SHG) and parametric generation (PG) by a laser beam in a uniaxial nonlinear crystal. Numerically computed curves show the dependence of the SHG power, and the reciprocal of the PG threshold power, on the parameter l/b, where l is the optical path length in the crystal and b is the confocal parameter (determined by the focal length of the focusing lens and the minimum radius of the laser beam, assumed to be in the TEM00 mode of an optical resonator). The calculations take full account of diffraction and double refraction. In the absence of double refraction, the optimum focusing condition is found to be l/b=2.84. For PG the optimization of the crystal length l is also discussed, and curves are given showing the dependence of the threshold on l for the case in which signal and idler have the same losses. It is shown that the computed functions are also relevant to the mixing of two Gaussian beams and to parametric amplificat...
28 citations
TL;DR: In this paper, the importance of noncollinear phase matching for noncollincale phase matching is demonstrated. But the absolute magnitude of the emitted noise has also been measured and is found to be in excellent agreement with theory.
Abstract: Measurements of optically excited parametric noise which demonstrate the importance of noncollinear phase matching are presented. The absolute magnitude of the emitted noise has also been measured and is found to be in excellent agreement with theory.
TL;DR: The main contributions of this paper are the extension of previous investigations of the unsupervised parametric pattern recognition problem to include cases where both constant and time-varying unknown parameter vectors are simultaneously present and the removal of the assumption of statistical independence between hypotheses for the sequence of observations.
Abstract: A Bayesian decision theory approach is applied to the solution of the problem of unsupervised parametric pattern recognition. The parametric model for this investigation includes the cases where both constant and time-varying unknown parameters are present, and, most significantly, the unknown hypotheses do not constitute a statistically independent sequence. They are restricted only to be from a source with finite-order Markov dependence. The resulting optimal learning system is found and shown to grow initially in size and memory until the N th observation (where N is the highest Markov order), and subsequently to remain of fixed size and memory. It can, therefore, operate indefinitely and continue to improve its ability to recognize patterns utilizing only a fixed size memory. In summary, the main contributions of this paper are the following: \begin{enumerate} \item the extension of previous investigations of the unsupervised parametric pattern recognition problem to include cases where both constant and time-varying unknown parameter vectors are simultaneously present; \item that the a priori probabilities of the hypotheses, the time-varying parameters, and their transition laws may, if constant, be expressed as functions of the constant unknown parameter and, thus, also be learned; and \item the removal of the assumption of statistical independence between hypotheses for the sequence of observations. \end{enumerate}
TL;DR: In this article, the authors considered the problem of testing the value of one parameter when the values of other parameters (nuisance parameters) are not specified, and established some results for testing hypotheses when the probability density of the observations does not constitute an exponential family under both the hypothesis and the alternative.
Abstract: We shall be concerned with the parametric problem of testing hypotheses concerning the value of one parameter when the values of other parameters (nuisance parameters) are not specified. Neyman [6] derived under certain conditions a locally most powerful two-sided test for this problem, i.e., he gave the form of the test maximizing the second derivative of the power function with respect to the parameter of interest at the point specified by the hypothesis. Generalizations of Neyman's results were given by Scheffe [7] and Lehmann [2], using the same technique as Neyman. They were also able to prove that the tests were UMP unbiased. A new technique for dealing with these problems was introduced by Sverdrup [9] and Lehmann and Scheffe [4] where the completeness of the sufficient statistics in an exponential family of densities is used to derive UMP unbiased tests. It is stated by Lehmann and Scheffe [4] that the conditions imposed earlier imply an exponential family of densities. When no UMP unbiased test exists we have little general theory. The problem is both one of principle and of technique. Most stringest tests exist under general conditions but are difficult to derive in particular cases. Lehmann [3] proposed maximin tests. Spjotvoll [8] has given an example of the form of a maximin test when no UMP unbiased and invariant test exists. This paper is an attempt to establish some results for testing hypotheses when the probability density of the observations does not constitute an exponential family under both the hypothesis and the alternative. The assumptions made in Section 2 are satisfied if we have an exponential family under the hypothesis, but do not say anything about the form of the density under the alternative. The results concern most powerful similar or unbiased tests, and under certain conditions the form of these tests for the particular family of densities studied, is given in Section 3. In Section 4 the theory in Section 3 is applied to the problem of testing serial correlation (not circular) in a first order autoregressive sequence. It is found that the usual tests are nearly UMP invariant. In Section 5 the problem of testing the value of the ratio of variances in the one-way classification variance components model is considered. Some numerical results are given for the power functions of the maximin test, the locally most powerful test and the standard $F$-test. The results indicate that the standard $F$-test performs well compared with the other tests.
TL;DR: In this paper, the effect of fast and slow parametric excitations on non-linear dynamical systems was studied and the results have asymptotic validity based on some recent mathematical results of Sethna.
Abstract: General non-linear dynamical systems with parametric excitations are studied. The study includes a detailed analysis of the effect of “fast” parametric excitations and also the effect of the simultaneous occurrence of “fast” and “slow” parametric excitation. The parametric excitations when they are “fast” and have frequency values close to each other are also studied and this gives results similar to the experimental results of Bogdanoff and Citron. The results have asymptotic validity based on some recent mathematical results of Sethna.
TL;DR: It is shown in this paper how the known function may be used to construct new systems, based on the original one, which are also asymptotically stable, and how the parametric perturbation and the synthesis procedures are generalised to include autonomous and non-autonomous non-linear systems.
TL;DR: In this paper, a canonical formalism with a new Hamiltonian function developed especially for application to the theory of geodesic fields of CARATHI~ODORY [2] was presented.
Abstract: As is well known there remain many unsolved problems in the CaIculus of Variations of multiple integrals; in particular, the theory for integrals in parametric form has not received much attention. This paper presents a canonical formalism with a new Hamiltonian function developed especially for application to the theory of geodesic fields of CARATHI~ODORY [2], or more precisely, to the form assumed by this theory for parametric integrals. As is pointed out by RUND [5], the canonical formalism given by CARATn~ODORY is not applicable to this case. Part one of the paper contains some brief immediate consequences of the parameter-invariance of the fundamental integral, and the definition and properties of the canonical variables and Hamiltonian function; these latter quantities being introduced by means of a certain contact transformation. In part two, some special features of geodesic fields of parametric integrals are pointed out, and an explicit characterization of geodesic fields by means of a generalized Hamilton-Jacobi equation is established. Finally a theorem concerning the integrability conditions of the field is proved, which restores an initial lack of determinism of the slope functions of a field.
TL;DR: Results of the simulation indicate quantitatively the superiority of the estimators over conventional decision-directed techniques, in terms of convergence rates and asymptotic performance characteristics.
Abstract: The problem of making measurements upon some available signal mixture in order to extract or estimate certain parametric data for subsequent signal detection using the measurement data is considered. The development is carried out for a formal binary signal observation mixture (no a priori classification of the observations into isolated category or class ensembles is assumed), with the parameters of the noise and pulse waveforms unknown. Two categories of multidimensional mixture-resolving estimators are treated: an optimized decision-directed category and a moment method category. In the former, the optimization is formulated to minimize a measure of distance and dispersion with a constraint adjustment to "maximize" a measure of convergence rate. An eigenvalue theory approach is applied to illustrate the relationship of the measurement data to the detector structure. An experimental case study is carried out via digital computer simulation, and a comparison of error probability performance characteristics with the conventional decision-directed and Bayes matched-filter techniques is made. Results of the simulation are presented which indicate quantitatively the superiority of the estimators over conventional decision-directed techniques, in terms of convergence rates and asymptotic performance characteristics.
TL;DR: In this article, a parametric probability model for order data on a set of objects is developed, which is appropriate for analysis of data with tree structure; the results of knockout tournaments are an example of such data.
Abstract: A parametric probability model for order data on a set of objects is developed, which is appropriate for analysis of data with tree structure; the results of knockout tournaments are an example of such data. The parameters of the model are the probabilities that the various objects will be ranked highest. An exact Bayes analysis is possible if the prior distribution of the parameters is Dirichlet. The 1965 Wimbledon tennis tournament is used as an example.
TL;DR: A distribution-free procedure applicable to the detection of a signal in some element of a multiple-resolution-element radar that is applicable to either a sequential or fixed-sample-size test; however, emphasis is placed on the sequential procedure.
Abstract: A distribution-free procedure applicable to the detection of a signal in some element of a multiple-resolution-element radar is described. The procedure is based on rank-order statistics and is applicable to either a sequential or fixed-sample-size test; however, emphasis is placed on the sequential procedure. Results are given showing the expected sample size and probability of detection for the case of envelope detection (square-law or linear) of a fluctuating signal (Swerling model 2). A comparison is made with the optimum parametric sequential procedure.
TL;DR: In this article, the transient growth of spin-wave populations with three-magnon nonlinear processes under perpendicular pumping was studied, assuming that the magnons are in thermal distribution before the electromagnetic pulse is applied.
Abstract: The transient growth of spin-wave populations with three-magnon non-linear processes under perpendicular pumping is studied. Calculations are made on the basis of second quantization of the magnetic system and the pumping microwave field, assuming that the magnons are in thermal distribution before the electromagnetic pulse is applied. General expressions describing transient evolution of the uniform mode and the parametric states are established in the case where the coincidence condition is satisfied (occurrence of the three-magnon transitions at resonance). The stationary state of the parametric magnons is also determined. To test experimentally the validity of the theory an expression for the transient power absorbed by the crystal at the beginning of the parametric excitation of the quasiparticles is derived. Basing on experimental data, the limits of the applicability of the theory are discussed.
TL;DR: Symmetrical formulation of quantum theory of three wave optical parametric interactions in crystals is presented in this paper, where the authors propose a solution to the problem of three-wave parametric interaction in crystals.
Abstract: Symmetrical formulation of quantum theory of three wave optical parametric interactions in crystals
01 Oct 1968
TL;DR: In this article, Earth resources satellite systems R and D planning, using case study approach in economic benefit analysis for parametric requirements determination, was performed using case-study approach for satellite system R&D planning.
Abstract: Earth resources satellite systems R and D planning, using case study approach in economic benefit analysis for parametric requirements determination
TL;DR: In this article, a structural distance between a scalar process and its model is introduced, and it is shown that it can be used to advantage for identification, although this distance is not known.
Abstract: A structural distance between a scalar process and its model is introduced, and it is shown that it can be used to advantage for identification. Although this distance is not known, it can be minimised by a particular algorithm. Examples of application and an appraisal of this method are given.
Proceedings Article•
01 Jan 1968TL;DR: Singular lines in parametric plane, discussing existence, equations and self adaptive designs as discussed by the authors, discussing self-adaptive designs in the context of parametric planes and singular lines.
Abstract: Singular lines in parametric plane, discussing existence, equations and self adaptive designs
01 Jan 1968
TL;DR: Much of the literature in numerical integration discusses the accuracy of an integration formula in terms of (a) the highest degree polynomial it can integrate exactly and (b) the coefficients of the lower order differences in the error term.
Abstract: Much of the literature in numerical integration discusses the accuracy of an integration formula in terms of (a) the highest degree polynomial it can integrate exactly and (b) the coefficients of the lower order differences in the error term. This information is of little value when the function to be integrated has nonpolynomial-like characteristics, such as an infinite value of ordinate or slope. Generally, methods which deal with such functions (e.g., see Fox1) demand a considerable degree of mathematical expertise to extract the needed expansions from the function's original form. Such methods are not well suited to automatic computation except when restricted to a very narrow class of functions.