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As part of the work performed under this contract, we have computed the 3- and 4-point correlation functions of the COBE-DMR 2-year and 4-year anisotropy maps. The results of our work showed that the 3-point correlation function is consistent with zero and that the 4-point function is not a very sensitive probe of non-Gaussian behavior in the COBE-DMR data.
Investigated here is this mapping problem: assign the tasks of a parallel program to the processors of a parallel computer such that the execution time is minimized. First, a taxonomy of objective functions and heuristics used to solve the mapping problem is presented. Next, we develop a highly parallel heuristic mapping algorithm, called Cyclic Pairwise Exchange (CPE), and discuss its place in the taxonomy. CPE uses local pairwise exchanges of processor assignments to iteratively improve an initial mapping. A variety of initial mapping schemes are tested and recursive spectral bipartitioning (RSB) followed by CPE is shown to result in the best mappings. For the test cases studied here, problems arising in computational fluid dynamics and structural mechanics on unstructured triangular and tetrahedral meshes, RSB and CPE outperform methods based on simulated annealing. Much less time is required to do the mapping and the results obtained are better. Compared with random and naive mappings, RSB and CPE reduce the communication time two fold for the test problems used. Finally, we use CPE in two applications on a CM-2. The first application is a data parallel mesh-vertex upwind finite volume scheme for solving the Euler equations on 2-D triangular unstructured meshes. CPE is used to map grid points to processors. The performance of this code is compared with a similar code on a Cray-YMP and an Intel iPSC/860. The second application is parallel sparse matrix-vector multiplication used in the iterative solution of large sparse linear systems of equations. We map rows of the matrix to processors and use an inner-product based matrix-vector multiplication. We demonstrate that this method is an order of magnitude faster than methods based on scan operations for our test cases.
The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given.
The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given.
The measurement of tropospheric carbon monoxide with gas filter radiometers is examined on the basis of the MAPS experiment. The performance characteristics of an instrument that uses the MAPS detectors, broadband filters, and gas cells in a system similar to the GASCOFIL system described by Morrow and Nicholls (1985) is determined. The signal function for two carbon monoxide channels of the MAPS instrument as it was flown in 1981 is shown. The measurements of the lower pressure channel are weighted to a higher altitude. The signal function, when integrated over altitude and multiplied by the normalization constant, yields the value of the signal. Both signal functions approach zero at the top because the gas concentration approaches zero. The present data reduction technique assumes that there are no clouds in the field of view. If clouds are present, the inferred carbon monoxide mixing ratio is too high, and those points must be rejected from the data set.
The ability of Landsat multispectral digital data to differentiate among 62 combinations of rock and alteration types at the Goldfield mining district of Western Nevada was investigated by using statistical techniques of cluster and discriminant analysis. Multivariate discriminant analysis was not effective in classifying each of the 62 groups, with classification results essentially the same whether data of four channels alone or combined with six ratios of channels were used. Bivariate plots of group means revealed a cluster of three groups including mill tailings, basalt and all other rock and alteration types. Automatic hierarchical clustering based on the fourth dimensional Mahalanobis distance between group means of 30 groups having five or more samples was performed. The results of the cluster analysis revealed hierarchies of mill tailings vs. natural materials, basalt vs. non-basalt, highly reflectant rocks vs. other rocks and exclusively unaltered rocks vs. predominantly altered rocks. The hierarchies were used to determine the order in which sets of multiple discriminant analyses were to be performed and the resulting discriminant functions were used to produce a map of geology and alteration which has an overall accuracy of 70 percent for discriminating exclusively altered rocks from predominantly altered rocks.
A method of minimizing fringe print-through in a phase-shifting interferometer, includes the steps of: (a) determining multiple transfer functions of pixels in the phase-shifting interferometer; (b) computing a crosstalk term for each transfer function; and (c) displaying, to a user, a phase-difference map using the crosstalk terms computed in step (b). Determining a transfer function in step (a) includes measuring intensities of a reference beam and a test beam at the pixels, and measuring an optical path difference between the reference beam and the test beam at the pixels. Computing crosstalk terms in step (b) includes computing an N-dimensional vector, where N corresponds to the number of transfer functions, and the N-dimensional vector is obtained by minimizing a variance of a modulation function in phase shifted images.
The ability of Landsat multispectral digital data to differentiate among 62 combinations of rock and alteration types at the Goldfield mining district of Western Nevada was investigated by using statistical techniques of cluster and discriminant analysis. Multivariate discriminant analysis was not effective in classifying each of the 62 groups, with classification results essentially the same whether data of four channels alone or combined with six ratios of channels were used. Bivariate plots of group means revealed a cluster of three groups including mill tailings, basalt and all other rock and alteration types. Automatic hierarchical clustering based on the fourth dimensional Mahalanobis distance between group means of 30 groups having five or more samples was performed using Johnson's HICLUS program. The results of the cluster analysis revealed hierarchies of mill tailings vs. natural materials, basalt vs. non-basalt, highly reflectant rocks vs. other rocks and exclusively unaltered rocks vs. predominantly altered rocks. The hierarchies were used to determine the order in which sets of multiple discriminant analyses were to be performed and the resulting discriminant functions were used to produce a map of geology and alteration which has an overall accuracy of 70 percent for discriminating exclusively altered rocks from predominantly altered rocks.
The Cosmic Background Explorer Satellite Differential Radiometer (COBE DMR) sky maps contain low-level correlated noise. We obtain estimates of the amplitude and pattern of the correlated noise from three techniques: angular averages of the covariance matrix, Monte Carlo simulations of two-point correlation functions and direct analysis of the DMR maps. The results from the three methods are mutually consistent. The noise covariance matrix of a DMR sky maps is diagonal to an accuracy of better than 1%. For a given sky pixel, the dominant noise covariance occure with the ring of pixels at an angular separation of 60 deg due to the 60 deg separation of the DMR horns. The mean covariance at 60 deg is 0.45%((sup +0.18)(sub -0.14)) of the mean variance. Additionally, the variance in a given pixel is 0.7% greater than would be expected from a single beam experiment with the same noise properties. Autocorrelation functions suffer from a approximately 1.5 sigma positive bias at 60 deg while cross-correlations have no bias. Published COBE DMR results are not significantly affected by correlated noise.
The advent of Very Large Scale Integration (VLSI) technology has rendered the gate level model impractical for many simulation activities critical to the design automation process. As an alternative, an approach to the modeling of VLSI devices at the chip level is described, including the specification of modeling language constructs important to the modeling process. A model structure is presented in which models of the LSI devices are constructed as single entities. The modeling structure is two layered. The functional layer in this structure is used to model the input/output response of the LSI chip. A second layer, the fault mapping layer, is added, if fault simulations are required, in order to map the effects of hardware faults onto the functional layer. Modeling examples for each layer are presented. Fault modeling at the chip level is described. Approaches to realistic functional fault selection and defining fault coverage for functional faults are given. Application of the modeling techniques to single chip and bit slice microprocessors is discussed.
In one approach to modeling brain function, sensorimotor integration is described as geometrical mapping among coordinates of non-orthogonal frames that are intrinsic to the system; in such a case sensors represent (covariant) afferents and motor effectors represent (contravariant) motor efferents. The neuronal networks that perform such a function are viewed as general tensor transformations among different expressions and metric tensors determining the geometry of neural functional spaces. Although the non-orthogonality of a coordinate system does not impose a specific geometry on the space, this "Tensor Network Theory of brain function" allows for the possibility that the geometry is non-Euclidean. It is suggested that investigation of the non-Euclidean nature of the geometry is the key to understanding brain function and to interpreting neuronal network function. This paper outlines three contemporary applications of such a theoretical modeling approach. The first is the analysis and interpretation of multi-electrode recordings. The internal geometries of neural networks controlling external behavior of the skeletomuscle system is experimentally determinable using such multi-unit recordings. The second application of this geometrical approach to brain theory is modeling the control of posture and movement. A preliminary simulation study has been conducted with the aim of understanding the control of balance in a standing human. The model appears to unify postural control strategies that have previously been considered to be independent of each other. Third, this paper emphasizes the importance of the geometrical approach for the design and fabrication of neurocomputers that could be used in functional neuromuscular stimulation (FNS) for replacing lost motor control.
Differential energy losses of fission fragments in thin carbon films as function of mass and initial energy mapped by time of flight method
The OH airglow has been observed in the infrared with a 0.14-micron bandpass filter centered at 1.65 micron. Spatial fluctuations of 2-11% and temporal fluctuations of 1-7% are found about the mean nightly level. These fluctuations are compared with similar variations observed previously at 2.2 micron, also attributed to OH airglow. Sky maps at 1.65 micron as a function of altitude, azimuth and time are presented.
The NASA P-3 aircraft with the L- and S-band radiometer system on board participated in the MARSEN experiments carried out between August 30 and September 23, 1979. Measurements of surface temperature and salinity were concentrated on freshwater outflows of the Rivers Weser and Elbe in the German Bight. Three missions were carried out, on September 19, 22, and 23. The values of salinity are plotted as a function of geographic position, and contour maps of the salinity distribution are generated from the value plots. It is noted that on September 22, during a noon flood-tide, two river-plume salinity fronts were detected when a body of water with higher salinity existed in front of the Weser delta near Bremerhaven generating with the river outflow of lower saline waters a front of delta-S equals 5 per thousand. Another pocket of lower saline waters was found in front of the Elbe delta at Cuxhaven, which in turn set up a strong front of delta-S equals 6 per thousand. The morning low tide of September 23 did not exhibit this extreme condition.
Low energy electron measurements collected by ISEE 1 reveal the frequent presence of field-aligned fluxes of few hundred eV electrons in he geomagnetic tail lobes. In the northern tail lobe these electrons are most prominent when the interplanetary magnetic field is directed away from the Sun. This characteristic helps identify the electrons as polar rain electrons. By mapping the tail lobe velocity distribution function into the solar wind, previous suggestions that the polar rain is indeed of solar wind origin and is due to the access of electrons to the magnetotail lobe were confirmed. It was demonstrated that the moe energetic component of the polar rain is composed of electrons from the solar wind strahl - a field-aligned component of the solar wind which is difficult to measure but which is thought to be caused by the collisionless transit of hundred eV electrons from the inner solar corona to 1 AU.
Low energy electron measurements collected by ISEE 1 reveal the frequent presence of field-aligned fluxes of few hundred eV electrons in the geomagnetic tail lobes. In the northern tail lobe these electrons are most prominent when the interplanetary magnetic field is directed away from the sun. This characteristic helps identify the electrons as polar rain electrons. By mapping the tail lobe velocity distribution function into the solar wind, previous suggestions that the polar rain is indeed of solar wind origin and is due to the access of electrons to the magnetotail lobe were confirmed. It was demonstrated that the more energetic component of the polar rain is composed of electrons from the solar wind strahl - a field-aligned component of the solar wind which is difficult to measure but which is thought to be caused by the collisionless transit of hundred eV electrons from the inner solar corona to 1 AU.
A hierarchical procedure for developing a leaf area index (LAI) map of deciduous boreal forests is studied. The collection of spectral reflectance data from the Boundary Waters Canoe area in Minnesota using helicopter-, high-altitude aircraft-, and Landsat-mounted spectral sensors is described. The relationship between LAI and biomass and the reflectance ratio is analyzed. The sensitivity of canopy reflectance in the visible and infrared to the LAI of the canopy for various boreal forest species is evaluated. The data reveal that Landsat data are useful for producing LAI maps of deciduous forest areas and the maps provide data which clarifies the function of vegetation in the global carbon cycle models.
Advances in remote sensing techniques are discussed. The benefits possible to remote sensing with the new Earth Observing System, which is composed of the Space Station and coorbiting and polar satellite platforms, are examined. Current changes in the remote sensing field, which involve a change from an industrial society to an informational society, force technology to high technology with high touch, short term to long term, centralized to decentralized, hierarchies to networks, and either/or to multiple option systems are studied. The explanatory and objective types of analyses for investigating biophysical, geochemical, and socioeconomic processes are described; the procedures include: morphometric, cause and effect, temporal and functional and ecological system analyses, inventory, mapping, monitoring, and modeling.