Search NASASearch

SEARCH · Search NASA

Results for “standard normal variate”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

Evaluation of Correction Methods for NASA GeneLab Transcriptomic Datasets

Conducting space biology experiments aboard the International Space Station, particularly those utilizing complex model organisms like mice, is expensive and difficult due to limited crew availability, hardware, and space. As a result, sample numbers from these studies are low, reducing the statistical power of any one experiment. Aggregating spaceflight datasets serves as a method to increase sample numbers, allowing for novel insights through bioinformatic analysis of ‘omics data from merged datasets. However, aggregating datasets can introduce unwanted variation including 1) differences in sample handling, processing, and sequencing platforms between datasets (technical variation) as well as 2) differences in experimental design between datasets. In the present study, NASA GeneLab-hosted RNAseq datasets from mouse liver tissues were used to evaluate several statistical methods to correct for this unwanted variation through two approaches, reference-based and standard. The following correction algorithms were applied with (reference-based) and/or without (standard) considering Universal Mouse RNA Reference samples: ComBat and ComBat_seq from the SVA package, median polish, empirical Bayes, and ANOVA-based algorithms from the MBatch package, and negative binomial regression normalization in the DESeq2 package. For each approach, after the correction algorithm was applied, differential gene expression (DGE) analysis of flight and ground control samples was performed with the combined data. The robustness of each tool was evaluated using BatchQC to determine statistical differences between datasets before and after correction, Principal Component Analysis to evaluate global gene expression in samples before and after correction, and by comparing DGE analysis of individual datasets and combined datasets before and after correction. The results showed that the reference-based approach introduced several additional (and likely artificial) DEGs when compared with the respective standard approach. Of the methods tested, standard ComBat and DESeq2 were identified as the most robust correction methods for combining spaceflight mouse liver RNAseq datasets hosted on GeneLab.

GeneLab

Evaluation of Non-Ozone-Depleting-Chemical Cleaning Methods for Space Mechanisms Using a Vacuum Spiral Orbit Rolling Contact Tribometer

Because CFC 113, an ozone depleting chemical (ODC), can no longer be produced, alternative bearing cleaning methods must be studied. The objective of this work was to study the effect of the new cleaning methods on lubricant lifetime using a vacuum bearing simulator (spiral orbit rolling contact tribometer). Four alternative cleaning methods were studied: ultra-violet (UV) ozone, aqueous levigated alumina slurry (ALAS), super critical fluid (SCF) CO2 and aqueous Brulin 815GD. Baseline tests were done using CFC 113. Test conditions were the following: a vacuum of at least 1.3 x 10(exp -6) Pa, 440C steel components, a rotational speed of 10 RPM, a lubricant charge of between 60-75 micrograms, a perfluoropolyalkylether lubricant (Z-25), and a load of 200N (44.6 lbs., a mean Hertzian stress of 1.5 GPa). Normalized lubricant lifetime was determined by dividing the total number of ball orbits by the amount of lubricant. The failure condition was a friction coefficient of 0.38. Post-test XPS analysis was also performed, showing slight variations in post-cleaning surface chemistry. Statistical analysis of the resultant data was conducted and it was determined that the data sets were most directly comparable when subjected to a natural log transformation. The natural log life (NL-Life) data for each cleaning method were reasonably normally (statistically) distributed and yielded standard deviations that were not significantly different among the five cleaning methods investigated. This made comparison of their NL-Life means very straightforward using a Bonferroni multiple comparison of means procedure. This procedure showed that the ALAS, UV-ozone and CFC 113 methods were not statistically significantly different from one another with respect to mean NL-Life. It also found that the SCF CO2 method yielded a significantly higher mean NL-Life than the mean NL-Lives of the ALAS, UV-ozone and CFC 113 methods. It also determined that the aqueous Brulin 815GD method yielded a mean NL-Life that was statistically significantly higher than the mean NL-Lives of each of the other four methods. Baseline tests using CFC 113 cleaned parts yielded a mean NL-Life 3.62 orbits/micro-g. ALAS and UV-ozone yielded similar mean NL-Life (3.31 orbits/mg and 3.33 orbits/micro-g, respectively). SCF CO2, gave a mean NL-Life of 4.08 orbits/mg and aqueous Brulin 8l5GD data yielded the longest mean NL-Life (4.66 orbits/micro-g).

Jansen, Mark J.

Discontinuous Mode Power Supply

A document discusses the changes made to a standard push-pull inverter circuit to avoid saturation effects in the main inverter power supply. Typically, in a standard push-pull arrangement, the unsymmetrical primary excitation causes variations in the volt second integral of each half of the excitation cycle that could lead to the establishment of DC flux density in the magnetic core, which could eventually cause saturation of the main inverter transformer. The relocation of the filter reactor normally placed across the output of the power supply solves this problem. The filter reactor was placed in series with the primary circuit of the main inverter transformer, and is presented as impedance against the sudden changes on the input current. The reactor averaged the input current in the primary circuit, avoiding saturation of the main inverter transformer. Since the implementation of the described change, the above problem has not reoccurred, and failures in the main power transistors have been avoided.

Lagadinos, John

Combining RNA-SEQ Datasets from NASA GENELAB: An Evaluation of Correction Methods

Background: Conducting space biology experiments aboard the International Space Station, particularly those utilizing complex model organisms like mice, is expensive and difficult due to limited crew availability, hardware, and space. As a result, sample numbers from these studies are low, reducing the statistical power of any one experiment. Aggregating spaceflight datasets serves as a method to increase sample numbers, allowing for novel insights through bioinformatic analysis of ‘omics data from merged datasets. However, aggregating datasets can introduce unwanted variation including 1) differences in sample handling, processing, and sequencing platforms between datasets (technical variation) as well as 2) differences in experimental design between datasets. Methods: In the present study, NASA GeneLab-hosted RNAseq datasets from mouse liver tissues were used to evaluate several statistical methods to correct for this unwanted variation through two approaches, reference-based and standard. The following correction algorithms were applied with (reference-based) and/or without (standard) considering Universal Mouse RNA Reference samples: ComBat and ComBat_seq from the SVA package, the median polish, empirical Bayes, and ANOVA-based algorithms from the MBatch package, and negative binomial regression normalization in the DESeq2 package. For each approach, after the correction algorithm was applied, differential gene expression (DGE) analysis of flight and ground control samples was performed with the combined data. The robustness of each tool was evaluated using BatchQC to determine statistical differences between datasets before and after correction, Principal Component Analysis to evaluate global gene expression in samples before and after correction, and by comparing DGE analysis of individual datasets and combined datasets before and after correction. Results: The results showed that the reference-based approach introduced several additional (and likely artificial) differentially expressed genes when compared with the respective standard approach. Conclusions: Of the methods tested, standard ComBat_seq and DESeq2 were identified as the most robust correction methods for combining spaceflight mouse liver RNAseq datasets hosted on GeneLab.

Finsam Samson

Estimation of intensity, footprint, and capacity of surface urban heat islands using a direction-enhanced adaptive synchronous extraction (DEASE) method

Here, the surface urban heat island (SUHI) effect, assessed through remotely sensed land surface temperature (LST), remains a focal point in urban climate research. Conventional indicators like SUHI intensity (SUHII) and footprint (SUHIF) capture peak values and spatial extent but fail to account for the cumulative thermal load—a critical dimension reflecting the total heat exposure imposed by spatially continuous warming, which directly limits a holistic assessment of ecological and societal impacts of the SUHI effect. Therefore, this study introduces an indicator termed SUHI capacity (SUHIC), designed to quantify the aggregated SUHI effect by integrating the magnitude of the warming signal across all affected areas, thereby enabling a more comprehensive evaluation of urban thermal environments. Furthermore, a direction-enhanced adaptive synchronous extraction (DEASE) method is proposed for the quantification of SUHIC. This method can dynamically identify the optimal background reference area based on the urban-rural LST gradients in various directions within the city, without relying on predefined mathematical models as previously. The results from 102 European cities first confirm that the directional variations in urban-rural LST gradients, and the DEASE method can effectively capture these distinctions for the simultaneous estimation of SUHII, SUHIF, and SUHIC. Secondly, the spatial patterns of absolute SUHIC values show strong associations with those of SUHIF (R2>0.86), while its relative values (normalized by the area of urban) align more closely with SUHII (R2 > 0.64). More importantly, SUHIC can serve as a crucial reference for assessing the urban thermal signal when SUHII and SUHIF diverge. The proposed method and framework contribute to standardizing the quantification of the SUHI effect.

Indicator

Flight Calibration of four airspeed systems on a swept-wing airplane at Mach numbers up to 1.04 by the NACA radar-phototheodolite method

The calibrations of four airspeed systems installed in a North American F-86A airplane have been determined in flight at Mach numbers up to 1.04 by the NACA radar-phototheodolite method. The variation of the static-pressure error per unit indicated impact pressure is presented for three systems typical of those currently in use in flight research, a nose boom and two different wing-tip booms, and for the standard service system installed in the airplane. A limited amount of information on the effect of airplane normal-force coefficient on the static-pressure error is included. The results are compared with available theory and with results from wind-tunnel tests of the airspeed heads alone. Of the systems investigated, a nose-boom installation was found to be most suitable for research use at transonic and low supersonic speeds because it provided the greatest sensitivity of the indicated Mach number to a unit change in true Mach number at very high subsonic speeds, and because it was least sensitive to changes in airplane normal-force coefficient. The static-pressure error of the nose-boom system was small and constant above a Mach number of 1.03 after passage of the fuselage bow shock wave over the airspeed head.

Thompson, Jim Rogers

NASA/American Cancer Society High-Resolution Flow Cytometry Project-I

BACKGROUND: The NASA/American Cancer Society (ACS) flow cytometer can simultaneously analyze the electronic nuclear volume (ENV) and DNA content of cells. This study describes the schematics, resolution, reproducibility, and sensitivity of biological standards analyzed on this unit. METHODS: Calibrated beads and biological standards (lymphocytes, trout erythrocytes [TRBC], calf thymocytes, and tumor cells) were analyzed for ENV versus DNA content. Parallel data (forward scatter versus DNA) from a conventional flow cytometer were obtained. RESULTS: ENV linearity studies yielded an R value of 0.999. TRBC had a coefficient of variation (CV) of 1.18 +/- 0.13. DNA indexes as low as 1.02 were detectable. DNA content of lymphocytes from 42 females was 1.9% greater than that for 60 males, with a noninstrumental variability in total DNA content of 0.5%. The ENV/DNA ratio was constant in 15 normal human tissue samples, but differed in the four animal species tested. The ENV/DNA ratio for a hypodiploid breast carcinoma was 2.3 times greater than that for normal breast tissue. CONCLUSIONS: The high-resolution ENV versus DNA analyses are highly reliable, sensitive, and can be used for the detection of near-diploid tumor cells that are difficult to identify with conventional cytometers. ENV/DNA ratio may be a useful parameter for detection of aneuploid populations.

NASA Center JSC

A comparative review of radiation aerosol models

Aerosol characteristics to be introduced into a set of models within a framework of a Standard Radiation Atmosphere (SRA) are reviewed, and a reconciliation of the Toon and Pollack (TP) global model with the SRA models is attempted. Among the topics discussed are physical and radiative characteristics, radiation aerosol models, albedo for single scattering, and phase function and spectral variation of extinction. Size distribution models are also covered, inclusive the Junge power law, and the modified gamma-, log normal-, and zold-distribution. Recommendations include modifying the SRA profile VI to resemble the Elterman profile modified in the TP model, improving discontinuity at the tropopause level for all SRA models, and retaining the same log-normal size distribution for all SRA components.

Lenoble, J.

Detecting Inter-Annual Variations in the Phenology of Evergreen Conifers Using Long-Term MODIS Vegetation Index Time Series

Long-term observations of vegetation phenology can be used to monitor the response of terrestrial ecosystems to climate change. Satellite remote sensing provides the most efficient means to observe phenological events through time series analysis of vegetation indices such as the Normalized Difference Vegetation Index (NDVI). This study investigates the potential of a Photochemical Reflectance Index (PRI), which has been linked to vegetation light use efficiency, to improve the accuracy of MODIS-based estimates of phenology in an evergreen conifer forest. Timings of the start and end of the growing season (SGS and EGS) were derived from a 13-year-long time series of PRI and NDVI based on a MAIAC (multi-angle implementation of atmospheric correction) processed MODIS dataset and standard MODIS NDVI product data. The derived dates were validated with phenology estimates from ground-based flux tower measurements of ecosystem productivity. Significant correlations were found between the MAIAC time series and ground-estimated SGS (R (sup 2) equals 0.36-0.8), which is remarkable since previous studies have found it difficult to observe inter-annual phenological variations in evergreen vegetation from satellite data. The considerably noisier NDVI product could not accurately predict SGS, and EGS could not be derived successfully from any of the time series. While the strongest relationship overall was found between SGS derived from the ground data and PRI, MAIAC NDVI exhibited high correlations with SGS more consistently (R (sup 2) is greater than 0.6 in all cases). The results suggest that PRI can serve as an effective indicator of spring seasonal transitions, however, additional work is necessary to confirm the relationships observed and to further explore the usefulness of MODIS PRI for detecting phenology.

Ulsig, Laura

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.

Characterization of Operational Performance of Ka-Band Links in Deep Space Network

This paper presents a characterization of performance of 32-GHz Ka-band link in an operational environment. The data come from tracking of Kepler spacecraft by the NASA Deep Space Network (DSN) in the past few years. Ka-band link offers a significant signal-to-noise advantage compared to the more common X- or S-band; however, it is subject to more signal fluctuation caused by the weather. Kepler is the first mission supported by the DSN that solely rely on the higher deep space Ka-band communications link to return its high-rate science data. A well characterization of the operational performance of Kepler would benefit future Ka-band missions, especially for those operating with smaller link margin. The study examines how weather conditions at the DSN facilities (e.g., winds, clouds, rains) affect the received signal, particularly on telemetry data. It addresses questions such as how often the weather affects the link and how much degradation the link could suffer. Among the 22 Ka-band passes in 2012, heavy clouds affected one pass and two passes were impacted by high winds. The adverse weather caused at time as much as 3-dB instantaneous change in the signal to noise ratio (SNR). Estimates of degradation to the SNR as a function of wind speeds are captured based on observations. This study also quantifies the probability distribution of the variation of received signal power. With such information, future missions can better plan their link design. An optimal link design aims for just having enough margin to realize the data return with a targeted probability, with neither having too much margin that it reduces the downlink data rate nor insufficient reserve that causes frequent data outages. The study tries to provide some answers to the questions such as how much does SNR vary from one tracking pass to the next, and what is the cumulative distribution of signal fluctuation. Regarding the signal variation over many tracking passes, we found that the averaged symbol SNR (SSNR) for each pass changed by as much as 4 dB. Some variations were due to geometry such as the changing distance between spacecraft and Earth and different antenna pointing elevations. Other variations seem to be random in nature, reflecting the randomness of operational environments. Some passes were found to be quite stable, with a standard deviation of symbol SNR around 0.25 dB while others had greater variation, up to 1.4 dB. Overall, the cumulative distribution of the symbol SNR reflects that 50% of the fluctuations was less than 0.6 dB, 90% of fluctuation was within 1.6 dB and 95% within 2.2 dB. Some of the challenges in data processing, validation and modeling were captured in this paper. We observed some inconsistent measurements where operational data significantly deviate from a normal expectation. These inconsistent measurements made it hard to develop an accurate and consistent performance model, such as the degradation of signal SNR as a function of high wind. The difficulty was compounded by the fact that there were only a few Ka-band passes observed in high winds.

Pham, Timothy

Airborne measurements of laser backscatter from the ocean surface

The data are taken with three different pulsed laser sources, one each in the ultraviolet (337.1 nm), visible (532.1 nm) and infrared (9.5 microns). The principal instrument is the airborne oceanographic lidar of the NASA Wallops Flight Facility. The data on mean laser backscatter and its variation with angle off nadir are found to be consistent with previous analytical work and some previous experimental work. The absolute calibration of this backscatter in terms of an effective Lambertian reflectance is less precise, but the data support values near nadir of approximately 0.20 for low wind speeds. It is noted that these values are 1 order of magnitude larger than the Fresnel reflectance for an air/water discontinuity in the refractive index. Whereas the normalized standard deviation (modulation factor) of backscatter is less well understood analytically, it is defined by these measurements to range from a few percent to over 50 percent at nadir and to increase off nadir as the tangent of theta or faster. The data are uncertain beyond 15 deg off nadir owing to a dynamic range limitation.

Bufton, J. L.

Assessment of variations in thermal cycle life data of thermal barrier coated rods

An analysis of thermal cycle life data for 22 thermal barrier coated (TBC) specimens was conducted. The Zr02-8Y203/NiCrAlY plasma spray coated Rene 41 rods were tested in a Mach 0.3 Jet A/air burner flame. All specimens were subjected to the same coating and subsequent test procedures in an effort to control three parametric groups; material properties, geometry and heat flux. Statistically, the data sample space had a mean of 1330 cycles with a standard deviation of 520 cycles. The data were described by normal or log-normal distributions, but other models could also apply; the sample size must be increased to clearly delineate a statistical failure model. The statistical methods were also applied to adhesive/cohesive strength data for 20 TBC discs of the same composition, with similar results. The sample space had a mean of 9 MPa with a standard deviation of 4.2 MPa.

Hendricks, R. C.

Hologic QDR 2000 whole-body scans: a comparison of three combinations of scan modes and analysis software

This study reports on the short-term in vivo precision and absolute measurements of three combinations of whole-body scan modes and analysis software using a Hologic QDR 2000 dual-energy X-ray densitometer. A group of 21 normal, healthy volunteers (11 male and 10 female) were scanned six times, receiving one pencil-beam and one array whole-body scan on three occasions approximately 1 week apart. The following combinations of scan modes and analysis software were used: pencil-beam scans analyzed with Hologic's standard whole-body software (PB scans); the same pencil-beam analyzed with Hologic's newer "enhanced" software (EPB scans); and array scans analyzed with the enhanced software (EA scans). Precision values (% coefficient of variation, %CV) were calculated for whole-body and regional bone mineral content (BMC), bone mineral density (BMD), fat mass, lean mass, %fat and total mass. In general, there was no significant difference among the three scan types with respect to short-term precision of BMD and only slight differences in the precision of BMC. Precision of BMC and BMD for all three scan types was excellent: < 1% CV for whole-body values, with most regional values in the 1%-2% range. Pencil-beam scans demonstrated significantly better soft tissue precision than did array scans. Precision errors for whole-body lean mass were: 0.9% (PB), 1.1% (EPB) and 1.9% (EA). Precision errors for whole-body fat mass were: 1.7% (PB), 2.4% (EPB) and 5.6% (EA). EPB precision errors were slightly higher than PB precision errors for lean, fat and %fat measurements of all regions except the head, although these differences were significant only for the fat and % fat of the arms and legs. In addition EPB precision values exhibited greater individual variability than PB precision values. Finally, absolute values of bone and soft tissue were compared among the three combinations of scan and analysis modes. BMC, BMD, fat mass, %fat and lean mass were significantly different between PB scans and either of the EPB or EA scans. Differences were as large as 20%-25% for certain regional fat and BMD measurements. Additional work may be needed to examine the relative accuracy of the scan mode/software combinations and to identify reasons for the differences in soft tissue precision with the array whole-body scan mode.

NASA Discipline Musculoskeletal

Rarefied aerodynamics and upper atmosphere density from multiple orbiter flight measurements

Flight data from six flights of the experimental High Resolution Accelerometer Package (HIRAP), a micro-g accelerometer system, have been analyzed to produce rarefied flow aerodynamic coefficients of the Orbiter and freestream density in the altitude range from 60 km to 160 km. The direct measurements of the lift to drag ratio (L/D) are used to obtain individual normalized body-axis force coefficients in a least-squares regression scheme. An aerodynamics model based on an exponential function of Knudsen number is used for the individual coefficients. The calculated L/D from the flight determined coefficients agree with the multiple flight data measurements to within about 5 percent. Simultaneously, an upper altitude density variation is also obtained from the data. Density altitude profiles exhibit a wave feature on all flights. The wave has an amplitude of about + or - 25 percent relative to the 1962 Standard atmosphere model.

Buck, G. M.

Reductions in Productivity Due to Land Degradation in the Drylands of the Southwestern United States

Dryland degradation has long been recognized at regional, national, and global scales, yet there are no objective assessments of its location and severity. An assessment of reductions in net primary production (NPP) due to dryland degradation in the southwestern United States is reported. The local NPP scaling (LNS) approach was applied to map the extent and magnitude of degradation. LNS seeks to identify reference sites in which there is no degradation that can be used as a standard for comparison with other sites that share the same environment, except for degradation. Twelve years were analyzed (2000–2011), using Normalized Difference Vegetation Index (NDVI) data (250 m) from the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite‐borne multispectral sensor. The results indicated that the total NPP reductions in the study area were about 35.9 ± 4.7 Tg C/yr, which equates to 0.31 ± 0.04 Mg C/ha·y. The NPP reductions in grassland‐savanna and livestock grazing areas were large and mostly consistent between years in spite of large variations in overall NPP caused by differences in land‐use, interannual variations in rainfall, and other aspects of weather. In comparison with other cover types, forested land generally had higher NPP reduction per unit area. The maps also enable attribution of degradation from the finest management units to entire agencies, such as the Bureau of Land Management, which had 50% less production per unit area than the U.S. Forest Service. The degradation within Native American land was low with total NPP reduction of about 2.41 ± 0.24 Tg C/yr and unit area reduction of productivity of just 0.21 ± 0.02 Mg C/ha·yr, yet the percent reduction from potential was in equivalence with other land management agencies.

Noojipady, Praveen

An Assessment of Five Modeling Approaches for Thermo-Mechanical Stress Analysis of Laminated Composite Panels

A study is made of the effects of variation in the lamination and geometric parameters, and boundary conditions of multi-layered composite panels on the accuracy of the detailed response characteristics obtained by five different modeling approaches. The modeling approaches considered include four two-dimensional models, each with five parameters to characterize the deformation in the thickness direction, and a predictor-corrector approach with twelve displacement parameters. The two-dimensional models are first-order shear deformation theory, third-order theory; a theory based on trigonometric variation of the transverse shear stresses through the thickness, and a discrete layer theory. The combination of the following four key elements distinguishes the present study from previous studies reported in the literature: (1) the standard of comparison is taken to be the solutions obtained by using three-dimensional continuum models for each of the individual layers; (2) both mechanical and thermal loadings are considered; (3) boundary conditions other than simply supported edges are considered; and (4) quantities compared include detailed through-the-thickness distributions of transverse shear and transverse normal stresses. Based on the numerical studies conducted, the predictor-corrector approach appears to be the most effective technique for obtaining accurate transverse stresses, and for thermal loading, none of the two-dimensional models is adequate for calculating transverse normal stresses, even when used in conjunction with three-dimensional equilibrium equations.

Noor, A. K.

Quadruple Lap Shear Processing Evaluation

The Thiokol, Science and Engineering Huntsville Operations (SEHO) Laboratory has previously experienced significant levels of variation in testing Quadruple Lap Shear (QLS) specimens. The QLS test is used at Thiokol / Utah for the qualification of Reusable Solid Rocket Motor (RSRM) nozzle flex bearing materials. A test was conducted to verify that process changes instituted by SEHO personnel effectively reduced variability, even with normal processing variables introduced. A test matrix was designed to progress in a series of steps; the first establishing a baseline, then introducing additional solvents or other variables. Variables included normal test plan delay times, pre-bond solvent hand-wipes and contaminants. Each condition tested utilized standard QLS hardware bonded with natural rubber, two separate technicians and three replicates. This paper will report the results and conclusions of this investigation.

Thornton, Tony N.