On the statistics of correlator outputs
Characteristic function, probability density function, and probability distribution function computations for correlation detector output, and correlator output statistics
Wintz, P. A.↗
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Spherical disharmonics in the Earth sciences and the spatial solution: Ridges, hotspots, slabs, geochemistry and tomography correlations
There is increasing use of statistical correlations between geophysical fields and between geochemical and geophysical fields in attempts to understand how the Earth works. Typically, such correlations have been based on spherical harmonic expansions. The expression of functions on the sphere as spherical harmonic series has many pitfalls, especially if the data are nonuniformly and/or sparsely sampled. Many of the difficulties involved in the use of spherical harmonic expansion techniques can be avoided through the use of spatial domain correlations, but this introduces other complications, such as the choice of a sampling lattice. Additionally, many geophysical and geochemical fields fail to satisfy the assumptions of standard statistical significance tests. This is especially problematic when the data values to be correlated with a geophysical field were collected at sample locations which themselves correlate with that field. This paper examines many correlations which have been claimed in the past between geochemistry and mantle tomography and between hotspot, ridge, and slab locations and tomography using both spherical harmonic coefficient correlations and spatial domain correlations. No conclusively significant correlations are found between isotopic geochemistry and mantle tomography. The Crough and Jurdy (short) hotspot location list shows statistically significant correlation with lowermost mantle tomography for degree 2 of the spherical harmonic expansion, but there are no statistically significant correlations in the spatial case. The Vogt (long) hotspot location list does not correlate with tomography anywhere in the mantle using either technique. Both hotspot lists show a strong correlation between hotspot locations and geoid highs when spatially correlated, but no correlations are revealed by spherical harmonic techniques. Ridge locations do not show any statistically significant correlations with tomography, slab locations, or the geoid; the strongest correlation is with lowermost mantle tomography, which is probably spurious. The most striking correlations are between mantle tomography and post-Pangean subducted slabs. The integrated locations of slabs correlate strongly with fast areas near the transition zone and the core-mantle boundary and with slow regions from 1022-1248 km depth. This seems to be consistent with the 'avalanching' downwellings which have been indicated by models of the mantle which include an endothermic phase transition at the 670-km discontinuity, although this is not a unique interpretation. Taken as a whole, these results suggest that slabs and associated cold downwellings are the dominant feature of mantle convection. Hotspot locations are no better correlated with lower mantle tomography than are ridge locations.
Ray, Terrill W.↗
Reaction of O2(+)(X 2Pi sub g) with H2, D2, and HD - Guided ion beam studies, MO correlations, and statistical theory calculations
Guided ion-beam mass spectrometry is used to examined the reactions of vibrationally cold ground-state O2(+)(X 2Pi sub g) with H2, D2, and HD. The energy dependence of the absolute integral cross sections from thermal energy to over 4 eV are measured in the center-of-mass frame of reference. Results are also presented for internally excited O2(+) ions reacting with D2 and HD. The results are consistent with the dominant state being the a 4Pi sub u electronic state. The experimental excitation functions are analyzed in detail and interpreted by extending the molecular orbital correlation arguments of Mahan (1971) and by comparison with results of statistical phase space theory and with a theory that predicts a tight transition state.
Weber, M. E.↗
Initiation of non-tropical thunderstorms by solar activity
A theory of thunderstorm initiation is proposed to account for the statistical correlation between solar activity and thunderstorm occurrence in middle to high latitudes. It is suggested that cosmic ray decreases and/or high-energy solar protons associated with active solar events enhance the electric field at low heights so that, if appropriate meteorological conditions are present during a solar event, the atmospheric electric field enhancement may be sufficient to trigger thunderstorm development. Statistical correlations and atmospheric electric effects are described. The theory could be tested if the possible forcing functions and the responding atmospheric electrical and ionic species' characteristics were measured.
Herman, J. R.↗
Dynamical computation of photon correlations and counting statistics
Dynamical computation of photon correlations and counting statistics
PHOTON↗
An apparent statistical relationship between polar heat budget and zonal circulation
Apparent statistical correlation between Arctic heat budget and zonal circulation
STATISTICAL CORRELATION↗
Study on development of techniques for resistance welding, phases I and II FINAL report, 20 Jun. 1966 - 28 Feb. 1967
Statistical correlation between infrared heat radiation and weld joint quality, and nondestructive inspection techniques
NONDESTRUCTIVE TESTING↗
A statistical analysis of the Martian wave of darkening and related phenomena.
Statistical correlation of latitude with time of maximum darkening of Mars dark areas, noting consistency of 2 models
STATISTICAL CORRELATION↗
Assessment of Thematic Mapper band-to-band registration by the block correlation method
Rectangular blocks of pixels from one band image were statistically correlated against blocks centered on identical pixels from a second band image. The block pairs were shifted in pixel increments both vertically and horizontally with respect to each other and the correlation coefficient to the maximum correlation was taken as the best estimate of registration error for each block pair. For the band combinations of the Arkansas scene studied, the misregistration of TM spectral bands within the noncooled focal plane lie well within the 0.2 pixel target specification. Misregistration between the middle IR bands is well within this specification also. The thermal IR band has an apparent misregistration with TM band 7 of approximately 3 pixels in each direction. The TM band 3 has a misregistration of approximately 0.2 pixel in the across-scan direction and 0.5 pixel in the along-scan direction, with both TM bands 5 and 7.
Card, D. H.↗
Assessment of Thematic Mapper Band-to-band Registration by the Block Correlation Method
Rectangular blocks of pixels from one band image were statistically correlated against blocks centered on identical pixels from a second band image. The block pairs were shifted in pixel increments both vertically and horizontally with respect to each other and the correlation coefficient to the maximum correlation was taken as the best estimate of registration error for each block pair. For the band combinations of the Arkansas scene studied, the misregistration of TM spectral bands within the noncooled focal plane lie well within the 0.2 pixel target specification. Misregistration between the middle IR bands is well within this specification also. The thermal IR band has an apparent misregistration with TM band 7 of approximately 3 pixels in each direction. The TM band 3 has a misregistration of approximately 0.2 pixel in the across-scan direction and 0.5 pixel in the along-scan direction, with both TM bands 5 and 7.
Card, D. H.↗
Examining the Impact of Local Constraint Violations on Energy Computations in DFT
ABSTRACT This work examines the impact of locally imposed constraints in Density Functional Theory (DFT). Using a metric referred to as the extent of violation index (EVI), we quantify how well exchange‐correlation functionals adhere to local constraints. Applying EVIs to a diverse set of molecules for GGA functionals reveals constraint violations, particularly for semi‐empirical functionals. We leverage EVIs to explore potential connections between these violations and errors in chemical properties. While no correlation is observed for atomization energies, a significant statistical correlation emerges between EVIs and total energies. Similarly, the analysis of reaction energies suggests weak positive correlations for specific constraints. However, definitive conclusions about error cancellation mechanisms cannot be made at this time. These observations revealed by EVIs may be useful for consideration when designing future generations of semilocal functionals.
Khanna, Vaibhav [Department of Chemistry Universit↗
Geometric Analysis and Visualization of Maxillofacial Anthropometry
As part of head borne systems, the maxillofacial and mandibular components are critical for Soldier protection in extreme and dynamic conditions. Often this equipment must not only cover the lower face of the wearer, but also accommodate motion of the lower jaw and resultant deformation of the face shape. Although the application is different, head borne equipmentdesigned for astronauts has similarly critical design requirements including comfort and protection from other environmental hazards while allowing for maximum performance. To improve the design of such systems and to ensure adequate accommodation of the user population, NASA Johnson Space Center is collaborating with the U.S. Army’s Development Command Soldier Center (DEVCOM SC) to statistically analyze facial landmark and measurement data from large Soldier anthropometric databases ( ANSUR 1988 and ANSUR II). Anthropometric measurements were incorporated from 5383 males and 3594 females for analysis, including individuals aged 17-58 across a range of races. Facial landmarks were analyzed, specifically the 3D coordinates of the Menton, Prementon, Gonion, Tragion, Stomion, Zygion, Pronasale, and Subnasale. These data were statistically correlated with demographiccharacteristics, such as sex and population origin. A statistical model of the lower head-face surface geometry is currently in development to describe the variance of head and face shape across the population. The model will be able to visually show the statistical trends of the different shapes and sizes of the head, along with the synthetically represented boundary cases. The specific analytical methods and outcomes will be detailed in the final proceeding. This study will provide a more comprehensive assessment of how face shape varies across the military population compared to traditional linear measurements. The outcome of this study is expected to provide critical insight and recommendations for improved protective equipment design and development, not only with Soldiers but also astronauts in future exploration missions, as well as first responders and others that require critical equipment fitted to the maxillofacial and or mandibular region.
W Green↗
Quantitative Measures for Software Independent Verification and Validation
As software is maintained or reused, it undergoes an evolution which tends to increase the overall complexity of the code. To understand the effects of this, we brought in statistics experts and leading researchers in software complexity, reliability, and their interrelationships. These experts' project has resulted in our ability to statistically correlate specific code complexity attributes, in orthogonal domains, to errors found over time in the HAL/S flight software which flies in the Space Shuttle. Although only a prototype-tools experiment, the result of this research appears to be extendable to all other NASA software, given appropriate data similar to that logged for the Shuttle onboard software. Our research has demonstrated that a more complete domain coverage can be mathematically demonstrated with the approach we have applied, thereby ensuring full insight into the cause-and-effects relationship between the complexity of a software system and the fault density of that system. By applying the operational profile we can characterize the dynamic effects of software path complexity under this same approach We now have the ability to measure specific attributes which have been statistically demonstrated to correlate to increased error probability, and to know which actions to take, for each complexity domain. Shuttle software verifiers can now monitor the changes in the software complexity, assess the added or decreased risk of software faults in modified code, and determine necessary corrections. The reports, tool documentation, user's guides, and new approach that have resulted from this research effort represent advances in the state of the art of software quality and reliability assurance. Details describing how to apply this technique to other NASA code are contained in this document.
Lee, Alice↗
Correlation between aircraft MSS and LIDAR remotely sensed data on a forested wetland in South Carolina
Wetlands in a portion of the Savannah River swamp forest, the Steel Creek Delta, were mapped using April 26, 1985 high-resolution aircraft multispectral scanner (MSS) data. Due to the complex spectral characteristics of the wetland vegetation, it was necessary to implement several techniques in the classification of the MSS imagery of the Steel Creek Delta. In particular, when performing unsupervised classification, an iterative cluster busting technique was used which simplified the cluster labeling process. In addition to the MSS data, light detecting and ranging (LIDAR) data were acquired by National Aeronautics and Space Administration (NASA) personnel along two flightlines over the Steel Creek Delta. These data were registered with the wetland classification map and correlated. Statistical analyses demonstrated that the laser derived canopy height information was significantly correlated with the Steel Creek Delta wetland classes encountered along the profiling transect of the LIDAR data.
Jensen, John R.↗
Correlation between aircraft MSS and LIDAR remotely sensed data on a forested wetland in South Carolina
Wetlands in a portion of the Savannah River swamp forest, the Steel Creek Delta, were mapped using April 26, 1985 high-resolution aircraft multispectral scanner (MSS) data. Due to the complex spectral characteristics of the wetland vegetation, it was necessary to implement several techniques in the classification of the MSS imagery of the Steel Creek Delta. In particular, when performing unsupervised classification, an iterative cluster busting technique was used which simplified the cluster labeling process. In addition to the MSS data, light detecting and ranging (LIDAR) data were acquired by National Aeronautics and Space Administration (NASA) personnel along two flightlines over the Steel Creek Delta. These data were registered with the wetland classification map and correlated. Statistical analyses demonstrated that the laser derived canopy height information was significantly correlated with the Steel Creek Delta wetland classes encountered along the profiling transect of the LIDAR data.
Jensen, John R.↗
Applications of flow models to the generation of correlated lattice QCD ensembles
Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these correlations can be exploited for variance reduction in the computation of observables. Three different proof-of-concept applications are demonstrated using a novel residual flow architecture: continuum limits of gauge theories, the mass dependence of QCD observables, and hadronic matrix elements based on the Feynman–Hellmann approach. In all three cases, it is shown that statistical uncertainties are significantly reduced when machine-learned flows are incorporated as compared with the same calculations performed with uncorrelated ensembles or direct reweighting. Published by the American Physical Society 2024
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Burst-error characteristics of the equatorial transionospheric channel
Analyses of AGC analog data from the Small Astronomy Satellite (SAS) at VHF (136 MHz) have shown amplitude fluctuations in the signals received at several equatorial tracking sites operated by NASA. Errors in data are shown to increase markedly for nighttime satellite passes around the periods of the two equinoxes as compared to the errors observed during other periods. Qualitative and quantitative correlations are established between the ionospheric scintillation phenomenon and the occurrence of errors. Strong time and geographic cause-and-effect relationships are established by determining the statistical correlation between scintillation indices and bit error rates. Detailed analyses of the AGC fading statistics and the fine grain error statistics, such as the block-error distribution and the bit-error autocorrelation function, establish the strong correlation between deep fades and their effects on the burst error structure associated with the transionospheric channel and the communication receiver being employed.
Blank, H. A.↗
Correlation of the Coronal Mass Ejection Productivity of Solar Active Regions with Measures of their Global Nonpotentiality from Vector Magnetograms: Baseline Results
Conventional magnetograms and chromospheric and coronal images show qualitatively that the fastest coronal mass ejections (CMEs) are magnetic explosions from sunspot active regions where the magnetic field is globally strongly sheared and twisted from its minimum-energy potential configuration. We present measurements from active region vector magnetograms that start to quantify the dependence of an active region's CME productivity on the global nonpotentiality of its magnetic field. From each of 17 magnetograms of 12 bipolar active regions, we measured the size of the active region (the magnetic flux content, phi) and three separate measures of the global nonpotentiality (L(sub SS), the length of strong-shear, strong-field main neutral line: I(sub N), the net electric current connecting one polarity to the other; and alpha = (mu)I(sub N)/phi), a flux normalized measure of the field twist). From these measurements and the observed CME productivity of the active regions, we find that: (1) All three measures of global nonpotentiality are statistically correlated with the active region flux content and with each other; (2) All three measures of global nonpotentiality are significantly correlated with CME productivity. The flux content correlates with CME productivity, but at a lower statistically significant confidence level (less than 95%); (3) The net current is less closely correlated with CME productivity than alpha and the correlation of CME productivity with flux content is even weaker. If these differences in correlation strength, and a significant correlation of alpha with flux content, persist to larger active regions, this would imply that the size of active regions does not affect CME productivity except through global nonpotentiality; and (4) For each of the four global magnetic quantities, the correlation with CME productivity is stronger for a two-day time window for the CME production than for windows half as wide or twice as wide. This plausibly is a result of the most counterproductive active regions producing less than one CME per day, and from the active region's evolution often significantly changing the global nonpotentiality over the course of several days. These results establish that measures of active region global nonpotentiality from vector magnetograms (such as L(sub SS), I(sub N), and alpha) should be useful for prediction a active region CMEs.
Falconer, D. A.↗