Showing papers by "RAND Corporation published in 1968"

Robustness of the F-Test to Errors of Both Kinds and the Correlation Between the Numerator and Denominator of the F-Ratio

Abstract: In this study of robustness the insensitivity of the F-test between means to its underlying assumptions (normally distributed populations with equal variances) is investigated. Using two nonnormal distributions (exponential and lognormal), it is found that the test is fairly insensitive for moderate and equal sample size (n = 32) when the variances are equal. Further, for small samples (n < 32), the test is conservative with respect to Type I error. It is also conservative with respect to Type II error for a large range of φ (noncentrality), depending on the size of the sample and α. When the within cell error variances are heterogenous, the test continues to be conservative for the upper values of φ and slightly biased toward larger Type II errors for smaller values of φ depending on the size of α. Analysis of the correlation between the numerator and denominator of F under the null hypothesis indicates that the robustness feature is largely due to this correlation. Analytic proofs under the non-null hyp...

Input-output relations in computer-simulated nerve cells. Influence of the statistical properties, strength, number and inter-dependence of excitatory pre-synaptic terminals.

Abstract: This communication examines, in digital computer simulated networks, the input-output relation established at synaptic level. It is restricted to excitatory junctions and analyzes the changes in post-synaptic discharge which occur when the number of pre-synaptic terminals increases while the EPSP size decreases, when the statistical structure or “form” (as measured by the interspike interval mean, standard deviation, histogram and by the autocorrelogram) of the spike train in each pre-synaptic fiber changes, and/or when the interdependence between pre-synaptic fibers varies from complete independence to strong dependence. 1Independent Pre-synaptic Terminals. When the number of pre-synaptic terminals increases and the EPSP size decreases proportionally (while the input form remains constant), the post-synaptic interspike interval mean increases slightly, the standard deviation decreases markedly, the histogram becomes sharp and narrow and the autocorrelogram becomes periodic. When, on the other hand, the pre-synaptic form varies (while the number of terminals and the EPSP size remain constant), the effect upon the post-synaptio output depends upon the given number of terminals and EPSP size. If terminals are few and EPSP's large, the output varies with the pre-synaptic form. The post-synaptic coefficient of variation is linearly related to the pre-synaptic coefficient of variation, the slope decreasing as the number of inputs increases. If terminals are numerous and weak, the pre-synaptic form ceases to be influential and the post-synaptic cell generates the same output regardless of the detailed structure of the corresponding input. The output common to any combination of independent weak input forms is a very regular train of evenly spaced spikes. (This conclusion is valid unless pre-synaptic terminals fire at extremely low rates.) Such results are mathematically predictable in a simple and realistic model of membrane potential and threshold dynamics (see Appendix). As the EPSP size increases, all other variables being equal, the post-synaptic interval mean decreases monotonically. The decrease is smooth or in steps depending on whether the pre-synaptic form is Poisson or pacemaker, respectively. Post-synaptic spikes are effectively blocked by relatively small numbers of inhibitory terminals. 2Dependent Pre-synaptic Terminals. When there is a physiological amount of interdependence between the presynaptic terminals that impinge upon the post-synaptic cell, the activity of the latter is a function of the statistical form of the input channels, even when the latter are numerous and weak. This happens when interdependence involves only a proportion of all terminals or only the terminals within separate and independent groups. In order to understand the transactions that take place in the nervous system, it is necessary to identify the presynaptic statistics that influence the corresponding post-synaptic discharge. When pre-synaptic terminals produce large PSP's their influence is dominant and exerted by way of the precise statistical form of the discharge. When terminals produce small PSP's their influence is contingent on their degree of interdependence. If they are uncorrelated, they act exclusively by way of their mean rates and provide a smooth adjustment of the post-synaptic membrane potential and firing rate. If terminals are correlated, they act by way of several statistical features and assume a dominant role that determines a precise relation between pre-synaptic timing and post-synaptic firing. The degree of inter-terminal correlation is thus a functionally significant variable.

Optimum Maintenance with Incomplete Information

Abstract: The maintenance of a system characterized by a discrete-parameter, non-stationary, finite-state Markov process is considered. Prior to each transition the decision maker selects one of a finite number of available actions replacements, repairs, inspections, etc. on the basis of a time sequence of noisy state measurements. The action selected and the system's age determine the subsequent one-step transition probabilities and the conditional on the system states distributions of the next measurement. Costs dependent on the action selected, the system's state, and age are assigned to each possible transition. It is shown that the action that minimizes the discounted value of expected immediate and future costs assuming optimum future actions is determined by the system's age and the posterior distribution over the states. With this result a dynamic-programming method is presented for the calculation of optimum maintenance policies.

Distortion and crosstalk of linearly filtered, angle-modulated signals

Abstract: An important problem in the theory and practice of receiving angle-modulated signals is the design of the filtering elements which must be employed. It has long been known that filtering introduces distortion and crosstalk into the signal. However, the computation of these effects is difficult. The methods customarily used employ approximations of one kind or another, and the equations used do not apply to all cases of practical interest. Here formulas are presented which enlarge somewhat the domain of cases amenable to calculation. In this analysis, an angle-modulated signal having an arbitrary phase function is applied to a general linear filter, and the phase of the output is expanded in a series having the linearly filtered input as the leading term. The expansion is then specialized to the case of a narrowband signal applied to a narrow, symmetrical, bandpass filter. A spectral analysis is performed by assuming a Gaussian input phase and examining terms through fifth order in the output phase expansion. This leads to the main results of the paper, namely expressions for the leading terms in the output spectrum. It is argued that these terms represent the principal contribution in the case where the distortion is small. To demonstrate their application to a practical problem, the formulas are used to calculate the distortion and crosstalk produced when an FM signal, having a flat baseband spectrum, is passed through a single-pole filter. This example is of some current interest because such a filter has been employed in the forward path of a feedback FM receiver used for satellite communication. A number of cases are considered, and the results of the computations are plotted.

Recombination, radiative energy loss, and level populations in nonequilibrium cesium discharges.

Abstract: The transition rate equations for the populations of cesium states in a homogenous, optically thin plasma have been solved for the excited-state populations, the effective ground-state ionization and recombination coefficients, and the effective electron kinetic-energy and radiative loss coefficients. A table of values is presented for the nonequilibrium steady-state plasma which is analogous to the Saha equation for the equilibrium plasma. Free electron densities from 1012 to 1015 cm-3 are considered, and a Maxwellian electron velocity distribution at temperatures from 1500 to 3000°K is assumed. These conditions are typical of those in thermionic and magnetohydrodynamic energy converters and other cesium discharges. The rate coefficients used for collision-induced and radiative atomic transitions are described. Molecular processes, diffusion, wall losses, etc., are discussed but not included explicitly in the model. The absorption of resonance radiation is simulated by reduction of the spontaneous emission coefficients. Other radiative absorption processes are neglected. The populations are seen to depart significantly from the Boltzmann distribution in steady state, and it is seen that many excited states participate in the ionization and recombination processes. The implications of these results for spectroscopic diagnostics, volume ion production, and energy loss in a cesium-discharge plasma are discussed.

Performance of Sidelobe Blanking Systems

Abstract: Sidelobe blanking systems are useful in preventing acquisition of strong targets in the antenna sidelobes and also in rejecting pulsed interference originating in the sidelobes. The analysis of a common two-channel system is presented in which the relationship between the probability of main-lobe detection and the probability of sidelobe detection are given in terms of false-alarm probability, signal-to-noise ratio, and the ratio of sidelobe levels of the two channels. The numerical results given provide a basis for the selection of the sidelobe blanking channel antenna gain and threshold levels.

Axiomatic Thermodynamics and Extensive Measurement.

Abstract: : The paper applies set theory to various phases of thermodynamics and measurement systems.

Microwave Oscillator Noise Reduction by a Transmission Stabilizing Cavity

Abstract: The theory of cavity stabilization of a microwave oscillator is reviewed and the appropriate design equations presented. The theory is verified with data taken on three different types of microwave oscillators: 1) a 10-GHz reflex klystron (stabilization factor achieved-22; FM noise reduction-28 dB; typical FM noise level-0.008 Hz in a 1-Hz bandwidth); 2) a 9.7-GHz low-noise two-cavity klystron oscillator (stabilization factor achieved-10; FM noise reduction--21.7 dB; typical FM noise level-0.0007 Hz in a 1-Hz bandwidth); 3) a 10-GHZ avalanche transit time diode oscillator (stabilization factor estimated at 30; FM noise reduction-29.5 dB; typical FM noise level--0.5 Hz in a 1-Hz bandwidth). Stabilization of the avalanche transit time diode oscillator produced a significant reduction in AM noise for modulation frequencies larger than the bandwidth of the stabilizing cavity.

Three-dimensional light beam scanner utilizing tandemly arranged diffraction gratings

Abstract: A light beam scanning apparatus including a rotatable disc having a plurality of focusing elements disposed in an annular or spiral pattern such that an impinging light beam is intercepted in succession by each of the focusing elements and deflected along a plurality of adjacent lines thereby providing, in accordance with the characteristics of the focusing elements, either a two-dimensional scan pattern oriented respectively transverse or parallel to the direction of the focused light or alternatively a three-dimensional scan pattern encompassing the areas of the orthogonal two-dimensional patterns.

Some patterns in the history of violence

Abstract: : The paper is aimed at describing systematic trends in the violence between political groups. The report is in two parts. Part one describes the formulation of an empirical test for the existence of (1) a short (15-30 year) term and (2) a long (80-120 year) term periodic fluctuation in the historical occurrence of war. The research described in part one is based, largely, on empirical (versus theoretical) generalizations. That is, not much concern is given to the 'why' of such patterns. The second part of the paper speculates about several possible reasons for these patterns. (Author)

A balanced optical heterodyne detector.

Abstract: In recent months optical heterodyning techniques have received considerable attention in communication and signal processing applications. Some of the proposed heterodyning techniques have employed balanced detection in order to reduce the effects of local oscillator noise on the detected signal output. We de­ scribe here a scheme of balanced detection in which the polariza­ tions of oscillator and signal waves are perpendicular. For this choice of polarizations, a suitable prism can be used to select the proper sum and difference terms of the impinging light before photodetection. The relative contribution of the local oscillator and signal to each detector can easily be controlled by a simple rotation of the prism. Because of its inherent freedom from alignment and vibration problems, and because of the sim­ plicity with which the output can be balanced, this scheme may find general usefulness in many optical systems, including optical signal processors. We analyze the performance of the balanced detector follow­ ing the schematic in Fig. 1. The signal S(t) is a plane wave, polarized with E field approximately out of the page (along z), which impinges on the face of a Wollaston prism along path OA. A local oscillator signal R(t) polarized nearly perpendicular to the signal, i.e., along ŷ, also propagates along path OA.

Scientific Applications: An algorithm for identifying the ergodic subchains and transient states of a stochastic matrix

Abstract: An algorithm for identifying the ergodic subchains and transient states of a stochastic matrix is presented. Applications in Markov renewal programming and in the construction of variable length codes are reviewed, and an updating procedure for dealing with certain sequences of stochastic matrices is discussed. Computation times are investigated experimentally and compared with those of another recently proposed method.

Data structures and techniques for remote computer graphics

Abstract: It has been adequately demonstrated that computer graphics systems need not require the dedication of a large scale computer for their operation. Computer graphics has followed the trends of computing in general, where remote access, time sharing, and multiprogramming have become the key phrases. The problems involved in providing a remotely accessed, interactive computer graphics system are more formidable than for a dedicated system, or even than for a local time shared system. The requirement is basically to obtain a real time response for the display console operator, while at the same time minimizing the overhead imposed on the central computer facilities. Also present, of course, are the classic graphical problems such as that of providing refresh data for cathode ray tube displays, and of relating the appearances of a picture on the tube face to its description in the data structure.

Statistical Estimation Procedures for the "Burn-In" Process*

Abstract: Thii study deals with the “burn-in” process. In this process, items whose failure rate is assumed to decrease with time are put on test (burnt-in) until a fixed amount of time has elapsed (truncated sampling) or until a fixed number of failures have occurred (censored sampling). The purpose is to identify and eliminate poor-quality or defective items. For both of the modes of observation described, we provide a conservative upper confidence bound for the failure rate at the time the burn-in process ends, and the maximum likelihood estimate (MLE) of the failure-rate function. These results are valid under quite general conditions. In particular, we do not require that the form of the life distribution be known. The MLE is obtained under the sole assumption that the failure-rate function is decreasing. The confidence bound is obtained under the even weaker assumption that the failure rate at the time observation ends is no larger than the failure rate throughout the period of observation. For the truncated ...

The Effect of Strain on the Susceptibility of Polycrystalline Ni–Fe Films

Abstract: Various ripple effects in uniaxial polycrystalline magnetic films have been related by several authors to an effective single‐grain crystalline anisotropy constant K. If either an isotropic planar stress σ or a uniaxial strain e33 is applied to such a film, the ripple properties are altered. We develop a simple model which includes the effects of such stresses and strains. We thereby evaluate K as an effective crystalline anisotropy given by K=[(K1+Bse33+¼Bσσ)2+(7/16)(Bσσ)2],1/2 where K1 is the fourth order magneto‐crystalline anisotropy constant, and B8 and Bσ are appropriate magnetoelastic coupling constants. A convenient ripple parameter is (HP‐HK), where HK is the uniaxial anisotropy field of the film and HP is the field in the hard direction at which the in‐phase component of the transverse differential susceptibility is a maximum. Measurements of (HP‐HK) vs e33 taken on electroplated cylindrical Ni–Fe films varying in thickness from 3000 A to a 10,000 A are presented. While the results are qualitati...

Discrete compound poisson processes and tables of the geometric poisson distribution.

Abstract: This paper discusses the properties of positive, integer valued compound Poisson processes and compares two members of the family: the geometric Poisson (stuttering Poisson) and the logarithmic Poisson. It is shown that the geometric Poisson process is particularly convenient when the analyst is interested in a simple model for the time between events, as in simulation. On the other hand, the logarithmic Poisson process is more convenient in analytic models in which the state probabilities (probabilities for the number of events in a specified time period) are required. These state probabilities have a negative binomial distribution. The state probabilities of the geometric Poisson process, known as the geometric Poisson distribution, are tabled for 160 sets of parameter values. The values of mean demand range from 0.10 to 10; those for variance to mean ratio from 1.5 to 7. It is observed that the geometric Poisson density is bimodal.

Derivation and Validation of an Initial-Value Method for Certain Nonlinear Two-Point Boundary-Value Problems.

Abstract: Much of the theory of invariant imbedding is devoted to transforming two-point boundary-value problems into Cauchy problems. Numerous references are given. In this paper, a proof is given that the solution of the Cauchy problem does indeed satisfy the boundary-value problem. The discussion is self-contained and general enough to cover many applications in optimal control and radiative transfer.

Three-dimensional nonlinear stability analysis of the sun-perturbed earth-moon equilateral points.

Abstract: Nonlinear analysis of earth-moon system motion stability in three dimensions near L4 libration point when perturbed by sun

Optimum Processing of Unequally Spaced Radar Pulse Trains for Clutter Rejection

Abstract: A train of radar pulses from one resolution cell can be processed coherently to reject echoes from external clutter and detect targets moving radially with respect to the clutter. Optimum methods of signal processing are defined for systems in which the interpulse spacings are multiply staggered to avoid target blind speeds. Likelihood ratio tests are developed for systems in which the target Doppler frequency is known a priori and for systems employing a bank of filters to cover the target Doppler band. To implement such tests, the N pulses in the train are added with complex weights and the amplitude of the sum compared with a detection threshold. The set of weights which maximizes the average signal-to-clutter ratio is also computed for a single-filter system with unknown target Doppler frequency. When the clutter autocorrelation function is exponential, the clutter covariance matrix can be inverted analytically. This latter result is useful for comparing different interpulse-spacing codes for a particular system application.