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NASA NTRS1980

ICAP: An Interactive Cluster Analysis Procedure for analyzing remotely sensed data

An Interactive Cluster Analysis Procedure (ICAP) was developed to derive classifier training statistics from remotely sensed data. The algorithm interfaces the rapid numerical processing capacity of a computer with the human ability to integrate qualitative information. Control of the clustering process alternates between the algorithm, which creates new centroids and forms clusters and the analyst, who evaluate and elect to modify the cluster structure. Clusters can be deleted or lumped pairwise, or new centroids can be added. A summary of the cluster statistics can be requested to facilitate cluster manipulation. The ICAP was implemented in APL (A Programming Language), an interactive computer language. The flexibility of the algorithm was evaluated using data from different LANDSAT scenes to simulate two situations: one in which the analyst is assumed to have no prior knowledge about the data and wishes to have the clusters formed more or less automatically; and the other in which the analyst is assumed to have some knowledge about the data structure and wishes to use that information to closely supervise the clustering process. For comparison, an existing clustering method was also applied to the two data sets.

Wharton, S. W.↗
NASA NTRS1994

Voids and constraints on nonlinear clustering of galaxies

Void statistics of the galaxy distribution in the Center for Astrophysics Redshift Survey provide strong constraints on galaxy clustering in the nonlinear regime, i.e., on scales R equal to or less than 10/h Mpc. Computation of high-order moments of the galaxy distribution requires a sample that (1) densely traces the large-scale structure and (2) covers sufficient volume to obtain good statistics. The CfA redshift survey densely samples structure on scales equal to or less than 10/h Mpc and has sufficient depth and angular coverage to approach a fair sample on these scales. In the nonlinear regime, the void probability function (VPF) for CfA samples exhibits apparent agreement with hierarchical scaling (such scaling implies that the N-point correlation functions for N greater than 2 depend only on pairwise products of the two-point function xi(r)) However, simulations of cosmological models show that this scaling in redshift space does not necessarily imply such scaling in real space, even in the nonlinear regime; peculiar velocities cause distortions which can yield erroneous agreement with hierarchical scaling. The underdensity probability measures the frequency of 'voids' with density rho less than 0.2 -/rho. This statistic reveals a paucity of very bright galaxies (L greater than L asterisk) in the 'voids.' Underdensities are equal to or greater than 2 sigma more frequent in bright galaxy samples than in samples that include fainter galaxies. Comparison of void statistics of CfA samples with simulations of a range of cosmological models favors models with Gaussian primordial fluctuations and Cold Dark Matter (CDM)-like initial power spectra. Biased models tend to produce voids that are too empty. We also compare these data with three specific models of the Cold Dark Matter cosmogony: an unbiased, open universe CDM model (omega = 0.4, h = 0.5) provides a good match to the VPF of the CfA samples. Biasing of the galaxy distribution in the 'standard' CDM model (omega = 1, b = 1.5; see below for definitions) and nonzero cosmological constant CDM model (omega = 0.4, h = 0.6 lambda(sub 0) = 0.6, b = 1.3) produce voids that are too empty. All three simulations match the observed VPF and underdensity probability for samples of very bright (M less than M asterisk = -19.2) galaxies, but produce voids that are too empty when compared with samples that include fainter galaxies.

Vogeley, Michael S.↗
NASA NTRS1974

Statistical analysis of catalogs of extragalactic objects. III - The Shane-Wirtanen and Zwicky catalogs

Statistical investigation of clustering in the galaxy catalogs compiled by Zwicki et al. (1961-1968) and Shane and Wirtanen (1967). The covariance and power spectrum of the angular distributions are estimated. The space region surveyed in the Zwicki catalog is found to represent a 'fair sample of the universe' in that the statistical nature of the clustering in this catalog is found to be mirrored at smaller angular scales in the deeper survey of Shane and Wirtanen.

Peebles, P. J. E.↗
NASA NTRS1976

Energy spectra of X-ray clusters of galaxies

A procedure for estimating the ranges of parameters that describe the spectra of X-rays from clusters of galaxies is presented. The applicability of the method is proved by statistical simulations of cluster spectra; such a proof is necessary because of the nonlinearity of the spectral functions. Implications for the spectra of the Perseus, Coma, and Virgo clusters are discussed. The procedure can be applied in more general problems of parameter estimation.

Avni, Y.↗
NASA NTRS1992

Systematic differences between the field and cluster elliptical galaxies

Multivariate statistical techniques and fundamental plane fits are used here to study possible systematic differences between field ellipticals (FEs) and cluster ellipticals (CEs). The FEs show more intrinsic scatter in their properties, especially when stellar population variables are included. Pairwise correlations for the two samples are different; the correlations are systematically better for the cluster sample, meaning that ellipticals in the two samples populate their fundamental planes in different ways. Bivariate correlations are different for the two samples, implying that they have different fundamental planes. This is especially true for the correlations which include the population variables Mg2 and (B-V), which are sensitive both to the enrichment history and the storm formation history.

De Carvalho, R. R.↗
NASA NTRS1991

A measurement of the mass fluctuation spectrum from the cluster X-ray temperature function

A statistically complete sample of galaxy clusters is presented which also has complete X-ray temperature information. Using this sample, the cluster bolometric luminosity and temperature functions are derived. The temperature function constrains the shape and amplitude of the mass fluctuation power spectrum. For a power law, i.e., with the fluctuation power spectrum proportional to k exp n, n = -(1.7 + 0.65, - 0.35), and an amplitude is obtained which implies that the rms value of delta-M/M is 0.59 + or - 0.02 on a scale of 8/h Mpc at the present epoch.

Henry, J. Patrick↗
NASA NTRS2019

Recently Formed Crater Clusters on Mars

This study maps and measures assorted properties of new dated crater clusters that formed recently when impactors fragmented in the atmosphere of Mars. We report these statistics for 77 clusters: number of craters, size of cluster, dispersion of cluster, direction (azimuth) from which the impactor approached, and an estimate of the angle from vertical of the impact. Clusters range from a few to hundreds of craters, with most containing tens of craters. They are most commonly dispersed over hundreds of meters, with extents ranging from a few meters to a few kilometers. We find that dispersion generally does not correlate with topographic elevation. However, when the highest elevations are disregarded, clusters are more dispersed at lower elevations, as expected. Impact azimuths are randomly distributed and do not express a clear directionality of incoming meteoroids. Results suggest impacts occur closer to horizontal than expected, which could be due to observational effects. The characteristics we report here provide important constraints for future work in understanding atmospheric fragmentation processes; properties of the impactors themselves, such as density and orbital parameters; and the seismic detectability of impacts. These are critical aspects to understand, as approximately half of current impacts are observed to be clusters.

Clusters↗
NASA NTRS2019

Recently Formed Crater Clusters on Mars

This study maps and measures assorted properties of new dated crater clusters that formed recently when impactors fragmented in the atmosphere of Mars. We report these statistics for 77 clusters:number of craters, size of cluster, dispersion of cluster, direction (azimuth) from which the impactor approached, and an estimate of the angle from vertical of the impact. Clusters range from a few to hundreds of craters, with most containing tens of craters. They are most commonly dispersed over hundreds of meters,with extents ranging from a few meters to a few kilometers. We find that dispersion generally does not correlate with topographic elevation. However, when the highest elevations are disregarded, clusters are more dispersed at lower elevations, as expected. Impact azimuths are randomly distributed and do not express a clear directionality of incoming meteoroids. Results suggest impacts occur closer to horizontal than expected, which could be due to observational effects. The characteristics we report here provide important constraints for future work in understanding atmospheric fragmentation processes; properties of the impactors themselves, such as density and orbital parameters; and the seismic detectability of impacts. These are critical aspects to understand, as approximately half of current impacts are observed to be clusters.

I. J. Daubar↗
NASA NTRS1984

A unified N-body and statistical treatment of stellar dynamics. I - The hybrid code. II - Applications to globular cluster cores

A unified N-body and statistical treatment of stellar dynamics is developed and applied to the late stages of core collapse and early stages of post collapse evolution in globular clusters. A 'hybrid' computer code is joined to a direct N-body code which is used to calculate exactly the behavior of particles in the inner spatial region, and the combination is used to follow particles statistically in the outer spatial region. A transition zone allows the exchange of particles and energy between the two regions. The main application results include: formation of a hard central binary system, reversal of core collapse and expansion due to the heat input from this binary, ejection of the binary from the core, and recollapse of the core; density profiles that form a one-parameter sequence during the core oscillations; and indications that these oscillations will eventually cease.

Mcmillan, S. L. W.↗
NASA NTRS1993

A catalog of intracluster gas temperatures

We have searched the Einstein Monitor Proportional Counter (MPC) data base for observations of clusters of galaxies. By coadding the MPC spectra obtained during all pointed observations of clusters with IPC count rates greater than 0.1 counts/s, we have obtained sufficient photon statistics to estimate the X-ray temperature of 84 clusters. Combining the MPC results with EXOSAT and Ginga results reported in the literature yields a combined sample of 104 clusters with known X-ray temperatures. One of the best studied X-ray correlations between clusters is that between their X-ray luminosity and gas temperature. We show that the best-fit power-law relation for our combined cluster sample can be explained by the observed increase in the gas-to-stellar mass ratio between low- and high-temperature clusters. The statistical significance of any evolution in our combined X-ray sample has been examined and compared with the statistical properties of clusters culled from optical catalogs. We find that there is strong evidence for a decrease in the X-ray luminosity of optically rich clusters beyond z approximately about 0.06. This result is used to estimate the normalization of the primordial power spectrum of density fluctuations.

David, L. P.↗
NASA NTRS1977

Alteration mapping at Goldfield, Nevada, by cluster and discriminant analysis of LANDSAT digital data

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.

Ballew, G.↗
NASA NTRS1977

Alteration mapping at Goldfield, Nevada, by cluster and discriminant analysis of Landsat digital data

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.

Ballew, G.↗
NASA NTRS1992

On the origin of globular clusters in elliptical galaxies

Multivariate statistical analysis is used to correlate the estimated total numbers of globular clusters in elliptical galaxies (N sub gc), and the numbers per unit luminosity (S sub N), with a variety of observed properties of the host galaxies. Both N sub gc and S sub N are correlated with the so-called fundamental plane of elliptical galaxies, suggesting that the processes which determine global properties of ellipticals also largely determine their globular cluster content, although a considerable residual scatter remians. The redder (presumably more metal-rich) galaxies were found to have more globular clusters, implying that a dissipative formation mechanism was involved. Galaxies which have more anisotropic velocity distributions were also found to have more clusters, suggesting that mergers may have been important in the production of globular systems.

Djorgovski, S.↗
NASA NTRS2026

The Thermal and Kinematic Sunyaev–Zeldovich Effect in Galaxy Clusters and Filaments Using Multifrequency Temperature Maps of the Cosmic Microwave Background A399–A401 Cluster Pair Case Study

We present a multifrequency and multi-instrument methodology to study the physical properties of galaxy clusters and cosmic filaments using cosmic microwave background observations. Our approach enables simultaneous measurement of both the thermal (tSZ) and kinematic Sunyaev–Zeldovich (kSZ) effects, incorporates relativistic corrections, and models astrophysical foregrounds such as thermal dust emission. We do this by jointly fitting a single physical model across multiple maps from multiple instruments at different frequencies, rather than fitting a model to a single Compton-y map. We demonstrate the success of this method by fitting the A399–A401 galaxy cluster pair and filament system using archival data from the Planck satellite and new, targeted deep data from the Atacama Cosmology Telescope, covering 11 different frequencies over 14 maps from 30 GHz to 545 GHz. Our tSZ results are consistent with previous work using Compton-y maps. We measure the line-of-sight peculiar velocities of the cluster–filament system using the kSZ effect and find statistical uncertainties on individual cluster peculiar velocities of ≲600 km s −1 , which are competitive with current state-of-the-art measurements. Additionally, we measure the optical depth of the filament component with a signal-to-noise of 8.5σ and reveal hints of its morphology. This modular approach is well-suited for application to future instruments across a wide range of millimeter and submillimeter wavebands.

Ajay S Gill↗
NASA NTRS1990

Clustered or regular cumulus cloud fields - The statistical character of observed and simulated cloud fields

The spatial distribution of cumulus clouds is assumed to be the result of the effects of convective activity on the thermodynamic environment. The effects can be parameterized in terms of a stabilization function representing the time rate of change of convective available potential energy. Using these results, a new inhibition hypothesis explaining the expected characteristics of the spatial distribution of cumulus clouds is postulated. This paper performs a verification of the inhibition hypothesis on real and simulated cloud fields. In order to do so, an objective measure of the spatial characteristics of cumulus clouds is introduced. Multiple cloud experiments are performed with a three-dimensional numerical cloud model. Skylab pictures of real cumuli are also used in the verification. Results of applying this measure to simulated and observed cumulus cloud fields confirm the inhibition hypothesis.

Ramirez, Jorge A.↗
NASA NTRS1993

Statistics of highly magnified gravitational images in clusters of galaxies. I - Implications for the clusters. II - Implications for the sources

A study is presently conducted of the probability distribution of observing images of background galaxies that are gravitationally lensed in the form of elongated arcs by clusters of galaxies, as a function of arc width, curvature radius, and the elongation's orientation. An upper limit is obtained on the size of the cores which is smaller than cluster core radii obtained for the gas from the X-ray surface brightness. It is argued that lensing clusters tend to be elongated along the line of sight; projection effects will enhance surface density. In the second part of this work, it is shown that the number of arcs expected in lensing clusters is primarily dependent on the angular size of the sources, since lower magnification is required to generate an arc of fixed length for a larger source.

Miralda-Escude, Jordi↗
NASA NTRS1989

The distribution of galaxies in Abell 1975

The distribution of galaxies in the field of Abell 1795 is studied, based on a red photograph obtained with the Palomar 1.2 m Schmidt telescope. A battery of statistical tests has been applied to the positional data of galaxies in A 1795, in order to assess the significance of asymmetry and subclustering. The large-scale distribution of galaxies is asymmetric, with an elongation to the north. Although there appear to be two, or possibly three, clumps of galaxies in the cluster core, various statistical tests provide no convincing evidence for subclustering. This may be due to the small number of galaxies in the core. These results are discussed in light of the recent observations by Hill et al. (1988) that the cD galaxy in A 1795 has a large peculiar velocity with respect to the cluster mean.

Oegerle, William R.↗