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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1987

Statistical tests for closure of plate motion circuits

Two methods, one based on a chi-square test and the second on an F-ratio test, of testing for the plate motion circuit closures are described and evaluated. The chi-square test is used to evaluate goodness of fit, and it is assumed that the assigned errors are accurate estimates of the true errors in the data. The F-ratio test is used to compare variances of distributions, and it is assumed that the relative values of assigned error are accurate. The two methods are applied to the data of Minster and Jordan (1978) on the motion of the three plates that meet at the Galapagos Triple Junction, and the motion of the three plates that meet at the Indian Ocean Triple Junction. It is noted that the F-ratio plate circuit closure test is more useful than the chi-square test for identifying systematic misfits in data because the chi-square test overestimates the errors of plate motion data.

Gordon, Richard G.↗
NASA NTRS1975

The effects of correlation on goodness of fit

Autocorrelated normal random variates were generated via computer and the effects of various levels of correlation on goodness of fit problems were studied. The results are useful in determining the distribution or estimating the parameters of populations that correlate observations such as wind speeds and temperature. The model used to generate the autocorrelated data is an autoregressive process of order 1. The Kolmogorov-Smirnov and chi-square statistics are used in the analysis. It was observed in the simulation that high positive correlations tend to shift the sample mean away from the population mean and negative correlations tend to shift the sample mean towards the population mean. In many cases, it was observed that positive and negative correlations tend to decrease the standard deviation. However, since this did not occur in all cases, no definite conclusion can be made regarding the standard deviation. Since the autoregressive process is a linear transformation, it is not surprising that normality was preserved. However, a possible extension of this problem could be to generate non-normal data and observe how the distribution is affected by correlation. Another extension might utilize another model such as autoregressive of order k or a moving average process of order k.

Kitchens, L. J.↗
NASA NTRS1987

Statistical analysis of secondary particle distributions in relativistic nucleus-nucleus collisions

The use is described of several statistical techniques to characterize structure in the angular distributions of secondary particles from nucleus-nucleus collisions in the energy range 24 to 61 GeV/nucleon. The objective of this work was to determine whether there are correlations between emitted particle intensity and angle that may be used to support the existence of the quark gluon plasma. The techniques include chi-square null hypothesis tests, the method of discrete Fourier transform analysis, and fluctuation analysis. We have also used the method of composite unit vectors to test for azimuthal asymmetry in a data set of 63 JACEE-3 events. Each method is presented in a manner that provides the reader with some practical detail regarding its application. Of those events with relatively high statistics, Fe approaches 0 at 55 GeV/nucleon was found to possess an azimuthal distribution with a highly non-random structure. No evidence of non-statistical fluctuations was found in the pseudo-rapidity distributions of the events studied. It is seen that the most effective application of these methods relies upon the availability of many events or single events that possess very high multiplicities.

Mcguire, Stephen C.↗
NASA NTRS1976

Multivariate normality

Sets of experimentally determined or routinely observed data provide information about the past, present and, hopefully, future sets of similarly produced data. An infinite set of statistical models exists which may be used to describe the data sets. The normal distribution is one model. If it serves at all, it serves well. If a data set, or a transformation of the set, representative of a larger population can be described by the normal distribution, then valid statistical inferences can be drawn. There are several tests which may be applied to a data set to determine whether the univariate normal model adequately describes the set. The chi-square test based on Pearson's work in the late nineteenth and early twentieth centuries is often used. Like all tests, it has some weaknesses which are discussed in elementary texts. Extension of the chi-square test to the multivariate normal model is provided. Tables and graphs permit easier application of the test in the higher dimensions. Several examples, using recorded data, illustrate the procedures. Tests of maximum absolute differences, mean sum of squares of residuals, runs and changes of sign are included in these tests. Dimensions one through five with selected sample sizes 11 to 101 are used to illustrate the statistical tests developed.

Crutcher, H. L.↗
NASA NTRS1973

Undergraduate research report

Studies are reported of the probability distribution of yield strength for mild steel, and the application of numerical techniques to solve mechanical vibration problems. Tensile experiments were conducted for 50 cold rolled and 38 hot rolled mild steel rods. Chi-square, Kolmogro-Smirnov and goodness-of-fit methods are used to test the normality or lognormality of the experimental results. As an example of the application of numerical techniques, a nonlinear dash-pot-speing system subjected to seismic excitation is analyzed by using the fourth-order Runge-Kutta integrated method.

Yeh, H. Y.↗
NASA NTRS1995

Gaussian statistics of the cosmic microwave background: Correlation of temperature extrema in the COBE DMR two-year sky maps

We use the two-point correlation function of the extrema points (peaks and valleys) in the Cosmic Background Explorer (COBE) Differential Microwave Radiometers (DMR) 2 year sky maps as a test for non-Gaussian temperature distribution in the cosmic microwave background anisotropy. A maximum-likelihood analysis compares the DMR data to n = 1 toy models whose random-phase spherical harmonic components a(sub lm) are drawn from either Gaussian, chi-square, or log-normal parent populations. The likelihood of the 53 GHz (A+B)/2 data is greatest for the exact Gaussian model. There is less than 10% chance that the non-Gaussian models tested describe the DMR data, limited primarily by type II errors in the statistical inference. The extrema correlation function is a stronger test for this class of non-Gaussian models than topological statistics such as the genus.

Kogut, A.↗
NASA NTRS2003

North Alabama Lightning Mapping Array (LMA): VHF Source Retrieval Algorithm and Error Analyses

Two approaches are used to characterize how accurately the North Alabama Lightning Mapping Array (LMA) is able to locate lightning VHF sources in space and in time. The first method uses a Monte Carlo computer simulation to estimate source retrieval errors. The simulation applies a VHF source retrieval algorithm that was recently developed at the NASA Marshall Space Flight Center (MSFC) and that is similar, but not identical to, the standard New Mexico Tech retrieval algorithm. The second method uses a purely theoretical technique (i.e., chi-squared Curvature Matrix Theory) to estimate retrieval errors. Both methods assume that the LMA system has an overall rms timing error of 50 ns, but all other possible errors (e.g., multiple sources per retrieval attempt) are neglected. The detailed spatial distributions of retrieval errors are provided. Given that the two methods are completely independent of one another, it is shown that they provide remarkably similar results. However, for many source locations, the Curvature Matrix Theory produces larger altitude error estimates than the (more realistic) Monte Carlo simulation.

Koshak, W. J.↗
NASA NTRS1975

Tables of critical values for examining compositional non-randomness in proteins and nucleic acids

A binomially distributed statistic is defined to show whether or not the proportion of a particular amino acid in a protein deviates from random expectation. An analogous statistic is derived for nucleotides in nucleic acids. These new statistics are simply related to the classical chi-squared test. They explicitly account for the compositional fluctuations imposed by the finite length of proteins, and they are more accurate than previous tables.

Laird, M.↗
NASA NTRS1979

Soft X-ray structure of the Coma cluster of galaxies

Results are reported for an observation of the Coma cluster with an imaging X-ray telescope system aboard a sounding rocket. A two-dimensional X-ray map of the cluster in the energy range from 0.15 to 2.0 keV is presented. The radial distribution, granularity, and ellipticity of the X-ray surface brightness are investigated, and the spectrum and flux within the field of view are analyzed. These properties are then examined quantitatively by comparing the observations with models through the use of a chi-squared test. It is found that: (1) no single galaxy contributes more than a few percent of the total X-ray flux of the Coma cluster; (2) the X-ray source is diffuse but granular on a scale of several arcmin, particularly in the central region; (3) the centroid of the X-ray source is at a local intensity minimum; and (4) the data are most consistent with an isothermal hydrostatic model.

Gorentstein, P.↗
NASA NTRS2000

Volcanic Signatures in Estimates of Stratospheric Aerosol Size, Distribution Width, Surface Area, and Volume Deduced from Global Satellite-Based Observations

Volcanic signatures in the stratospheric aerosol layer are revealed by two independent techniques which retrieve aerosol information from global satellite-based observations of particulate extinction. Both techniques combine the 4-wavelength Stratospheric Aerosol and Gas Experiment (SAGE) II extinction measurements (0.385 <= lambda <= 1.02 microns) with the 7.96 micron and 12.82 micron extinction measurements from the Cryogenic Limb Array Etalon Spectrometer (CLAES) instrument. The algorithms use the SAGE II/CLAES composite extinction spectra in month-latitude-altitude bins to retrieve values and uncertainties of particle effective radius R(sub eff), surface area S, volume V and size distribution width sigma(sub R). The first technique is a multi-wavelength Look-Up-Table (LUT) algorithm which retrieves values and uncertainties of R(sub eff) by comparing ratios of extinctions from SAGE II and CLAES (e.g., E(sub lambda)/E(sub 1.02) to pre-computed extinction ratios which are based on a range of unimodal lognormal size distributions. The pre-computed ratios are presented as a function of R(sub eff) for a given sigma(sub g); thus the comparisons establish the range of R(sub eff) consistent with the measured spectra for that sigma(sub g). The fact that no solutions are found for certain sigma(sub g) values provides information on the acceptable range of sigma(sub g), which is found to evolve in response to volcanic injections and removal periods. Analogous comparisons using absolute extinction spectra and error bars establish the range of S and V. The second technique is a Parameter Search Technique (PST) which estimates R(sub eff) and sigma(sub g) within a month-latitude-altitude bin by minimizing the chi-squared values obtained by comparing the SAGE II/CLAES extinction spectra and error bars with spectra calculated by varying the lognormal fitting parameters: R(sub eff), sigma(sub g), and the total number of particles N(sub 0). For both techniques, possible biases in retrieved-parameters caused by assuming a unimodal functional form are removed using correction factors computed from representative in situ measurements of bimodal size distributions. Some interesting features revealed by the LUT and PST retrievals include: (1) Increases in S and V (but not R(sub eff)) after the Ruiz and Kelut injections, (2) Increases in S, V, R(sub eff) after Pinatubo, (3) Post-Pinatubo increases in S, V, and R(sub eff) that are more rapid in the tropics than elsewhere, (4) Mid-latitude post-Pinatubo increases in R(sub eff) that lag increases in S and V, (5) S and V returning to pre-Pinatubo values sooner than R(sub eff) does, (6) Sharp increases in sigma(sub g), after Pinatubo and slight increases in sigma(sub g) after Ruiz, Etna, Kelut, Spurr and Rabaul, and (7) Gradual declines in the heights at which R(sub eff), S and V peak after Pinatubo.

Bauman, J. J.↗
NASA NTRS2001

Accuracy for detection of simulated lesions: comparison of fluid-attenuated inversion-recovery, proton density--weighted, and T2-weighted synthetic brain MR imaging

OBJECTIVE: The objective of our study was to determine the effects of MR sequence (fluid-attenuated inversion-recovery [FLAIR], proton density--weighted, and T2-weighted) and of lesion location on sensitivity and specificity of lesion detection. MATERIALS AND METHODS: We generated FLAIR, proton density-weighted, and T2-weighted brain images with 3-mm lesions using published parameters for acute multiple sclerosis plaques. Each image contained from zero to five lesions that were distributed among cortical-subcortical, periventricular, and deep white matter regions; on either side; and anterior or posterior in position. We presented images of 540 lesions, distributed among 2592 image regions, to six neuroradiologists. We constructed a contingency table for image regions with lesions and another for image regions without lesions (normal). Each table included the following: the reviewer's number (1--6); the MR sequence; the side, position, and region of the lesion; and the reviewer's response (lesion present or absent [normal]). We performed chi-square and log-linear analyses. RESULTS: The FLAIR sequence yielded the highest true-positive rates (p < 0.001) and the highest true-negative rates (p < 0.001). Regions also differed in reviewers' true-positive rates (p < 0.001) and true-negative rates (p = 0.002). The true-positive rate model generated by log-linear analysis contained an additional sequence-location interaction. The true-negative rate model generated by log-linear analysis confirmed these associations, but no higher order interactions were added. CONCLUSION: We developed software with which we can generate brain images of a wide range of pulse sequences and that allows us to specify the location, size, shape, and intrinsic characteristics of simulated lesions. We found that the use of FLAIR sequences increases detection accuracy for cortical-subcortical and periventricular lesions over that associated with proton density- and T2-weighted sequences.

NASA Discipline Neuroscience↗
NASA NTRS1992

The polar cap structure of the X-ray pulsar 4U 1538 - 52

We compare the pulse-phase-dependent spectral observations of 4U 1538 - 52 obtained from Ginga to a series of static model atmospheres of curved accreting polar caps, utilizing a magnetized radiative transfer code with relativistic polarized cross sections. A chi-squared fit was performed on the symmetrized pulse shapes, allowing the parameters of the two polar caps to vary independently. We find evidence for a significant difference between the caps, both in terms of opening angle and temperature, while the optical depth is similar and compatible with radiative deceleration models. The polar caps appear larger than what is usually estimated from dipole fields, and are not located at the antipodes of each other. A broader distribution of magnetic fields is required than expected from a dipolar field at constant radius. If the magnetic field is indeed dipolar, it should be off-center in respect to the star and the accretion shock height exhibits an unusual dependence on the polar angle. An alternative possibility is that the magnetic field is disordered on scales small compared to the polar cap radius.

Bulik, T.↗
NASA NTRS2002

Protein Kinase Classification with 2866 Hidden Markov Models and One Support Vector Machine

The main application considered in this paper is predicting true kinases from randomly permuted kinases that share the same length and amino acid distributions as the true kinases. Numerous methods already exist for this classification task, such as HMMs, motif-matchers, and sequence comparison algorithms. We build on some of these efforts by creating a vector from the output of thousands of structurally based HMMs, created offline with Pfam-A seed alignments using SAM-T99, which then must be combined into an overall classification for the protein. Then we use a Support Vector Machine for classifying this large ensemble Pfam-Vector, with a polynomial and chisquared kernel. In particular, the chi-squared kernel SVM performs better than the HMMs and better than the BLAST pairwise comparisons, when predicting true from false kinases in some respects, but no one algorithm is best for all purposes or in all instances so we consider the particular strengths and weaknesses of each.

Weber, Ryan↗
NASA NTRS1993

Inverse sequential procedures for the monitoring of time series

Climate changes traditionally have been detected from long series of observations and long after they happened. The 'inverse sequential' monitoring procedure is designed to detect changes as soon as they occur. Frequency distribution parameters are estimated both from the most recent existing set of observations and from the same set augmented by 1,2,...j new observations. Individual-value probability products ('likelihoods') are then calculated which yield probabilities for erroneously accepting the existing parameter(s) as valid for the augmented data set and vice versa. A parameter change is signaled when these probabilities (or a more convenient and robust compound 'no change' probability) show a progressive decrease. New parameters are then estimated from the new observations alone to restart the procedure. The detailed algebra is developed and tested for Gaussian means and variances, Poisson and chi-square means, and linear or exponential trends; a comprehensive and interactive Fortran program is provided in the appendix.

Radok, Uwe↗
NASA NTRS2002

A Lightning Channel Retrieval Algorithm for the North Alabama Lightning Mapping Array (LMA)

A new multi-station VHF time-of-arrival (TOA) antenna network is, at the time of this writing, coming on-line in Northern Alabama. The network, called the Lightning Mapping Array (LMA), employs GPS timing and detects VHF radiation from discrete segments (effectively point emitters) that comprise the channel of lightning strokes within cloud and ground flashes. The network will support on-going ground validation activities of the low Earth orbiting Lightning Imaging Sensor (LIS) satellite developed at NASA Marshall Space Flight Center (MSFC) in Huntsville, Alabama. It will also provide for many interesting and detailed studies of the distribution and evolution of thunderstorms and lightning in the Tennessee Valley, and will offer many interesting comparisons with other meteorological/geophysical wets associated with lightning and thunderstorms. In order to take full advantage of these benefits, it is essential that the LMA channel mapping accuracy (in both space and time) be fully characterized and optimized. In this study, a new revised channel mapping retrieval algorithm is introduced. The algorithm is an extension of earlier work provided in Koshak and Solakiewicz (1996) in the analysis of the NASA Kennedy Space Center (KSC) Lightning Detection and Ranging (LDAR) system. As in the 1996 study, direct algebraic solutions are obtained by inverting a simple linear system of equations, thereby making computer searches through a multi-dimensional parameter domain of a Chi-Squared function unnecessary. However, the new algorithm is developed completely in spherical Earth-centered coordinates (longitude, latitude, altitude), rather than in the (x, y, z) cartesian coordinates employed in the 1996 study. Hence, no mathematical transformations from (x, y, z) into spherical coordinates are required (such transformations involve more numerical error propagation, more computer program coding, and slightly more CPU computing time). The new algorithm also has a more realistic definition of source altitude that accounts for Earth oblateness (this can become important for sources that are hundreds of kilometers away from the network). In addition, the new algorithm is being applied to analyze computer simulated LMA datasets in order to obtain detailed location/time retrieval error maps for sources in and around the LMA network. These maps will provide a more comprehensive analysis of retrieval errors for LMA than the 1996 study did of LDAR retrieval errors. Finally, we note that the new algorithm can be applied to LDAR, and essentially any other multi-station TWA network that depends on direct line-of-site antenna excitation.

Koshak, William↗
NASA NTRS1999

Lidar Altimeter Measurements of Canopy Structure: Methods and Validation for Closed Canopy, Broadleaf Forests

Lidar altimeter observations of vegetated landscapes provide a time-resolved measure of laser pulse backscatter energy from canopy surfaces and the underlying ground. Airborne lidar altimeter data was acquired using the Scanning Lidar Imager of Canopies by Echo Recovery (SLICER) for a successional sequence of four, closed-canopy, deciduous forest stands in eastern Maryland. The four stands were selected so as to include a range of canopy structures of importance to forest ecosystem function, including variation in the height and roughness of the outer-most canopy surface and the vertical organization of canopy stories and gaps. The character of the SLICER backscatter signal is described and a method is developed that accounts for occlusion of the laser energy by canopy surfaces, transforming the backscatter signal to a canopy height profile (CHP) that quantitatively represents the relative vertical distribution of canopy surface area. The transformation applies an increased weighting to the backscatter amplitude as a function of closure through the canopy and assumes a horizontally random distribution of the canopy components. SLICER CHPs, averaged over areas of overlap where lidar ground tracks intersect, are shown to be highly reproducible. CHP transects across the four stands reveal spatial variations in vegetation, at the scale of the individual 10 m diameter laser footprints, within and between stands. Averaged SLICER CHPs are compared to analogous height profile results derived from ground-based sightings to plant intercepts measured on plots within the four stands. Tbe plots were located on the segments of the lidar ground tracks from which averaged SLICER CHPs were derived, and the ground observations were acquired within two weeks of the SLICER data acquisition to minimize temporal change. The differences in canopy structure between the four stands is similarly described by the SLICER and ground-based CHP results, however a Chi-square test of similarity documents differences that are statistically significant. The differences are discussed in terms of measurement properties that define the smoothness of the resulting CHPs and Lidar Altimeter Measurements of Canopy Structure - Harding et al. canopy properties that may vertically bias the CHP representations of canopy structure. The statistical differences are most likely due to the more noisy character of the ground-based CHPs, especially high in the canopy where ground-based sightings are rare resulting in an underestimate of canopy surface area and height, and to departures from the assumption of horizontal randomness which bias the CHPs toward the observer (upward for SLICER and downward for ground-based CHPs). The results demonstrate that the SLICER observations reliably provide a measure of canopy structure that reveals ecologically interesting structural variations such as those characterizing a successional sequence of closed-canopy, broadleaf forest stands.

Harding, D. J.↗
NASA NTRS2003

Application of a data-mining method based on Bayesian networks to lesion-deficit analysis

Although lesion-deficit analysis (LDA) has provided extensive information about structure-function associations in the human brain, LDA has suffered from the difficulties inherent to the analysis of spatial data, i.e., there are many more variables than subjects, and data may be difficult to model using standard distributions, such as the normal distribution. We herein describe a Bayesian method for LDA; this method is based on data-mining techniques that employ Bayesian networks to represent structure-function associations. These methods are computationally tractable, and can represent complex, nonlinear structure-function associations. When applied to the evaluation of data obtained from a study of the psychiatric sequelae of traumatic brain injury in children, this method generates a Bayesian network that demonstrates complex, nonlinear associations among lesions in the left caudate, right globus pallidus, right side of the corpus callosum, right caudate, and left thalamus, and subsequent development of attention-deficit hyperactivity disorder, confirming and extending our previous statistical analysis of these data. Furthermore, analysis of simulated data indicates that methods based on Bayesian networks may be more sensitive and specific for detecting associations among categorical variables than methods based on chi-square and Fisher exact statistics.

NASA Discipline Neuroscience↗
NASA NTRS1997

Modeling the effects of exercise during 100% oxygen prebreathe on the risk of hypobaric decompression sickness

BACKGROUND: Several previous studies indicated that exercise during prebreathe with 100% O2 decreased the incidence of hypobaric decompression sickness (DCS). We report a meta-analysis of these investigations combined with a new study in our laboratory to develop a statistical model as a predictive tool for DCS. HYPOTHESIS: Exercise during prebreathe increases N2 elimination in a theoretical 360-min half-time compartment decreasing the incidence of DCS. METHODS: A dose-response probability tissue ratio (TR) model with 95% confidence limits was created for two groups, prebreathe with exercise (n = 113) and resting prebreathe (n = 113), using nonlinear regression analysis with maximum likelihood optimization. RESULTS: The model predicted that prebreathe exercise would reduce the residual N2 in a 360-min half-time compartment to a level analogous to that in a 180-min compartment. This finding supported the hypothesis. The incidence of DCS for the exercise prebreathe group was significantly decreased (Chi-Square = 17.1, p < 0.0001) from the resting prebreathe group. CONCLUSIONS: The results suggested that exercise during prebreathe increases tissue perfusion and N2 elimination approximately 2-fold and markedly lowers the risk of DCS. Based on the model, the prebreathe duration may be reduced from 240 min to a predicted 91 min for the protocol in our study, but this remains to be verified. The model provides a useful planning tool to develop and test appropriate prebreathe exercise protocols and to predict DCS risks for astronauts.

NASA Program Environmental Health↗